Bulletin of the Malaysian Mathematical Sciences Society最新文献

In this paper, we consider the 3D tropical climate model with damping terms in the equation of u, v and (theta ), respectively. Firstly, we get some uniform estimates of strong solution. Secondly, we derive the result of the continuity of the semigroup ({S(t)}_{tge 0}) in case of (4le alpha ,beta <5) and (frac{13}{5}<gamma <5) via some usual inequalities. Finally, the system (1.1) is shown to possess an (({mathbb {V}},{mathbb {V}}))-global attractor and an (({mathbb {V}},{textbf{H}}^{2}))-global attractor.

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.

Let H(G) be the harmonic index of a graph G, which is defined as:

In this note, we define a new graph parameter (xi (G)) satisfying some properties and prove that (xi (G) le 2H(G)), with equality if and only if G is a non-trivial complete graph, possibly plus some additional isolated vertices. In particular, (xi (G)) can be the chromatic number (chi (G)), the choice number (chi _{ell }(G)), the DP-chromatic number (chi _{text {DP}}(G)), the DP-paint number (chi _{text {DPP}}(G)), the weak coloring number (text {wcol}(G)), the coloring number (text {col}(G)). Our result generalizes some corresponding known results.

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.

Abstract

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 (mathbb R^n) . 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.

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.

This paper discusses a variational principle on subsets for topological pressure of non-autonomous dynamical systems. Let ((X, f_{1,infty })) be a non-autonomous dynamical system and (psi ) be a continuous potential on X, where (X, d) is a compact metric space and (f_{1,infty }=(f_n)_{n=1}^infty ) is a sequence of continuous maps (f_n: Xrightarrow X). We define the Pesin–Pitskel topological pressure (P_{f_{1,infty }}^{B}(Z,psi )) and weighted topological pressure (P_{f_{1,infty }}^{mathcal {W}}(Z,psi )) for any subset Z of X. Also, we define the measure-theoretic pressure (P_{mu ,f_{1,infty }}(X,psi )) for any (mu in mathcal {M}(X)), where (mathcal {M}(X)) denotes the set of all Borel probability measures on X. Then, for any nonempty compact subset Z of X, we show the following variational principle for topological pressure

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.

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 ({mathbb {H}}^{M}). We obtain a sufficient condition on phase retrieval frames for quaternionic left Hilbert module (big ({mathbb {H}}^{M},,(cdot ,,cdot )big )) of the form ({e_{m}T_{n}g}_{m,,nin {mathbb {N}}_{M}}), where ({e_{m}}_{min {mathbb {N}}_{M}}) is an orthonormal basis for (big ({mathbb {H}}^{M},,(cdot ,,cdot )big )) and ((cdot ,,cdot )) is the Euclidean inner product on ({mathbb {H}}^{M}). It is worth noting that ({e_{m}}_{min {mathbb {N}}_{M}}) is not necessarily (left{ frac{1}{sqrt{M}}e^{frac{2pi imcdot }{M}}right} _{min {mathbb {N}}_{M}}), and that our method also applies to phase retrievability in ({mathbb {C}}^{M}). For the real Hilbert space (big ({mathbb {H}}^{M},,langle cdot ,,cdot rangle big )) induced by (big ({mathbb {H}}^{M},,(cdot ,,cdot )big )), we present a sufficient condition on phase retrieval frames ({e_{m}T_{n}g}_{min {mathbb {N}}_{4M},,nin {mathbb {N}}_{M}}), where ({e_{m}}_{min {mathbb {N}}_{4M}}) is an orthonormal basis for (big ({mathbb {H}}^{M},,langle cdot ,,cdot rangle big )). We also give a method to construct and verify general phase retrieval frames for (big ({mathbb {H}}^{M},,langle cdot ,,cdot rangle big )). Finally, some examples are provided to illustrate the generality of our theory.

In this paper, we consider the following quasilinear chemotaxis system involving nonlocal effect

where (Omega =B_{R}(0)subset {mathbb {R}}^n (nge 3)) with (R>0,) the parameters (mu , alpha ) are positive constants and diffusion function ( varphi (u)le C_{0}(1+u)^{-m}) for all (uge 0) with (C_{0}>0) and (m> -1.) It has been shown that if

then there exist suitable initial data (u_{0}) 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.

Here, considering (-infty<a<frac{N-p}{p}), (ale ele a+1), (d=1+a-e) and (p^*:=p^*(a,e)=frac{Np}{N-dp}), the existence of positive solution of a weighted p-Laplace equation involving vanishing potentials

in ({mathbb {R}}^N) is proved, where the potential V can vanish at infinity with exponential decay and f is a function with subcritical growth of class (C^1). 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 ( L^{infty }({mathbb {R}}^N). )