Contemporary Mathematics

Fixed Point Results for Generalized (α, β)-Nonexpansive Type-1 Mapping in Hyperbolic Space

Asifa Tassaddiq — 2024-11-25

In this article, we define several fundamental characteristics and put forward some basic fixed point results in the context of hyperbolic space for generalized (α, β)-nonexpansive type-1 mappings. Additionally, we present ∆-convergence and strong convergence results within the framework of hyperbolic space for these types of mappings. Lastly, we provide some numerical examples to highlight our main result and comparison the iterative procedures that we use in our study with various iterative techniques from the literature. The results in this study enhance, broaden and unite corresponding results in the literature.

Approximate and Exact Solutions of Some Nonlinear Differential Equations Using the Novel Coupling Approach in the Sense of Conformable Fractional Derivative

Muhammad Imran Liaqat — 2024-09-30

Several scientific fields utilize fractional nonlinear partial differential equations to model various phenomena. However, most of these equations lack exact solutions. Consequently, techniques for obtaining approximate solutions, which sometimes yield exact solutions, are essential. In this research, we develop a new approach by combining the homotopy perturbation method (HPM) and the conformable natural transform to solve the gas-dynamic equation (GDE), the Fokker-Planck equation (FPE), and the Swift-Hohenberg equation (SHE) in the context of conformable derivatives. The proposed approach is called the conformable natural homotopy perturbation method (CNHPM). This approach has the advantage of not requiring assumptions about significant or minor physical factors. Consequently, it eliminates some of the constraints associated with conventional perturbation methods and can solve both weak and highly nonlinear problems. We consider the absolute, relative, and residual errors numerically and graphically to assess the correctness of our approach. The results show that our approach serves as a suitable alternative to the approximate methods in the literature for solving fractional differential equations.

Fekete-Szegö Functional Problem for Analytic and Bi-Univalent Functions Subordinate to Gegenbauer Polynomials

Omar Alnajar — 2024-12-02

This article aims to introduce a new qualitative subclass of bi-univalent and analytic functions that are intricately linked to Gegenbauer polynomials. These polynomials, known for their significant role in various areas of mathematics, provide a robust framework for exploring the properties of analytic functions. In our exploration, we will address the Fekete-Szego problem, which is pivotal in the field of complex analysis. By doing so, we will derive the coefficient bounds |h₂| and |h₃| for functions within this newly defined subclass, thereby enhancing our understanding of their behavior. Furthermore, by concentrating on the specific parameters that were utilized to achieve our primary results, we expect to generate a variety of additional outcomes. These results will not only deepen our insight into the characteristics of these functions but also contribute to the broader discourse on analytic function theory. We anticipate that the findings presented in this article will pave the way for future research and applications, particularly in the realms of mathematical analysis and applied mathematics.

On the Existence of Solutions to a Fractional Hybrid Thermostat Model

Kiran Kumar Saha — 2024-12-19

This work is concerned with the existence of solutions to a nonlinear fractional hybrid thermostat model in the settings of Atangana-Baleanu derivatives. We also consider the boundary conditions of this model in the form of hybrid conditions. Imposing some suitable conditions on the given data, we establish the existence result of continuous solutions based on the Dhage fixed-point theorem in Banach algebra. Moreover, an example is constructed to illustrate our theoretical result.

Theta Pairing of Hypersurface Rings

Mohammad Reza Rahmati — 2024-10-21

In this article, we prove a conjecture on the positive definiteness of the Hochster Theta pairing over a general isolated hypersurface singularity, namely: Let R be an admissible isolated hypersurface singularity of dimension n. If n is odd, then is positive semi-definite on . The conjecture is expected to be true for the polynomial ring over any field. We prove this conjecture over any field of arbitrary characteristic. We also provide two different proofs of the above conjecture overusing the Hodge theory of isolated hypersurface singularities and structural facts about the category of matrix factorizations. The first proof overis a more complete and developed version of a former work of the author. We have extended some of the former results in this article. The second proof overis quite direct and uses a former result of the author on Riemann-Hodge bilinear relations for Grothendieck residue pairing of isolated hypersurface singularities.

Inequalities of Coefficients and the Fekete-Szegö Problem Associated with λ-Pseudo Starlike Functions

Musthafa Ibrahim — 2024-12-12

We introduce a new subclass of starlike functions, denoted by , that are influenced by the Janowski functions, which are well-known in the literature. Our main results are the coefficient estimates of the inverse function and the Fekete-Szegö inequality for this subclass. We also present some special cases of our results that are of interest.

Solution of Non-Autonomous Bloch Equation via Multistage Differential Transformation Method

Noufe H. Aljahdaly — 2024-12-11

This study explores the multistage differential transformation method (MsDTM) as an efficient approach for solving non-autonomous differential equations. The proposed method demonstrates wide-ranging applicability in fields such as computer graphics, quantum optics, biomathematics, and image processing. Specifically, the Bloch equations, which describe the interaction of a spin-1/2 system (or two-level atom) with a mono- or bichromatic laser field in the presence of an off-resonant broad-band squeezed vacuum (SV), are examined. As a system of non-autonomous ordinary differential equations, the Bloch model captures the quantum dynamics between matter and electromagnetic fields, offering insights into more complex and experimentally relevant models. The MsDTM is employed to obtain numerical solutions with high precision and computational efficiency, outperforming the classical 4th-order Runge-Kutta (RK4) method. A key advantage of the MsDTM is its adaptability; its accuracy can be further enhanced by either increasing the number of iterations or refining the time-step in the numerical scheme. Consequently, MsDTM emerges as a robust tool for computing solutions to a broad class of non-autonomous equations.

An Axial-Vector Photon in a Mirror World

Rasulkhozha S. Sharafiddinov — 2024-11-22

We discuss a theory in which the left- and right-handed axial-vector photons refer to long- and short-lived bosons of true neutrality, respectively. Such a difference in lifetimes expresses the unidenticality of masses, energies, and momenta of axial-vector photons of the different components, generalizing the classical Klein-Gordon equation to the case of C-odd types of particles with a nonzero spin. Together with a new Dirac equation for truly neutral particles with the half-integral spin, the latter admits the existence of the second type of the local axial-vector gauge transformation responsible for origination in a Lagrangian of an interaction Newton component, which gives an axial-vector mass to all the interacting particles and fields. The quantum axial-vector mass, energy, and momentum operators constitute herewith a new Schrödinger equation, confirming that each of them can individually influence on the matter field. They define at the new level, namely, at the level of the mass-charge structure of gauge invariance another Euler-Lagrange equation such that it has an axial-vector nature.

Recursive and Explicit Formulas for Expansion and Connection Coefficients in Series of Classical Orthogonal Polynomial Products

H. M. Ahmed — 2024-11-06

Coefficient Estimates for New Subclasses of Bi-Univalent Functions Associated with Jacobi Polynomials

Ala Amourah — 2024-11-01

Our research introduces new subclasses of analytical functions that are defined by Jacobi polynomials. We then proceed to estimate the Fekete-Szegö functional problem and the Maclaurin coefficients for this specific subfamily, denoted as |a₂| and |a₃|. Furthermore, we demonstrate several new results that emerge when we specialize the parameters used in our main findings.

Analyzing Feedback M/G/1 Double Retrial Orbit with Two-Phase Optional Service and Repair under Working Vacation Policy

A. Baskar — 2024-12-04

This research presents a comprehensive analysis of the M/G/1 double retrial queue model with a two-phase optional service and repair, under a working vacation policy. The model addresses scenarios where patients are willing to pay more for enhanced comfort and care. To accommodate this, an optional service phase is introduced, allowing patients to choose between ordinary and premium service levels. The system is further refined by a two-phase service mechanism: in the first phase, patients receive an initial level of service, and depending on their satisfaction or specific needs, they may opt for an enhanced second phase of service. Additionally, the model incorporates feedback and repair processes, reflecting a more realistic representation of queue dynamics. Patients who are dissatisfied with the service or encounter issues can re-enter the system for further attention. The non-Markovian model equations are solved using the probability-generating function approach, which facilitates the analysis of complex queue behaviors and the calculation of key performance indicators, such as expected system length and queue length. The paper includes detailed numerical results with test data to demonstrate the accuracy of the model’s predictions and validate the proposed system design’s effectiveness.

More on Externally q-Hyperconvex Subsets of T₀-Quasi-Metric Spaces

Collins Amburo Agyingi — 2024-10-16

We continue earlier research on T₀-quasi-metric spaces which are externally q-hyperconvex. We focus on external q-hyperconvex subsets of T₀-quasi-metric spaces in particular. We demonstrate that a countable family of pairwise intersecting externally q-hyperconvex subsets has a non-empty intersection that is external q-hyperconvex under specific requirements on the underlying space (see Proposition 22). Last but not least, we demonstrate that if A is a subset of a supseparable and externally q-hyperconvex space Y, where Y ⊆ X, then A is also externally q-hyperconvex in X (Proposition 25).

Efficient Collocation Algorithm for High-Order Boundary Value Problems via Novel Exponential-Type Chebyshev Polynomials

Galal I. El-Baghdady — 2024-10-22

This paper presents an innovative collocation algorithm designed to effectively handle a specific class of boundary value problems with high-order characteristics. The approach involves utilizing a novel variant of exponential type Chebyshev polynomials that meet all the necessary equation conditions. A key aspect of the algorithm is the transformation of both linear and nonlinear forms of the equations, along with their respective boundary conditions, into systems of algebraic equations. By solving these systems, a unique iterative technique is employed that significantly reduces the computational time required for solving these types of equations. To validate the effectiveness of the algorithm, numerous experiments using various examples with differing orders and types are conducted. The proposed technique is compared against other similar methods. The results obtained demonstrate the exceptional accuracy of the proposed approach and its potential for extension to other models in the future. Additionally, a comprehensive and detailed error analysis of the proposed method is developed, further confirming its robustness and precision in practical applications.

Novel Temperature-Based Topological Indices for Certain Convex Polytopes

Sakander Hayat — 2024-10-24

A topological index is a number that assists in understanding various physical characteristics, chemical reactivities, and boiling activities of a chemical compound by characterizing the whole molecular graph structure. These indices are essential for quantifying different chemical properties of chemical compounds in chemical graph theory. The choice of convex polytopes in this work is an important feature due to its structural adaptability, easy accessibility and astonishing capacity to identify its numerical values. In this paper, we present exact analytical expressions for the general first temperature index, the general second temperature index, the first hyper-temperature index, the second hyper-temperature index, the sum-connectivity temperature index, the product-connectivity temperature index, the reciprocal product-connectivity temperature index, the arithmetic-geometric temperature index and the F-temperature index of convex polytopes.

Solutions for a New Fractional Differential Dynamical System and Yosida Quasi-Inverse Variational Inequality in Hilbert Space

Faizan Ahmad Khan — 2024-10-11

In this article, first we introduce and study a Yosida Quasi-inverse variational inequality problem (in short, YQIVI) in Hilbert space and then developed a new fractional differential dynamical system for the YQIVI. We prove the existence and uniqueness of solution for the suggested dynamical system. Further, using the Lyapunov function we also prove the asymptotic stability of the new dynamical system at the equilibrium point. Furthermore, using Rothe's time discretization method we investigate existence and uniqueness of solution of the proposed dynamical system. Finally, we provide a numerical example to demonstrate the credibility and efficacy of the dynamical system in solving the YQIVI.

Support Based Essential and Core Based Superfluous Fuzzy Modules

Abhishek Kumar Rath — 2024-10-18

In this paper, we introduce and explore several novel concepts within the framework of fuzzy module theory. First, we define the notion of a support based essential fuzzy module, establishing its foundational properties. We then investigate the essentiality of alpha cuts and the quotient fuzzy modules arising from support based essential fuzzy modules. Additionally, we demonstrate that under specific conditions, the product of a fuzzy ideal and a fuzzy module results in a support based essential fuzzy module. Further, we define the concept of a support based essential fuzzy monomorphism and provide a detailed characterization. We also introduce the fuzzy injective hull and prove that the direct sum of the fuzzy injective hulls of a class of fuzzy modules coincides with the fuzzy injective hull of the direct sum of the same class. Finally, we define the core based superfluous fuzzy module as a dual concept to the support based essential fuzzy module and establish corresponding dual results.

