This study examines the magnetohydrodynamic and heat transfer capabilities of a water-based Ternary hybrid nanofluid, composed of Alumina, Graphene, and Titanium Dioxide, interacting with a slender stretching sheet within a porous matrix. The theoretical model takes into consideration a number of physical constraints, such as the Hall effect, Darcy-Forchheimer resistance, chemical reaction and temperature-dependent heat source. To analyze the system, similarity transformations were used to transform the governing partial differential equations into nonlinear ordinary differential equations; these were then solved numerically using the solver bvp4c of the MATLAB software. The analysis reveals a unique crossover effect in concentration profiles; kinematic effects like the Hall effect cause a `Low-High-Low' distribution, while porosity causes a counter `High-Low-High' zonal distribution. Furthermore, the data shows that the flow acceleration in both the axial and transverse directions is controlled by the variable thickness of the sheet and the Hall parameter. Conversely, porosity represents a drag force that slows down momentum while widening the thermal boundary layer. These observations suggest that optimization of the velocity power index in conjunction with the use of ternary nanofluids can play an important role in improving the cooling performance of next generation electromagnetic systems.
This study presents a numerical analysis of the magnetohydrodynamic flow of water-based mono, hybrid, and ternary hybrid nanofluids over a non-linearly stretching sheet. The physical model incorporates the Darcy-Forchheimer porous medium approximation along with heat source effects to simulate realistic transport phenomena. By employing similarity transformations, the governing partial differential equations are converted into a system of non-linear ordinary differential equations, which are subsequently solved using the implicit finite difference Keller-box method. The investigation rigorously evaluates the influence of critical physical parameters, including Brownian motion, thermophoresis, magnetic field strength, and porous resistance parameter on the fluid's velocity, temperature, and concentration profiles. The numerical results reveal that the ternary hybrid nanofluid exhibits the highest thermal profile, whereas the mono nanofluid (silicon dioxide) demonstrates the superior heat transfer rate, making it more efficient for specific cooling applications. It is further observed that intensifying the magnetic field and porous parameter generates resistive forces that suppress fluid velocity but enhance the thermal boundary layer. Additionally, the nanoparticle concentration profile displays a distinctive crossover behavior, where the trends observed near the bounding surface reverse in the far-field region.
In this paper, we consider a based on the presence of a mathematical sequential reduction of three compartmental (Susceptible, Infected, Recovered) model to the logistic (Verhulst) equation with parameter estimated by the basic characteristic of the epidemic process, this model is being tested in the application of the data on the outbreak of COVID-19 reported by the European Center for Disease Control and Prevention. We show that such a simple model sufficiently reproduces the epidemic dynamics not only qualitatively, but India qualitatively with a high degree of correlation that allows to use it for forecast estimations. In additional exponential and poisson model using to regression parameters are estimated. Finally, some aspects of the SIR model are discussed in context, and how its conditions and parameters ns reflect efforts to prevention disease development are clearly indicated by deviations from such model solutions.
In this paper, we propose an algorithm of an interior point methods to solve a linear problem. The study is based on the new kernel function with exponential-hyperbolic logarithmic barrier term, We prove that the proposed kernel function belongs to the eligible class introduced by Bai et al. in [11].We show that the algorithm has complexity results for large-update methods, respectively. These are the best known complexity results for such methods.
This paper investigates the existence and uniqueness of solutions for impulsive fractional differential equations involving the Caputo fractional derivative with nonlocal conditions in an abstract Banach space. The main results are proved by using the Banach contraction principle theorem and the topological degree theory for condensing maps. Additionally, an example is provided to illustrate the application of the obtained results.
This study investigates the joint relationship between Social performance (SP), Business and Financial performance (FB), and operational risk capital within the Moroccan banking sector over the period 2013-2023 (77 bank-year observations). Operational risk is modeled under the Basel III Standardized Approach (SA), where capital requirements are determined by the Business Indicator (BI), its scaled Business Indicator Component (BIC), and, where applicable, the Internal Loss Multiplier (ILM). This framework allows us to examine how income-based regulatory capital proxies interact with profitability outcomes. Using panel fixed-effects regressions with bank-level controls (size, macroeconomic conditions), we estimate the impact of SP, FB components (ILDC, FC, BI, BIC), and operational risk exposure (operational RWA to total RWA) on ROA, ROE, and ROTE. Results indicate that SP exerts a positive and economically significant effect on profitability. Business indicator variables display strong explanatory power, with BI and BIC significantly associated with higher returns. Operational risk exhibits a non-linear and regulatory-mediated effect: while improved operational efficiency enhances profitability, higher BI- and BIC-driven capital requirements increase regulatory burden, moderating marginal returns. These findings highlight a capital-channel transmission mechanism whereby Basel III operational risk calibration influences bank performance.
