Bulletin of the Malaysian Mathematical Sciences Society最新文献

In this paper, we mainly establish two supercongruences involving truncated hypergeometric series by using some hypergeometric transformation formulas. The first supercongruence confirms a recent conjecture of the second author. The second supercongruence confirms a conjecture of Guo, Liu and Schlosser partially, and gives a parametric extension of a supercongruence of Long and Ramakrishna.

This paper addresses the adaptive wavelet estimations for density derivatives by using data-driven methods. Based on the classical linear wavelet estimator of density derivatives, we provide a point-wise estimation under the local Hölder condition firstly. Moreover, we introduce a data-driven wavelet estimator for adaptivity and prove a point-wise oracle inequality, which does not require any assumption on the underlying function. Finally, by using the point-wise oracle inequality, the point-wise estimation under the local Hölder condition and (L^p)-risk ((1le p<infty )) estimation on Besov spaces are investigated respectively.

In this paper, we investigate the existence of traveling wave solution for temporally discrete Lotka Volterra competitive system with delays. By using the cross iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The obtained results makes up and improves the results of the existence of traveling wave solutions for this systems.

In this paper, we show the equality of the (local) (textrm{v})-number and Castelnuovo-Mumford regularity of certain classes of Gorenstein algebras, including the class of Gorenstein monomial algebras. Also, for the same classes of algebras with the assumption of level, we show that the (local) (textrm{v})-number serves as an upper bound for the regularity. As an application, we get the equality between the ({{,mathrm{textrm{v}},}})-number and regularity for Stanley-Reisner rings of matroid complexes. Furthermore, this paper investigates the (textrm{v})-number of Frobenius powers of graded ideals in prime characteristic setup. In this direction, we demonstrate that the (textrm{v})-numbers of Frobenius powers of graded ideals have an asymptotically linear behaviour. In the case of unmixed monomial ideals, we provide a method for computing the (textrm{v})-number without prior knowledge of the associated primes.

In this paper, we are interested in the following Kirchhoff type equation

where (a,lambda >0,alpha in (0,2)) and (pin (2alpha +2,6).) The potential V(|x|) is radial and bounded below by a positive number. By introducing the Gersgorin Disc’s theorem, we prove that for each positive integer k, Eq. (0.1) has a radial nodal solution (U_k^{lambda }) with exactly k nodes. Moreover, the energy of (U_k^{lambda }) is strictly increasing in k and for any sequence ({lambda _n}) with (lambda _nrightarrow 0^+,) up to a subsequence, (U_k^{lambda _n}) converges to (U_k^0) in (H^{1}({mathbb {R}}^3)), which is also a radial nodal solution with exactly k nodes to the classical Schrödinger equation

Our results can be viewed as an extension of Kirchhoff equation concerning the existence of nodal solutions with any prescribed numbers of nodes.

Let R be the ({mathbb {F}}_q)-algebra ({mathbb {F}}_qtimes ({mathbb {F}}_q+v{mathbb {F}}_q)) of order (q^3) where (v^2=v) and ({mathbb {F}}_q) is a finite field of q elements. We study the MacWilliams identities of the linear codes over R related to complete, Hamming, symmetric, Gray and Lee weight enumerators.

In this paper, we provide several new characterizations of the maximal right ring of quotients of a ring by using the relatively dense property. As a ring is embedded in its maximal right ring of quotients, we show that the endomorphism ring of a module is embedded into that of the rational hull of the module. In particular, we obtain new characterizations of rationally complete modules. The equivalent condition for the rational hull of the direct sum of modules to be the direct sum of the rational hulls of those modules under certain assumption is presented. For a right H-module M where H is a right ring of quotients of a ring R, we provide a sufficient condition under which (text {End}_R(M)=text {End}_H(M)). Also, we give a condition for the maximal right ring of quotients of the endomorphism ring of a module to be the endomorphism ring of the rational hull of the module.

In this paper, we consider the critical problem involving local and nonlocal operator with critical exponent under the zero mass case. First, we establish the continuous and compactness Sobolev embedding results. Second, we establish the non-existence result by Pohožaev identity. Finally, we prove the existence results for upper-crtical and lower-crtical cases via Sobolev embedding theorem, Mountain-pass theorem and Nehari manifold.

A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in (textbf{ZF}) a new characterization of iso-dense spaces in terms of special quasiorders. For a non-empty family (mathcal {A}) of subsets of a set X, a quasiorder ({{,mathrm{lesssim },}}_{mathcal {A}}) on X determined by (mathcal {A}) is defined. Necessary and sufficient conditions for (mathcal {A}) are given to have the property that the topology consisting of all ({{,mathrm{lesssim },}}_{mathcal {A}})-increasing sets coincides with the generalized topology on X consisting of the empty set and all supersets of non-empty members of (mathcal {A}). The results obtained, applied to the quasiorder ({{,mathrm{lesssim },}}_{mathcal {D}}) determined by the family (mathcal {D}) of all dense sets of a given (generalized) topological space, lead to a new characterization of non-trivial iso-dense spaces. Independence results concerning resolvable spaces are also obtained.

In this paper, we investigate the Cauchy problem of one-dimensional compressible Euler–Fourier–Korteweg system. The global unique strong solutions are established in the critical Besov spaces with small initial data close to a constant equilibrium state. This extends the recent work of Kawashima et al. (Commun Partial Differ Equ 47:378–400, 2022) on the dissipative structure of linear Euler–Fourier–Korteweg system to the non-linear system in critical space.