Contemporary Mathematics

Cubic Splines with Least-Squares and Conditioned Curvature and Applications

2024-11-27T10:43:08+08:00

In this article is detailed reviewed cubic splines with least-squares method and it is proposed a strategy for the interpolating spline obtained to have a conditioned curvature. The control of this curvature is done from a discrete point of view, resulting in an optimization problem. In the last part, some illustrative experiments and with practical applications have been exposed.

A New Higher-Order Scheme for Multiple Roots with Unknown Multiplicity

2025-01-19T14:55:33+08:00

In this work, we propose a new efficient iterative method to find multiple roots of nonlinear equations with unknown multiplicity n. The new scheme is free from the second derivative and consists of three steps derived from Enhanced Halley’s method introduced by the contributors and a Newton step. To increase efficiency, the first derivatives were approximated using forward difference, central difference, and Hermite interpolation techniques. It is demonstratedthat the implemented method achieves sixth order of convergence. As an application, we apply the new method to chemical engineering problem (volume from van der Waals), biomedical engineering (blood rheology model) and ten academic problems. Comparisons and examples clarify that the new method outperforms existing methods with the same order of convergence.

Markov Modelling of Small Cell Base Station Sleep Strategies with Disaster and Repairable Server

2024-12-17T14:48:12+08:00

A network of Base Station (BS) is required in order to function mobile phones and other mobile devices. A large number of BSs will be deployed in advanced networks namely Long-Term Evolution (LTE-A) to achieve high data rates which result in heavy energy usage in cellular networks. The energy consumption can be reduced by BS sleep strategy. A Markov model (MM) is proposed for the strategy with disaster and repairable server, as a system may encounter a disaster at any stage. The proposed model efficiently calculates the energy saving factor with disaster and the results shows that the amount of power saved in BS increases with the number of light sleep cycles. The expressions for steady-state probabilities (SSP) and transient probabilities are derived . Moreover for the proposed model, mean and variance are computed. Numerical illustration on energy saving factor with disaster is presented to show the effectiveness.

Application of Neutrosophic Case-Based Reasoning and Neutrosophic Best-Worst Method for Product Cost Estimation

2025-01-20T09:25:09+08:00

The problem of product cost estimation is one of the crucial issues in contemporary manufacturing systems when new products arrive as customer orders. Product cost estimation determines the success of manufacturers. An overestimation causes them to lose sales and competitiveness and an underestimation results in a financial crisis. This should be done at the early of production to reduce the potential costs that can be incurred in the production, distribution, consumption, and disposal of products. In previous studies, this problem was addressed using different mathematical, heuristics, multiple-criteria decision-making (MCDM), and artificial intelligence (AI) methods. These methods have their advantages and disadvantages as stated by several studies. Referring to the previous studies, the integration of neutrosophic case-based reasoning (N-CBR) and neutrosophic best-worst method (N-BWM) was not applied to solve the problem of product cost estimation. This study aims to develop a decision support system (DSS) by integrating the neutrosophic versions of CBR and BWM to solve the problem of product cost estimation at the early production stage. This implies that the proposed system contributes additional knowledge to the current literature in product cost estimation and decision-making. This is because, nowadays, neutrosophic set theory (NST) is getting more attention to represent the knowledge of experts in MCDM. In this study, product orders were treated as multiple-attributed cases incorporating neutrosophic-based verbal terms, and numeric and categorical cost drivers as case attributes. In addition, this study applied an object-oriented programming (OOP) approach to represent part-order arrivals as cases with multiple attributes. Optimal weights of case attributes were determined using a group-based N-BWM. Neutrosophic-based verbal terms of cost drivers and neutrosophic BWM terms were converted into equivalent single-valued trapezoidal neutrosophic numbers (SVTNNs). From managerial implication, the proposed system can be applied to estimate the cost of new product orders at the early production stage in real manufacturing environments by integrating the proposed methodological approaches. In this study, a numerical example was illustrated in a simulated machining environment to test the soundness of the proposed system.

On the Maximum Number of Connected Induced Subgraphs of a Graph

2024-10-16T15:39:32+08:00

We characterize the structure of graphs of a given order that maximize the number of connected induced subgraphs across seven different graph classes, each with specific parameters such as minimum degree, independence number, vertex cover number, vertex connectivity, edge connectivity, chromatic number, and the number of bridges. This work contributes to filling a gap in the existing literature.

Quiescent Optical Solitons for the Concatenation Model Having Nonlinear Chromatic Dispersion and Kerr Law of Self-Phase Modulation

2025-01-22T09:31:19+08:00

This paper focuses on the retrieval of quiescent optical solitons within the framework of the concatenation model, incorporating nonlinear chromatic dispersion and the Kerr law of self-phase modulation. These solitons, which remain stable and maintain their shape over time, are crucial for understanding the behavior of light in nonlinear optical media. The retrieval of these solitons is achieved through two distinct techniques. Each of these integration schemes offers a systematic way to derive analytical solutions, ensuring that the underlying dynamics of the optical solitons are accurately captured. In addition to the analytical solutions, this study presents numerical simulations to validate the theoretical findings. These simulations illustrate the behavior of the recovered quiescent solitons, confirming their stability and showcasing their dynamics under the influence of self-phase modulation and nonlinear chromatic dispersion. By bridging analytical methods with computational validation, the paper offers a thorough examination of these soliton structures and their real-world relevance, particularly in the design of advanced optical fiber networks and nonlinear optical devices.