In this paper, we introduce a parametric extension of geometric mean labelling called k-Geometric Mean Labelling (k-GML) or Generalised Geometric Mean Labelling (GGML). For a simple graph G = (V, E), a k-GML consists of an injective vertex labelling f : V → N with the induced edge labelling g_k(uv) = \lfloor(f(u)f(v))^k\rfloor , 0 < k < 1, such that all edge labels are distinct. The classical geometric mean labelling appears as the special case k = 1/2 . We investigate the structural properties of graphs that admit k-GML and present characterisations for several fundamental graph families, including paths, cycles, stars, complete graphs and complete bipartite graphs. A significant contribution of this work is the study of GGML under graph operators such as disjoint union, join, corona product, shadow graph and line graph. We further analyse how the parameter k influences edge-label distributions, collisions and injectivity intervals. The results demonstrate that GGML is a flexible and unifying framework for extending geometric mean labelling and motivates further research.
Digital images play a critical role in numerous domains, serving as a key source of information for analysis and decision-making. With advancements in technology, image acquisition, processing, and transmission now occur at remarkable speeds. However, these images are frequently susceptible to corruption caused by technical malfunctions or human errors. Common challenges include improper camera angles, suboptimal lighting conditions, and low-visibility scenarios such as nighttime capture, all of which introduce noise and signal distortions. Given these challenges, noise removal remains a critical and ongoing research problem in the field of image processing. Numerous studies have demonstrated that digital image denoising is a prominent research area, with various techniques and algorithms being developed to enhance image quality by mitigating noise effects. Addressing these issues is essential to ensure the reliability and quality of image-based applications. The digital image represents visual information captured by sensors, commonly used in fields ranging from photography to medical diagnostics. During acquisition, unwanted noise (e.g., Gaussian, speckle, salt and pepper) can degrade image quality and hinder subsequent analysis. Wavelet theory based technique, particularly the Discrete Wavelet Transform, have proven highly effective for denoising, enabling recovery of crucial visual details and underlying structures. This research presents the best algorithm for the denoising of noisy digital images by using the discrete wavelet transform combined with various wavelets like db-2, sym-5, coif4, bior2.4, and Coiflet 3. The algorithm assesses performance using Signal-to-Noise Ratio (SNR) along with L1 and L2 norms to quantify both noise suppression and digital image detail preservation.
In this paper, we introduce and systematically study a new class of linear operators called Cohen-Lorentz $((r,s);(p,q))$-nuclear operators. This concept unifies and generalizes the classical theory of Cohen $(p,q)$-nuclear operators by incorporating the framework of Lorentz sequence spaces. We provide a comprehensive set of equivalent characterizations and establish the ideal properties of this new class. The relationships with other known operator ideals, such as Cohen-Lorentz summing and Cohen-Lorentz strongly summing operators, are investigated in detail. We prove that, under specific conditions on the indices, this class forms a Banach ideal. Furthermore, we provide a tensor product characterization for operators with values in a dual space and establish a fundamental factorization theorem.
A family of generalized modulus-based iterative schemes incorporating an acceleration mechanism is proposed for large-scale sparse linear complementarity problems. The proposed approach is based on a generalized matrix splitting strategy involving an acceleration parameter, which extends several existing accelerated modulus-based methods as special cases. Convergence of the proposed schemes is guaranteed under certain conditions when the coefficient matrix belongs to the class of $P$-matrices or $H_{+}$-matrices, and several numerical experiments are included to illustrate their computational performance. The numerical results show that the generalized accelerated methods significantly reduce the number of iterations and CPU time compared with existing approaches, thereby improving convergence performance for large-scale sparse problems.
This study addresses the Darboux integrability of a newly developed four-dimensional hyperchaotic system. Systems of this type are of considerable interest in the study of nonlinear dynamics due to their high-dimensional complexity and potential applications in secure communications, control theory, and cryptography. In this work, the proposed system is examined from the perspective of Darboux theory of integrability to identify its algebraic and analytic structures. The analysis indicates that the system lacks invariant algebraic surfaces and has only one Darboux element, which is an exponential factor. These results demonstrate that the system is non-integrable in the Darboux sense. Furthermore, it is demonstrated that under certain parameter constraints, the system fails to admit polynomial or rational first integrals.