Optimization of Fuzzy Mathematical Model of Regular Octagon-Shaped Parking Space

Arun Prasath GM — 2024-10-23

In the vigorous development of the city population, there is a need to set up clear dimensions for the parking space. Car parking plays a significant part in the residential apartments and commercial buildings. Roadside parking spaces will create a huge traffic problem if the parking lots are not properly designed. Sometimes, it leads to the accident. Hence, keeping all these causes in mind, the flexible parking space is the necessary of the time. In the proposed research work, the parking space considered in the problem is of a regular octagon shape, and the mathematical model is developed under a fuzzy environment. LINGO Optimization Software is used to solve the mathematical model and MATLAB(Matrix Laboratory) is used to define the fuzzy variable. At the outset, the results will reveal the importance of making the length of the parking lot under fuzzy environment.

Impact of Imputation on Performance of Goodness-of-Fit Tests for the Logistic Panel Data Model

Opeyo Peter Otieno — 2024-10-30

Goodness-of-fit tests aim at discerning model misspecification and identifying a model which is poorly fitting a given data set. They are methods used to determine the suitability of the fitted model. The subject of assessment of goodness-of-fit in logistic regression model has attracted the attention of many scientists and researchers. Several methods for assessing how well observed data can fit into logistic regression models have been proposed and discussed where test statistics are functions of the observed data values and their corresponding estimated values after parameter estimation. Considering a correctly specified panel data model with balanced data set, the conditional maximum likelihood estimates of the parameters are less biased and the estimated response variable values are actually in the neighborhood of the observed values. Relative to the induced biases of the parameter estimates resulting from imputation of missing covariates, the performances of the goodness-of-fit tests may be misjudged. This study looks at the susceptibility of the goodness-of-fit tests for logistic panel data models with imputed covariates. Simulation results show that Bayesian imputation impacts less on the goodness-of-fit test statistics and therefore stands out as the better technique against other classical imputation methods. An increased proportion of missingness however appeared to reduce the confidence interval of the test statistics which in turn reduces the chances of adopting the model under study.

Analysis of a Markovian Queue of Single Server Performing in MultiPhase Subject to Disaster, Recovery and Repair

C.T Dora Pravina — 2024-11-12

In this paper, we can study about Markovian single-server queue with servers in distinct phases of disaster and repair. The server can stay in full-active Phase or passive Phase randomly and alternately. The server is set to serve in two Phases, such as the full active Phase and passive Phase. When the server operates in full active Phase, the customers arrive and served in First Come: First Serve (FCFS) queue discipline. However, when the server switches from full active to passive Phase, it can only offer to provide service at a rate lower than that of the server in full active Phase. During passive Phase, customers are not allowed to join the system. The server moves to repair Phase immediately after the last customer is served, irrespective of the Phase. The customers will be restricted from joining the queue in repair Phase. After the repair Phase, the server will enter the full active Phase. The server remains in the system for a random period of time. In the event of a disaster, in full active and passive Phases, all customers in system aredropped out, and system moves to repair Phase. The expressions for the steady state probabilities and some key performance metrics are obtained. A numerical illustration is made to study the effects of server shifting from full active phase to passive phase that affects the customers in the system and the occurrence of disaster which has an adverse effect on the customers in that phase.

Caputo Fractional Order Nonlinear Incidence HIV Infection Model with Optimal Control

David Yaro — 2024-12-04

Examining mathematical models is a crucial aspect of research in comprehending the dynamics and managing the transmission of Human Immunodeficiency Virus (HIV). This study presents a Caputo fractional order HIV infection model with optimal control. We demonstrate that this model exhibits solutions that are always nonnegative. Additionally, we provide a comprehensive examination of the elasticity of both zero disease and viral-persistence equilibrium location. We also delve into the numerical method proposed by Atanackovic and Stanckovic for solving Generalized Inverse Method and provide numerical simulations to validate the findings.

Biharmonic Extensions on Infinite Trees

Ibtesam Bajunaid — 2024-11-27

In the investigation of harmonic and potential functions on the Euclidean spaces, the Runge-type approximation theorem and Laurent decomposition theorem for harmonic functions are important. Their extensions to subharmonic functions are also crucial. In this note, we investigate various aspects of these results in the context of discrete potential theory on infinite trees. Given an infinite tree T with positive potentials, we prove that for a harmonic function h outside a finite set, there exists a harmonic function H on T such that h − H is bounded outside a finite set. Developing other results based on this theorem, we investigate in detail biharmonic functions on T and study their properties. The thrust is to extend these results to the study of discrete biharmonic and bisuperharmonic functions on infinite trees. This is always true in Rⁿ, n ≥ 5 because the fundamental solution of ∆²on this case tends to 0 at infinity. Based on this property we also define the notion of a tapered biharmonic space.

Decision-Making of Fredholm Operator on a New Variable Exponents Sequence Space of Supply Fuzzy Functions Defined by Leonardo Numbers

Salah H. Alshabhi — 2024-11-27

In this article, we will use a weighted regular matrix formed by Leonardo numbers and variable exponent sequence spaces to build a new stochastic space. We have proposed various geometric and topological structures for this new space, as well as the multiplication operator that operates on it.

Some Identities for the (a, b; k)-Nacci Sequences

Monrudee Sirivoravit — 2024-12-04

In this paper, we introduce a generalization of the k-generalized Fibonacci sequence, called the (a, b; k)-nacci sequence, where a and b are real numbers and k ≥ 2 is an integer. The (a, b; k)-nacci sequence is defined recursively as follows:

We also provide some identities involving the sum of the (a, b; k)-nacci terms and investigate the sums of the squares of the (a, b; k)-nacci numbers.

Black-Box Adversarial Attacks Against SQL Injection Detection Model

Maha Alqhtani — 2024-11-14

Structured Query Language (SQL) injection attacks represent a substantial threat to the security of web applications, making the development of effective detection techniques crucial. These techniques have evolved from traditional signature-based techniques to more advanced techniques based on machine learning models. Machine learning detection models are often vulnerable to adversarial examples. Adversarial examples are deliberately crafted inputs designed to deceive models into making incorrect predictions by subtly altering the original dataset in ways that are typically imperceptible to humans. To train and test these machine learning models, datasets comprising both malicious and normal data are indispensable. However, the lack of sufficient and balanced datasets presents a significant challenge, particularly for models intended to detect SQL injection attacks. Most network traffic datasets exhibit a substantial class imbalance, with a disproportionate amount of normal traffic compared to malicious traffic, making it difficult to train effective and reliable detection models. This study addressed the shortcomings of current SQL injection detection techniques and proposed a conditional tabular generative adversarial network adversarial attack method. We evaluated the effectiveness of the generated adversarial SQL injection examples using qualitative and quantitative methods, measuring their ability to evade the detection model. A conventional neural network algorithm detection model was built and tested, and the generated adversarial examples successfully bypassed the detection model at a rate of up to 6%. The evidence demonstrated that the conditional tabular generative adversarial network successfully captures the statistical properties of real data and generates synthetic data that accurately represents the real data. This method is also expected to address the problem of insufficient and imbalanced SQL injection datasets, which could aid in training various machine learning models beyond the one used in our study.

Unveiling of Highly Dispersive Dual-Solitons and Modulation Instability Analysis for Dual-Mode Extension of a Non-Linear Schrödinger Equation

Abeer S. Khalifa — 2024-11-20

The two-mode equations are nonlinear models that describe the behavior of two-way waves moving simultaneously while being affected by confined phase velocity. This article expands a non-linear Schrödinger equation (NLSE) by constructing it as a dual-mode structure. Applying the modified extended direct algebraic method (MEDAM) yields exact and explicit solutions. The results of this investigation have significant implications for the propagation of solitons in nonlinear optics. There are multiple resulted solutions that comprise singular periodic solutions, Weierstrass elliptic doubly periodic solutions, Jacobi elliptic function (JEF), singular soliton, bright soliton, dark soliton, and rational solutions, moreover, hyperbolic wave solutions. We show our acquired traveling wave solutions’ uniqueness and significant addition to current research by contrasting them with the body of existing literature. The method’s effectiveness shows that it may be used to address a wide variety of nonlinear problems across multiple disciplines, particularly in the theory of soliton, as the studied model appears in many applications. Additionally, we display the outlines of some of these discovered solution behaviors in 3D and 2D graphs to help with comprehension. Finally, we analyze modulation instability to examine the stability of the discovered solutions.

Controllability of Impulsive Nonlinear Fractional Dynamical System with Delays in State and Control

G. Arthi — 2024-12-19

In this paper, the controllability of nonlinear impulsive fractional dynamical system with delays in state and control is analyzed by using a delayed Mittag Leffler (M-L) function. Controllability Grammian matrix is used to establish the controllability of linear system. The sufficient conditions of the considered nonlinear system are derived by utilizing the fixed point techniques. Finally, an example is provided for the illustration of the obtained result.

Reliable Computational Method for Systems of Fractional Differential Equations Endowed with ψ-Caputo Fractional Derivative

Mariam Al-Mazmumy — 2024-11-12

This study develops a highly convergent computational method, the ψ-Laplace Adomian Decomposition Method (ψ-LADM), for solving coupled systems ofψ-Caputo Fractional Differential Equations (FDEs). The effectiveness of the proposed method has been assessed using various numerical test examples, including a real-world application for atmospheric convection models utilizing Lorenz chaotic dynamical systems. Notably, the method consistently produced solutions that matched the true solutions of the governing models. In the case of the Lorenz chaotic system, the obtained solutions accurately portrayed the characteristic phase portraits of a true chaotic system.

Fractional View Analysis of Coupled Whitham-Broer-Kaup Equations Arising in Shallow Water with Caputo Derivative

Abdulrahman B. M. Alzahrani — 2024-11-27

This research explores the analysis of the nonlinear fractional systems described by the Whitham-Broer-Kaup equations using novel mathematical tools like the Aboodh transform iteration method and the Aboodh residual power series method in light of the Caputo operator theory. The Whitham-Broer-Kaup equations are critical for describing the nonlinear propagation of dispersive waves and have enormous practical relevance. In the application of the Aboodh transform iteration method and the Aboodh residual power series method, as well as the introduction of the Caputo operator, the modelling accuracy is improved by calculating the fractional derivatives. The study has proven the usefulness of these techniques in providing solutions to fractional nonlinear systems that are only approximate but are insightful concerning dynamic behaviour. The insertion of the Caputo operator in the modelling method gives it some sophistication, simulating the non-locality inherent in fractional calculus. Consequently, this study enriches mathematical models and computational approaches, bringing in solid tools for researchers who want to examine complex nonlinear systems with fractional nature.

Detection of Prenatal Cardiac Disease using Computer Vision and Artificial Intelligence

P. Megana Santhoshi — 2024-11-18

Prenatal cardiac anomalies, commonly referred to as congenital heart defects (CHDs), comprise a spectrum of pathologies that adversely affect cardiac function. There is a correlation between the numerous risks of cardiovascular diseases and the pressing requirement for precise, reliable, and efficient methods of early detection. The contemporary epoch of voluminous data presents a plethora of novel prospects for clinicians to utilize artificial intelligence in order to identify and enhance treatment for pediatric patients and those afflicted with congenital heart disease. Machine learning, a prevalent technique in the field of artificial intelligence, has been utilized to forecast various outcomes in obstetrics. The application of artificial intelligence in real-time electronic health recording and predictive modelling has demonstrated promising outcomes in the domain of fetal monitoring. The present research provides an in-depth review of recent advancements and challenges in the application of artificial intelligence techniques, such as deep learning and computer vision, for the detection of congenital heart disease.

A Mixed Neuro Graph Approach with Gradient Boosting to Hybrid Job-Shop Scheduling to Minimize a Regular Function of Job Completion Times and Numbers of Used Machines

Yuri Sotskov — 2024-11-18

The paper considers a multi-stage processing system including sets of identical (parallel) machines and a set of dedicated machines processing different operations of the given jobs in any sectors of economy. Based on the weighted Mixed Neuro graph model, the paper proposes adaptive algorithms for solving this problem via appropriate Mixed Neuro graph transformations. The main novelty is (1) low demands on the source data-unlike classical machine learning algorithms, the approach can offer stable interpretable results even with a short dataset size; (2) the number of new matrix multiplication operations that make up the main load when training models increases linearly with the number of new data from 0 to 999 time periods; (3) the results of the model are repeatable due to the stability of the coefficients of the model. These algorithms are able to solve (exactly or heuristically) the tested instances with N jobs and W types of parallel identical machines within on the personal computer. The gradient boosting result is in interval 5.9677410-3.4982093.