Computing the Edge Metric Dimension of the Line Graph of the Molecular Graphs of Some Classes of Antiviral Drugs, with Focus on Mpox Treatments

2024-11-18T10:34:16+08:00

The study of viral infections, particularly those caused by monkeypox (Mpox), is crucial due to its significant public health impact and awareness. Graph theory, which is instrumental in understanding the topology of networks in various disciplines, is applied to studying antiviral drug structures to explore these antiviral drugs' structural and physicochemical properties using invariants such as metric dimension and edge metric dimension. These invariants offer insights into their mechanisms of action and potential for developing more effective therapies. The edge metric dimension is a graph theoretical parameter or invariant that allows for uniquely identifying all edges in a graph or bonds in a molecular graph through a chosen subset of vertices or atoms in a molecular graph, known as the edge resolving set. Line graphs can be applied in chemistry (modeling molecular structures), network theory, and computer science to solve problems like edge coloring and matching. In this paper, we specifically focus on the concept of edge metric dimension in a line graph of antiviral drug structures, which allows for the distinct identification of edges of their corresponding antiviral drug structures through the use of edge-resolving sets. This approach and results obtained not only enhances our knowledge and understanding of molecular interactions but also supports the advancement of effective therapeutic solutions in response to emerging health challenges such as Mpox disease. The following antiviral drug structures, namely Acyclovir, Brincidofovir, Cidofovir, Famciclovir, Tecovirimat, and Valacyclovir, are investigated in this study.

Some New Fractional Interval-Valued Inequalities for Set-Valued H(α, 1 − α)-Godunova-Levin Mappings with Applications

2025-01-13T15:07:19+08:00

Convex integral inequalities are an area of substantial interest in mathematical analysis because of their applications to a variety of fields such as optimization, probability theory, and functional analysis. This study derives general forms of convex integral inequalities and presents several new results in the context of H(α, 1−α)-Godunova-Levin mappings via AB fractional integral operators, including Jensen's, Pachapatte, Ostrowski, and Hermite-Hadamard. Additionally, we developed a new type of Jensen-type inequality in sequential form as well as a new Ostrowki-type inequality using a Moore-metric Hausdorff distance approach, which is really an innovative approach to such inequality. Our analysis of convex integral inequalities introduces novel bounds and constraints that characterize the behavior of generalized convex functions. We have further developed several remarks to demonstrate the accuracy of our results that lead to several other generalized convex mappings that have never been introduced so far for this type of generalized mapping, as well as several interesting non-trivial examples.

Mathematical Analysis of Non-Autonomous HIV/AIDS Transmission Dynamics with Efficient and Cost-Effective Intervention Strategies

2025-01-17T09:15:39+08:00

This study focuses on the analysis of a controlled dynamical system for the time evolution of Human Immunodeficiency Virus/Acquired Immunodeficiency Syndrome (HIV/AIDS) incorporating vertical (mother-to-child) transmission route of HIV and saturated treatment as two distinguishing factors. The impact of key epidemiological parameters of the model on the basic reproduction number is assessed via sensitivity analysis based on the normalized forward sensitivity approach. As a consequence of the sensitivity analysis, three time-dependent control intervention strategies including, therapeutic measure responsible for blocking vertical transmission route of HIV, condom usage measure, and treatment efforts with highly active anti-retroviral treatment (HAART) are considered to hinder HIV/AIDS transmission in the population. The non-autonomous system is analysed using optimal control theory, the existence of optimal control is qualitatively analysed and the optimal control triple is characterized by the famous Pontryagin’s maximum principle. The optimal control triple considered are categorized into three different policies combining any two of the interventions namely, Policy A (combination of vertical transmission preventive effort and control intervention for condom measure); Policy B (combination of vertical transmission preventive effort and treatment measure with HAART); and Policy C (combination of condom usage measure and treatment effort), and detailed analyses of the efficiency and economic methodologies are explored. It is shown among other findings that Policy C is the most efficient and most cost-effective intervention. Therefore, the policy that averts highest cases of HIV/AIDS is recommended. The study emphasizes the importance of cost-effective intervention policies in resource-limited settings, which is crucial for policymakers.

On Laplace Equation Solution in Orthogonal Similar Oblate Spheroidal Coordinates

2025-01-20T09:33:27+08:00

Orthogonal coordinate systems enable expressing the boundary conditions of differential equations in accord with the physical boundaries of the problem. It can significantly simplify calculations. The orthogonal similar oblate spheroidal (SOS) coordinate system can be particularly useful for a physical processes description inside or in the vicinity of the bodies or particles with the geometry of an oblate spheroid. The interior solution of the Laplace equation in the SOS coordinates was recently found; however, the exterior solution was missing. The exterior solution of the azimuthally symmetric Laplace equation in the SOS coordinates is derived. In the steps leading to this solution, important formulas of the SOS algebra are found. Various forms of the Laplace operator in the SOS coordinates in azimuthally symmetric case are shown. General transformation between two different SOS coordinate systems is derived. It is determined that the SOS harmonics are physically the same as the solid harmonics. Further, a formula expressing any generalized Legendre polynomial as a finite sum of monomials is found. The reported relations have potential application in geophysics, astrophysics, electrostatics, electromagnetism, fluid flow and solid state physics (e.g., ferroic inclusions).

