{"title":"Global Attractors for the Three-Dimensional Tropical Climate Model with Damping Terms","authors":"Rongyan Mao, Hui Liu, Fahe Miao, Jie Xin","doi":"10.1007/s40840-024-01667-7","DOIUrl":"https://doi.org/10.1007/s40840-024-01667-7","url":null,"abstract":"<p>In this paper, we consider the 3D tropical climate model with damping terms in the equation of <i>u</i>, <i>v</i> and <span>(theta )</span>, respectively. Firstly, we get some uniform estimates of strong solution. Secondly, we derive the result of the continuity of the semigroup <span>({S(t)}_{tge 0})</span> in case of <span>(4le alpha ,beta <5)</span> and <span>(frac{13}{5}<gamma <5)</span> via some usual inequalities. Finally, the system (1.1) is shown to possess an <span>(({mathbb {V}},{mathbb {V}}))</span>-global attractor and an <span>(({mathbb {V}},{textbf{H}}^{2}))</span>-global attractor.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"7 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008601","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 Pre-Schwarzian Norm of Certain Logharmonic Mappings","authors":"Md Firoz Ali, Sushil Pandit","doi":"10.1007/s40840-024-01668-6","DOIUrl":"https://doi.org/10.1007/s40840-024-01668-6","url":null,"abstract":"<p>We connect the pre-Schwarzian norm of logharmonic mappings to the pre-Schwarzian norm of an analytic function and establish some necessary and sufficient conditions under which locally univalent logharmonic mappings have a finite pre-Schwarzian norm. We also obtain a necessary and sufficient condition for a logharmonic function to be Bloch. Furthermore, we obtain the pre-Schwarzian norm and growth theorem for logharmonic Bloch mappings and their analytic and co-analytic parts.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"30 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980325","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 Relation Between the Harmonic Index and Some Coloring Parameters","authors":"Dazhi Lin","doi":"10.1007/s40840-024-01662-y","DOIUrl":"https://doi.org/10.1007/s40840-024-01662-y","url":null,"abstract":"<p>Let <i>H</i>(<i>G</i>) be the harmonic index of a graph <i>G</i>, which is defined as: </p><span>$$begin{aligned} H(G) = sum _{uv in E(G)}frac{2}{d_{G}(u) + d_{G}(v)}. end{aligned}$$</span><p>In this note, we define a new graph parameter <span>(xi (G))</span> satisfying some properties and prove that <span>(xi (G) le 2H(G))</span>, with equality if and only if <i>G</i> is a non-trivial complete graph, possibly plus some additional isolated vertices. In particular, <span>(xi (G))</span> can be the chromatic number <span>(chi (G))</span>, the choice number <span>(chi _{ell }(G))</span>, the DP-chromatic number <span>(chi _{text {DP}}(G))</span>, the DP-paint number <span>(chi _{text {DPP}}(G))</span>, the weak coloring number <span>(text {wcol}(G))</span>, the coloring number <span>(text {col}(G))</span>. Our result generalizes some corresponding known results.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"21 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979826","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":"Two Relaxed CQ Methods for the Split Feasibility Problem with Multiple Output Sets","authors":"Nguyen Thi Thu Thuy, Tran Thanh Tung","doi":"10.1007/s40840-023-01647-3","DOIUrl":"https://doi.org/10.1007/s40840-023-01647-3","url":null,"abstract":"<p>In this paper, two relaxed CQ algorithms with non-inertial and inertial steps are proposed for solving the split feasibility problems with multiple output sets (SFPMOS) in infinite-dimensional real Hilbert spaces. The step size is determined dynamically without requiring prior information about the operator norm. Furthermore, the proposed algorithms are proven to converge strongly to the minimum-norm solution of the SFPMOS. Some applications of our main results regarding the solution of the split feasibility problem are presented. Finally, we give two numerical examples to illustrate the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980472","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":"Proximal Subgradient Algorithm for a Class of Nonconvex Bilevel Equilibrium Problems","authors":"","doi":"10.1007/s40840-024-01664-w","DOIUrl":"https://doi.org/10.1007/s40840-024-01664-w","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we propose an algorithm for a bilevel problem of solving a monotone equilibrium problem over the solution set of a mixed equilibrium