Study of multiobjective fractional variational formulation using η-Approximation Method

Sony Khatri — 2024-11-20

This paper investigates the idea of the η-approximated technique for converting the nonlinear and nonconvex multiobjective fractional variational dual problems (MFP) and (MFD) with inequality constraints to the linear and convex counterparts of the problems, namely, (MFP)_η and (MFD)_η, respectively. Weak, strong, and converse duality theorems are obtained for the original as well as the η-approximated dual pair under invexity for weak Pareto as well as Pareto solutions. Furthermore, the connection between the original and modified problems has also been established. A suitable numerical example is constructed to bolster the research paper.

Some Parallel Surfaces in Three-Dimensional Minkowski Space as the Discriminant Set of a Certain Family of Functions

Patriciu Alina-Mihaela — 2024-11-27

In this paper we prove that, in three-dimensional Minkowski space, the family of parallel surfaces to a given surface at a certain distance can be obtained as the discriminant set of a certain family of functions. As consequence, we obtain that Minkowski spheres with prescribed radius, having contact of order 1 with a surface, have the centers on the parallel surface at distance equal to the radius. We give an example showing that the parallel surface to a timelike flat surface admits cuspidal edge as singularity

Third-Kind Chebyshev Spectral Collocation Method for Solving Models of Two Interacting Biological Species

M. A. Taema — 2024-12-16

This paper develops numerical methods for solving a system of two nonlinear integro-differential equations that arise in biological modeling. A spectral collocation method utilizing third-kind Chebyshev polynomials forms the basis of the solution methodology, which efficiently converts the integro-differential system into a collection of nonlinear algebraic equations. To guarantee precise and effective calculation, these algebraic equations are subsequently numerically solved using Newton’s method. In comparison to current methods, the suggested approach offers notable gains in computational efficiency and precision. The spectral collocation method’s accuracy is confirmed by contrasting the outcomes with those derived from other numerical methods that are published in the literature. To further illustrate the applicability, dependability, and computational efficiency of the suggested approach in resolving complicated biological systems, a number of illustrative instances are provided. The ability of spectral collocation techniques based on third-kind Chebyshev polynomials to solve integro-differential equations in a variety of scientific and engineering applications is highlighted by this work.

A Mathematical Model for Controlling SARS-COV 2 by Triplet Oxygen Molecules, Spinning Bubbles and Other Spinors

Massimo Fioranelli — 2024-11-22

Background: One of best ways to repel harmful viruses like corona is using of repulsive force between spinors which are existed within structures of cells and viruses. These spins could be induced within virus and cell structures by external magnetic fields which are emitted from currents of ions within blood cells. Motions of charges and ions within blood vessels produces magnetic fields. These fields force on spinors within cell and virus structures within alveolus and make them parallel. These spinning viruses interact with triplet spins of oxygen molecules within alveolus. According to the Pauli exclusion principle, parallel spinors repel each other and anti parallel spinors attract each other. Thus the triplet state of spinors of oxygen molecules could help cells to repel viruses with the same induced spin states. On the other hand, by using external waves, one can induce virtual viruses with opposite induced spins within alveolus and cancel effects of real viruses. We use of this property in controlling viral diseases. Purpose: Our aim is to 1. propose a mathematical model which use of repulsive force between parallel spinors and attractive force between anti parallel spinors within structures of oxygen molecules; alveolar cells and viruses to control COVID-19 disease. 2. We also introduce a mechanism mathematically to induce virtual viruses with opposite spinor states around real viruses within alveolus. These virtual viruses cancel effects of real viruses and form harmless bubbles. 3. We introduce a quantum mask to use of spinor interactions and repel viruses. Method: In this model, hemoglobin molecules and their irons, take special spins from heart waves, move along vessels and induce them to spinors within the structure of other cells like alveolar ones. These spinors select oxygen triplet molecules with opposite spins and repel parallel spin ones. Also, spinors which form RNAs and proteins of viruses could take parallel or opposite spins of any external magnetic field. These spinning viral structures are attracted by opposite spinors of alveolar cells and repel the oxygen molecules with parallel spins. This causes to a decrease in number of needed oxygen molecules within human’s body. To control these viruses, we build a system which includes: 1. A vessel of water and oxygen molecules which be located near the face and is open. 2. A vessel of viruses which is located far from the face and is closed. 3. A heater-cooler system which connects two vessels. Results: During the respiration, alveolar air molecules go out, collide with vessels, attract oxygen and viral molecules with opposite spins and repel parallel ones. Consequently, viruses which could be attracted by alveolar cells go away from the face and build a mask against any similar spinning virus in another end of system. On the other hand, spinors around the viruses in second and closed vessel which couldn’t be attracted by alveolar cells, form some bubbles. By heating and cooling the system these bubble shapes are induced in open vessel of system, make virtual viruses and bubbles which fly towards the face and alveolus. These virtual viruses attract real viruses and make spin-less bubbles which are harmless and go out of human‘s body. We formulate the model and obtain related currents. Conclusion: By using repulsive forces between triplet oxygen states and spinors within viral structures and induction of virtual viruses with opposite spins around real viruses; harmful effects of these viruses could be cancelled. Because; spinors of viruses are surrounded by anti parallel spinors of oxygen molecules and virtual viruses and harmless bubbles and pairs are formed. We have formulate the mechanism and obtained frequencies of waves which induce virtual viruses within alveolus.

Estimation of Tensile Strength of Carbon Fibers Using Exponentiated Exponential Weibull-Dagum Distribution Model (EEWD) and Its Properties

Vidya P — 2024-11-14

The tensile strength of Carbon fibers was investigated. Tested EEWD distribution ability to fit with data and observed the skewness of data. The T-R{.} framework has been recently used to generalize various distributions, but the viability of using Dagum distribution has not been investigated. Three distributions are combined in the T-R{.}, through one serving as a baseline distribution. The combined potency of each distribution, which is a weighted hazard function of the baseline distribution, would have more parameters but would also be highly flexible in handling bimodality in datasets. Thus, this paper used the quantile function of the Weibull distribution to generalize the Dagum distribution. In this present research work a novel generalized 6P (six parameter) model called Exponentiated Exponential Weibull Dagum Distribution (EEWD) has been introduced. Appropriate distributions including PDF, CDF, moments, Moment Generating Function (MGF) of EEWD distribution, stochastic ordering, Cumulant Generating Function (CGF) of EEWD distribution, mean, mean deviations and their sub-models have been given. Further EEWD model has been applied in the real-time data admissible.

New Oscillation Conditions Test for Neutral Differential Equations

Omar Bazighifan — 2024-11-13

In this work, we investigate new oscillation conditions of delay differential equations of second-order. We start by finding new relations and inequalities between the corresponding function and its solution, also with its derivatives. The new inequalities allow us to improve the asymptotic and oscillation conditions of the solutions of the this equation. By using an improved method and approach, we obtain new criteria that test the all solutions oscillation. The article provides some examples that highlight the significance of new conditions and properties.

An Experimental Analysis of Traditional Machine Learning Algorithms for Maize Yield Prediction

Souand P.G. Tahi — 2024-12-19

Maize plays a significant role in the African diet and is one of the main staple foods in many parts of the continent. Accurate yield estimations ensure an adequate food supply, contributing to food security and reducing the risk of food shortages. They also enable market planning and price setting. Machine learning is well known as one of the most advanced statistical methods for predicting crop yields. This paper provides extensive experiment results of machine learning models on maize production. Thirteen basic supervised learning algorithms classified into classic and ensemble learning are compared using three datasets of different sizes and from various sources (Kaggle, Zenodo). These datasets are from three main origins: experimentation, specifically covering crop data with 240 observations; predictions on crop yield from the FAO (Food and Agriculture Organization) and World Data Bank with 4,121 observations; and historical data from China with 975 observations. The metrics used to evaluate the models are the coefficient of determination, the mean absolute error, the root mean square error, and the explained variance score. Moreover, permutation importance is used on the best models to identify the most relevant predictors for the models according to the data. The results show that extremely randomized trees (ERT) and extreme gradient boosting (XGBoost) are more suitable for predicting maize yield with a coefficient of determination between 0.75 and 0.96 and 0.73 and 0.96, respectively. With the other metrics, the ERT model shows a low performance. Its training time varies between 2,547 and 7,814 seconds as obtained from a computer with characteristics of HP core i5, CPU @ 1.00 GHz, 1.9 GHz, and 8 GB RAM under 134 Windows 10. ERT and XGBoost are best suited to these databases of varying dimensions, making them perfect for predicting maize yield and streamlining decision-making processes.

An Inverse Inequality for Fractional Sobolev Norms in Unbounded Domains

Radostin H. Lefterov — 2024-12-06

The nonlocal operators have found applications in various areas of contemporary science. The anomalous diffusion phenomena have been modeled by the fractional Poisson boundary-value problem. Electromagnetic fluids have been described by fractional differential equations. The fractional differential operators have found applications in material sciences, planar and space elasticity, probabilistic theory, harmonic analysis, and even in finance. The inverse inequality plays an important role in Numerical Analysis. The well-known results on inverse inequalities have been obtained in bounded domains and finite-dimensional spaces. Naturally, a new challenge arises to obtain inverse inequalities in the fractional Sobolev spaces. This paper is devoted to differential inequalities between fractional Sobolev norms. We expand the notion of a monotone function into a new notion supermonotone function and rigorously prove an inverse inequality for a class of differentiable functions in unbounded domains. Examples that demonstrate the theory are presented.

Decision-Making on Deferred Statistical Convergence of Measurable Functions of Two Variables

Devia Narrania — 2024-11-27

In this paper, we define and study strongly deferred Cesàro summable, strongly Cesàro summable, m-statistical convergence and m-deferred statistical convergence of real-valued Lebesgue measurable functions of two variables. Further, we present illustrative examples in support of our definitions. Also, we examine some properties and relations among these concepts under some restrictions. In addition, we present illustrative examples to show the essentiality of these restrictions.

Health Insurance Provider Selection Through Novel Correlation Measure of Neutrosophic Sets Using TOPSIS

B.S. Mahapatra — 2024-10-22

Risk monitoring aims to recognize and control potential threats to our assets or health activities. Insurance is vital, as it compensates for any unexpected loss of property or life. Clients selecting the best health insurance provider must consider various factors and their relative significance to their circumstances. Multi-criteria decision-making (MCDM) helps people analyze and compare policy alternatives to find the best option. This research aims to assist potential health policy purchasers by addressing the selection of health insurance providers as an MCDM problem. The correlation coefficient is useful for identifying the importance of several conflicting criteria. The idea of correlation coefficients is extended in a neutrosophic context to capture the indeterminacy and incomplete information in the relationship among the criteria. The technique for order preference by similarity to an ideal solution (TOPSIS) approach is a useful and straightforward approach to solving MCDM problems. However, it often became ambiguous to researchers due to its involvement in the distance measure technique. The proposed neutrosophic correlation measure may also replace the ambiguity of using a suitable distance measure in the TOPSIS approach. This study extends the TOPSIS method by using the proposed neutrosophic correlation coefficient on single-valued neutrosophic sets (SVNSs). The criteria preferences are computed using a method based on the removal effects of the criteria (MEREC) approach. Some valuable concepts, like the weighted closeness measure of type I and type II and the weighted index parameter, are introduced with their properties to establish the proposed neutrosophic TOPSIS approach. An MCDM approach for health insurance providers has been constructed to illustrate the proposed approach numerically. The proposed method suggest that the health insurance provider ϒ₂ is the most beneficial alternative, whereas ϒ₁ is the least suitable. The client considers the terms and conditions for non-coverage and the facilities provided for pediatric and maternity care while buying health insurance. The comparative analysis of the suggested technique demonstrates the merit of the research in terms of consistency. The sensitivity analysis demonstrates the flexibility and robustness of the obtained results.

On the Solutions of Nonlinear Implicit ω-Caputo Fractional Order Ordinary Differential Equations with Two-Point Fractional Derivatives and Integral Boundary Conditions in Banach Algebra

Yousuf Alkhezi — 2024-11-06

This article delves into the analysis of nonlinear implicit ω-Caputo fractional-order ordinary differential equations (NLIFDEs) with two-point fractional derivatives and integral boundary conditions within the context of Banach algebra. The primary focus is on demonstrating the existence and uniqueness of solutions for these complex fractional differential equations by utilizing Banach's and Krasnoselskii's fixed point theorems. Furthermore, the study explores the stability of these solutions through the Ulam-Hyers and Ulam-Hyers-Rassias stability criteria, thereby assessing the robustness of the proposed model. To illustrate the versatility of the generalized model, several special cases are examined, showcasing its ability to encompass various classical models. The practical applicability of the theoretical findings is underscored through a numerical example, which demonstrates the feasibility and relevance of the proposed methodology. This thorough investigation advances the comprehension of nonlinear fractional differential equations with integral boundary conditions, highlighting the intricate relationship between fractional derivatives, nonlinearities, and integral terms. The results offer significant insights into the behavior and stability of solutions within this demanding mathematical framework.