Improved Passive Synchronization for Complex Dynamical Networks with Randomly Occurring Distributed Coupling Time-Varying Delays via State Feedback Control

2025-03-05T11:26:11+08:00

The improved synchronization of complex dynamical networks under passivity performance is the main topic of this paper. To distinguish between simple and complex dynamics in real-world scenarios, the effect of randomly occurring time-varying delays is specifically considered. The study is based on the development of a feedback controller and a Lyapunov-Krasovskii functional (LKF) with novel integral terms. Finally, a useful example is provided to illustrate the effectiveness of the proposed approach.

Improving Model Fitting for Applicable Medical Data: A Novel Exponentiated Transformation of BURR XII

2025-01-20T09:21:56+08:00

This paper presents a novel extension of the Exponentiated Transformation of the BURR XII (ETBXII) distribution. In this paper, we explore the need for improved model fitting to applicable data and present a literature review on existing distributions that researchers modified. The proposed extension is introduced, and its properties, such as its hazard rate and distribution function, are addressed. The results demonstrate that the suggested extension can better match data than existing distributions and present an empirical application to demonstrate its utility. The conclusion of the manuscript discusses the potential effects of the suggested expansion on statistical modelling in several domains.

Novel Approaches to Positive Solutions for Fractional Nonlinear Boundary Value Problems

2025-02-11T09:48:56+08:00

This study explores a fractional boundary value problem based on Riemann-Liouville derivatives and integrals. New results are derived to begin the necessary and adequate circumstances for the existence and uniqueness of positive solutions, leveraging fixed-point theorems on right circular cones. A convergent iterative sequence for solving the problem is presented, along with a numerical scheme. The validity of the results is demonstrated through illustrative examples.

An ASCII Value Based Data Encryption Using Coloring Tripartite Graph

2024-12-12T16:04:17+08:00

In current network systems, cryptography plays a vital role in ensuring a secure data transfer. Robust encryption is essential to safeguard data during transmission, making it a top priority. Encryption transforms readable data into an unreadable format and is commonly used for data protection. Modern cryptography incorporates graph theory principles to enhance the security of information-sharing over networks. This study introduces an ASCII-based data encryption system that utilizes a Coloring Tripartite Graph (CTG) as a confidential key to facilitate secure data exchange. In addition to detailing the security protocols, the recipient receives encrypted data in the form of CTG. The adoption of this encryption technology significantly enhances the security of data transmissions.

(k, g)-Fractional Integral Hermite-Hadamard Type Inequalities Involving Convex and Symmetric Functions

2025-02-06T09:36:08+08:00

This paper examines the importance of generalised (k, g) fractional integral operators within the framework of mathematical inequalities. We introduce innovative generalised fractional integral Hermite-Hadamard inequalities, which, to our knowledge, constitute a new advancement in the area. These inequalities are formulated using contemporary generalised fractional integral operators and underscore the complex interconnections among convexity, symmetry, and fractional calculus. align, we present fractional integral Hermite-Hadamard-type inequalities that utilise these generalised operators, offering an expanded framework for comprehending the characteristics of convex and symmetric functions. Our discoveries enhance theoretical understanding and possess prospective applications in optimisation, numerical analysis, and diverse areas of applied mathematics. Furthermore, we enhance this work by discussing several special cases pertinent to this paper.

Enhancing Voltage Stability and Power Quality in Hybrid MPPT Algorithm Based SPV-Wind Hybrid Microgrid System Tied Utility Grid Integrating Modified STATCOM

2024-11-24T03:44:19+08:00

Voltage sags can lead to equipment malfunction, decreased performance, and operational disruptions. They are typically caused by short circuits, motor start-ups, or sudden load increases, affecting power system reliability. Voltage stability of the proposed system has been improved by implementing modified Static Synchronous Compensator (m-STATCOM) by reducing voltage sags resulting power quality of the proposed system has been enhanced during breakdowns in electrical systems. The Voltage-Source Inverter (VSI) technology of m-STATCOM allows for quick reaction. At the Point of Common Coupling (PCC), it stabilizes voltage to avoid equipment damage from voltage fluctuations. m-STATCOM boosts reactive power regulation, renewable energy stability, and fault ride-through for dependable grid performance. Hybrid Incremental Conductance and Ripple Correlation Control (INC-RCC) for MPPT in PV and wind farms tracks Maximum Power Point Tracking (MPPT) under diverse situations to reduce power losses and fluctuations resulting improve efficiency and reaction speed as compared to Penguin Search (PS) optimization. System stability and performance improve with the Solar Photovoltaic (SPV)-Wind farm and Sinusoidal Pulse Width Modulation (SPWM)-Voltage Source Inverter (VSI)-based m-STATCOM controller. This integrated solution assists in minimizing LLG failure voltage drops.1KW SPV and 2.5 kW wind farm hybrid system connected to 400 V, 50 Hz utility grid integrated to the SPWM-VSI based m-STATCOM controller has been designed using MATLAB/Simulink.