This research paper aims to investigate a few coupled fixed point results in dislocated quasi b-metric spaces. We have established a coupled fixed point theorem for maps satisfying contraction condition using linear and rational expression in dislocated quasi b-metric space. To support our stated theorem and its corollaries, we have included an example.
This paper investigates the Laplacian spectral properties of the Cartesian product of graph Km□Kg, focusing on the trace, energy, and characteristic polynomial coefficients of Laplacian matrix of the graph. We derive general formulas for the trace of Laplacian matrix powers and provide recursive relations for the Laplacian coefficients of characteristic polynomial using trace identities for Km□Kg graph, also found upper bounds of eigenvalue of Laplacian matrix of Km□Kg.
Transportation Management Systems (TMS) need regular and effective access to transportation data such as route cost, travel distance and CO_2 emissions to support route planning, freight pricing, dispatch scheduling and real time logistics operations. As transportation databases expand in size and query frequency increases, SQL query performance becomes a critical factor affecting overall system responsiveness. This study presents a standardized relational schema intended for query intensive TMS workloads and examines how SQL optimization techniques affect the efficiency of origin destination (OD) based transportation data retrieval. The proposed schema is assessed using an extensive synthetic transportation dataset through typical TMS style queries, including OD cost lookup, least cost route determination from a specified origin and emission restricted route filtering. Query performance is evaluated under baseline and indexed configurations using execution time measurements and analysis of query execution plans. The findings provide insights into how schema design and indexing strategies influence SQL execution efficiency for high frequency OD queries, providing pragmatic guidelines for the development of scalable and performance centric transportation databases.
The purpose of this book is to serve students, teachers, and researchers who seek a clear and accessible introduction to modern methods in Partial Differential Equations (PDEs), particularly in regions where advanced mathematical material is not always readily available. Over the past decades, I have taught these topics in Brazil using lecture notes that grew organically from classroom experience. These notes have now been reorganized, expanded, and translated into English with a single goal in mind: to other mathematical knowledge to readers in developing countries, especially in some poor countries all over the world, where access to updated material is often limited. The topics presented here range from the classical linear theory to nonlinear analysis, monotonicity methods, compactness techniques, evolution equations, and a large variety of applied PDE models. Every chapter was written with great care for clarity and pedagogy. Technical proofs are included when necessary, but always with an effort to preserve intuition and motivation. Many of the problems re ect real questions arising from physics, engineering, and contemporary mathematical research. This book is also the result of a personal commitment. I firmly believe that mathematics is a universal language - one that should not be restricted by geographical or economic barriers. The possibility of translating these materials into English and making them accessible to students around the world is, to me, an act of gratitude and service. If these pages help even a single student develop confidence and inspiration to pursue further studies, then this work will have fulfilled its purpose. I am deeply grateful to Valéria Neves Domingos Cavalcanti, whose support, friendship, and mathematical insight have shaped much of my academic life. My thanks also go to the countless students whose questions and enthusiasm gave life to these notes. It is my sincere hope that this book becomes a bridge - connecting people, ideas, and opportunities - and that it might illuminate the path for those who, like me, believe in the transformative power of education.
The theory of semigroups of operators is undoubtedly one of the most powerful and elegant tools in modern functional analysis for the study of evolution equations. From the classical heat diffusion to complex wave propagation phenomena and quantum mechanics, the abstract language of semigroups allows us to unify diverse problems under a common framework, providing robust methods for establishing existence, uniqueness, and asymptotic behavior of solutions. This book, Linear and Nonlinear Semigroups and Applications, is the result of years of teaching and research at the State University of Maringá. It has been conceived to serve both as a textbook for graduate students in Mathematics and as a reference for researchers interested in the analysis of partial differential equations. The text is structured to guide the reader from the foundations to the frontiers of the theory. We begin with a review of differential and integral calculus in Banach spaces, setting the stage for the theory of C0-semigroups of linear operators. Here, the classical theorems of Hille-Yosida and Lumer-Phillips are presented not just as abstract results, but as operational tools essential for solving linear Evolution problems. However, nature is inherently nonlinear. A distinctive feature of this volume is the substantial treatment dedicated to nonlinear analysis. We introduce the theory of monotone and accretive operators, multivalued mappings, and the crucial Crandall-Liggett Theorem, which generalizes the generation of semigroups to the nonlinear setting. This transition is handled with care, highlighting the geometric and analytic subtleties that arise when linearity is abandoned. Throughout the book, the abstract theory is constantly motivated by and applied to concrete problems. We explore in detail the heat equation, the wave equation with various types of damping (frictional, viscoelastic, and boundary damping), and the Schrödinger equation. Special attention is given to the regularity of solutions and to the concept of weak and generalized solutions, bridging the gap between abstract functional analysis and applied mathematics. We assume the reader has a background in basic functional analysis and Lebesgue integration theory. Our goal is that, by the end of this journey, the reader will not only understand the "how" and "why" of semigroup theory but will also be equipped to apply these powerful techniques to their own research problems. We are grateful to our colleagues and students whose questions and feedback over the years have helped shape this material. We hope this book serves as a solid foundation for those venturing into the vast and dynamic field of evolution equations.
