Bulletin of the Malaysian Mathematical Sciences Society最新文献

Let (mathbb {B}_X) be a bounded symmetric domain realized as the open unit ball of a JB*-triple X. First, we extend the definition for pluriharmonic Bloch functions to (mathbb {B}_X) by using the infinitesimal Kobayashi metric. Next, we develop some methods to investigate Bloch functions, and composition operators of pluriharmonic Bloch spaces on bounded symmetric domains. The obtained results provide the improvements and extensions of the corresponding known results.

The shadowable points of dynamical systems have been well-studied by Morales in his recent paper (2016). This paper aims to generalize the main results obtained by Morales to free semigroup actions. To this end, we introduce the notion of shadowable points of a free semigroup action. Let G be a free semigroup generated by finite continuous self-maps acting on compact metric space. We will prove the following results for G on compact metric spaces. The set of shadowable points of G is a Borel set. G has the pseudo-orbit tracing property (POTP) if and only if every point is shadowable point of G. The chain recurrent and non-wandering sets of G coincide when every chain recurrent point is shadowable point of G. The space X is totally disconnected at every shadowable point of G under certain condition.

In this paper, an efficient lopsided double-step (LDS) iteration scheme is proposed to quickly solve complex symmetric linear systems, by using the real part and imaginary part of the coefficient matrix. We give detailed analysis of the spectral radius of the iteration matrix and the quasi-optimal parameter for the LDS method. In addition, a modified version of the LDS (MLDS) method is developed by using only one matrix inversion in each iteration, and the convergence properties of the MLDS method are discussed. Particularly, under suitable conditions, the convergence factors of the LDS and the MLDS methods are no more than 0.1768, and this number is less than that of many exiting methods. Numerical experiments are implemented and the results support the contention that the LDS and the MLDS methods are more efficient than several classical methods. Furthermore, we also explore the fixed parameters for the LDS and the MLDS methods in practice, and the numerical results are very satisfactory.

The graph (aK_{m,m}nabla C_{n}) is named the generalized double-wheel graph. A graph G is said to be M-integral (resp. A-integral, D-integral, (D^L)-integral or (D^Q)-integral) if all eigenvalues of its matrix M (resp. adjacency matrix A(G) , distance matrix D(G) , distance Laplacian matrix (D^L(G)) or distance signless Laplacian matrix (D^Q(G))) are integers. In this paper, we completely determine all D-integral, (D^L)-integral and (D^Q)-integral generalized double-wheel graphs respectively.

Let (G_S) be the graph obtained by attaching a self-loop at every vertex in (S subseteq V(G)) of a simple graph G of order n. In this paper, we explore several new results related to the line graph (L(G_S)) of (G_S.) Particularly, we show that every eigenvalue of (L(G_S)) must be at least (-2,) and relate the characteristic polynomial of the line graph L(G) of G with the characteristic polynomial of the line graph (L({widehat{G}})) of a self-loop graph ({widehat{G}}), which is obtained by attaching a self-loop at each vertex of G. Then, we provide some new bounds for the eigenvalues and energy of (G_S.) As one of the consequences, we obtain that the energy of a connected regular complete multipartite graph is not greater than the energy of the corresponding self-loop graph. Lastly, we establish a lower bound of the spectral radius in terms of the first Zagreb index (M_1(G)) and the minimum degree (delta (G),) as well as proving two Nordhaus–Gaddum-type bounds for the spectral radius and the energy of (G_S,) respectively.

For any non-negative integer k and any graph G, a subset (Ssubseteq V(G)) is said to be a (K_{1,k+1})-isolating set of G if (G-N[S]) does not contain (K_{1,k+1}) as a subgraph. The (K_{1,k+1})-isolation number of G, denoted by (iota _k(G)), is the minimum cardinality of a (K_{1,k+1})-isolating set of G. Recently, Zhang and Wu (2021) proved that if G is a connected n-vertex graph and (Gnotin {P_3,C_3,C_6}), then (iota _1(G)le frac{2}{7}n). In this paper, we characterize all extremal graphs attaining this bound, which resolves a problem proposed by Zhang and Wu (Discrete Appl Math 304:365–374, 2021).

Let (mathbb {A}) be the (2times 2) diagonal operator matrix determined by a positive Hilbert space operator A. We give several upper bounds for the (mathbb {A})-Berezin number of (2times 2) block matrices on a reproducing kernel Hilbert space and prove inequalities for the A-Berezin number of Hilbert space operators. Our results in this paper generalize and refine earlier the A-Berezin number inequalities.

In this paper, we consider the following nonlinear Schrödinger equation with an (L^2)-constraint:

where (Nge 3), (a,mu >0), (2<q<2+frac{4}{N}<p<2^*), (2q+2N-pN<0) and (lambda in mathbb {R}) arises as a Lagrange multiplier. We deal with the concave and convex cases of energy functional constraints on the (L^2) sphere, and prove the existence of infinitely solutions with positive energy levels.

We study nuclear embeddings for spaces of Morrey type, both in its sequence space version and as smoothness spaces of functions defined on a bounded domain (Omega subset {{mathbb {R}}}^{{d}}). This covers, in particular, the meanwhile well-known and completely answered situation for spaces of Besov and Triebel-Lizorkin type defined on bounded domains which has been considered for a long time. The complete result was obtained only recently. Compact embeddings for function spaces of Morrey type have already been studied in detail, also concerning their entropy and approximation numbers. We now prove the first and complete nuclearity result in this context. The concept of nuclearity has already been introduced by Grothendieck in 1955. Again we rely on suitable wavelet decomposition techniques and the famous Tong result (1969) which characterises nuclear diagonal operators acting between sequence spaces of (ell _r) type, (1le rle infty ).