Some Properties of Analytic Functions Associated with Erdély-Kober Integral Operator

2024-12-25T10:29:08+08:00

The target of this paper is to discuss a new subclass of schlicht mappings with negative coefficients correlated to Erdely-Kober Integral Operator in the unit disk U = {w ∈ C : |w| < 1}. For mappings in our class, we learn fundamental properties like the Hadamard product, the coefficient inequality, the distortion and covering theorem, the radii of starshapeness, the convexity and close-to-convexity, the extreme points, and the closure theorems.

Common Fixed Point Theorems for Generalized Contractions in Ordered M-Metric Spaces

2025-02-11T09:07:21+08:00

This paper seeks to investigate and derive fixed point and common fixed point results for almost generalized contractive mappings and Reich contractions within the framework of partially ordered M-metric spaces. Furthermore, the practical utility and applicability of these findings are demonstrated through illustrative examples. The results presented herein build upon and substantially generalize several foundational studies in the existing literature.

On Topological Structures on Γ-BCK-Algebras

2025-01-20T09:28:47+08:00

In this paper, we first study topological structures on Γ-BCK-algebras and obtain some of its properties. Next, we introduce the notion of quotient Γ-BCK-algebra by ideals and investigate some of topological properties on a quotient Γ-BCK-algebra. Finally, we define a quotient Γ-BCK-algebras by dual ideals of a Γ-BCK-algebra and give uniform structures on quotient Γ-BCK-algebras.

Digital Image Watermarking for Image Integrity Verification and Tamper Correction

2025-01-03T17:12:05+08:00

Images transmitted through internet can be easily tampered by the available image editing tools. This article proposes a Hamming code based watermarking approach for tamper localization and correction of images. The original image is divided into various blocks with 8 consecutive pixels. The 64 bits of the 8 pixels are arranged into an 8 × 8 matrix of bits. A modified (7,4) Hamming code (MHC) is applied on first 7 most significant bits (MSBs) of each row of the matrix. The first 4 MSBs are data bits. The next 3 bits are redundant bits. The watermark bits are calculated from the 4 MSBs and stored in 3 redundant bits. Furthermore, the column parity for the first 7 columns of the 8 × 8 matrix is computed and embedded in the least significant bits (LSBs) of the 7 rows. Thereafter the column parity of the first 7 bits of 8th column is stored in 8th bit location of 8th column. This technique can detect 1-bit error or 2-bit error if it occurs in one of the 8 pixels of the block. Experimental outcomes prove that this proposed scheme maintains 4.0 bits per pixel with 36.94 dB peak signal-to-noise ratio (PSNR) and 0.9781 structural similarity (SSIM).

Cut-Free Sequent Calculus for Multi-Agent Logic of Common Knowledge

2025-03-19T15:16:33+08:00

Cut-free sequent calculi are handy tools for backward proof-search of logical formulas or sequents. In the present paper, we introduce a Gentzen-type sequent calculus for the logic of common knowledge. To maintain a deterministic backward proof-search process, we do not include cut or cut-like rules in the introduced calculus. Also, derivation loops are used to define provable sequents and to establish termination of backward proof-search. Using this sound and complete finitary loop-type sequent calculus we construct a decision procedure for the logic of common knowledge. The procedure allows to efficiently determine whether an arbitrary formula or sequent is valid in the logic.

Optical Solitons with Dispersive Concatenation Model Having Fractional Temporal Evolution

2025-02-17T09:28:55+08:00

This paper adopts the direct algebraic method to recover and enlist a full spectrum of optical 1-soliton solutions for the dispersive concatenation model that comes with Kerr law of nonlinear refractive index change. The temporal evolution for the model is taken to be fractional so that the model is viable for controlling the Internet bottleneck-a growing problem in telecommunications industry. The numerical simulations supplement the soliton solutions that are obtained analytically.

Bifurcation Analysis and Quenching Chaos in Brushless DC Motor Based on Dither Signals

2025-01-14T10:45:25+08:00

This study investigates bifurcation and chaos dynamics in brushless direct current (DC) motor (BLDCM) through analyses of time response, Poincare' maps and frequency spectra. A chaos suppression approach is then proposed and detailed. To identify the initiation of chaotic motion in BLDCM, Lyapunov exponents and dimensions are utilized. Subsequently, the study implements the suggested method by introducing an external input, referred to as a dither signal, into the chaotic BLDCM system. The effectiveness of the proposed control method was determined by simulations.

Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics

2025-01-26T15:18:23+08:00

The paper addresses the latest form of Boussinesq equation with generalized form of cubic nonlinearity. The solitary waves are recovered from the model using traveling wave hypothesis. The conservation laws are recovered from the model. The conservation laws are obtained using the method of multipliers. Finally, the complete discriminant method yields shock waves and cnoidal waves as well. The numerical simulations supplement the analytical results.