A Bayesian Shrinkage Approach for the Inverse Weibull Distribution under the Type-II Censoring Schemes

Mojtaba Delavari — 2024-12-02

One main challenge in the application of the lifetime distribution models, such as inverse Weibull (IW) distribution is the need for an appropriate estimation method based on experimental conditions. When prior information and certain guessed values are available for model parameters the Bayesian shrinkage (BS) method becomes a valuable approach in this situation. This study considered the BS estimation method in the two-parameter IW distribution under the squared error loss function (SELF) and the type-II censored data. The maximum likelihood (ML), the least squares (LS), and Bayes estimation methods were also examined for a comparative study. Due to the complexity of calculations, the Lindley approach was utilized to approximate the Bayes estimates. The BS estimates were derived and a score test for the guessed value was presented. Additionally, a Monte Carlo simulation was conducted to evaluate the efficiency of all estimation methods. Furthermore, a real data set was implemented to illustrate and compare the BS estimates with the other estimates. The simulation study indicated the consistency of the estimators. The numerical studies also demonstrated that the BS estimators outperform the others.

A φ-Contractivity Fixed Point Theory and Associated φ-Invariant Self-Similar Sets

Nifeen H. Altaweel — 2024-10-14

In this paper, we apply a generalized variant of the concept of fixed point theory due to contraction mappings on metric spaces to construct a general class of iterated function systems relative to the so-called φ-contraction mappings on a metric space. In particular, we give a general framework to the Hutchinson method of constructing self-similar sets as fixed points of suitable mappings issued from the φ-contractions on the metric space. The results may open a new axis in the generalization of self-similar sets and associated self-similar functions. Moreover, our results may be extended to general metric spaces with suitable assumptions. The theoretical results are applied for the computation of the fractal dimension of a concrete example of the new self-similar sets.

Peristaltic Transport of a Jeffrey Nanofluid in a Vertical Layer with Suction and Injection: Effect of Velocity No-Slip, Temperature and Concentration with Application

S. Sivaranjani — 2024-10-17

This study explores the peristaltic motion of a Jeffrey nanofluid in a vertical channel, as well as the effects of suction and injection at the walls. The non-Newtonian behavior of the fluid is described using the Jeffrey fluid model. Which includes both relaxation and retardation times. Nanoparticles are used to improve the fluid’s thermal conductivity and overall heat transfer qualities. The governing equations, such as continuity, momentum, energy, and nanoparticle concentration, are based on incompressible and laminar flow assumptions. Peristaltic flow has been extensively employed for a range of biological fluids, with a particular emphasis on non-Newtonian fluids due to their industrial implications. The intricacy of non-Newtonian fluids has led to the development of numerous models, including the Jeffrey fluid. Model which is one of the simplest linear models that accurately capture non-Newtonian properties, making it suitable for analytical solutions. Nanofluids, which consist of nanoparticles dispersed in a base fluid, are innovative materials. With numerous applications in engineering, biology, medicine, and other fields. These fluids have unique properties that make them particularly useful in a range of applications. The resulting partial differential equations are mathematically turned into dimensionless by applying appropriate transformations. The results demonstrate that peristaltic waves have significant influence on velocity and temperature, and nanoparticles improve thermal conductivity, which increases heat transfer rate, yet the elasticity of Jeffrey fluid gives unique flow features. Using MATLAB software, the effects of all physical factors on temperature, velocity, and concentration fields are visually investigated.

Regularity of Weak Solutions to a Class of Nonlinear Parabolic Equations in Fractional Sobolev Spaces

Huimin Cheng — 2024-11-29

In this article, we study regularity of weak solutions to a class of nonlinear parabolic equations in divergence form. The main purpose is to present a regularity estimate with more general conditions on coefficients, N-functions and non-homogeneous terms in the fractional Sobolev spaces. By deriving a higher integrability estimate of weak solutions, we obtain the desired regularity estimate. In addition, the results of this article expand the regularity theory of parabolic equations in fractional Sobolev spaces and Besov spaces.

Application of Sumudu Transform and New Iterative Method to Solve Certain Nonlinear Ordinary Caputo Fractional Differential Equations

Amandeep Singh — 2024-10-30

By combining the new iteration method (NIM) and Sumudu transform (ST) methods, together known as the new iteration ST method (NISTM), a semi-analytical or series solution for various fractional differential equations, in which new iteration method (NIM) is used to decompose the nonlinear operator prior to performing the ST, is produced in this script. Using the Caputo sense to account for the fractional derivative, this method computes series solutions for a variety of nonlinear fractional differential equation instances. While in many convergence issues a solution is achieved for just a small number of series terms, our series solution merges with the exact solution differential equation of fractional order in many example problems.

On the Fekete-Szegö Inequalities of the Generalized Mittag-Leffler Function Associated with a Lambert Series

Jamal Salah — 2024-10-15

This study aims to investigate the Fekete-Szegö problem for the linear operator generated by the convolution (the Hadamard product) involving one of the generalized forms of the Mittag-Leffler function and the well-known Lambert series. The findings will mainly apply on some subclasses of starlike and convex functions.

Painlevé Analysis and Chiral Solitons from Quantum Hall Effect

Nikolay A. Kudryashov — 2024-10-18

This study examines the generalized Schrödinger equation governing chiral solitons. We assess its integrability using the Painlevé test for nonlinear partial differential equations. Our analysis shows that the equation fails the Painlevé test, suggesting the Cauchy problem cannot be solved using the inverse scattering transform. However, through a traveling wave reduction, we find that the resulting nonlinear ordinary differential equation does satisfy the Painlevé test. Therefore, we establish a general solution for this reduced equation, which we outline accordingly.

A Time-Delayed Model and Estimation in Parabolic-Trough Solar Collectors

Sharefa Asiri — 2024-12-11

The dynamics of the parabolic-trough solar collectors are described by a differential equation model. Based on this model, different control strategies have been proposed to manage the heat production. However, the time delay between the solar irradiance (input) and the outlet temperature (output) has not yet been incorporated into the model. Considering this parameter will improve the model-based control techniques that strongly depend on the solar irradiance function. This paper develops a mathematical model for the parabolic-trough solar collectors in which the time delay is included. Since this parameter is unknown in practice, a method based on a cross-convolution approach is proposed to estimate it accurately. Moreover, the efficiency of the proposed method is improved by combining it with a filtering methodology. The proposed model's effectiveness and the estimation method's performance are demonstrated through numerical simulations.

Characteristic Equations of Chebyshev Polynomials of Third and Fourth Kinds and Their Generating Matrices

Anu Verma — 2024-10-14

The main goal of the article is to obtain matrix representation for the third and fourth kinds of Chebyshev polynomials by using a tridiagonal matrix. We present a connection between the determinant of the tridiagonal matrix and the third and fourth kinds of Chebyshev polynomials. We also determine the characteristic equations for the third and fourth kinds of the Chebyshev polynomials up to degree three. We also prove some properties relating to matrix representation. We obtain a connection between the second, third kind and fourth kinds of Chebyshev polynomials and matrix power. It elaborates the theorem to validate through examples. The applications of the Chebyshev polynomials is also discussed. The practical application of the Chebyshev polynomials of the third kind in approximation theory is also detailed.

Three-Dimensional Multiphase Peristaltic Flow Through a Porous Medium with Compliant Boundary Walls

Nouman Ijaz — 2024-11-07

In this communication, we focus on the peristaltic propulsion of multiphase fluid flowing in a three-dimensional rectangular channel with compliant walls. The flow is influenced by porosity and magnetic effects, and the formulation is based on lubrication theory. The governing equations for both fluid and particulate phases are derived for continuity and momentum, assuming a long wavelength (λ → ∞) and a creeping flow regime (R_e→ 0). Exact solutions of the partial differential equations for both solid and liquid velocities are obtained using the eigenfunction expansion method. We analyze the influence of several relevant parameters on the velocities and profiles graphically. It is found that fluid velocity increases with greater damping and mass effects. Conversely, wall tension and wall elastance have an inverse effect on velocity distribution. While wall tension tends to reduce the size of the boluses, wall stiffness tends to enhance the trapping of boluses. Additionally, the size of the trapped bolus increases due to the combined effects of the magnetic field and porosity.

Certain Weighted Fractional Integral Inequalities Involving Convex Functions

Majid K. Neamah — 2024-12-09

A comprehensive examination of applied sciences and their advancement necessitates an expansion of analytical studies. Our objective in this article is to unveil and present a fresh perspective on weighted integral inequalities by introducing the concept of the weighted proportional Hadamard fractional integral operator. To achieve this generalization, we have used positive and continuous functions, while some of the functions used during our generalization of these inequalities must fulfill the condition of being convex over a certain period that represents the range of functions used for the generalization. Additionally, we establish some novel inequalities using this fractional integral operator. We also delve into specific instances of the findings we present. This study significantly contributes to the literature by bridging gaps in the understanding of fractional integrals and their relationship with convex functions, thereby paving the way for future research in this dynamic area.

Nonlinear Schrödinger Equations with Delay: Closed-Form and Generalized Separable Solutions

Andrei D. Polyanin — 2024-12-04

Nonlinear Schrödinger equations with constant delay are considered for the first time. These equations are generalizations of the classical Schrödinger equation with cubic nonlinearity and the more complex nonlinear Schrödinger equation containing functional arbitrariness. From a physical point of view, considerations are formulated about the possible causes of the appearance of a delay in nonlinear equations of mathematical physics. To construct exact solutions, the principle of structural analogy of solutions of related equations was used. New exact solutions of nonlinear Schrödinger equations with delay are obtained, which are expressed in elementary functions or in quadratures. Some more complex solutions with generalized separation of variables are also found, which are described by mixed systems of ordinary differential equations without delay or ordinary differential equations with delay. The results of this work can be useful for the development of new mathematical models described by nonlinear Schrödinger equations with delay, and the given exact solutions can serve as the basis for the formulation of test problems designed to evaluate the accuracy of numerical methods for integrating nonlinear partial differential equations with delay.

Families of Graceful Spiders with 3ℓ, 3ℓ + 2 and 3ℓ – 1 Legs

N. B. Huamaní — 2024-11-07

We say that a tree is a spider if has at most one vertex of degree greater than two. We prove the existence of families of graceful spiders with 3ℓ, 3ℓ+2 and 3ℓ−1 legs. We provide specific labels for each spider graph, these labels are constructed from graceful path graphs that have a particular label, so there is a correspondence between some paths and graceful spiders that we are studying, this correspondence is described in an algorithm outlined in the preliminaries.

Stable Truncated Trigonometric Moment Problems

Luminita Lemnete Ninulescu — 2024-11-22

Let , be an one dimensional complex sequence of degree at most 2n. In the present paper we give a necessary condition such that admits on an atomic representing measure with a finite number of atoms. The necessary condition is expressed in terms of "stability" of the Riesz linear non-negative functional, , associated to the given sequence. We also give a necessary and sufficient condition such that the extended sequence to admit on an unique atomic representing measure with a finite number of atoms. The "stability" condition of the introduced Riesz functional is an adaption of the concept "dimension stability" by Vasilescu introduced for solving Hamburger moment problems in [5]. In section 3 of the present paper, we apply the main existence theorem for determining representing measures with 1, 2, 3 atoms, according to the rank of the moment matrix. The representing measures of the data of the quadratic moment problem have the support in the unit circle.

A Class of p-Valent Close-to-Convex Functions Defined Using Gegenbauer Polynomials

Waleed Al-Rawashdeh — 2024-12-12

A new class of p-valent close-to-convex functions is introduced in this paper, which is defined using Gegenbauer Polynomials within the open unit disk D. This investigation sheds light on the properties and behaviors of these p-valent close-to-convex functions, providing estimations for the modulus of the coefficients a_p+1 and a_p+2, with p being a natural number, for functions falling under this particular class. Additionally, this paper also investigates the classical Fekete-Szegö functional problem for functions f that are part of the aforementioned class.

