Bulletin of the Malaysian Mathematical Sciences Society最新文献

Given a simple, finite graph with vertex set V(G), we define a zero forcing set of G as follows. Choose (Ssubseteq V(G)) and color all vertices of S blue and all vertices in (V(G) - S) white. The color change rule is if w is the only white neighbor of blue vertex v, then we change the color of w from white to blue. If after applying the color change rule as many times as possible eventually every vertex of G is blue, we call S a zero forcing set of G. Z(G) denotes the minimum cardinality of a zero forcing set. We show that if G is 2-edge-connected, claw-free, and cubic, then . We also study a similar graph invariant known as the loop zero forcing number of a graph G which happens to be the dual invariant to the Grundy domination number of G. Specifically, we study the loop zero forcing number in two particular types of planar graphs.

The t-path ideal (I_t(G)) of a graph G is the square-free monomial ideal generated by the monomials which correspond to the paths of length t in G. In this paper, we prove that the Stanley–Reisner complex of the 2-path ideal (I_2(G)) of an (undirected) tree G is vertex decomposable. As a consequence, we show that the Alexander dual (I_2(G)^{vee }) of (I_2(G)) has linear quotients. For each (t ge 3), we provide a counterexample of a tree for which the Stanley–Reisner complex of (I_t(G)) is not vertex decomposable.

In this article, we investigate a class of nonsmooth multiobjective mathematical optimization problems with switching constraints (abbreviated as, (NMMPSC)) in the framework of Hadamard manifolds. Corresponding to (NMMPSC), the generalized Guignard constraint qualification (abbreviated as, (GGCQ)) is introduced in the Hadamard manifold setting. Karush–Kuhn–Tucker (abbreviated as, KKT) type necessary conditions of Pareto efficiency are derived for (NMMPSC). Subsequently, we introduce several other constraint qualifications for (NMMPSC), which turn out to be sufficient conditions for (GGCQ). We have furnished non-trivial illustrative examples to justify the significance of our results. To the best of our knowledge, constraint qualifications for (NMMPSC) have not yet been studied in the Hadamard manifold framework.

In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived. A probabilistic generalization of a series transformation formula and some interesting examples are discussed. A connection between the probabilistic Fubini polynomials and Bernoulli, Poisson, and geometric random variables are also established. Finally, a determinant expression formula is presented.

We study the long-time dynamics of a wave equation with nonlocal weak damping, nonlocal weak anti-damping and sup-cubic nonlinearity. Based on the Strichartz estimates in a bounded domain, we obtain the global well-posedness of the Shatah–Struwe solutions. To overcome the difficulties brought by the nonlinear weak damping term, we present a new-type Gronwall’s lemma to obtain the dissipative for the Shatah–Struwe solutions semigroup of this equation. Finally, we establish the existence of a time-dependent exponential attractor with the help of a more general criteria constructed by the quasi-stable technique.

The aim of this paper is to introduce Clairaut conformal submersions between Riemannian manifolds. First, we find necessary and sufficient conditions for conformal submersions to be Clairaut conformal submersions. In particular, we obtain Clairaut relation for geodesics on the total manifolds of conformal submersions, and prove that Clairaut conformal submersions have constant dilation along their fibers, which are totally umbilical, with mean curvature being gradient of a function. Further, we calculate the scalar and Ricci curvatures of the vertical distributions of the total manifolds. Moreover, we find a necessary and sufficient condition for Clairaut conformal submersions to be harmonic. For a Clairaut conformal submersion we find conformal changes of the metric on its domain or image, that give a Clairaut Riemannian submersion, a Clairaut conformal submersion with totally geodesic fibers, or a harmonic Clairaut submersion. Finally, we give two non-trivial examples of Clairaut conformal submersions to illustrate the theory and present a local model of every Clairaut conformal submersion with integrable horizontal distribution.