Wang, Yan Fang, Xin Gui Hsu, D. F.
Published in
Acta Mathematica Sinica

A G-Frobenius graph Γ, as defined by Fang, Li, and Praeger, is a connected orbital graph of a Frobenius group G = K ⋊ H with Frobenius kernel K and Frobenius complement H. Γ is also shown to be a Cayley graph, Γ = Cay(K, S) for K and some subset S of the group K. On the other hand, a network N with a routing function R, written as (N,R), is an undi...

Ma, Li Chen, De Zhong Yang, Yang
Published in
Acta Mathematica Sinica

In this paper, we consider the principal eigenvalue problem for Hormander’s Laplacian on Rn, and we find a comparison principle for such principal eigenvalues. We also study a related semi-linear sub-elliptic equation in the whole Rn and prove that, under a suitable condition, we have infinitely many positive solutions of the problem.

Park, Chun-Gil Rassias, Themistocles M.
Published in
Acta Mathematica Sinica

We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach modules over a unital C*-algebra. The main purpose of this paper is to investigate N-isometric C*-algebra isomorphisms between linear N-normed C*-algebras, N-isometric Poisson C*-algebra isomorphisms between linear N-normed Poisson C*-algebras, N-isometric Lie C*-alg...

Hai, Jin Ke Zhu, Yi Xin
Published in
Acta Mathematica Sinica

Alperin and Brouá have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.

Wang, Yu You, Hong
Published in
Acta Mathematica Sinica

This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d(u), u]n is central, for all u ∈¸ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Fil...

Staněk, Svatoslav
Published in
Acta Mathematica Sinica

The paper presents the conditions which guarantee that for some positive value of ì there are positive solutions of the di.erential equation (φ(x'))'+μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0,∞) × (ℝ \ {0}) of the semipositone type and Q is singular at the v...

Ding, Xie Ping
Published in
Acta Mathematica Sinica

Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known...

Yang, Ying
Published in
Acta Mathematica Sinica

M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the upper and lower bounds of the smoothing parameter selected by the proposed criterion are established. The main contribution of this ...

Chen, Yi Chao Liu, Yan Pei Wang, Tao
Published in
Acta Mathematica Sinica

Total embedding distributions have been known for only a few classes of graphs. In this paper the total embedding distributions of the cacti and the necklaces are obtained. Furthermore we obtain the total embedding distributions of all graphs with maximum genus 1 by using the method of this paper.

Bie, Rong Fang Wang, Shi Qiang
Published in
Acta Mathematica Sinica

In this paper, by using model-theoretic methods, it is shown that some systems of unsolved cubic diophantine equations in number theory can have solutions in certain inductive extension rings of the ring I of rational integers. These inductive rings are not fields, and every element of them is a sum of 4 cubes and a sum of 3 squares. Also some of t...