Contemporary Mathematics

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

Y. H. Youssri — 2025-02-28

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.

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

Narmadha Venkatesan — 2025-03-03

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.

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

Shun-Chang Chang — 2025-02-27

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.

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

Samson Olaniyi — 2025-02-27

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.

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

Majid K. Neamah — 2025-03-05

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.

CMWH-On Topological Structures on Γ-BCK-Algebras

I. Ibedou — 2025-03-05

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.

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

Nibedita Ghosh — 2025-02-27

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.

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

Sastry Kodanda Rama Jammalamadaka — 2025-02-27

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.

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

M. Kaviyarasu — 2025-02-27

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.

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

Donlaporn Triamwichanon — 2025-03-03

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.

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

Johana Gamez — 2025-03-05

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.

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

Sergio Vidal-Beltrán — 2025-02-27

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.

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

Xiaoyu Li — 2025-02-27

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.