Mathematical Methods in the Applied Sciences最新文献

{"title":"The Kinetics and Mechanism of Inhibitor Drugs in the Treatment of Alzheimer's Disease","authors":"Yasser Alzahrani,&nbsp;Shantia Yarahmadian,&nbsp;Vaghawan Prasad Ojha,&nbsp;Trey Leonard","doi":"10.1002/mma.70029","DOIUrl":"https://doi.org/10.1002/mma.70029","url":null,"abstract":"<div>\u0000 \u0000 <p>The etiology of Alzheimer's disease (AD) remains elusive. From a pathological point of view, several complex hypotheses, such as impaired neurotransmission, oxidative stress, and aggregation of amyloid-\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math> (A\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math>), are considered crucial contributors to the pathophysiology of AD. Recent studies have primarily focused on AD treatment strategies targeting drugs that intervene in cerebral deposition of aggregated amyloid-\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math> (A\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math>) polymers, often found in the form of amyloid plaques. In this paper, we present intuitive mathematical models that clarify the treatment of AD in the presence of inhibitory drugs. These models elucidate the intricate kinetics involved in A\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math> formation and the interaction of drugs with these processes. We discuss two categories of drugs: first, anti-inflammatory drugs (NSAIDs), which act as monomer inhibitors of A\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math> aggregation, and second, drugs that directly interact with A\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math> aggregated polymers. We initially analyze each drug independently and then assess their combined effects. Our numerical simulations demonstrate that the first type of drug reduces the equilibrium state value of aggregated filaments, whereas the second model of drug exhibits even greater efficacy in reducing the equilibrium state value of aggregated filaments. Furthermore, we conduct simulations of the simultaneous application of both drugs. The results are compared with the experimental data.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15474-15492"},"PeriodicalIF":1.8,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear Sequential Fractional Integro-Differential Systems: Caputo-Type Derivatives and Boundary Constraints","authors":"Saud Fahad Aldosary,&nbsp;Manigandan Murugesan,&nbsp;Hami Gündoğdu","doi":"10.1002/mma.70009","DOIUrl":"https://doi.org/10.1002/mma.70009","url":null,"abstract":"<p>In recent years, the study of sequential fractional differential equations (SFDEs) has become increasingly important in multiple domains of science and engineering. This work investigates a new class of boundary value problems (BVPs) characterized by nonlocal closed boundary conditions involving SFDEs with Caputo fractional integral operators. The existence of solutions is established using the Leray–Schauder alternative, while the uniqueness is demonstrated through the Banach fixed point theorem. To illustrate the main findings, several examples are presented, along with a discussion of specific cases that arise from the analysis.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15194-15218"},"PeriodicalIF":1.8,"publicationDate":"2025-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well-Posedness and Qualitative Properties","authors":"K. Mitra,&nbsp;S. Sonner","doi":"10.1002/mma.11221","DOIUrl":"https://doi.org/10.1002/mma.11221","url":null,"abstract":"<p>We analyze nonlinear degenerate coupled partial differential equation (PDE)-PDE and PDE-ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion. The other equations are either of advection-reaction-diffusion type or ODEs. Under very general assumptions, the existence of weak solutions is proven by considering regularized systems, deriving uniform bounds, and using fixed point arguments. Assuming additional structural assumptions we also prove the uniqueness of solutions. Global-in-time well-posedness is established for Dirichlet and mixed boundary conditions, whereas, only local well-posedness can be shown for homogeneous Neumann boundary conditions. Using a suitable barrier function and comparison theorems, we formulate sufficient conditions for finite-time blow-up or uniform boundedness of solutions. Finally, we show that solutions of the degenerate parabolic equation inherit additional global spatial regularity if the diffusion coefficient has a power-law growth.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14890-14908"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11221","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blow-Up Phenomenon for a Pseudo-Parabolic Equation With Positive Initial Energy","authors":"Khadijeh Baghaei","doi":"10.1002/mma.70021","DOIUrl":"https://doi.org/10.1002/mma.70021","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the blow-up phenomenon associated with a specific class of pseudo-parabolic equations. We demonstrate that solutions to the corresponding initial boundary value problem exhibit blow-up in finite time under the conditions that the initial energy is positive and the initial values are sufficiently large.