Semantic Segmentation Based on Geometric Calibration Using AI and AR in Health Care

G. Ganesan — 2024-11-12

In the medical field, medical imaging is essential for precise diagnosis, treatment planning, and condition monitoring. The goal of this work is to improve the field of healthcare imaging by investigating the complementary applications of augmented reality (AR) and artificial intelligence (AI) in semantic segmentation. More precise identification and delineation of anatomical structures and abnormalities in medical images is made possible by AI-driven semantic segmentation, opening the door to more precise diagnosis and treatment plans. Modern AI algorithms are employed in the suggested methodology to perform semantic segmentation in a variety of medical imaging modalities, including ultrasound, CT, and MRI scans. The detection of anomalies such as tumours, irregularities in organs, and neurological disorders is made easier by these algorithms. The foundation for integrating augmented reality technologies into the healthcare ecosystem is provided by the segmented medical images. AR enhances the interaction and visualization of segmented medical data in the context of healthcare. Real-time augmented reality overlays help surgeons by improving surgical navigation and precision. Additionally, AR apps help with medical education by offering professionals and students alike an immersive learning environment. AR provides interactive visualizations to help patients understand their medical conditions when they are going for therapy and rehabilitation. The difficulties in integrating these technologies in the healthcare industry are discussed in this paper, with a focus on the significance of data privacy, regulatory compliance, and easy integration with current healthcare systems. The successful deployment of AI technologies necessitates interdisciplinary collaboration among AI developers, healthcare professionals, and AR specialists to ensure compliance with ethical, legal, and clinical standards mandated in the healthcare domain. The proposed Segmentation mask is redefined with geometric calibration and used with U-Net for image segmentation. The segmentation is experimented on Cityscapes and PASCAL VOC 2012 datasets. The experimental results show that proposed semantic segmentation based on geometric calibration yields more accuracy than its counterparts.

Structure of (σ, ρ)-n-Derivations on Rings

Abu Zaid Ansari — 2024-11-29

The goal of this research is to describe the structure of Jordan (σ, ρ)-n-derivations on a prime ring. By (σ, ρ)- n-derivations, we mean n-additive maps ℑ : Rⁿ→R satisfying the following property in each n-slot:

ℑ(pq, ϖ1, ··· , ϖn−1) = ℑ(p, ϖ1, ··· , ϖn−1)σ(q) +ρ(p)ℑ(q, ϖ1, ··· , ϖn−1),

for every p, q, ϖ1, ··· , ϖ_n−1∈ R. We find the conditions under which every Jordan (σ, ρ)-n-derivation becomes a (σ, ρ)-n-derivation. Moreover, the concept of ∗-n-centralizers on ∗-ring has given. The ∗-ring is also used for examining some outcomes, where left and right ∗-n-centralizers are significant

Statistical Evaluation of Survival Rates in Lung Cancer Utilizing Gaussian and Logistic Regression Techniques

Pitta Shankaraiah — 2024-11-19

Cancer is the second most prevalent cause of mortality globally as per the World Health Organization. Among the various types of cancer, lung cancer is particularly fatal and ranks third in terms of frequency. Its impact on healthcare systems and individuals’ quality of life is enormous. This sort of cancer is particularly problematic because it has a very poor survival rate compared to other types of cancer. The focus of the present research is to examine the correlation between lung cancer and survival time, in addition to the different characteristics of the cancer dataset. The purpose of the present investigation is to determine the optimal modeling strategy for accurately assessing the survival probabilities and other statistical measures. A set of Gaussian and Logistic parametric regression survival models to calculate probability values, average survival time, and other relevant statistical metrics have been used in the present research study. The data of 168 patients and nine essential variables related to advanced lung cancer, including age, gender, and other clinical factors have been included in the study. The proposed estimation methods are compared by assessing significant factors, such as mean survival probability, mean cumulative survival probability, and model fit indices viz, the Akaike Information Criterion and Bayesian Information Criterion. The family of Logistic Regression models exhibited higher performance across these parameters, reflecting their resilience and appropriateness for this particular set of survival data.

The Nonlinear Schrödinger Equation Derived from the Third Order Korteweg-de Vries Equation Using Multiple Scales Method

Murat Koparan — 2024-11-14

Nonlinear equations of evolution (NLEE) are mathematical models used in various branches of science. As a result, nonlinear equations of evolution have served as a language for formulating many engineering and scientific problems. For this reason, many different and effective techniques have been developed regarding nonlinear equations of evolution and solution methods. Although the origin of nonlinear equations of evolution dates back to ancient times, there have been significant developments regarding these equations from the past to the present. The main reason for this situation is that nonlinear equations of evolution involve the problem of nonlinear wave propagation. In recent years, equations of formation have become increasingly important in applied mathematics. This work focuses on the perturbation approach, often known as many scales, for nonlinear evolution equations. The article focuses on the analysis of the (1+1) dimensional third-order nonlinear Korteweg-de Vries (KdV) equation using the multiple scales method, which resulted in obtaining nonlinear Schrödinger (NLS) type equations.

On q Sturm Liouville Operator with Periodic Boundary Conditions

Olgun Cabri — 2024-10-16

In this study, we consider q-Sturm Liouville operator with periodic boundary conditions. An asymptotic expression of the solution is obtained. With the help of this asymptotic representation, an asymptotic solution of the characteristic equation is presented. An application of the Rouche theorem, asymptotic expressions of eigenvalues are obtained.

Dynamic Analysis of Extinction and Stationary Distribution of a Stochastic Dual-Strain SEIR Epidemic Model with Double Saturated Incidence Rates

S. Saravanan — 2024-12-12

This study aims to enhance and extend the mathematical model of a dynamic stochastic dual-strain SEIR epidemic with a double-saturated incidence rate. The model is represented by a nonlinear system of differential equations that describe the dynamics of susceptible, exposed, infected and recovered individuals, with the exposed and infected compartments further divided into sub-classes for the first and second strains. We develop an innovative stochastic epidemic model where drug-sensitive and drug-resistant infected groups interact through mutation. The primary objective is to determine the existence and uniqueness of a positive global solution using a well-deservedly constructed Lyapunov function, enabling a deeper analysis of the system’s complexities. This analytical framework reveals the interactions between disease transmission, treatment dynamics, and stochastic influences. A significant contribution to this work is defining the stochastic basic reproduction number as a threshold for the progression of both strains. Under low noise conditions and , the model predicts the emergence of an ergodic stationary distribution, offering insights into longterm disease trends. Conversely, in high-noise scenarios, , the analysis explores the extinction and persistence of drug-sensitive and drug-resistant infections. Our analytical results are further confirmed by simulations of epidemics spreading across drug-sensitive and drug-sensitive populations. Based on our simulations and theoretical predictions, we find that they are closely aligned.

Calculus for the Delta Distribution

Fred Brackx — 2024-11-20

A compendium of interesting identities involving the delta distribution in higher dimensional Euclidean space is presented, ready to use as a reference work whenever modelling with the delta function is involved. The formulæ are expressed as well in vector, as in Cartesian and spherical variables, the latter case being especially important since distributions in spherical coordinates have to be treated with the utmost care. Special attention is paid to an alter ego of the delta distribution, the so-called delta signumdistribution, acting on test functions showing a singularity at the origin, which appears, mostly unnoticed, when radial functions and negative powers of the radial distance are used.

Certain Class of P-Valent Analytic Function Associated with Derivative Operator and Their Properties

Ma'moun I. Y. Alharayzeh — 2024-11-11

This study aims to define a new subclass of multivalent analytic functions in the open unit disk. Jackson's derivative operator has been used to generate this subclass. Before getting coefficient characterization, we look at certain needs for the functions related to this subclass. We can see several fascinating features, including coefficient estimates, growth and distortion theorem, extreme points, and the radius of starlikeness and convexity of functions belonging to the subclass are shown using this technique.

Two Iterates of Symmetric Generalized Skew 3-Derivation

Abu Zaid Ansari — 2024-10-21

Our goal in this study is to validate the following finding: Assume that a prime ring R having , D is a symmetric skew 3-derivation on R with automorphisms α. If ∇₁, ∇₂ : R³ → R are symmetric generalized skew 3-derivations with α and associated skew 3-derivations D₁, D₂ respectively such that for every , then either ∇₁ = 0 or ∇₂ = 0 on R, where ∂₁ and ∂₂ stands for the traces of ∇₁ and ∇₂ respectively.

Modeling Occupational Stress on Employee Performance with Mediating and Moderating Roles of Social Support: Structural Equation Modeling and Multivariate Analysis

KDV Prasad — 2024-10-23

Purpose: This empirical study investigated the relationship between occupational stress and employee performance and the mediating and moderating effects of social support on the relationship between occupational stress and the performance of IT sector employees in Bangalore city. Methodology: A quantitative methodology was used. The data were collected via a questionnaire to measure the three reflective constructs of the study: occupational stress, employee performance, and social support. Factor loadings > 0.5 for the items of all three constructs were considered for analysis. The questionnaire's internal consistency was measured by assessing Cronbach's alpha and the split-half correlation coefficient. SEM analysis was carried out on the valid responses of 500 responses via AMOS version 28. Findings: The results of the Shapiro-Wilk test for normality indicated normally distributed data. Excellent model fit was observed, as indicated by the model fit statistics. A statistically significant direct effect between occupational stress and employee performance and social support was observed, with both the variable performance of occupational stress and social support explaining 28% of the variance in the dependent variable. performance This study also examined the moderating role of social factors in the relationship between occupational stress and employee performance. Social support also moderated the performance of the IT sector employees. Positive and statistically significant moderating effects of social support on the relationship between occupational stress and employee performance were observed. The slope analysis revealed that social support strengthens the relationship between occupational stress and employee performance. The authors suggest that organizations adopt social support strategies, such as breaks, meditation, and yoga, to relieve stress and increase social support among employees. Originality: This study assessed the effects of modeling occupational stress on employee performance with mediating and moderating roles of social support via structural equation modeling analysis and multivariate analysis.

On a General Subclass of q-Starlike and q-Convex Analytic Functions

Amnah E. Shammaky — 2024-12-10

We introduce a certain subclass of analytic functions in the open unit disk U involving the q-derivative operator. Some convolution results and Fekete-Szegö inequalities for the analytic functions belonging to this class are derived. We have also provided some results as corollaries of our theorems.

Controllability of Impulsive Damped Fractional Order Systems Involving State Dependent Delay

Arthi G. — 2024-11-11

In this article, the concept of controllability on fractional order impulsive systems involving state dependent delay and damping behavior is analysed by utilizing Caputo fractional derivative. The main motivation is to derive the sufficient conditions for the controllability of the considered systems. Based on the Laplace transform and inverse Laplace transform, the solution of fractional-order dynamical systems are obtained. The results are established by utilizing basic ideas of fractional calculus, Mittag-Leffler function and Banach fixed point theorem. Finally, an application is provided to illustrate the derived result.

Bayesian Modeling of INGARCHX Models for Cellulitis Related to Meteorological Factors in Mahasarakham and Roi-Et Hospitals

Khemmanant K — 2024-10-31

The objective of this research is to develop integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models to represent the weekly incidence of cellulitis cases in relation to two exogenous variables: seasonality and the weekly average of either relative humidity or maximum temperature. The key to the proposed model is its capacity to explain overdispersion and lag dependence. For predictions and model parameters, we employ the Bayesian Markov Chain Monte Carlo (MCMC) approach, as supported by both a simulation study and an empirical study. To assess different models, we apply the deviance information criterion (DIC) criterion to the weekly cellulitis case sample data with two independent variables. In addition, we offer a one-week prediction to help Mahasarakham and Roi-Et Hospitals manage the increasing volume of hospital admissions by estimating the weekly cellulitis case incidence rate.

Generation of Fractal Attractor for Controlled Metric Based Dynamical Systems

C. Thangaraj — 2024-12-12

Mandelbrot initiated the term “Fractal” in 1975, and it has since gained popularity among mathematicians and physicists alike. The mathematical properties of fractals are available and applied in the chaotic structures of various systems, which are generally experienced in science and technology. The iterated function system (IFS) evolved as a practical application of the theory of discrete dynamical systems and is a valuable tool to generate fractal attractors. In this context, the Hutchinson-Barnsley (HB) theory is generalized to construct fractal sets using an IFS of contractions on a controlled metric space (CMS). The HB theorem of IFS is proved in a Hausdorff controlled metric space (HCMS), and it is also guaranteed that the HB operator has merely a single fixed point in a Hausdorff controlled metric space, known as a controlled fractal. This study also links the extended rectangular b-metric space (ERbMS) and the controlled metric space to create a new metric space, the controlled extended rectangular b-metric space (CERbMS), by incorporating the control factor as a function in the rectangular inequality. In addition, the fixed point theorem is also proved with specific conditions for contractions in the proposed metric space CERbMS and illustrated with an example. Finally, the structure of IFS is defined in CERbMS to construct the HB theory for generating the controlled extended rectangular b-fractals.