problem involving prox-convex functions in finite dimensional Euclidean space <span> <span>(mathbb R^n)</span> </span>. The proposed algorithm is based on the proximal method for mixed variational inequalities by using proximal operators of prox-convex functions. The convergence of the sequences generated by the proposed algorithm is established. Furthermore, some consequences of the main result are given. Finally, we provide numerical examples to illustrate our algorithm;s convergence and compare it with others. As an application, we apply the proposed algorithm to solve a modified oligopolistic Nash–Cournot equilibrium model. </p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"175 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139968955","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 Submanifolds as Riemann Solitons","authors":"Adara M. Blaga, Cihan Özgür","doi":"10.1007/s40840-024-01661-z","DOIUrl":"https://doi.org/10.1007/s40840-024-01661-z","url":null,"abstract":"<p>We provide some properties of Riemann solitons with torse-forming potential vector fields, pointing out their relation to Ricci solitons. We also study those Riemann soliton submanifolds isometrically immersed into a Riemannian manifold endowed with a torse-forming vector field, having as potential vector field its tangential component. We consider the minimal and the totally geodesic cases, too, as well as when the ambient manifold is of constant sectional curvature. In particular, we prove that a totally geodesic submanifold isometrically immersed into a Riemannian manifold endowed with a concircular vector field is a Riemann soliton if and only if it is of constant curvature. Furthermore, we show that, if the potential vector field of a minimal hypersurface Riemann soliton isometrically immersed into a Riemannian manifold of constant curvature and endowed with a concircular vector field is of constant length, then it is a metallic shaped hypersurface.\u0000</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139951955","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":"Variational Principle for Topological Pressure on Subsets of Non-autonomous Dynamical Systems","authors":"Javad Nazarian Sarkooh","doi":"10.1007/s40840-024-01656-w","DOIUrl":"https://doi.org/10.1007/s40840-024-01656-w","url":null,"abstract":"<p>This paper discusses a variational principle on subsets for topological pressure of non-autonomous dynamical systems. Let <span>((X, f_{1,infty }))</span> be a non-autonomous dynamical system and <span>(psi )</span> be a continuous potential on <i>X</i>, where (<i>X</i>, <i>d</i>) is a compact metric space and <span>(f_{1,infty }=(f_n)_{n=1}^infty )</span> is a sequence of continuous maps <span>(f_n: Xrightarrow X)</span>. We define the Pesin–Pitskel topological pressure <span>(P_{f_{1,infty }}^{B}(Z,psi ))</span> and weighted topological pressure <span>(P_{f_{1,infty }}^{mathcal {W}}(Z,psi ))</span> for any subset <i>Z</i> of <i>X</i>. Also, we define the measure-theoretic pressure <span>(P_{mu ,f_{1,infty }}(X,psi ))</span> for any <span>(mu in mathcal {M}(X))</span>, where <span>(mathcal {M}(X))</span> denotes the set of all Borel probability measures on <i>X</i>. Then, for any nonempty compact subset <i>Z</i> of <i>X</i>, we show the following variational principle for topological pressure </p><span>$$begin{aligned} P_{f_{1,infty }}^{B}(Z,psi )=P_{f_{1,infty }}^{mathcal {W}}(Z,psi )=sup {P_{mu ,f_{1,infty }}(X,psi ):mu in mathcal {M}(X), mu (Z)=1}. end{aligned}$$</span><p>Moreover, we show that the Pesin–Pitskel topological pressure and weighted topological pressure can be determined by the measure-theoretic pressure of Borel probability measures. In particular, we have the same results for topological entropy.\u0000</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139951950","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":"Phase Retrieval in Quaternion Euclidean Spaces","authors":"Ming Yang, Yun-Zhang Li","doi":"10.1007/s40840-024-01660-0","DOIUrl":"https://doi.org/10.1007/s40840-024-01660-0","url":null,"abstract":"<p>Quaternion algebra is a noncommutative associative algebra. Noncommutativity limits the flexibility of computation and makes analysis related to quaternions nontrivial and challenging. Due to its applications in signal analysis and image processing, quaternionic Fourier analysis has received increasing attention in recent years. This paper addresses phase