Mathematical Methods in the Applied Sciences最新文献

{"title":"Construction of Bernstein-Based Words and Their Patterns","authors":"Irem Kucukoglu,&nbsp;Yilmaz Simsek","doi":"10.1002/mma.11066","DOIUrl":"https://doi.org/10.1002/mma.11066","url":null,"abstract":"<p>In this paper, with inspiration of the definition of Bernstein basis functions and their recurrence relation, we give construction of a new word family that we refer Bernstein-based words. By classifying these special words as the first and second kinds, we investigate their some fundamental properties involving periodicity and symmetricity. Providing schematic algorithms based on tree diagrams, we also illustrate the construction of the Bernstein-based words. For their symbolic computation, we also give computational implementations of Bernstein-based words in the Wolfram Language. By executing these implementations, we present some tables of Bernstein-based words and their decimal equivalents. In addition, we present black–white and four-colored patterns arising from the Bernstein-based words with their potential applications in computational science and engineering. We also give some finite sums and generating functions for the lengths of the Bernstein-based words. We show that these functions are of relationships with the Catalan numbers, the centered \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math>-gonal numbers, the Laguerre polynomials, certain finite sums, and hypergeometric functions. We also raise some open questions and provide some comments on our results. Finally, we investigate relationships between the slopes of the Bernstein-based words and the Farey fractions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 13","pages":"12819-12836"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11066","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767499","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":"Regularity Criterion Involving the Middle Eigenvalue of the Strain Tensor to the 3D Micropolar Bénard Equations","authors":"Bo Xu,&nbsp;Fan Wu,&nbsp;Jiang Zhou","doi":"10.1002/mma.11203","DOIUrl":"https://doi.org/10.1002/mma.11203","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, by using energy methods and the Littlewood-Paley decomposition theory, we obtain regularity criteria for the strong solution of the 3D micropolar Bénard equations, which only involves the positive part of the middle eigenvalue of the strain matrix in two classes of Besov spaces. Specifically, the criteria are \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>+</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>;</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mover>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <mo>˙</mo>\u0000 </mover>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 <mo>)</mo>\u0000 <mspace></mspace>\u0000 <mtext>or</mtext>\u0000 <mspace></mspace>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>+</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>;</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mov","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14632-14639"},"PeriodicalIF":1.8,"publicationDate":"2025-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012279","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 Hybrid Identification Method for Mathematical Models for Zika Virus","authors":"S. Buitrago,&nbsp;R. Escalante,&nbsp;M. Villasana","doi":"10.1002/mma.11176","DOIUrl":"https://doi.org/10.1002/mma.11176","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies some deterministic mathematical models that seek to explain the expansion of Zika virus, as a viral epidemic, using published data for Brazil. Three SIR type models considering several aspects in the spread of the disease are considered with 3, 6, and 10 unknown parameters, respectively. The parameter identification is carried through a search algorithm based on a combination of a stochastic domain exploration and a heuristic calculation of a descent direction, in order to avoid stopping the algorithm at a local optimum. The models are validated using the epidemic data found. Finally, it was confirmed that the basic reproductive ratio \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ℜ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathfrak{Re}}_0 $$</annotation>\u0000 </semantics></math> is consistent with those previously reported in the literature. We conclude that the proposed optimization method improves computation time with respect to a genetic algorithm or an exhaustive search in the parameter space.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14264-14275"},"PeriodicalIF":1.8,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012407","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":"Subsonic Solutions for the Multidimensional Euler-Poisson System of Plasma","authors":"Yan Zhou","doi":"10.1002/mma.11190","DOIUrl":"https://doi.org/10.1002/mma.11190","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we investigate the steady Euler-Poisson system that governs the dynamics of a collisionless ion-electron plasma. We establish the unique existence and structural stability of subsonic potential flow in a multidimensional nozzle. This is accomplished by prescribing the electric potential difference on a noninsulated boundary from a fixed point at the exit, along with specifying the pressure at the exit. The Euler-Poisson system is reformulated into a second-order quasilinear elliptic system, and the key ingredient of the analysis is to gain the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}&amp;amp;#x0005E;{1,alpha } $$</annotation>\u0000 </semantics></math> estimate of the corresponding linearized system.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14449-14458"},"PeriodicalIF":1.8,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012166","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":"Complex and Real Valued Solutions for Fractional Helmholtz Equation","authors":"Zifei Shen,&nbsp;Shuijin Zhang","doi":"10.1002/mma.11197","DOIUrl":"https://doi.org/10.1002/mma.11197","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation: \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>Δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mi>u</mi>\u0000 <mo>−</mo>\u0000 <mi>λ</mi>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mspace></mspace>\u0000 <mtext>in</mtext>\u0000 <mspace></mspace>\u0000 <mspace></mspace>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {left(-Delta right)}&amp;amp;amp;#x0005E;su-lambda u&amp;amp;amp;#x0003D;fleft(x,uright),kern0.60em mathrm{in}kern0.60em {mathbb{R}}&amp;amp;amp;#x0005E;n $$</annotation>\u0000 </semantics></math>, where \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>λ</mi>\u0000 <mo>&lt;</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$$ nge 3,kern0.3em 0&amp;amp;lt;lambda &amp;amp;lt;&amp;amp;amp;#x0002B;infty $$</annotation>\u0000 </semantics></math> and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>&lt;</mo>\u0000 <mi>s</mi>\u0000 <mo>&lt;</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$$ frac{n}{n&amp;amp;amp;#x0002B;1}&amp;amp;lt;s&amp;amp;lt;frac{n}{2} $$</annotation>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14549-14562"},"PeriodicalIF":1.8,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012167","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":"Analysis and Backstepping Control of a Novel 4D Fractional Chaotic Oscillator","authors":"Amin Jajarmi,&nbsp;Majid Akbarian,&nbsp;Dumitru Baleanu","doi":"10.1002/mma.11211","DOIUrl":"https://doi.org/10.1002/mma.11211","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we introduce a new 4D fractional model to extract the chaotic attractors of a biological oscillator. The proposed description includes a recently developed \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ψ</mi>\u0000 </mrow>\u0000 <annotation>$$ psi $$</annotation>\u0000 </semantics></math>-Caputo fractional derivative. To explore the model, we employ the time domain analysis and the phase plane method, both of which exhibit the chaotic attractors for some fractional orders. Furthermore, we implement a robust approximation scheme based on a sequential substitution rule and investigate its convergence. The last step is to design a stabilizing backstepping controller to eliminate undesired chaotic behaviors. We then show that the closed-loop system is globally asymptotically stable, as stated in Theorem 5.1, and use experiments to confirm that it works.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14750-14762"},"PeriodicalIF":1.8,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243114","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 Two-Warehouse Deteriorating Inventory Model With Credit Period and Price-Dependent Demand Under Partially Backlogged Shortages","authors":"Partha Halder,&nbsp;Rajan Mondal,&nbsp;Goutam Mandal,&nbsp;Asoke Kumar Bhunia","doi":"10.1002/mma.11183","DOIUrl":"https://doi.org/10.1002/mma.11183","url":null,"abstract":"<div>\u0000 \u0000 <p>This work is the demonstration of a two-storage inventory model for deteriorating items, considering bilevel trade credit facility. The customers' demand is dependent on selling price of the item and credit period offered by the retailer. Further, the items are deteriorating at a constant rate during stock-in situation, but the deterioration rates of the items in different warehouse are different. According to the credit period provided by the supplier to retailer, three distinct scenarios may arise among which are discussed in detail. The corresponding optimization problems are solved with the help of three tournament-based hybrid algorithms (tournament differential evolution [TDE], tournament teaching learning-based optimization [TTLBO], and tournament RAO-3 algorithms). Further, the feasibility of the proposed model is validated by considering a numerical example. Finally, the impacts of different system parameters on optimal policy are studied with the help of sensitivity experiment, and its impacts are shown graphically.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14353-14366"},"PeriodicalIF":1.8,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012168","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":"Solutions to Two Problems on a Class of Sequences Converging to the Number e","authors":"Stevo Stević","doi":"10.1002/mma.11196","DOIUrl":"https://doi.org/10.1002/mma.11196","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We solve two problems concerning the family of real sequences \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;ℕ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {a}_n&amp;amp;amp;#x0005E;{left(alpha right)}&amp;amp;amp;#x0003D;{left(1&amp;amp;amp;#x0002B;frac{1}{n}right)}&amp;amp;amp;#x0005E;nleft(1&amp;amp;amp;#x0002B;frac{alpha }{n}right),kern0.3em nin mathbb{N} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ alpha in left[0,infty right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, considerably improving and complementing the results in the literature. Namely, we find all the values of the parameter \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ alpha $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14543-14548"},"PeriodicalIF":1.8,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012340","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":"The BV Solution for a Nonlocal Diffusion Equation and Its Application on Multiplicative Noise Removal","authors":"Yi Ran,&nbsp;Zhichang Guo,&nbsp;Jingfeng Shao,&nbsp;Yao Li,&nbsp;Boying Wu","doi":"10.1002/mma.11184","DOIUrl":"https://doi.org/10.1002/mma.11184","url":null,"abstract":"<div>\u0000 \u0000 <p>Multiplicative Gamma denoising is always a critical challenge in image processing. The multiplicative mechanism and the heavy-tailed distribution of the Gamma noise significantly complicate its removal. To address these two characteristics, this paper proposes a novel gray value indicator function, which is inserted into a new nonlocal diffusion equation model that combines the strengths of the Perona–Malik model and the regularized Perona–Malik model. Furthermore, the concept of generalized Young measure is used to prove the existence for BV solutions and the maximum principle of the proposed model when the initial value \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <mi>B</mi>\u0000 <mi>V</mi>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 <mo>∩</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {u}_0in BVleft(Omega right)cap {L}&amp;amp;amp;#x0005E;{infty}left(Omega right) $$</annotation>\u0000 </semantics></math>. We employ the explicit finite difference method to implement our model, and comparative experiments are conducted.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14367-14384"},"PeriodicalIF":1.8,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012583","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 Source Identification Problem for Subdiffusion Equations Involving Delays","authors":"Nguyen Van Dac,&nbsp;Lam Thi Thoa","doi":"10.1002/mma.11186","DOIUrl":"https://doi.org/10.1002/mma.11186","url":null,"abstract":"<div>\u0000 \u0000 <p>We are concerned with a problem of parameter identification in a subdiffusion equation involving time-varying delays. The solvability of problem is proved by using final state observation, which is possibly nonlocal data. The state function is shown to be Hölder continuous, and the stability result in the case of local data is testified. Finally, an application for a class of nonlinearities is given.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14401-14412"},"PeriodicalIF":1.8,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012584","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}