Kolmogorov-Arnold Representation Based Informed Orchestration in Solving Partial Differential Equations for Carbon Balance Sustainability

Charles Z. Liu — 2024-11-14

This paper introduces the Kolmogorov-Arnold Credit Informed Network Orchestration (KACINO), a novel framework proposed to comprehensively structure and analyze the carbon dynamic system. By synthesizing dynamic processes such as carbon emission and sequestration, a credit information of carbon dynamics is built accumulation, KACINO provides a holistic approach to model the complexities inherent in carbon dynamics. Through systematic analysis and scenario simulations, KACINO facilitates informed policy recommendations aimed at optimizing carbon credit utilization and achieving sustainable environmental outcomes. This paper outlines the theoretical foundation, methodology, and practical applications of KACINO, highlighting its potential to support transformative strategies in climate change mitigation and sustainable development.

Asymptotic Behavior of Trajectories in Some Models of Ecnomic Dynamics

S. I. Hamidov — 2024-10-24

Asymptotic behavior of trajectories in Neumann type models of economic dynamics with average growth rate is studied. Index set is introduced and the sequence of cones generated by the cone Z of the Neumann-Gale model is considered. The concept of quasi rate of the model z_i is introduced. The relationship between the concepts of average growth rate and quasi rate is found. The relationship between the turnpikes M_α for different values of х and the set A_z of conic hulls of the sets of all angular distance limit points is examined. Upper and lower estimates for a non-empty turnpike are obtained. Under some additional conditions, more accurate lower estimate is obtained which allows to conclude that in most cases the set M_αis a subset of the set A_z. Algorithm is proposed for constructing a trajectory X_i, which has the point x among its angular distance limit points. Theorem on the existence of a turnpike which has the point х among its angular distance limit points is proved.

Hybrid PLM and ADRC Control for Sensorless Induction Motor Drive with Nine-Level Converter Employing SVPWM

Abdellah Oukassi — 2024-10-21

This paper outlines the design of a predictive controller combined with an active disturbance rejection control (ADRC)-type controller to enhance the dynamic performance of the induction motor powered by a nine-level converter. The predictive control law proposed is derived from the Poisson Laguerre model, based on predictive control. The motor is controlled using indirect field-oriented control, both with and without a speed sensor. For speed estimation, the Luenberger observer of order 4 is used. The predictive method utilized allows for the dynamic adjustment of control parameters based on those of the induction motor. The paper aims to eliminate internal and external disturbances and reduce total harmonic distortion (THD) through the use of a Nine-level cascaded H-bridge inverter. Space vector pulse width modulation (SVPWM) signals are generated using the logic of hexagon decomposition. The SVPWM method operates by decomposing higher-level hexagons into multiple two-level hexagons. The Poisson-Laguerre model (PLM) is also compared with the ADRC and the proportional-integral (PI) control. Simulations with MATLAB/SIMULINK software for an induction motor are performed to test the performance of each controller and the validity of the observer.

Numerical Computation and Statistical Interpretations of Heat Transfer of Tween-20/ethyl Acetate Nanofluid Flow with Melting Rheological Quality and Activation Energy

Aamir Farooq — 2024-11-11

Tween-20 plays a significant role in the biological, food, and pharmaceutical industries. Additionally, it plays a vital role in improving the quality of reverse mechanisms of multi-drug resistance. This paper uses artificial neural computing to examine Tween-20 nanoparticles’ behaviors in a base fluid called ethyl acetate to enhance the applications in nanomedicine, drug delivery and biotechnology. The study focuses on the nonlinear model of a viscous fluid at the stagnation point, where mixed convection processes and activation energy are present. The study incorporates slip velocity and melting boundary conditions to examine heat and mass transfer, taking into account thermal and solutal stratification. Various fields of research and technology, specially in industrial engineering that include hydrodynamics, panto-graph systems, and biomedical mathematics, extensively utilize artificial computing. The datasets are based on velocity, temperature, and concentration outlines. The fourth-order Runge-Kutta method is used to generate the datasets. To validate the LMM-ABNNs, we have compared them with a numerical solution, showing a high level of agreement. We utilize the error histogram and mean square error results to validate the performance, scrutinize the training and testing methods, and explore the validity of the approximate answer. Furthermore, the quality characteristics such as skin friction, rate of heat, and mass movement (Nusselt and Sherwood numbers) are statistically analyzed to forecast the model’s durability. This article is the best example of investigating different fluid parameters with the latest artificial neural computing.

Analysis of Interested Subjects in New Energy Vehicle Industry-Based on Game Theory Perspective

Zhu Meng — 2024-12-12

This paper analyzes the stakeholders of the new energy vehicle industry strategic choices in market competition using Nash equilibrium and cooperative game theory from game theory, employing mathematical models. First, This paper constructs a game model containing multiple competitors to determine the optimal strategy of the industry in the non-cooperative situation. Secondly, the cooperative game theory is introduced to analyze the distribution of various stakeholders in the new energy vehicle industry under the condition of cooperation, and to discuss how to achieve win-win results through cooperation.Verifying the model's effectiveness through empirical analysis, we suggest competitive strategies to be employed in the tripartite game. Our research demonstrates that game theory can provide a scientific basis for the new energy vehicle industry to devise effective competitive tactics in the intricate market environment.

Modelling Climate Change in a Stochastic Extreme Values Framework

Mathieu Tiene — 2024-11-07

This article presents a contribution to modelling of rainfall hazards in a stochastic framework. The independence of the realizations of a process conditionally on the latent random effect, which also allowing us to calculate the likelihood of the observed annual maxima. We also showed the predominance of the moment estimator over the Hill estimator. Furthernore, we used a stochastic model to provide a temporal framework for modeling extreme events, as well as the evolution of extreme rainfall in west Africa from 2019 to 2169, which shows a significant decrease over the entire range of the different stations.

Numerical Treatment for the Distributed Order Fractional Optimal Control Coronavirus (2019-nCov) Mathematical Model

Nehaya R. Alsenaideh — 2024-10-31

In this paper, we presented the distributed order fractional optimal control of the Coronavirus (2019-nCov) mathematical model. The distributed order fractional operator is defined in the Caputo sense. Control variables are considered to reduce the transmission of infection to healthy people. The discretization of the composite Simpson's rule and Grünwald-Letnikov nonstandard finite difference method is constructed to solve the obtained optimality system numerically. The stability analysis of the proposed method is studied. Numerical examples and comparative studies for testing the applicability of the utilized method and to show the simplicity of this approximation approach are presented. Moreover, by using the proposed method we can conclude that the model given in this paper describes well the confirmed real data given in Spain and Wuhan.

Existence Results and Trajectory Controllability of Conformable Hilfer Fractional Neutral Stochastic Integro-differential Equations

A. Jalisraj — 2024-11-25

This manuscript commits to analyzing the existence and uniqueness of mild solution and trajectory controllability of conformable Hilfer fractional neutral stochastic integro-differential system with infinite delay through Lipschitz, growth conditions and properties of semigroup theory, controllability theory, stochastic analysis techniques, and Banach fixed point theorem with example. This manuscript mainly focuses on fractional system provide the mathematical foundation to understand and control complex, real-world systems with memory, and randomness.

Mathematical Evaluation and Dynamic Transmissions of a Tumor Growth Model Using a Generalized Singular and Non-Local Kernel

Rakhi Singh — 2024-10-15

Currently, fractional calculus plays a critical role in improving control techniques, analyzing disease transmission dynamics, and solving several other real-world problems. This research investigates the time-fractional tumor growth model using an innovative approach. The new modified fractional derivative operator employs a singular and non-local kernel, based on Atangana and Baleanu's concepts with the Caputo derivative. The tumor growth model used the newly modified fractional operator, which provided numerical simulation. With the introduction of this new operator, we provide significant analysis for the tumor growth epidemic model. We have proven the uniqueness and stability conditions of the model by utilizing Banach's fixed point theory and the Picard successive approximation method. Using the Laplace-Adomian decomposition method (LADM), we found the numerical solution to the Modified Atangana-Baleanu-Caputo derivative model. We have verified the convergence analysis of the suggested scheme. We ultimately utilize the suggested method to obtain numeric outcomes and simulations for the tumor growth model. The study investigates the effect of multiple biological variables on the transmission of tumor growth dynamics.

Optimizing Group Size using Percentile Based Group Acceptance Sampling Plans with Application

Abdullah M. Almarashi — 2024-11-05

The present paper focuses on optimizing the sample size and the acceptance number which are commonly known as design parameters for the group acceptance sampling plan (GASP). Design parameters are analyzed under the assumption that the characteristic of interest for the product follows Another Generalized Transmuted-Exponential (AGTransmuted-Exponential) distribution. Using different values of the quality levels (median lifetime), the values of the Operating Characteristic function is determined. The proposed plan satisfies two types of risks based on producer's point of view and consumer’s point of view at varied stipulated quality levels. Optimization of the sample size, group size and acceptance numbers is obtained through Monte Carlo simulation, for which relevant R codes were developed. Specific R codes are appended for future usage by academia and practitioners from various fields of life. The simulated results of the study are exhibited in the form of tables and explained with relevant examples. Results of the proposed GASP are compared with plan parameters obtained using MLE estimates of AGTransmuted-Exponential distribution and also by design parameters obtained using mean as quality level. Results of the study exhibited that Median as a quality parameter resulted in the decrease of group size and acceptance number simultaneously at all quality levels. Easy to follow the methodology of the current paper will open new vistas for applying the proposed GASP to a family of transmuted probability distributions. For illustration purposes, a real data set for fatigue fracture stress is analyzed using MLE estimates of AGTransmuted-Exponential distribution to demonstrate the implementation of the proposed sampling plan.

Optimizing Stochastic Transportation Networks with Mixed Constraints Using Pareto Distribution

Pullooru Bhavana — 2024-12-10

We propose a novel solution approach combining stochastic programming techniques with Pareto distribution characteristics. This approach involves reformulating the problem into a tractable optimization model using probabilistic constraints and employing advanced algorithms to solve the resulting mixed-integer programming problem. Numerical experiments illustrate the effectiveness of the proposed method and highlight its practical implications for transportation network design and management under uncertain conditions. The results demonstrate that incorporating Pareto-distributed uncertainties into the transportation problem provides a more realistic and adaptable framework for decision-making. The proposed solution approach offers valuable insights for managing complex transportation systems where both stochastic and deterministic factors play a crucial role.

Existence Results for Multivalued Contractive Type Mappings Involving w_b -Distances

Abdul Latif — 2024-12-09

We present some new results on the existence of fixed points for multivalued contractive type mappings involving generalized distance on metric type spaces. In support of our main results, some examples are also given. Finally, we conclude that our new presented results either improve or generalize some interesting fixed point results of the existing literature.

Solving Multi-objective Bi-item Capacitated Transportation Problem with Fermatean Fuzzy Multi-Choice Stochastic Mixed Constraints Involving Normal Distribution

Elakkiya Kumar — 2024-11-05

The transportation problem (TP) is an important type of linear programming problem. The aim of TP is to optimize the objective function by allocating product shipments from various sources to multiple destinations. When limitations exist during transportation in the number of products transported from a source to destination due to a variety of factors, such as storage limitations, budgetary constraints, and so on, then TP becomes the capacitated transportation problem (CTP). The business entrepreneurs are keen on transporting multiple items with multiple objectives to generate maximum revenue for an organization, which leads to the development of a multi-objective bi-item capacitated transportation problem (MOBICTP). If a supplier's resources significantly increase or decrease, and the demand needs also significantly increase or decrease, the MOBICTP transforms into a MOBICTP with mixed constraints. Most real-world problems have uncertain parameters due to insufficient data, fluctuating market costs for an item, variation in weather conditions, and so on. Such uncertain parameters are addressed using fuzzy, multi-choice, or stochastic programming. In this article, we examined a novel integrated model for a multi-objective bi-item capacitated transportation problem, which includes a fermatean fuzzy multi-choice stochastic mixed constraint that follows normal distribution. First, the Fermatean fuzzy multi-choice stochastic parameter in the constraints is transformed into a multi-choice stochastic parameter in the constraints by using the (α, β )-cut technique and accuracy function. Then the improved chance-constrained method is developed using Newton divided difference interpolation polynomial. The improved chance-constrained method is used to transform the multi-choice stochastic parameter in the constraints into its equivalent deterministic constraints. Secondly, we propose a novel approach, the improved global weighted sum method, which transforms a multi-objective problem into a single objective problem and utilizes Lingo 18.0 software to find the optimal compromise solution to the equivalent deterministic problem. The main aim of this paper is to help business entrepreneurs improve their profit margins by optimizing the quantity of multiple items while minimizing damage costs, labor costs, transportation time, and transportation costs, and maximizing discounts. To show the model’s validity and significance, a numerical example is solved using the Lingo 18.0 software. In order to emphasize the proposed method, a comparative analysis is conducted with other existing methods. The final component includes a sensitivity analysis and conclusions with future research directions.