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15364-15371"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Generalization of Bivariate Sampling Kantorovich Operators and Applications to Image Processing","authors":"Metin Turgay,&nbsp;Tuncer Acar","doi":"10.1002/mma.70025","DOIUrl":"https://doi.org/10.1002/mma.70025","url":null,"abstract":"<p>In this paper, we introduce bivariate modified sampling Kantorovich operators, which extend the classical sampling Kantorovich operators by incorporating a transformation function \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 </mrow>\u0000 <annotation>$$ rho $$</annotation>\u0000 </semantics></math>. The paper begins by presenting essential definitions, including to introduce new bivariate weighted modulus of continuity, and its fundamental properties. The newly constructed operators are studied in terms of pointwise and uniform convergence in spaces of continuous functions. We investigate weighted approximation properties of the family of operators in weighted spaces of functions constructed by \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 </mrow>\u0000 <annotation>$$ rho $$</annotation>\u0000 </semantics></math>. Moreover, we study modular convergence of these operators in Orlicz spaces \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>η</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mfenced>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ {L}&amp;amp;#x0005E;{eta}left({mathbb{R}}&amp;amp;#x0005E;2right) $$</annotation>\u0000 </semantics></math>. Finally, we present some \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 </mrow>\u0000 <annotation>$$ rho $$</annotation>\u0000 </semantics></math>-kernels and applications to image processing. The newly constructed operators present better process and higher PSNR value for some parameters \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>w</mi>\u0000 </mrow>\u0000 <annotation>$$ w $$</annotation>\u0000 </semantics></math> and function \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 </mrow>\u0000 <annotation>$$ rho $$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15413-15432"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical and Theoretical Approximation Through Riemann–Liouville-Type Fractional Kantorovich Operators","authors":"Priya Sehrawat,&nbsp;S. A. Mohiuddine,&nbsp;Arun Kajla,&nbsp;Abdullah Alotaibi","doi":"10.1002/mma.70033","DOIUrl":"https://doi.org/10.1002/mma.70033","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents the Riemann–Liouville-type fractional \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 <annotation>$$ alpha $$</annotation>\u0000 </semantics></math>-Bernstein–Kantorovich operators based on a sequence \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {tau}_{mathfrak{n}} $$</annotation>\u0000 </semantics></math>. To establish the uniform convergence of these operators, we employ the Korovkin-type theorem, Lipschitz-type space, and modulus of continuity. Additionally, we demonstrate global approximation by utilizing the Ditzian–Totik modulus of smoothness. An approximation result related to the Korovkin theorem is also provided by using Fibonacci \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 <annotation>$$ mathfrak{f} $$</annotation>\u0000 </semantics></math>-statistical convergence. Finally, we illustrate the convergence of the proposed operators through graphical representations created using Maple.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15533-15542"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parallel Additive Schwarz Preconditioner for a Discrete Nonlinear Plate Vibration Problem Using a θ-Scheme in Time and Finite Difference in Space","authors":"Yassin Khali,&nbsp;Samir Khallouq,&nbsp;Nabila Nagid","doi":"10.1002/mma.11227","DOIUrl":"https://doi.org/10.1002/mma.11227","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we propose a numerical scheme for solving the two-dimensional fourth-order partial differential equation (PDE) with variable coefficients, governing the transverse vibrations of a simply supported thin plate. By introducing a new variable, the equation is transformed into a system of two second-order equations. In the discretization of the spatial derivative, second-order centered finite difference operators are considered, then a three-level \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <annotation>$$ theta $$</annotation>\u0000 </semantics></math>-scheme is considered for the resulting semi-discretized equations. The stability and convergence of the scheme are proved in the discrete \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>l</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {l}_2 $$</annotation>\u0000 </semantics></math> norm and in the discrete maximum norm using the energy method. To accelerate the resolution of the linear system derived from the discretization of the plate equation, the overlapping additive Schwarz preconditioner (ASP) is applied and analyzed. Numerical experiments are provided showing the effectiveness of the preconditioner and the convergence properties of the scheme.