Contemporary Mathematics

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

2024-06-28T08:43:40+08:00

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.

Controllability of Impulsive Damped Fractional Order Systems Involving State Dependent Delay

2023-03-25T16:54:19+08:00

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.

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

2024-08-01T16:18:25+08:00

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.

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

2024-02-26T10:53:11+08:00

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).

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

2024-08-08T10:38:21+08:00

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.

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

2024-03-12T15:22:41+08:00

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.

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

2024-08-13T10:11:34+08:00

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.

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

2024-05-23T17:25:41+08:00

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.

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

2024-07-30T14:43:34+08:00

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.

Two Iterates of Symmetric Generalized Skew 3-Derivation

2024-06-12T10:56:29+08:00

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.

New Oscillation Conditions Test for Neutral Differential Equations

2024-08-26T16:47:44+08:00

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.

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

2024-06-24T11:42:50+08:00

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.

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

2024-10-10T08:54:26+08:00

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.

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

2023-05-16T14:14:18+08:00

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.

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

2024-07-11T11:32:59+08:00

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.

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

2023-09-18T10:29:46+08:00

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.

Support Based Essential and Core Based Superfluous Fuzzy Modules

2024-08-01T15:23:03+08:00

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.

Modelling Climate Change in a Stochastic Extreme Values Framework

2023-12-21T11:18:03+08:00

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.

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

2024-09-18T11:27:05+08:00

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.

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

2024-04-12T08:52:07+08:00

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.

D-Continuity

2024-08-05T15:13:03+08:00

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.

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

2024-06-09T09:16:10+08:00

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.

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

2024-08-02T22:55:37+08:00

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.

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

2024-07-15T10:51:42+08:00

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.

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

2024-09-19T09:00:20+08:00

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.

Goal Programming Model Using Data Envelopment Analysis for Human Development Index

2024-07-29T09:06:44+08:00

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.

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

2023-06-21T09:49:08+08:00

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.

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

2024-07-29T14:27:23+08:00

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.

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

2023-09-26T12:08:53+08:00

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.

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

2024-09-04T10:06:16+08:00

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.

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

2024-03-29T08:58:06+08:00

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.

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

2024-07-17T09:26:26+08:00

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.

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

2024-05-11T16:04:42+08:00

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.

Painlevé Analysis and Chiral Solitons from Quantum Hall Effect

2024-07-24T09:55:43+08:00

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.

Theta Pairing of Hypersurface Rings

2024-06-12T15:40:16+08:00

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.

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

2024-08-26T09:53:04+08:00

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.

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

2024-09-02T15:25:25+08:00

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

2023-03-27T08:57:52+08:00

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.

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

2024-08-05T11:28:16+08:00

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.

Asymptotic Behavior of Trajectories in Some Models of Ecnomic Dynamics

2023-09-28T17:57:22+08:00

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.

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

2023-12-01T16:36:57+08:00

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.

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

2024-08-06T16:36:21+08:00

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.

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

2024-05-06T16:33:24+08:00

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.

Black-Box Adversarial Attacks Against SQL Injection Detection Model

2024-08-01T10:21:22+08:00

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.

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

2024-05-31T16:03:57+08:00

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.

Novel Temperature-Based Topological Indices for Certain Convex Polytopes

2024-09-18T11:10:14+08:00

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.

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

2024-06-05T15:13:07+08:00

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.

Detection of Prenatal Cardiac Disease using Computer Vision and Artificial Intelligence

2024-10-27T23:39:45+08:00

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.

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

2023-02-27T17:19:16+08:00

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.

Study of multiobjective fractional variational formulation using η-Approximation Method

2024-08-02T17:40:02+08:00

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.

Sequential Kannan Type Contractions in Partial b-Metric Spaces

2023-10-19T11:50:00+08:00

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.

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

2024-07-01T11:55:22+08:00

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.

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

2023-10-25T09:37:22+08:00

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.

On q Sturm Liouville Operator with Periodic Boundary Conditions

2024-08-21T08:41:02+08:00

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.

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

2024-06-27T09:06:06+08:00

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.

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

2024-07-11T11:41:49+08:00

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.

Calculus for the Delta Distribution

2024-05-28T15:01:48+08:00

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.

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

2024-08-21T08:58:04+08:00

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.

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

2024-05-27T10:12:44+08:00

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.

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

2024-08-26T14:46:42+08:00

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.

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

2024-07-24T11:37:22+08:00

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.