Journal of Mathematical Analysis and Applications最新文献

{"title":"A novel dimensionality reduction iterative method for the unknown coefficient vectors in TGFECN solutions of unsaturated soil water flow problem","authors":"Xiaoli Hou ,&nbsp;Yuejie Li ,&nbsp;Qiuxiang Deng ,&nbsp;Zhendong Luo","doi":"10.1016/j.jmaa.2024.128930","DOIUrl":"10.1016/j.jmaa.2024.128930","url":null,"abstract":"<div><div>The main purpose of this paper is to reduce the dimensionality of unknown coefficient vectors in finite element (FE) solutions of two-grid FE Crank-Nicolson (CN) (TGFECN) format for the unsaturated soil water flow (USWF) problem with two strong nonlinear terms by using proper orthogonal decomposition (POD). For this purpose, our first step involves designing a time semi-discrete CN (TSDCN) scheme for the USWF problem and demonstrate the existence, boundedness, and error estimations of TSDCN solutions. Thereafter, we discretize the TSDCN scheme using the two-grid FE method to create a new TGFECN format and prove the existence, boundedness, and error estimations of TGFECN solutions. The primary focus should be on reducing the dimension of unknown coefficient vectors of TGFECN solutions through the utilization of the POD technique in creating a novel format, referred to as dimension reduction iterative TGFECN (DRITGFECN) format, while establishing the existence, boundedness, and error estimations for DRITGFECN solutions. Lastly, we use two sets of numerical tests to exhibit the advantage of the DRITGFECN format. Due to the presence of two highly nonlinear terms in the unsaturated soil flow problem, the development and analysis of DRITGFECN format pose greater challenges and necessitates more advanced technical skills compared to previous studies. However, the significance and broad applications of this research make it a valuable subject for investigation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445603","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":"Existence and concentration of positive solutions to generalized Chern-Simons-Schrödinger system with critical exponential growth","authors":"Liejun Shen ,&nbsp;Marco Squassina","doi":"10.1016/j.jmaa.2024.128926","DOIUrl":"10.1016/j.jmaa.2024.128926","url":null,"abstract":"<div><div>We are concerned with a class of generalized Chern-Simons-Schrödinger systems<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>+</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>u</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></munderover><msubsup><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mo>∂</mo></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><msub><mrow><mo>∂</mo></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><msub><mrow><mo>∂</mo></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mo>∂</mo></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mo>∂</mo></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><msub><mrow><mo>∂</mo></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> denotes a sufficiently large parameter, <span><math><mi>V</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mi>R</mi></math></span> admits a potential well <span><math><mi>Ω</mi><mo>≜</mo><mtext>int</mtext><msup><mrow><mi>V</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mn>0</mn><mo>)</mo></math></span> and the nonlinearity <em>f</em> fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. Under some suitable assumptions on <em>V</em> and <em>f</em>, based on variational method together with some new technical analysis, we are able to get the existence of positive solutions for some large <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span>, and the asymptotic behavior of the obtained solutions is also investigated when <span><math><mi>λ</mi><mo>→</mo><mo>+</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417530","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":"A Fourier approach to tomographic reconstruction of tensor fields in the plane","authors":"David Omogbhe","doi":"10.1016/j.jmaa.2024.128928","DOIUrl":"10.1016/j.jmaa.2024.128928","url":null,"abstract":"<div><div>We consider the problem of inversion of the X-ray transform for sums of 1-forms and symmetric 2-tensor fields. Such a problem arises after linearization of a related travel time tomography problem, described via Mañé's action potential of the energy level 1/2 for a magnetic flow. In a strictly convex bounded domain in the Euclidean plane, we show when and how to recover simultaneously both unknown 1-tensor and symmetric 2-tensor field uniquely from measurement of radiating flux at the boundary. The approach to reconstruction is based on the Cauchy problem for a Beltrami-like equation associated with <em>A</em>-analytic maps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433168","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":"Coordinate-update algorithms can efficiently detect infeasible optimization problems","authors":"Jinhee Paeng ,&nbsp;Jisun Park ,&nbsp;Ernest K. Ryu","doi":"10.1016/j.jmaa.2024.128925","DOIUrl":"10.1016/j.jmaa.2024.128925","url":null,"abstract":"<div><div>Coordinate update/descent algorithms are widely used in large-scale optimization due to their low per-iteration cost and scalability, but their behavior on infeasible or misspecified problems has not been much studied compared to the algorithms that use full updates. For coordinate-update methods to be as widely adopted to the extent so that they can be used as engines of