A Spectral Collocation Approach for Time-Fractional Korteweg-de Vries-Burgers Equation via First-Kind Chebyshev Polynomials

2025-02-06T11:03:13+08:00

The time-fractional Korteweg-de Vries-Burgers (TFKdVB) problem is solved numerically in this study. The approach makes use of the shifted first-kind Chebyshev polynomials (SFKCPs) collocation method. By utilizing Caputo's formulation to approximate the time-fractional derivatives and impose boundary conditions, we arrive at a spectral solution. Numerical examples are presented to illustrate the precision and effectiveness of the suggested approach.

Some Notes on Generalized P-Derivations with Ideals in Factor Rings

2025-02-21T08:54:44+08:00

The main goal of this article is to delve deeper into the discussion of the commutativity of a factor ring R/P by analyzing certain differential identities that involve generalized P-derivations and P-multipliers connecting I to P. Here, I represents a non-zero ideal of an arbitrary ring R, and P is a prime ideal of R such that P ⊊ I. Furthermore, we will explore some outcomes from our various theorems. To underscore the necessity of the primeness assumption in our theorems, we will provide some illustrative counterexamples.

Moore-Penrose Pseudo-Inverse Applied to the Decoding of 5G and Beyond (B5G) Communication Systems

2025-01-20T09:12:13+08:00

This work uses the Moore-Penrose pseudo-inverse (PINV) properties to improve the decoding of signals in the uplink channel of a 5th-Generation mobile communication technology (5G) and Beyond (B5G) communication system. The results of computational simulations show an improvement in the bit error rate (BER) and in the Error Vector Magnitude (EVM) under adverse conditions of the wireless communication channel, which is of great importance to meet the high transmission rate and high reliability requirements of 5G and B5G systems.

Efficient Training Scheme for Neural Network Based 4K-QAM Soft Demapper

2025-01-02T14:32:33+08:00

The practicality of the densely packed and spectrally efficient 4096-Quadrature Amplitude Modulation (4K-QAM) is obstructed by the ultra-high computational complexity of its soft demapper, which is essential for generating the soft outputs required by channel decoders. In this paper, we propose an efficient training scheme to build a highly effective neural network based 4K-QAM soft demapper that can offer significantly lower computational complexity. The results demonstrate that this alternative demapper can achieve comparable decoding performance in coded 4K-QAM systems, while reducing computational complexity by up to 20% compared with the well-known low-complexity max-logarithm of maximum a posteriori (log-MAP) demapper.

Finding Negative Associations from Medical Data Streams Based on Frequent and Regular Patterns

2025-02-05T17:52:12+08:00

Medical data flows in streams as the data related to clinical tests and administered drugs by the doctors flows continuously. The doctors must be immediately alerted if negative associations are found among the drugs they prescribe. Data streams are to be processed in single scans as it is not possible to rescan the data for any iterative processing. To detect negative drug connections, regular and frequent drug patterns must be processed. Negative correlations between disease-curing medications might create adverse responses that kill patients. This paper proposes an algorithm that finds the negative associations among regular and frequent patterns mined from medical data streams. The algorithm mines the most effective and critical negative associations. By enforcing optimum frequency and regularity, the number of negative associations reduced to 0.43 from 0.73 for 1,000 item sets mined.

El-Zaki Transform Method for Solving Applications of Some Integral Differential Equations

2024-09-20T14:21:56+08:00

Integral equations have close contact with many different science and engineering problems, such as contact problems in the theory of elasticity, potential theory, fluid mechanics, quantum mechanics, healthcare, and others. So, in this presentation, we will study the following models: determining the blood glucose concentration by using Volterra integral equations. Integral equations are used in electrical engineering applications. Abel's integral equation has applications in a variety of scientific domains, including plasma diagnostics, radio astronomy, and optical fibre evaluation. This is an ancient example of an integral equation. The El-Zaki transformation method is used to solve three models and compare the exact and approximate results. The findings are calculated using Maple 18.

Quantum Public-Key Cryptosystem Using Orthogonal Product States with High Channel Capacity

2025-01-19T08:57:40+08:00

A public-key cryptosystem using orthogonal product states is presented. It is based on the non-locality of some orthogonal product states in an untangled two-particle quantum system. Every user creates a group of two-particle quantum systems and shares them with a key management center (KMC) in which the first particle of the two-particle systems are held by the user and the second particle of the two-particle systems are held by KMC. This is the user's (private key, public key) pair. Two users can exchange secret message by this cryptosystem. The laws of quantum physics guarantees that this cryptosystem has unconditional security. There are no entangled states needed in this public-key cryptosystem. Moreover both users and KMC needn't perform complex quantum operations except quantum measurements on a particle or a two-particle system. So the public-key cryptosystem is feasible to implement by today's technology. One orthogonal product quantum system contributes three bits to the key. So the cryptosystem has a high channel capacity.

