Ricerche di Matematica最新文献

{"title":"Energy decay of wave equations with infinite memory effects versus supercritical frictional dampings","authors":"Menglan Liao","doi":"10.1007/s11587-023-00832-7","DOIUrl":"https://doi.org/10.1007/s11587-023-00832-7","url":null,"abstract":"<p>In this paper, a class of damped viscoelastic wave equations </p><span>$$begin{aligned} u_{tt}-k(0)Delta u-int _0^infty k'(s)Delta u(t-s)ds+|u_t|^{m-1}u_t=|u|^{p-1}u end{aligned}$$</span><p>is considered in a bounded domain <span>(Omega subset {mathbb {R}}^3)</span>. Uniform energy decay was discussed which depends on the relaxation function <span>(-k'(s))</span> in the previous work (Guo et al., Z Angew Math Phys 69:65, 2018) for <span>(1le mle 5)</span>. Depending on a key integral inequality obtained by Martinez (ESAIM Control Optim Calc Var 4:419–444, 1999), we establish the decay estimate of the total energy for <span>(m&gt;5)</span>. Our results improve and complement the previous one. As an example, a logarithmic energy decay is also presented.</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"56 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138565956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hyperbolic reaction–diffusion model of chronic wasting disease","authors":"Elvira Barbera, Annamaria Pollino","doi":"10.1007/s11587-023-00831-8","DOIUrl":"https://doi.org/10.1007/s11587-023-00831-8","url":null,"abstract":"<p>A hyperbolic reaction–diffusion model is developed in the framework of Extended Thermodynamics in order to describe the spatio-temporal dynamics of populations afflicted by chronic wasting diseases. The hyperbolic structure of the system guarantees that the wave processes occur at finite velocity, so that the paradox of instantaneous diffusion, typical of parabolic systems, is removed. The character of steady states, together with the Hopf bifurcation, are investigated through linear stability analysis. The model is integrated numerically to valuate the behavior of the populations. Finally, the propagation of acceleration waves is analyzed.\u0000</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138563906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nilpotent groups whose difference graphs have positive genus","authors":"Parveen, Jitender Kumar","doi":"10.1007/s11587-023-00830-9","DOIUrl":"https://doi.org/10.1007/s11587-023-00830-9","url":null,"abstract":"<p>The power graph of a finite group <i>G</i> is a simple undirected graph with vertex set <i>G</i> and two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group <i>G</i> is a simple undirected graph whose vertex set is the group <i>G</i> and two vertices <i>a</i>, <i>b</i> are adjacent if there exists <span>(c in G)</span> such that both <i>a</i> and <i>b</i> are powers of <i>c</i>. In this paper, we study the difference graph <span>(mathcal {D}(G))</span> of a finite group <i>G</i> which is the difference of the enhanced power graph and the power graph of <i>G</i> with all isolated vertices removed. We characterize all the finite nilpotent groups <i>G</i> such that the genus (or cross-cap) of the difference graph <span>(mathcal {D}(G))</span> is at most 2.</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"64 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some notes on the algebraic structure of linear recurrent sequences","authors":"Gessica Alecci, Stefano Barbero, Nadir Murru","doi":"10.1007/s11587-023-00826-5","DOIUrl":"https://doi.org/10.1007/s11587-023-00826-5","url":null,"abstract":"<p>Several operations can be defined on the set of all linear recurrent sequences, such as the binomial convolution (Hurwitz product) or the multinomial convolution (Newton product). Using elementary techniques, we prove that this set equipped with the termwise sum and the aforementioned products is an <i>R</i>-algebra, given any commutative ring <i>R</i> with identity. Moreover, we provide explicitly a characteristic polynomial of the Hurwitz product and Newton product of any two linear recurrent sequences. Finally, we also investigate whether these <i>R</i>-algebras are isomorphic, considering also the <i>R</i>-algebras obtained using the Hadamard product and the convolution product.\u0000</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"84 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of solutions for the problem of microwave heating and a Liapunoff criteria for stability and instability","authors":"Giovanni Cimatti","doi":"10.1007/s11587-023-00825-6","DOIUrl":"https://doi.org/10.1007/s11587-023-00825-6","url":null,"abstract":"<p>The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"62 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the dynamics of a Leslie–Gower predator–prey ternary model with intraguild","authors":"C. Accarino, F. Capone, R. De Luca, G. Massa","doi":"10.1007/s11587-023-00822-9","DOIUrl":"https://doi.org/10.1007/s11587-023-00822-9","url":null,"abstract":"Abstract In this paper, a predator–prey model with intraguild predation describing the evolution between three interacting species—namely prey, mesopredator and top predator—is investigated, with the aim to model a complete food web. In particular, the longtime behaviour of the solutions is analysed, proving the existence of an absorbing set, and the linear and nonlinear stability analyses of the coexistence equilibrium are performed.