Deriving Optimal Skew Polycyclic Codes Over F_q Using Skew Polycyclic Linear Codes Over R = R₁ ×R₂ ×R₃

Sassia Makhlouf — 2024-11-29

This paper investigates the theory and applications of linear and skew polycyclic codes over the ring = 1 ×2 ×3, where i (0 ≤ i ≤ 3) are finite commutative rings. We first explore the structure of linear codes over , establishing foundational properties. Then, we introduce skew polycyclic codes over , a generalization of polycyclic code over a finite field. We delve into the algebraic structure of these codes and demonstrate how they differ from their classical counterparts. Furthermore, we examine the dual codes ofskew polycyclic codes over , providing necessary and sufficient conditions for a code to be self-dual. Finally, we investigate the Gray images of skew polycyclic codes over , focusing on codes with optimal parameters. We provide explicit construction of Gray maps that yield images with good properties,such aslarge minimum distances and favorable automorphism groups. These results have potential applications in constructing new classes of error-correcting codes. We demonstrate this through an example of skew polycyclic codes applied in secret sharing schemes.

The Spectra of Multiplication Operators and Weighted Composition Operators on Iterated Weighted-Type Banach Spaces of Analytic Functions

Shams Alyusof — 2024-10-11

This research aims to analyze the spectral of multiplication operators acting on weighted Banach spaces of analytic functions defined on the unit disk. These spaces, denoted by Sn : n ∈ N, include well-known cases such as the Bloch space and the Zygmund space for n = 1 and n = 2, respectively. Additionally, we offer a description of the spectra of weighted composition operators within these spaces. The outline of this paper provides a structured framework for organizing the research, starting from the introduction to the conclusion and references. The main section is to investigate the spectrum of multiplication operators on Sn spaces, and it followed by a section that is designed to build upon the previous one, leading to characterize the spectrum of weighted composition operators on the same spaces.

D-Continuity

Mohammad Zailai — 2024-11-20

We call a map f : X → Y D-continuous if its restriction to any set of points that do not possess compact neighborhoods is continuous. We investigate this weaker version of continuity and provide examples to compare D-continuity with other types of continuity. Let f : X → Y be a D-continuous bijective map such that f(A) is locally finite, where A is the set of all points that do not possess compact neighborhoods in X. Then, we show that f|A is a homeomorphism. We also show that if X is a countably generated topological space, then any D-continuous f : X → Y is continuous. We discuss C-normality, illustrating the relationship between this property and D-continuity. Finally, we investigate the space of all real-valued D-continuous maps of an arbitrary topological space X and obtain some results.

On Impulsive Nonlocal Nonlinear Fuzzy Integro-Differential Equations in Banach Space

Najat H.M Qumami — 2024-10-18

The aim of this article is to investigate the existence, uniqueness and other qualitative properties of the solution of first-order nonlocal impulsive nonlinear fuzzy integro-differential equations in Banach space by using the concept of fuzzy numbers whose values are normal, upper semicontinuous, compact, and convex. The result is attained by utilizing a modified version of the Banach contraction principle. We offer an example as an application of the results.

Finite Sum of Integral Operators from the Fractional Cauchy Spaces to Bloch-Type and Zygmund-Type Spaces

Rita A. Hibschweiler — 2024-10-15

The family of fractional Cauchy transforms, defined on the open unit disc in the complex plane, is of classical and modern interest. Membership of an analytic function in the family is determined by the requirement that the function can be expressed as an integral of a certain kernel against a complex Borel measure on the disc. Such an integral representation imposes a growth condition on the function and its derivatives. This exposes a connection between the families of Cauchy transforms and familiar spaces of analytic functions, such as the Bloch spaces and the Zygmund space. The notion of a composition operator has been a fruitful area of study. More generally, many authors have studied weighted composition operators, the differentiation operator, integral-type operators, and various products of such operators, acting from one normed linear space of analytic functions to another such space. A common theme of such works is to characterize the operator-theoretic notions of boundedness and compactness in terms of the inducing symbols of the operator. We extend these studies to a specific linear transformation which will be defined as the sum of finitely many integral operators. Our conclusions include a complete characterization of boundedness and compactness of the integral sum, acting from the fractional Cauchy spaces to the Bloch-type and Zygmund-type spaces.

Application of Natural Transform Decomposition Method for Solution of Fractional Richards Equation

K. Raghavendar — 2024-12-09

This study employs the natural transform decomposition method (NTDM) to examine analytical solutions of the nonlinear time-fractional Richards equation (TFRE). The NTDM is an innovative and attractive hybrid integral transform strategy that elegantly combines the Adomian decomposition method and the natural transform method. This solution strategy effectively generates rapidly convergent series-type solutions through an iterative process involving fewer calculations. The convergence and uniqueness of the solutions are presented. To demonstrate the efficiency of the considered solution method, two test cases of the TFRE are investigated within the framework of the Caputo-Fabrizio and Atangana-Baleanu-Caputo derivatives whose definitions incorporate nonsingular kernel functions. Numerical comparisons between the obtained approximate solutions, exact solutions, and those from existing related literature are presented to show the validity and accuracy of the technique. Graphical representations demonstrating the effect of varying non-integer, temporal, and spatial parameters on the behavior of the obtained model solutions are also presented. The results indicate that the execution of the method is straightforward and can be employed to explore complex physical systems governed by time-fractional nonlinear partial differential equations.

Essential Analysis of New SEVIR Model: A Five Case Epidemic Model

Kalpana Umapathy — 2024-12-03

In this work, we introduce a new SEVIR epidemic model to analyze the dynamics of infectious diseases by incorporating the key compartments such as susceptible, exposed, vaccinated, infected, and recovered populations. We add the vaccination compartment in the current model and calculate the consequences concerning the disease spreading; it is significantly relevant at the present day considering the general policies of worldwide vaccinations. For a stringent assessment of stability, it should involve derivation of a basic reproduction number, as this parameter characterizes whether an infection will be spread at all. Our results demonstrate that when we have R₀ < 1, the disease-free equilibrium is locally asymptotically stable, which implies that an infection will eventually die out. We also identify two distinguished disease-dependent equilibrium points for the first time, giving much deeper insight into long term behavior of the disease. Numerical simulations show the efficacy of vaccination toward reducing the newly infected individuals and suggest the model can predict stabilization for all compartments over time. The exposed and recovered population increases and stabilizes as the susceptible, infected, and vaccinated populations decline. In this regard, these are valuable insights into the progression of epidemics and put emphasis on vaccination programs. Our model provides a perspective on disease control by taking into account the interplay between vaccination and infection dynamics. It can be very useful for predicting future outbreaks and can guide public health policy. Future work will extend the model by adding quarantine measures to further hone our understanding of disease transmission.

Sequential Kannan Type Contractions in Partial b-Metric Spaces

Yaé U. Gaba — 2024-10-18

This paper presents the concept of the "sequential condition" in the context of fixed point results for self-maps in partial b-metric spaces. We demonstrate the existence of a unique fixed point when this condition is satisfied. Additionally, we provide illustrative examples to showcase the application and effectiveness of our findings.

Goal Programming Model Using Data Envelopment Analysis for Human Development Index

Yasmine Salama — 2024-10-24

United Nations' Human Development Index measures human development and has significant positive correlation with abundance in natural resource. Data Envelopment Analysis is used for composite indicators' development and overcomes weighting techniques' limitations. It has limitations in existence of missing records that Goal Programming can overcome. Accordingly, this paper introduces a new Human Development Index that improves upon the United Nations' Human Development Index by incorporating natural resource abundance and addressing missing data issues through Goal Programming. To address these issues, a model is proposed that combines Data Envelopment Analysis and Goal Programming. The model first estimates missing values and then calculates weights for the Human Development Index using Data Envelopment Analysis, which integrates standardized human development dimensions with natural resource factors. This revised Human Development Index results in new country rankings and is validated through a correlation analysis with the United Nations' Human Development Index and a Wilcoxon Signed-Rank test. The correlation analysis shows strong agreement in rankings despite different weighting methods, while the Wilcoxon test indicates significant differences in median rankings. Our proposed index offers a more comprehensive measure of human development by considering both human development dimensions and natural resources, enhancing the accuracy of the Human Development Index and suggesting areas for future research into additional factors affecting human development, beside others.

A Wavelet Multi-Scale Takagi-Sugeno Fuzzy Approach for Financial Time Series Modeling

Anouar Ben Mabrouk — 2024-11-25

Fuzzy logic has been introduced as a modeler suitable for many situations where the data may be uncertain, and difficult to be described via the existing exact and analytic tools. However, although fuzzy models have succeeded to fit many situations, they fail in many others especially nonlinear, non-stationary, volatile, fuzzy, and fluctuated data such as financial time series. In this context, the need has emerged for more effective models to describe the data while preserving the fuzzy model as a basic descriptor of data fuzziness. In the present work, we develop a hybrid approach combining the Takagi-Sugeno fuzzy model with the wavelet decomposition to investigate financial time series as complex systems. The new approach showed effectively a high performance compared to existing methods via error estimates and Lyapunov theory of stability. The model is applied empirically to the Saudi Arabia Tadawul market traded over the period January 01, 2011, to December 31, 2022, a period characterized by many critical movements and phenomena such as the Arab Spring, Qatar embargo, Yemen war, NEOM project, 2030 KSA vision and the last COVID-19 pandemic, which makes its study of great importance to understand markets situations and also for policymakers, managers and investors.

A Multi-Model Survival Analysis of Lung Cancer Using Parametric Techniques

Pitta Shankaraiah — 2024-11-25

Lung cancer remains one of the leading causes of cancer-related mortality worldwide, underscoring the critical need for effective prognostic tools. This study utilizes survival analysis to explore the factors that influence the survival outcomes of North Central Cancer Treatment data related to lung cancer. The main goal of this study is to compare and contrast various statistical models, including the Weibull, Exponential, Log-gaussian, Gumbel, and Rayleigh models. We have computed important functions, such as the survival function, the hazard function, and the cumulative hazard function, for all the considered distributions. The Anderson-Darling and Cramer Von-Mises tests, which are Goodness of fit tests, effectively compare and assess various parametric regression survival models. The Weibull survival model is interpreted to be the most effective and efficient way to study the lung cancer dataset, which is concluded upon evaluating the results of Anderson-Darling statistic 0.28745, Cramer Von-Mises statistic 0.0450, Mean Survival Probability 0.9697, Mean Cumulative Survival Probability 0.0303, Akaike Information Criterion 1,650.753 and Bayesian Information Criterion 1623.329 of the Weibull, Exponential, Log-gaussian, Gumbel, and Rayleigh parametric regression survival models.

A Mathematical Model for Inducing Delays in Transmissions of Information Between Spinors Within the Heart, Hemoglobin Molecules and Cells by Mobile Waves

Massimo Fioranelli — 2024-10-31

Biological systems like the heart, hemoglobin and cells are built from entangled spinors. Entangled spinors exchange information through two ways: (i) Spinor waves with the velocity of infinity; and (ii) Photons with the limited velocity of the speed of light. If any spin in a pair reverses, then the other spin changes sogn immediately. However, initial exchanged photons do not understand these changes, and retain the memory of the previous stage. Thus, when they reach the spinors, the spinors repel them. With time, the new emitted photons from the spinors obtain the correct information, and absorb other spinors in a pair. This repelling and absorbing causes the oscillation of heart cells and the motions of blood cells including hemoglobin. These molecules transmit information and oxygen and pass them on to cells. A mobile wave could break the entanglement between the spinors of the hemoglobin, and cause a delay in information and oxygen transmission from the heart to some cells, thereby creating non-normal cells like tumor ones. The reason for this is that without information, cells have to act independently of other cells. Also, without oxygen, cells have to use other mechanisms for respiration like the ones which were used by tumor cells in the Warburg proposal. This does not depend on the wavelength because the wavelength only determines the probability of existence of photons at each point and waves with any wavelength (even bigger than cell size) are formed from many photons with smaller size than cells. However, after some time, after establishing electromagnetic towers, the spinor structure of the body could resist these wave-fronts, and the probability for the emergence of tumors decreases. Without this resistance and according to the Warburg proposal, generated tumor cells produce different numbers of spinors which help them to diagnose the motion of T-cells, making them ready to respond. To avoid this event, we may use again some mobile waves which produce some noise around tumor cells.