Discrete Prediction of Grain Evolution in Solid-State Welding of Ti₆Al₄- V Alloy

2025-01-20T09:20:41+08:00

Titanium (Ti) alloys, known for their high strength and low weight, are essential in aircraft and aerospace applications. This study focuses on friction spot welding as an innovative, efficient process that creates robust Ti alloys joints while minimizing the carbon footprint. The research aims to develop a cellular automata (CA) model to analyze grain evolution during the friction stir spot welding of Ti₆Al₄V alloy. The methodology involved simulating the welding process at rotational speeds ranging from 800 to 1,200 rpm using a complex curved-thread shoulder. The CA model incorporated both deterministic and probabilistic approaches to capture the dynamic recrystallization (DRX) behavior. Grain nucleation and growth were modeled based on dislocation density, allowing for an in-depth assessment of the alloy's microstructural changes driven by hardening and softening mechanisms. Validation was performed by comparing the model's predictions with experimental measurements of temperature and grain size. The findings indicate that heat and deformation during welding significantly influence grain size evolution, enhancing the understanding of microstructural behavior in high-strength titanium joints. This work contributes valuable insights into optimizing welding techniques for titanium alloys in aerospace engineering.

Quiescent Optical Soliton Perturbation for Fokas-Lenells Equation with Nonlinear Chromatic Dispersion and Generalized Quadratic-Cubic Form of Self-Phase Modulation Structure

2025-02-14T17:44:46+08:00

This paper retrieves perturbed quiescent optical solitons for the Fokas-Lenells equation that is considered with generalized quadratic-cubic form of self-phase modulation and nonlinear chromatic dispersion. The model is taken up with linear temporal evolution as well as with generalized temporal evolution. Two integration approaches are implemented to make this retrieval possible. The enhanced Kudryashov’s approach and the projective Riccati equation scheme recovers a wide range of such solitons. The numerical scheme displays a few simulations to such solitons.

Prey and Predators in Mathematical Model Under Caputo Fractional Derivative

2024-11-25T15:15:35+08:00

The main concentration of ours as writers of this paper is finding the relation between two predators and one prey in a fractional mathematical model governed by Caputo fractional derivative (CFD). To achieve the above-mentioned goal the fractional reduced transform method (FRTM) has been utilized. When we use the CFD there will be no need to use Adomian's polynomials to calculate the nonlinear terms. To prove the reliability of CFD method, we have compared the outcomes of the fractional derivative orders with the ordinary derivative order index 0 < ω < 1. For further confirmation, we have presented our findings by showing graphs simulating the series solution. Moreover, we have also compared the error estimation with Rung Kutta and different orders. The Matrix Laboratory (MATLAB) software package was used as a tool for the above-mentioned process.

Structure of Algebras Satisfying an ω-Polynomial Identity of Degree Six

2025-02-24T08:55:22+08:00

This paper is devoted to the study of a class of commutative non-associative algebras characterized by the identity:

where α ∈ [0, 1]. In this study, we strongly use the Peirce decomposition technique. This allowed us to determine the conditions for an algebra of this class to be Bernstein, principal train, or evolution.

Signature Transform Application in Time Series Analysis: An Introduction to Classification and Reconstruction Problems

2025-01-13T09:09:50+08:00

The goal of this paper is to analyze comprehensively how the Signature Transform can be used for the classification of time series. Data preprocessed with the signature transform can theoretically be classified using only linear models, which represents an advantage over more traditional algorithms. Unlike existing papers, our goal is to offer a self-contained, compact work that is accessible to audiences with a more limited mathematical background. The exposition is deliberately soft, and the experiments are short and clear, aiming to provide all the details necessary for full reproducibility. In our illustrative example, we work with sine waves (signals) of only two different possible frequencies, carefully pointing out every step of the methodology. Remarks on how to visualize time series in a simple two dimensional (2D) plane are included, as visualization represents an important step in developing an intuitive understanding of the problem. Finally, we discuss an alternative application in signal reconstruction, with the aim of building an encoder/decoder system. Important limitations arise in this final section, which nevertheless open a way to improve a clear and intuitive interpretation of such a transform.

The Hybrid and Interaction Solutions with Resonance Y-Type Solitons for the (2 + 1)-Dimensional KdV Equation

2025-02-07T10:39:16+08:00

The hybrid solutions and interaction solutions with resonance Y-type solitons are mainly investigated for the (2 + 1)-dimensional Korteweg-de Vries (KdV) equation, concerning lumps, resonance Y-type solitons and interaction solutions. Firstly, by the Hirota bilinear form, we deduce the periodic solitary wave solutions through modified three-wave method. Consequently, the lumps are gained in virtue of the parameter limit approach. Secondly, when applying some constraint conditions to the N-solitons, the resonance Y-type solitons are obtained. They are new types of soliton solutions for this system. Thirdly, adding other constraint conditions to the resonanceY-type solitons, the novel interaction phenomena of resonanceY-type solitons with breathers, and resonanceY-type solitons with the lumps arise. Finally, two types of hybrid solutions are obtained for this system, including the solitons, breathers and lumps; resonance Y-type solitons, breathers and lumps, respectively.