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"12 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135773372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hopf bifurcation and Turing patterns for a diffusive predator–prey system with weak Allee effect","authors":"Wenbin Yang, Xin Chang","doi":"10.1007/s11587-023-00824-7","DOIUrl":"https://doi.org/10.1007/s11587-023-00824-7","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"36 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Group identities on symmetric units under oriented involutions in group algebras","authors":"Alexander Holguín-Villa, John H. Castillo","doi":"10.1007/s11587-023-00809-6","DOIUrl":"https://doi.org/10.1007/s11587-023-00809-6","url":null,"abstract":"Abstract Let $$mathbb {F}G$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; denote the group algebra of a locally finite group G over the infinite field $$mathbb {F}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;/mml:math&gt; with $$mathop {textrm{char}}nolimits (mathbb {F})ne 2$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mtext&gt;char&lt;/mml:mtext&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;≠&lt;/mml:mo&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , and let $$circledast :mathbb {F}Grightarrow mathbb {F}G$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;⊛&lt;/mml:mo&gt; &lt;mml:mo&gt;:&lt;/mml:mo&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mo&gt;→&lt;/mml:mo&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; denote the involution defined by $$alpha =Sigma alpha _{g}g mapsto alpha ^circledast =Sigma alpha _{g}sigma (g)g^{*}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;α&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;Σ&lt;/mml:mi&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;α&lt;/mml:mi&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mo&gt;↦&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;α&lt;/mml:mi&gt; &lt;mml:mo&gt;⊛&lt;/mml:mo&gt; &lt;/mml:msup&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;Σ&lt;/mml:mi&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;α&lt;/mml:mi&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mi&gt;σ&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mrow /&gt; &lt;mml:mo&gt;∗&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , where $$sigma :Grightarrow {pm 1}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;σ&lt;/mml:mi&gt; &lt;mml:mo&gt;:&lt;/mml:mo&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mo&gt;→&lt;/mml:mo&gt; &lt;mml:mo&gt;{&lt;/mml:mo&gt; &lt;mml:mo&gt;±&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo&gt;}&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; is a group homomorphism (called an orientation) and $$*$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mrow /&gt; &lt;mml:mo&gt;∗&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; is an involution of the group G . In this paper we prove, under some assumptions, that if the $$circledast $$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mo&gt;⊛&lt;/mml:mo&gt; &lt;/mml:math&gt; -symmetric units of $$mathbb {F}G$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; satisfies a group identity then $$mathbb {F}G$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; satisfies a polynomial identity, i.e., we give an affirmative answer to a Conjecture of B. Hartley in this setting. Moreover, in the case when the prime radical $$eta (mathbb {F}G)$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;η&lt;/mml:mi&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:m","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"40 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Turing instability for a Leslie–Gower model","authors":"F. Capone, R. De Luca, L. Fiorentino, V. Luongo, G. Massa","doi":"10.1007/s11587-023-00819-4","DOIUrl":"https://doi.org/10.1007/s11587-023-00819-4","url":null,"abstract":"Abstract The aim of this paper is to investigate a reaction-diffusion Leslie–Gower predator–prey model, incorporating the intraguild predation and both self and cross-diffusion. The longtime behaviour of the solutions is analysed, proving the existence of an absorbing set. The existence of patterns is investigated by looking for conditions guaranteeing that an equilibrium, stable in the absence of diffusion, becomes unstable when diffusion is allowed.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136209027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction: A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect","authors":"Marzia Bisi, Maria Groppi, Giorgio Martalò, Cinzia Soresina","doi":"10.1007/s11587-023-00818-5","DOIUrl":"https://doi.org/10.1007/s11587-023-00818-5","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136291817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}