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14990-15014"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Quaternionic Integer Reversible Dual-Hahn Transform and a New Hyperchaotic System for Medical Image Protection via Zero-Watermarking","authors":"Karim El-Khanchouli,&nbsp;Nour-Eddine Joudar,&nbsp;Mhamed Sayyouri","doi":"10.1002/mma.70018","DOIUrl":"https://doi.org/10.1002/mma.70018","url":null,"abstract":"<div>\u0000 \u0000 <p>Discrete orthogonal moments, such as the dual-Hahn moments, often exhibit limitations in accurately reconstructing signals, which reduces their effectiveness in applications that require precise recovery, particularly for 1D signals and color images. To address this limitation, this paper introduces a novel transform called the quaternionic integer reversible dual-Hahn transform (QIRDHT). This innovative approach enables simultaneous and lossless processing of 1D signals and color images, while being particularly well suited for resource-constrained environments. Furthermore, chaotic systems play a crucial role in cryptography, especially for secure key generation. However, the classical Hénon system has several drawbacks, including a restricted range of control parameters, limited sensitivity to initial conditions, and a tendency to generate periodic sequences. To overcome these limitations, we propose an enhanced hyperchaotic system that combines the dynamics of the Hénon system and logistic maps. This new hyperchaotic system exhibits richer dynamic behavior and a broader range of control parameters, significantly improving the security of encryption schemes. By integrating QIRDHT with this hyperchaotic map, we develop an efficient scheme for generating and extracting multiple zero-watermarks. The robustness of the proposed algorithm is evaluated against various geometric and common signal processing attacks using different medical images. Experimental results demonstrate that the proposed method outperforms existing approaches in terms of PSNR, BER, and NC, ensuring enhanced protection of medical images.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15311-15337"},"PeriodicalIF":1.8,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Impact of Cross-Diffusion and Nonlocal Competition on a Predator–Prey Model With Harvesting","authors":"Lakpa Thendup Bhutia,&nbsp;Samir Biswas,&nbsp;Bidhan Bhunia,&nbsp;Tapan Kumar Kar","doi":"10.1002/mma.70006","DOIUrl":"https://doi.org/10.1002/mma.70006","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we examine the influence of nonlocal competition on the spatiotemporal dynamics of a predator–prey system. The nonlocal term is introduced in the intraspecific competition among the predator species. A density-dependent cross-diffusion is considered to model the movement behavior of species. First, the temporal system is examined, where the existence, boundedness, and stability of the equilibrium points are ascertained. Bifurcation analysis also reveals the presence of saddle-node, transcritical, Hopf bifurcations, and codimension-2 bifurcation such as the Bogdano–Takens bifurcation. The behavior of the system is inspected both in the presence and absence of nonlocal interaction. It is observed that the nonlocal interaction tends to destabilize the coexisting equilibrium. For lower values of diffusion coefficient, spatially nonhomogeneous solutions are detected. For higher values of diffusion coefficient, domain-induced Turing instability switching is observed. Moreover, when the domain size is small, the coexisting equilibrium is stable irrespective of the value of the diffusion coefficient. Furthermore, the stabilizing effect of harvesting effort is also seen. The formulated system is numerically solved using the operator splitting method. Extensive numerical simulations are conducted to validate all the theoretical findings.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15151-15171"},"PeriodicalIF":1.8,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Harmonic Growth—The Harmonic Number Applied to ROI, Business Scaling, Nth Plant Economics, Micro Combined Heat and Power (mCHP), Biorefineries, and Biochar Production","authors":"Micah N. Jasper","doi":"10.1002/mma.11156","DOIUrl":"https://doi.org/10.1002/mma.11156","url":null,"abstract":"<p>Scaling is a topic of utmost importance in business. When to scale and how has been the subject of countless books and seminars. This paper looks at modular businesses that have income and costs directly proportional to the number of units. This work assumes that all of the plants or units have the same capital cost, operating costs, and revenue and that the company reinvests all net profit into purchasing more units. Furthermore, this model ignores depreciation, inflation, fluctuating market prices, and market saturation. With these assumptions, the question of when the company can afford to scale and purchase the next unit is directly related to the payback period and the harmonic number. This work describes a novel growth function called the harmonic growth function based on harmonic numbers. This function is related to the standard ROI. The harmonic growth function is explained and applied to a micro combined heat and power (mCHP) station, a biomass company expanding the number of biorefineries, and biochar retort kilns for biochar production.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"13999-14013"},"PeriodicalIF":1.8,"publicationDate":"2025-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11156","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}