Modeling and Position Control of a Marine Vehicle with Omnidirectional Configuration

2025-03-26T09:29:02+08:00

One of the main means of monitoring aquatic bodies are buoys, most of which are fixed, so they are not flexible enough to perform tasks such as: cleaning; rescue; exploration and surveillance. Therefore, this work is dedicated to the mathematical modeling and design of control schemes for a compact buoy with omnidirectional configuration to move between two desired points in a given time; this configuration allows the buoy to converge accurately and quickly to desired positions and routes, however, disturbances due to waves must be considered, which directly affect the movement of the buoy. These disturbances can be compensated by a robust motion controller. Thus, the dynamic model of the buoy is obtained and two control schemes are developed: Proportional-Derivative-Plus controller and Backstepping controller. These controllers base their design on a Lyapunov candidate function, which guarantees the stability of the system; however, they depend on the parameters of the dynamic model. Therefore, the dynamic buoy model is obtained considering environmental disturbances such as wind and waves. The mathematical model and the control algorithms are simulated and compared in MATLAB/Simulink. The comparison is made considering the presence of environmental disturbances from waves and wind. In addition, the evaluation was carried out using performance indicators such as variation in control efforts and those based on error: integral error, absolute integral error, and mean square error.

Boosted Whittaker-Henderson Graduation of Order 1: A Graph Spectral Filter Using Discrete Cosine Transform

2025-01-20T09:33:11+08:00

The Whittaker-Henderson (WH) graduation of order 1 is a smoothing/filtering method for equally spaced one-dimensional data. Inspired by Phillips and Shi, this paper introduces the boosted version of the WH graduation of order 1. We show that it is a graph spectral filter using the discrete cosine transform, and then provide a simple formula for the (i, j) entry of its smoother matrix. We also show that it is a linear smoother such that the filter weights sum to unity and the smoother matrix is bisymmetric, i.e., symmetric and centrosymmetric. GNU Octave user-defined functions based on the obtained results are also provided.

Perturbation of Solitary Waves and Shock Waves with Surface Tension

2025-01-16T15:59:44+08:00

This manuscript is designed with an extensive aim to investigate solitary waves in shallow water with surface tension. The governing model is the perturbed sixth-order Boussinesq equation, which incorporates higher-order dispersion effects and perturbative terms that influence wave dynamics. The G′/G-expansion procedure is employed to systematically retrieve exact solitary wave solutions, providing a diverse set of wave structures that depend on the interplay between dispersion, nonlinearity, and perturbative effects. The study further establishes the necessary parameter constraints for the existence of such solitary waves, ensuring the physical viability of the obtained solutions. Additionally, a detailed analysis of the influence of perturbation terms on the soliton characteristics is provided, revealing novel behaviors and stability conditions that were previously unexplored. These findings contribute to a deeper understanding of wave propagation in shallow water systems, with potential applications in engineering and fluid dynamics.

Exploring the Insurance-Growth Nexus: Life vs. Non-Life Insurance in Saudi Arabia

2024-10-29T09:35:07+08:00

This paper explores the relationship between insurance and economic growth in Saudi Arabia from 1992 to 2022, focusing on the distinct impacts of life and non-life insurance sectors. Using a nonlinear autoregressive distributed lag (NARDL) model, the research analyzes the insurance-growth nexus while capturing asymmetries in both short and long-term relationships. The analysis shows a significant positive correlation between life insurance penetration and GDP per capita growth, whereas no substantial link is observed for non-life insurance penetration. These results underscore the potential of life insurance in diversifying income sources and reducing oil dependency within the Saudi economy. The research indicates that increased life insurance penetration could create a multiplier effect, fostering financial stability, encouraging savings, and stimulating economic growth. This effect may also extend to other regions with similar economic structures. The findings have important implications for policymakers and stakeholders in the insurance industry, particularly in economies seeking to reduce their reliance on natural resources and diversify their economic base by highlighting the role of the life insurance sector in economic development.

Optical Solitons with the Concatenation Model Having Fractional Temporal Evolution with Depleted Self-Phase Modulation

2025-02-10T09:00:40+08:00

This paper investigates the recovery of optical soliton solutions for the concatenation model, incorporating fractional temporal evolution while excluding self-phase modulation effects. To achieve this, we employ the enhanced direct algebraic method and the new projective Riccati equation approach, both of which prove effective in extracting a comprehensive spectrum of optical soliton solutions. The obtained soliton families include bright solitons, dark solitons, singular solitons, and straddled soliton structures, each characterized by distinct parameter constraints. Additionally, the impact of fractional temporal evolution on soliton behavior is analyzed, revealing how variations in the fractional order influence soliton amplitude, width, and stability. The derived parameter conditions governing the existence of these solitons provide deeper insight into the dynamics of optical pulse propagation in nonlinear media. These findings contribute to a broader understanding of soliton behavior in optical fiber systems and may offer potential applications in fiber-optic communication and photonic signal processing.