This study examines neural network systems exponential stability, a critical characteristic that guarantees the bounded ness and long-term convergence of network states. Using Linear matrix inequality and Lyapunov functional methods, we prove sufficient conditions for exponential stability. The system's state trajectory converges exponentially to an equilibrium point under suitable conditions, as demonstrated by the stability criteria derived from the network's weight matrices, activation functions, and time delays. Our results are validated by theoretical proofs and numerical simulations, showing the usefulness of the findings for control systems, computational neuroscience, and deep learning architectures.
This paper presents the steady flow of an incompressible magnetohydrodynamic viscous fluid past a viscous fluid sphere placed in a porous medium. The dynamics of fluid motion are determined by the Stokes equation within the fluid domain, accompanied by the Lorentz force resulting from an external magnetic field. The flow is assumed to exhibit uniform characteristics when situated at a certain distance from the fluid sphere, and the no-slip boundary condition is applied at the fluid sphere surface. The solution is obtained by applying these boundary conditions. Expressions for the stream functions and fluid sphere's drag force are derived using an analytical method. We provide a graphical presentation and discuss the relationship among the coefficient of drag, Hartmann number, and porosity parameter. It is noted that a raise in the porosity parameter and Hartmann number values raises the drag. It is also noticed that the drag in magnetohydrodynamic viscous fluid flow past a fluid sphere in a porous medium is more significant than in magnetohydrodynamic flow past a fluid sphere without a porous medium. This is attributed to the combined resistance of Lorentz forces and the permeability of the porous medium. The current study subsequently obtains some findings that correspond with previous research.
One of the most dominant spatial processes in the transformation of land surfaces in newly emerging cities in India is urban expansion. The current research focuses on the pattern and extent of urban growth in the newly emerging city of Jhajjar, located in the state of Haryana. A mathematical and geospatial modelling technique using Land Use Land Cover (LULC) change analysis is applied to understand the pattern and extent of urban growth. Multi-temporal Landsat 8 and 9 OLI and TIRS Collection 2 Level 2 data for the years 2015, 2020, and 2025 were downloaded from the USGS Earth Explorer platform. Supervised classification using the Maximum Likelihood Classification algorithm is applied to classify the land surface into four major land cover classes, namely Built-up Area, Vegetation, Barren Land, and Water Bodies. From the analysis, it is evident that the built-up area is showing rapid growth, increasing from 3.34 km2 (37%) in 2015 to 6.85 km2 (76%) in 2025. Simultaneously, vegetation cover shows a sharp decline, reducing from 4.62 km2 (51%) in 2015 to 0.69 km2 (8%) in 2025. Moreover, the extent of water bodies and barren land also shows significant changes. Using the mathematical model, the Urban Growth Rate (UGR), Land Use Change Rate (LUCR), and Annual Expansion Rate (AER) were applied to understand urban transformation. The results indicate that the Urban Growth Rate is 105.09%, with an average annual expansion of 0.351 km2.
This paper analyses technical efficiency and technology gaps among 305 smallholder farmers cultivating gherkin, paddy, and groundnut in northern Tamil Nadu using a dual-frontier framework. Crop-specific technical efficiency is estimated via input-oriented Data Envelopment Analysis under variable returns to scale with bootstrap bias correction. To account for technology heterogeneity across crops, a DEA meta-frontier is constructed and Technology Gap Ratios are derived. In parallel, Quantile Random Forests are employed to estimate flexible nonparametric production frontiers at the 95th conditional quantile, and a pooled machine-learning meta-frontier is obtained. Results indicate high technical efficiency across all crops, with paddy and groundnut operating closer to their group frontiers, while gherkin exhibits greater dispersion. Meta-frontier estimates show minimal technology gaps, with gherkin technology lying closest to the global frontier. Strong agreement between DEA- and ML-based frontiers confirms the robustness of the findings.