general-purpose solvers, it is necessary to also understand their behavior under pathological problem instances. In this work, we show that the normalized iterates of randomized coordinate-update fixed-point iterations (RC-FPI) converge to the infimal displacement vector and use this result to design an efficient infeasibility detection method. We then extend the analysis to the setup where the coordinates are defined by non-orthonormal basis using the Friedrichs angle and then apply the machinery to decentralized optimization problems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417464","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":"Dynamics and backward bifurcations of SEI tuberculosis models in homogeneous and heterogeneous populations","authors":"Wei Li ,&nbsp;Yi Wang ,&nbsp;Jinde Cao ,&nbsp;Mahmoud Abdel-Aty","doi":"10.1016/j.jmaa.2024.128924","DOIUrl":"10.1016/j.jmaa.2024.128924","url":null,"abstract":"<div><div>The main difference between tuberculosis (TB) and other infectious diseases is that the transmission of the bacterium should be considered not only as the development of a primary infection, but also as exogenous reinfection or endogenous reactivation. Moreover, individuals in the population may have heterogeneous contact rates, which can be described by complex networks. To this end, we present two differential equation-based TB models in homogeneous and heterogeneous populations. The first model assumes that the number of contacts per unit time is constant for the whole population, whereas the second model considers the heterogeneous number of contacts per unit time for each individual. We derive the basic reproduction number of each model using the next-generation matrix method, and analyze the dynamical properties of each model in detail. We find that the two models undergo backward bifurcations and have the same threshold condition for backward bifurcation. From this threshold condition, we see that the reduced rate of exogenous reinfection of individuals plays an important role in causing the backward bifurcation. Interestingly, the second model allows the threshold condition for backward bifurcation to be independent of network parameters. Thus, unlike other infectious disease models on complex networks, in controlling the spread of tuberculosis among populations with different numbers of contacts, we only need to focus on disease parameters during treatment. Finally, numerical simulations more intuitively demonstrate the impact of parameter changes on the prevalence of tuberculosis and reveal the model's richer and more interesting dynamical properties, such as bistability. Sensitivity analysis indicates that the basic reproduction number is highly correlated with both the relapse rate of latent individuals progressing to active infection and the probability of healthy individuals becoming infected after contact with the pathogen. Therefore, enhancing the detection and treatment of latent cases and reducing contact between infected and uninfected individuals are the most crucial public health interventions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433252","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":"Energy balance and scale truncation of the approximate deconvolution with correction","authors":"Alexander E. Labovsky","doi":"10.1016/j.jmaa.2024.128929","DOIUrl":"10.1016/j.jmaa.2024.128929","url":null,"abstract":"<div><div>We present the similarity theory of Approximate Deconvolution with Correction (ADC) - a member of the recently proposed family of turbulence models called LES-C. This model stems from a combination of a well-known Approximate Deconvolution Model (ADM) with a defect correction procedure. We derive the energy equality for the ADC in a way that highlights the enhanced accuracy of the ADC, as compared to the ADM. Using the proposed definitions of the ADC energy and dissipation rates, we investigate the energy cascade of the ADC; we show that it correctly predicts the energy cascade in the inertial range, and acts to dissipate the small scales at a higher rate than the ADM. The micro-scale of the ADC is then found; we prove it to be larger than the micro-scale of the ADM, which also explains the previously established efficiency of the ADC.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417379","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":"Global existence in a two-dimensional chemotaxis-(Navier)-Stokes system with sub-logarithmic sensitivity","authors":"Ruina He,&nbsp;Zhongping Li","doi":"10.1016/j.jmaa.2024.128921","DOIUrl":"10.1016/j.jmaa.2024.128921","url":null,"abstract":"<div><div>This paper considers the following chemotaxis-(Navier)-Stokes system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>n</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>n</mi><mo>=</mo><mi>Δ</mi><mi>n</mi><mo>−</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>n</mi><mi>χ</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mi>∇</mi><mi>c</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>c</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>c</mi><mo>=</mo><mi>Δ</mi><mi>c</mi><mo>−</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mi>c</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>κ</mi><mo>(</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mo>)</mo><mi>u</mi><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>∇</mi><mi>P</mi><mo>+</mo><mi>n</mi><mi>∇</mi><mi>Φ</mi></mtd></mtr></mtable></mrow></math></span></span></span> in