Fermatean Neutrosophic Soft Structure and its Ideals in Hyper BCK-Algebras

2025-01-20T09:15:55+08:00

The goal of this paper is to investigate the use of fermatean neutrosophic soft sets (FNSSs) in the context of hyper BCK-algebras. While examining their characteristics and connections, it presents several ideas, including fermatean neutrosophic soft hyper BCK-ideals (FNSH BCK-ideals), fermatean neutrosophic soft weak hyper BCK-ideals (FNSWH BCK-ideals), fermatean neutrosophic softs-weak hyper BCK-ideals (FNSs-WH BCK-ideals), and fermatean neutrosophic soft strong hyper BCK-ideals (FNSSH BCK-ideals). The criteria under which an FNSWH BCK-ideal can be categorized as an FNSs-WH BCK-ideal are also investigated, along with the classification of FNSWH BCK-ideals. Furthermore, standards are given for determining if an FNSS is an FNSSH BCK-ideal.

Grüss-Type Inequalities Involving Bounds Constant via Analytic Kernel Fractional Integral

2025-02-18T08:52:18+08:00

The primary aim of this study is to derive a generalization of certain Grüss-type inequalities under constant constraints via a generalized Analytical kernel Riemann-Liouville fractional integral. We derived new Grüss-type inequalities with constant limits using generalized fractional integral operators with identical and varying parameters. The results acquired are more broadly applicable.

Integration of Fuzzy Techniques and Formal Representation of Domain and Expert Knowledge in AI Systems: A Comprehensive Review

2025-01-14T10:19:03+08:00

The integration of domain and expert knowledge into AI systems represents a critical advancement, with profound implications for solving complex, multidisciplinary challenges. The formal representation of domain and expert knowledge in these systems, combined with AI techniques, has enabled the fusion of human expertise with technologies such as machine learning (ML) and natural language processing (NLP), significantly enhancing decision-making and predictive capabilities. This paper provides a systematic review of the mathematical and computational techniques employed to integrate domain and expert knowledge into artificial intelligence (AI) systems for the development of expert systems, evaluating a total of 907 studies. The results demonstrate substantial growth in the mathematical andalgorithmic foundations of expert systems since the 1980s, highlighting key trends in the integration of AI technologies. The challenges and benefits of these approaches across various domains are discussed, emphasizing their mathematical rigor and practical significance.

Global Existence of Smooth Solutions to the Incompressible 2D Navier-Stokes-Landau-Lifshitz Equations with the Dzyaloshinskii-Moriya Interaction and V-Flow Term

2025-02-19T09:03:32+08:00

The paper focuses on the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations, incorporating the Dzyaloshinskii-Moriya (DM) interaction and a V-flow term, derived as models for magnetovi-scoelastic materials. It is demonstrated that under assumption small initial data there exist the global smooth solutions for this coupled system posed on T² or R² .

Decision-Making in the Age of AI: A Review of Theoretical Frameworks, Computational Tools, and Human-Machine Collaboration

2025-03-25T09:21:53+08:00

Decision-making, a critical process across all disciplines, is undergoing significant transformation with the integration of advanced computational techniques. This review examines the evolution of decision-making, from its theoretical foundations to the implementation of optimization algorithms, neural networks, and artificial intelligence (AI). The review first explores the contrasting paradigms of normative and descriptive decision-making theories. Normative theories propose ideal decision-making processes based on rational calculations, while descriptive theories aim to explain real-world human decision-making, often incorporating cognitive biases and heuristics. Subsequently, the review investigates optimization techniques focusing on neural networks and deep learning. These powerful tools enable machines to learn complex patterns from data, facilitating tasks such as classification, prediction, and decision-making. Various neural network architectures, including feedforward networks, convolutional networks, and recurrent networks, are examined, highlighting their distinctive strengths and limitations. The review further explores the integration of AI in decision-making processes, examining its impact on organizational structures and the inherent challenges of human-machine collaboration within uncertain environments. While AI excels at analyzing vast datasets and identifying patterns, human judgment remains indispensable for strategic decisions, particularly in areas requiring implicit knowledge, ethical considerations, and navigating complex uncertainties. The review concludes by examining the ethical implications of AI-driven decisions and explores the potential for a future where AI effectively augments human capabilities. The need for AI literacy, transparency, and a thoughtful approach to integrating AI into decision-making processes is emphasized, aiming to maximize its benefits while mitigating risks. The review highlights the emergence of human-AI partnerships, where AI enhances human capabilities. Still, human oversight and judgment remain critical for navigating the complexities of strategic decision-making in a world marked by increasing uncertainty.

Generalized Geometric Analysis of Blood Vessel Subdivisions and Fluid Mechanics

2025-02-24T11:16:08+08:00

This study proposes simplified geometric analyses of the subdivisions of blood vessels and extends the fluid-mechanical analysis to derive generalized equilibrium solutions. Departing from the traditional emphasis on symmetrical subdivisions in which one vessel splits into two, we delve into a broader scenario in which a single vessel divides into multiple branches. This exploration advances our understanding of blood vessel fluid mechanics and extends its application to biomechanical contexts. Methodologically, we integrate principles from physics, physiology, geometry, and optimality analysis. The results reveal generalized optimal solutions for the original radius of the vessel compared to bifurcated radii and optimal solutions for bifurcated angles. These findings play a significant and pivotal role in evolution, improving our comprehension of vascular mechanics and paving the way for further applications in understanding hemodynamics and the evolutionary processes of vascular systems in various animals.