Bulletin of the Malaysian Mathematical Sciences Society最新文献

We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail’s ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity.

Let G be a finite group, and let (pi ) be a set of primes. The aim of this paper is to obtain some results concerning how much information about the (pi )-structure of G can be gathered from the knowledge of the sizes of conjugacy classes of its (pi )-elements and of their multiplicities. Among other results, we prove that this multiset of class sizes determines whether G has a hypercentral Hall (pi )-subgroup.

On reproducing kernel Hilbert spaces with normalized complete Pick kernel, we establish an equivalent result to the Gleason–Kahane–Żelazko theorem without assuming linearity. On the way of establishing this, we observe that linearity on a multiplier algebra is enough to conclude linearity on the whole Hilbert space. By constructing a counter-example, we show that the condition of complete Pick kernel can not be removed. Also, we demonstrate the automatic continuity of such functionals. Leveraging these findings, we extend the Kowalski–Słodkowski theorem in this setup.

In a recent study, Kim established a general identity which implies a generalization of the modular equations of degrees 3, 5, 11 and 23, and derived some identities for partitions. In this paper we provide proofs for some new modular equations of composite degrees and degree of 7 by methods of elementary algebra and Kim’s generalization of theta-function identities. In addition, we derive many partition identities, which are proved depending upon these modular equations and reciprocation.

In this paper we introduce and study a new graph-theoretic invariant called the bi-Wiener index. The bi-Wiener index (W_b(G)) of a bipartite graph G is defined as the sum of all (shortest-path) distances between two vertices from different parts of the bipartition of the vertex set of G. We start with providing a motivation connected with the potential uses of the new invariant in the QSAR/QSPR studies. Then we study its behavior for trees. We prove that, among all trees of order (nge 4), the minimum value of (W_b) is attained for the star (S_n), and the maximum (W_b) is attained at path (P_n) for even n, or at path (P_n) and (B_n(2)) for odd n where (B_n(2)) is a broom with maximum degree 3. We also determine the extremal values of the ratio (W_b(T_n)/W(T_n)) over all trees of order n. At the end, we indicate some open problems and discuss some possible directions of further research.

In this paper, we extend the findings of recent studies on k-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the k-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the k-rainbow total domination number of the corona product (G*H), provided that H has enough vertices.

In this article we study the solution u(t, x) of the Cauchy problem of linear damped wave equation. We obtain the sufficient and necessary condition of the boundedness of the solution u(t, x) on the Triebel–Lizorkin space at a fixed time t.

The variety of Moufang loops is axiomatized by any one of four well known (equivalent) identities. We prove that this axiomatic harmony holds in a broader setting by obtaining two alternate, generalized versions of the (traditional) definition of a Moufang loop using four “local” identities, each derived from one of the four “global” Moufang identities, one for loops, the other for magmas with the right or left inverse property.

We determine the sharp bounds on the second Hankel determinants of logarithmic coefficients and the third Hankel determinants for Ozaki close-to-convex functions.

This paper focuses on the stability and decay rates of solutions to the three dimensional anisotropic magnetohydrodynamic equations with horizontal velocity dissipation and magnetic damping phenomenon. By fully exploiting the structure of the system, the energy methods and the method of bootstrapping argument, we prove the global stability of solutions to this system with initial data small in (H^{3}(mathbb {R}^{3})). Furthermore, we make use of the integral representation approach to obtain the optimal decay rates of these global solutions and their derivatives. This result along with its proof offers an effective approach to the large-time behavior on partially dissipated systems and reveals the stabilizing phenomenon exhibited by electrically conducting fluids.