retrievability in quaternion Euclidean spaces <span>({mathbb {H}}^{M})</span>. We obtain a sufficient condition on phase retrieval frames for quaternionic left Hilbert module <span>(big ({mathbb {H}}^{M},,(cdot ,,cdot )big ))</span> of the form <span>({e_{m}T_{n}g}_{m,,nin {mathbb {N}}_{M}})</span>, where <span>({e_{m}}_{min {mathbb {N}}_{M}})</span> is an orthonormal basis for <span>(big ({mathbb {H}}^{M},,(cdot ,,cdot )big ))</span> and <span>((cdot ,,cdot ))</span> is the Euclidean inner product on <span>({mathbb {H}}^{M})</span>. It is worth noting that <span>({e_{m}}_{min {mathbb {N}}_{M}})</span> is not necessarily <span>(left{ frac{1}{sqrt{M}}e^{frac{2pi imcdot }{M}}right} _{min {mathbb {N}}_{M}})</span>, and that our method also applies to phase retrievability in <span>({mathbb {C}}^{M})</span>. For the real Hilbert space <span>(big ({mathbb {H}}^{M},,langle cdot ,,cdot rangle big ))</span> induced by <span>(big ({mathbb {H}}^{M},,(cdot ,,cdot )big ))</span>, we present a sufficient condition on phase retrieval frames <span>({e_{m}T_{n}g}_{min {mathbb {N}}_{4M},,nin {mathbb {N}}_{M}})</span>, where <span>({e_{m}}_{min {mathbb {N}}_{4M}})</span> is an orthonormal basis for <span>(big ({mathbb {H}}^{M},,langle cdot ,,cdot rangle big ))</span>. We also give a method to construct and verify general phase retrieval frames for <span>(big ({mathbb {H}}^{M},,langle cdot ,,cdot rangle big ))</span>. Finally, some examples are provided to illustrate the generality of our theory.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"10 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923993","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":"Blow-up Analysis to a Quasilinear Chemotaxis System with Nonlocal Logistic Effect","authors":"Chang-Jian Wang, Jia-Yue Zhu","doi":"10.1007/s40840-024-01659-7","DOIUrl":"https://doi.org/10.1007/s40840-024-01659-7","url":null,"abstract":"<p>In this paper, we consider the following quasilinear chemotaxis system involving nonlocal effect </p><span>$$begin{aligned} left{ begin{array}{ll} u_{t}=nabla cdot (varphi (u)nabla u)-nabla cdot (unabla v)+mu u left( 1-int _{Omega }u^{alpha }text {d}xright) , {} &{} xin Omega , t>0,[2.5mm] 0=Delta v-m(t)+u, m(t)=frac{1}{|Omega |}int _{Omega } u(x,t)text {d}x, {} &{} xin Omega , t>0,[2.5mm] u(x,0)=u_{0}(x), {} &{} xin Omega , end{array} right. end{aligned}$$</span><p>where <span>(Omega =B_{R}(0)subset {mathbb {R}}^n (nge 3))</span> with <span>(R>0,)</span> the parameters <span>(mu , alpha )</span> are positive constants and diffusion function <span>( varphi (u)le C_{0}(1+u)^{-m})</span> for all <span>(uge 0)</span> with <span>(C_{0}>0)</span> and <span>(m> -1.)</span> It has been shown that if </p><span>$$begin{aligned} 0<alpha <min left{ 2,frac{n}{2},frac{n(m+1)}{2}right} , end{aligned}$$</span><p>then there exist suitable initial data <span>(u_{0})</span> such that the corresponding radially symmetric solution blows up in finite time. In this work, we extend the blow-up result established by previous researchers.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"49 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768167","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}
Abdolrahman Razani, Gustavo S. Costa, Giovany M. Figueiredo
{"title":"A Positive Solution for a Weighted p-Laplace Equation with Hardy–Sobolev’s Critical Exponent","authors":"Abdolrahman Razani, Gustavo S. Costa, Giovany M. Figueiredo","doi":"10.1007/s40840-024-01657-9","DOIUrl":"https://doi.org/10.1007/s40840-024-01657-9","url":null,"abstract":"<p>Here, considering <span>(-infty<a<frac{N-p}{p})</span>, <span>(ale ele a+1)</span>, <span>(d=1+a-e)</span> and <span>(p^*:=p^*(a,e)=frac{Np}{N-dp})</span>, the existence of positive solution of a weighted <i>p</i>-Laplace equation involving vanishing potentials </p><span>$$begin{aligned} -Delta _{ap}u+V(x)|x|^{-ep^*}|u|^{p-2}u=|x|^{-ep^*}f(u) end{aligned}$$</span><p>in <span>({mathbb {R}}^N)</span> is proved, where the potential <i>V</i> can vanish at infinity with exponential decay and <i>f</i> is a function with subcritical growth of class <span>(C^1)</span>. We use Del Pino & Felmer’s arguments to overcome the lack of compactness and the Moser iteration method with Caffarelli–Kohn–Nirenberg inequality to obtain estimates of the solution in <span>( L^{infty }({mathbb {R}}^N). )</span></p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773567","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}