a smooth bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with no-flux/no-flux/Dirichlet boundary conditions, where<span><span><span><math><mi>χ</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>c</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></mfrac><mspace></mspace><mtext>and</mtext><mspace></mspace><mspace></mspace><mi>f</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>γ</mi></mrow></msup></math></span></span></span> with <span><math><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> and <span><math><mi>γ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>. We proved that if <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub><mo>&lt;</mo><mn>1</mn></math></span>, then for any <span><math><mi>κ</mi><mo>∈</mo><mi>R</mi></math></span> the problem possesses a global classical solution.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417528","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":"On the Cauchy problem for a weakly coupled system of semi-linear σ-evolution equations with double dissipation","authors":"Yingli Qiao ,&nbsp;Tuan Anh Dao","doi":"10.1016/j.jmaa.2024.128919","DOIUrl":"10.1016/j.jmaa.2024.128919","url":null,"abstract":"<div><div>In this paper, we would like to consider the Cauchy problem for a multi-component weakly coupled system of semi-linear <em>σ</em>-evolution equations with double dissipation for any <span><math><mi>σ</mi><mo>≥</mo><mn>1</mn></math></span>. The first main purpose is to obtain the global (in time) existence of small data solutions in the supercritical condition by assuming additional <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> regularity for the initial data and using multi-loss of decay wisely. For the second main one, we are interested in establishing the blow-up results together with sharp estimates for lifespan of solutions in the subcritical case. The proof is based on a contradiction argument with the help of modified test functions to derive the upper bound estimates. Finally, we succeed in catching the lower bound estimate by constructing Sobolev spaces with the time-dependent weighted functions of polynomial type in their corresponding norms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433167","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":"Level sets of nonsmooth functions, Part 2: Lipschitz and piecewise-differentiable manifolds","authors":"Suzane M. Cavalcanti,&nbsp;Paul I. Barton","doi":"10.1016/j.jmaa.2024.128920","DOIUrl":"10.1016/j.jmaa.2024.128920","url":null,"abstract":"<div><div>This paper introduces piecewise-differentiable (<span><math><mi>P</mi><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span>) manifolds according to a unified general framework that also applies to nonsmooth Lipschitz manifolds and smooth manifolds. We present definitions of nonsmooth manifolds and embedded submanifolds for abstract sets as well as for subsets of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, and explore the relationships between them. The <span><math><mi>P</mi><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> and Lipschitz Rank Theorems from Part 1 of this series, in terms of the Clarke Jacobian and B-subdifferential generalized derivative sets, are used to characterize level sets of functions between nonsmooth manifolds as embedded submanifolds. We illustrate how the Level Set Theorems developed in this paper can be applied to functions on Euclidean space, including a piecewise-differentiable process model for distillation columns.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417380","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":"On c-lineability","authors":"Stanisław Kowalczyk,&nbsp;Małgorzata Turowska","doi":"10.1016/j.jmaa.2024.128916","DOIUrl":"10.1016/j.jmaa.2024.128916","url":null,"abstract":"<div><div>In the paper we study <span><math><mi>c</mi></math></span>-lineability and <span><math><mi>c</mi></math></span>-spaceability of some families <span><math><mi>F</mi></math></span> of real functions defined on an interval <em>I</em>. The main goal is to formulate general conditions under which any non-empty family <span><math><mi>F</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>I</mi></mrow></msup></math></span> of functions is <span><math><mi>c</mi></math></span>-spaceable or <span><math><mi>c</mi></math></span>-lineable. Generally, we consider the families of function of the form <span><math><mi>F</mi><mo>=</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∖</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. In most cases, families of functions for which lineability and spaceability are studied have such a form. Most often, family <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is seemingly “very close” to <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or consists of “almost all” functions. The results obtained in this paper are a generalization of previous ideas. The main idea of our constructions is to “reproduce” one function to obtain <span><math><mi>c</mi></math></span>-dimensional (closed) linear space. For this “reproduction” we use the Fichtenholz-Kantorovich Theorem, applied to a countable family of pairwise disjoint intervals contained in the domain of functions from the considered class. The initial function is “squashed” and “pasted” into disjoint intervals included in the domain of constructed function.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417461","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}