Exact Time-Dependent Thermodynamic Relationships for a Brownian Particle Navigating Complex Networks

Mesfin Asfaw Taye — 2024-11-14

The thermodynamic characteristics of systems driven out of equilibrium are examined for M Brownian ratchets organized in a complex network. The precise time-dependent solution reveals that the entropy S, entropy production ep(t), and entropy extraction hd(t) of the system in complex networks increase with system size, which is plausible as these thermodynamic quantities display extensive properties. In other words, as the number of lattice sites increases, the entropy S, entropy production ep(t), and entropy extraction hd(t) increase, demonstrating that these complex networks cannot be reduced to the corresponding one-dimensional lattice. Conversely, the rates for thermodynamic quantities such as velocity V, entropy production rate e˙p(t), and entropy extraction rate h˙ d(t) become independent of the network size in the long-term limit. The exact analytic results also indicate that the free energy decreases with system size. The model system is further analyzed by incorporating heat transfer via kinetic energy. Since heat exchange via kinetic energy does affect the energy extraction rate, the heat dumped to the cold reservoirs also contributes to internal entropy production. Consequently, such systems exhibit a higher degree of irreversibility. The thermodynamic features of a system operating between hot and cold baths are also compared and contrasted with a system functioning in a heat bath where temperature varies linearly along the reaction coordinate. Regardless of the network arrangements, the entropy, entropy production, and extraction rates are significantly larger for the linearly varying temperature case than for a system operating between hot and cold baths.

Geometric Properties and Neighborhoods of Certain Subclass of Analytic Functions Defined by Using Bell Distribution

Ala Amourah — 2024-11-25

A differential operator is defined on an open unit disk D using the innovative Bell Distribution operator. This operator introduces a new perspective in the study of complex functions within the disk. In this research, the established concept of neighborhoods plays a crucial role. By utilizing these neighborhoods, we aim to derive inclusion relations specifically concerning the (t, n)-neighborhoods of the classes defined by this operator. This approach allows for a deeper understanding of how these classes interact and overlap, providing valuable insights into their structural properties and potential applications in geometric function theory. Through this analysis, we hope to uncover new relationships and behaviors that can enhance our comprehension of differential operators in complex analysis.

A Generalized Number-Theoretic Transform for Efficient Multiplication in Lattice Cryptography

Ahmad Al Badawi — 2024-10-14

The Number Theoretic Transform (NTT) has emerged as a powerful tool for efficiently computing convolutions of digital signals, due to its inherent advantages such as numerical stability, reliance on simple integer operations, and proven efficiency. Its applications have extended to accelerating polynomial multiplication in lattice-based cryptography. However, existing NTT multiplication algorithms impose restrictions on the underlying moduli, potentially affecting key and ciphertext sizes as well as computational overhead. Therefore, enabling NTT with small moduli holds significant potential for enhancing the overall system performance. This study introduces a novel reduction framework for NTT computation in cyclotomic rings employing field extensions. Our approach replaces the underlying polynomial ring with a two-dimensional isomorphic ring, effectively relaxing the restrictions imposed on the NTT moduli. The proposed framework is evaluated through two case studies relevant to the LAC and NTTRU lattice-based cryptographic schemes. Comprehensive theoretical analysis is provided, demonstrating the effectiveness of our approach in enabling NTT with small moduli and its potential to improve the efficiency of lattice-based cryptography.

The Control Policy M/M/c/N Interrelated Queue with Manageable Incoming Rates, Reverse Balking and Impatient Customers

Immaculate Samuel — 2024-11-25

This study explores an interconnected M/M/c/N queueing model that incorporates reverse balking, reneging, a control technique, and adjustable arrival rates. In reverse balking, the likelihood of a visitor deciding to join or leave a queue is influenced by the current system size, with a higher probability of joining as the system size grows. Conversely, long wait times can lead to customer impatience, causing them to leave the queue before receiving service (reneging). Service begins with the arrival of the initial customer (T_L) and continues until the system is empty. We are developing a multi-server queueing system with adjustable arrival rates that includes reverse balking and considers impatient customers. For this model, we determine the steady-state condition and performance metrics such as average waiting time and average system size.

Derivation of Sawada-Kotera and Kaup-Kupershmidt Equations KdV Flow Equations from Modified Nonlinear Schrödinger Equation (MNLS)ns from Modfied Nonlinear Schrödinger Equation (MNLS)

Murat Koparan — 2024-10-14

Mathematical models of problems that arise in almost every branch of science are nonlinear evolution equations (NLEE). As a result, nonlinear evolution equations have served as a language for formulating many engineering and scientific problems. For this reason, many different and effective techniques have been developed regarding nonlinear evolution equations and solution methods. The main reason for this situation is that nonlinear evolution equations involve the problem of nonlinear wave propagation. In this study, (1 + 1) dimensional fifth-order nonlinear Korteweg-de Vries (fKdV) type equations were obtained by applying the multi-scale method known as the perturbation method for the modified nonlinear Schrödinger (MNLS) equation. Thus, we showed the relationship between KdV equations and MNLS type equations.

Computing Quadratic Eigenvalues and Solvent by a New Minimization Method and a Split-Linearization Technique

Chein-Shan Liu — 2024-10-22

To solve quadratic eigenvalue problems (QEPs), especially the gyroscopic systems, two methods are proposed: an iterative direct detection method (DDM) of the complex eigenvalues of the original QEP, and a split-linearization method (SLM) for finding the solvent matrix, which results to a standard linear eigenvalue problem (LEP) being solved to compute all eigenvalues by the symmetry extension. Reducing the dimension to one-half, the LEP is recast in a simpler QEP involving the square of the solvent. We set up two new merit functions which are minimized to detect the complex eigenvalues from the original QEP and a simpler QEP. For each eigen-parameter the merit function consists of the Euclidean norm of each derived eigen-equation, whose vector variable is solved from a derived inhomogeneous linear system. Then, the golden section search algorithm is employed to minimize the merit functions and locate the complex eigenvalue as a local minimal point. The results are compared with that computed by the cyclic-reduction-based solvent (CRS) method.

On a Model for Solving Mixed Fractional Integro Differential Equation

Azhar Rashad Jan — 2024-12-11

In this work, the mixed fractional integro differential equation (MfrIo-DE) of the second kind, under certain condition is considered, in the space L₂(−1, 1)× C [0, T]; T < 1 T is the time. The position kernel k (|x−y|) of IE has a singularity. After integrating and using the properties of fractional integral, we have a MIE in position and time, where the kernel of position takes the singular form k (|x−y|), and the kernel of time takes the singular Abel form (t −τ)^α−1 , 0 < α < 1. Then, using separation of variable method, under certain substitution, we obtain FIE in position, with variable fractional coefficients in time. Using the Toeplitz matrix method (TMM), we have a nonlinear algebraic system (NAS). Moreover, numerical results are obtained and discussed, especially when 0 < α < 1. Also, the solutions of the mixed equation are considered when α = 0, α = 1. Finally, the error estimate, in each case, is computed.

Geometric Features of a Multivalent Function Pertaining to Fractional Operators

K. Divya Priya — 2024-11-25

The Prabhakar fractional operator is commonly acclaimed as the queen model of fractional calculus. The distinction between univalent and multivalent functions became more formalized as part of the broader field of geometric function theory. This area of mathematics focuses on the study of analytic functions with specific geometric properties, such as injectivity, and their applications in various domains, including conformal mapping and potential theory. This paper’s goal is to discover new results of the harmonic multivalent functions defined in the open unit disc . Let present , the class of multivalent harmonic functions of the form in the open unit disc. Analyzing convolution with prabhahar fractional differential operator with multivalent harmonic function to be in the class . The coefficient inequality, growth rates, distortion properties, closure characteristics, neighborhood behaviors, and extreme points, all pertinent to this class were explored.

Airport Flight-Gate Allocation Assignment Using Local Antimagic Vertex Coloring

G. Muthumanickavel — 2024-12-05

The management of aviation gate assignments may significantly affect the overall productivity of an airport. This work presents a novel approach to enhancing gate assignment algorithms. The methodology used in this study incorporates graph theory and other intricate techniques, with specific focus on the concept of local antimagic vertex coloring. This study presents a comprehensive methodology for identifying optimal gate locations, which incorporates several factors such as aircraft characteristics, passenger capacity, and resource availability. Based on the results of this study, the incorporation of local antimagic vertex coloring exhibits the capacity to significantly enhance the operational effectiveness of airports via the reduction of passenger line wait times and alleviation of traffic congestion challenges. The aforementioned result was derived by using comprehensive models of the physical cosmos and conducting a meticulous analysis of empirical facts. This novel concept has the capacity to enhance the efficacy of airport gate allocation, resulting in heightened levels of customer contentment and reduced operational costs. The implementation of this procedure will facilitate the preservation of the efficiency of the operational networks for air transportation.

Optimizing Factory Workers Work Shifts Scheduling Using Local Antimagic Vertex Coloring

G. Muthumanickavel — 2024-11-28

Optimization of industrial processes, reduction of worker costs, and protection of workers well-being are significantly dependent on effective work shifts scheduling. This article introduces a new approach to work shifts scheduling by combining Local Antimagic Vertex Coloring. In the provided model, workers are diagrammed as edges, while work shifts are shown as vertices. In order to ensure that adjacent vertices are allocated distinct weights that correspond to non-overlapping work shifts, the Local Antimagic Vertex Coloring approach is used to assign uniform weights to vertices. To optimize the effectiveness of scheduling, regular graphs are used, offering a methodical and fair framework for administrating shift allocations. Adopting this comprehensive approach ensures fair allocation of responsibilities among all workers, minimizes conflicts over shift schedules, and meets operational requirements such as skill levels, shift lengths, and staff availability. By virtue of its versatility, this model may be tailored to various industrial environments, therefore enhancing both scheduling efficiency and staff satisfaction. The actual applications of this method clearly demonstrate its durability, identifying significant improvements in shift planning, reduction of scheduling errors, and a more effective work shifts management process. This paper proposes a comprehensive solution to the complex problem of scheduling work shifts for industrial workers, including both theoretical and practical benefits.

A Semi-Analytical Solution to a Generalized Nonlinear Van Der Pol Equation in Plasma By MsDTM

Noufe Aljahdaly — 2024-11-28

This article examines the effectiveness of the multistage differential transform method (MsDTM) in solving equations with a very strong nonlinear term. It introduces MsDTM as a method for solving the generalized nonlinear Van der Pol equation, which features strong nonlinearity. The generalized nonlinear Van der Pol equation arises in plasma and describes the propagation of various nonlinear phenomena, such as wave propagation in astrophysical plasma. MsDTM demonstrates greater accuracy compared to other analytical and numerical methods, such as the 4th-order Runge-Kutta Method (4thRKM), due to its ability to enhance accuracy through two factors: the number of iterations and the time step size. Most numerical methods rely solely on reducing the time step size to improve accuracy, but for some types of equations, this requires an impractically small time step size, causing the method to fail. In contrast, MsDTM offers an additional means of improving accuracy by increasing the number of iterations. The paper successfully applies MsDTM to solve the Van der Pol equation and presents the results, demonstrating that the method is highly effective for equations with very strong nonlinearity.

New Solutions to the Fractional Perturbed Chen Lee Liu Model with Time-Dependent Coefficients: Applications to Complex Phenomena in Optical Fibers

Farah M. Al-Askar — 2024-10-31

In this paper, we consider the fractional perturbed Chen Lee Liu model with time-dependent coefficients (FPCLLM-TDCs). We apply the mapping method in order to get hyperbolic, elliptic, trigonometric and rational fractional solutions. These solutions are vital for understanding some fundamentally complicated phenomena. The obtained solutions will be very helpful for applications such as fiber optics and plasma physics. Finally, we show how the conformable fractional derivative order affect the exact solutions of the FPCLLM-TDCs. Furthermore, we examine the effects of time-dependent coefficients when these coefficients take on special cases such as random variables, polynomials, and hyperbolic functions.