Bulletin of the Malaysian Mathematical Sciences Society最新文献

Let ({p_n}_{nge 1}) and ({ d_n}_{nge 1}) be two sequences of integers such that (|p_n|>|d_n|>0) and ({d_n}_{nge 1}) is bounded. It is proven by Deng and Li that the Moran-type Bernoulli convolution

is a spectral measure if and only if the numbers of factor 2 in the sequence (big {frac{p_1p_2dots p_n}{2d_n}big }_{nge 1}) are different from each other. Unfortunately, there is a gap in the proof of the sufficiency. Here we give a new proof to close the gap.

Let (Asubseteq B) be an extension of integral domains, (B[![X]!]) be the power series ring over B, and (R=A + XB[![X]!]) be a subring of (B[![X]!].) In this paper, we give a complete description of v-invertible v-ideals (with nonzero trace in A) of R. We show that if B is a completely integrally closed domain and I is a fractional divisorial v-invertible ideal of R with nonzero trace over A, then (I = u(J_1 + XJ_2[![X]!])) for some (uin qf(R),) (J_2) an integral divisorial v-invertible ideal of B and (J_1subseteq J_2) a nonzero ideal of A.

A family (Delta ) of subsets of ({1,2,ldots ,n}) is a simplicial complex if all subsets of F are in (Delta ) for any (Fin Delta ,) and the element of (Delta ) is called the face of (Delta .) Let (V(Delta )=bigcup _{Fin Delta } F.) A simplicial complex (Delta ) is a near-cone with respect to an apex vertex (vin V(Delta )) if for every face (Fin Delta ,) the set ((Fbackslash {w})cup {v}) is also a face of (Delta ) for every (win F.) Denote by (f_{i}(Delta )=|{Ain Delta :|A|=i+1}|) and (h_{i}(Delta )=|{Ain Delta :|A|=i+1,nnot in A}|) for every i, and let (text {link}_{Delta }(v)={E:Ecup {v}in Delta , vnot in E}) for every (vin V(Delta ).) Assume that p is a prime and (kgeqslant 2) is an integer. In this paper, some extremal problems on k-wise L-intersecting families for simplicial complexes are considered. (i) Let (L={l_1,l_2,ldots ,l_s}) be a subset of s nonnegative integers. If (mathscr {F}={F_1, F_2,ldots , F_m}) is a family of faces of the simplicial complex (Delta ) such that (|F_{i_1}cap F_{i_2}cap cdots cap F_{i_k}|in L) for any collection of k distinct sets from (mathscr {F},) then (mleqslant (k-1)sum _{i=-1}^{s-1}f_i(Delta ).) In addition, if the size of every member of (mathscr {F}) belongs to the set (K:={k_1,k_2,ldots ,k_r}) with (min K>s-r,) then (mleqslant (k-1)sum _{i=s-r}^{s-1}f_i(Delta ).) (ii) Let (L={l_1,l_2,ldots ,l_s}) and (K={k_1,k_2,ldots ,k_r}) be two disjoint subsets of ({0,1,ldots ,p-1}) such that (min K>s-2r+1.) Assume that (Delta ) is a simplicial complex with (nin V(Delta )) and (mathscr {F}={F_1, F_2,ldots , F_m}) is a family of faces of (Delta ) such that (|F_j|pmod {p}in K) for every j and (|F_{i_1}cap F_{i_2}cap cdots cap F_{i_k}|pmod {p}in L) for any collection of k distinct sets from (mathscr {F}.) Then (mleqslant (k-1)sum _{i=s-2r}^{s-1}h_i(Delta ).) (iii) Let (L={l_1,l_2,ldots ,l_s}) be a subset of ({0,1,ldots ,p-1}.) Assume that (Delta ) is a near-cone with apex vertex v and (mathscr {F}={F_1, F_2,ldots , F_m}) is a family of faces of (Delta ) such that (|F_j|pmod {p}not in L) for every j and (|F_{i_1}cap F_{i_2}cap cdots cap F_{i_k}|pmod {p}in L) for any collection of k distinct sets from (mathscr {F}.) Then ( mleqslant (k-1)sum _{i=-1}^{s-1}f_i(text {link}_Delta (v)).)

This manuscript demonstrates robust optimality conditions, Wolfe and Mond–Weir type robust dual models for a robust mathematical programming problem involving vanishing constraints (RMPVC). Further, the theorems of duality are examined based on the concept of generalized higher order invexity and strict invexity that establish relations between the primal and the Wolfe type robust dual problems. In addition, the duality results for a Mond–Weir type robust dual problem based on the concept of generalized higher order pseudoinvex, strict pseudoinvex and quasiinvex functions are also studied. Furthermore, numerical examples are provided to validate robust optimality conditions and duality theorems of Wolfe and Mond–Weir type dual problems.

For (1le p<infty ), let (L_p({mathcal {M}},tau )) be the non-commutative (L_p)-space associated with a von Neumann algebra ({mathcal {M}}), where ({mathcal {M}}) admits a normal semifinite faithful trace (tau ). Using the trace (tau ), Banach duality formula and Gâteaux derivative, this paper characterizes an element (ain L_p({mathcal {M}},tau )) such that

where ({mathcal {B}}_p) is a closed linear subspace of (L_p({mathcal {M}},tau )) and (Vert cdot Vert _p) is the norm on (L_p({mathcal {M}},tau )). Such an a is called ({mathcal {B}}_p)-minimal. In particular, minimal elements related to the finite-diagonal-block type closed linear subspaces

(converging with respect to (Vert cdot Vert _p)) are considered, where ({e_i}_{i=1}^{infty }) is a sequence of mutually orthogonal and (tau )-finite projections in a (sigma )-finite von Neumann algebra ({mathcal {M}}), and ({mathcal {S}}) is the set of elements in ({mathcal {M}}) with (tau )-finite supports.

The smallest M-eigenvalue (tau _M ({mathcal {A}})) of a fourth-order partial symmetric tensor ({mathcal {A}}) plays an important role in judging the strong ellipticity condition (abbr. SE-condition) in elastic mechanics. Specifically, if (tau _M ({mathcal {A}})>0), then the SE-condition of ({mathcal {A}}) holds. In this paper, we establish lower and upper bounds of (tau _M ({mathcal {A}})) via extreme eigenvalues of symmetric matrices and tensors constructed by the entries of ({mathcal {A}}). In addition, when ({mathcal {A}}) is an elasticity Z-tensor, we establish lower bounds for (tau _M ({mathcal {A}})) via the extreme C-eigenvalues of piezoelectric-type tensors. Finally, numerical examples show the efficiency of our proposed bounds in judging the SE-condition of ({mathcal {A}}).

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.