We establish two inequalities concerning the weakly convergent sequence WCS(X) and Jordan-von Neumann type constants C't(X), C_∞(X), which enable us to obtain some sufficient conditions for normal structure. The results obtained in this paper represent an extension as well as refinement of previous known results. Meanwhile, the Jordan-von Neumann type constants C't(X), C_∞(X) for the Bynum space l2,∞ are computed, and are used to show that our results are sharp.
In this paper, by constructing a partial sum of ζ(k) on the Riemann Zeta function, using the ζn(k) power series function, Binomial expression and Cauchy product formula, some important sums are calculated. By extending the power series function from one variable to multivariate, some relationships of high order sums on Riemann Zeta function are established. By using the relationship between the logarithmic function and Stirling numbers of the first kind, and some other related equations, 18 seven-order sums of Riemann Zeta function and some other high order sums are obtained.
The purpose of this paper is to find out the deep and rich structure of the set of Parseval frame wavelets with special dilation matrices (M-PFW). We study the all kinds of properties of M-PFW, semi-orthogonal M-PFW and MRA M-PFW based on shift-invariant space and the dimension function. We investigate various subclass of the set of M-PFWs. Several constructive examples illustrating the various possibilities are given.
In this paper, an extragradient-type method proposed by Wang, Xiu and Zhang [Modified extragradient-type method for variational inequalities and verification of the existence of solutions, J. Optim. Theory Appl., 2003, 119: 167-183] for solving variational inequalities in Euclidean spaces is extended to Banach spaces. The operator involved in the variational inequality is not necessarily uniformly continuous. The main advantage lies in that the proposed algorithm is well defined no matter whether the variational inequality problem has a solution or not. Furthermore, the existence of the solution to the variational inequality problem can be verified through the behavior of the generated sequence. Under some suitable assumptions, the sequence generated by the proposed method is strongly convergent to the solution of the variational inequality, which is closest to the initial iterate in the sense of Bregman distance. The main results presented in this paper generalize and improve the recent ones in the literature.
We study the multiplicity of positive solutions to a p-Kirchhoff equation with sign-changing weight functions. These positive solutions are obtained by the variational methods and the decomposition of the Nehari manifold.
Based on anisotropic Sobolev space and compensated compactness methods, we obtain the homogenization of nonlinear elliptic equations with general anisotropic diffusivity.
Different type of continuous functions of unbounded variation have been discussed. According to the local structure, all continuous functions have been classified. Meanwhile, certain examples of different kinds of fractal functions have been given. Properties of those fractal functions have also been discussed. Definition of singular continuous functions has been given and an equivalent theorem which can be used to describe whether a function is a singular continuous function or not has been set up. Based on definition of singular continuous functions, we make research on definition of local fractal functions and fractal functions. Fractal functions are composed of singular fractal functions, irregular fractal functions and regular fractal functions. Finally, definition of fractal functions corresponding to discontinuous functions has been explored.
We mainly discuss the average sampling and reconstruction of signals in weighted reproducing kernel subspaces of Lνp . First, the sampling stability for two kinds of average sampling functionals are established. Then, we give a general iterative algorithm based on probability measure, which provides a unified treatment for iterative approximation projection algorithm and iterative frame algorithm. Finally, the asymptotic pointwise error estimate is presented for reconstructing a signal from its average samples corrupted by white noise.
Suppose that k ≥ 2 is an integer. In this note, we prove that every graph with m edges admits a partition V1, V2, . . ., Vk such that e(V1, V2, . . ., Vk) ≥ (k-1)/k·m + (k-1)/(2k)·(√2m + 1/4-1/2)-((k-2)2)/(8k), and max{e(Vi) : 1 ≤ i ≤ k} ≤ m/(k2) + (k-1)/(2k2) (√2m + 1/4-1/2)+ 3/8-(7k-4)/(8k2). This improves the main result of [Fan G., Hou J., Zeng Q., A bound for judicious k-partitions of graphs, Discrete Appl. Math., 2014, 179: 86-99].
We study the generalized Roper-Suffridge operator (F(z1)+f'(z1)Σk =2nakzkpk, f' (z1)1/(p2)z2, . . ., f' (z1)1/(pn)zn)', and prove that it can preserve the properties of almost spirallikeness of type β and order α, spirallikeness of type β and order α, and strongly spirallikeness of type β on the following Reinhardt domain in complex Euclidean space Ωn,p2,...,pn = {z = (z1, . . ., zn) ∈ Cn : |z1|2 +Σk=2n |zk|pk < 1, pk ∈ N+, k = 2, . . ., n} under some special conditions, respectively.
Batch codes were first proposed by Ishai et al., an (n,N, k,m)-combinatorial batch code was defined by Peterson et al. as a purely combinatorial version of batch codes. It is a system consisting of m subsets of an n-element set such that any k elements can be retrieved by reading at most one (or in general, t) elements from each subset and the number of total elements in m subsets is N. For given parameters n, k,m, the minimum N, denoted by N(n, k,m), is of particular interest, which has both theoretical interests and strong practical motivation. So far, for k ≥ 5, m+3 ≤ n <.jpg){kind=small}
, precise values of N(n, k,m) have not been established except for some special settings of the parameters. In this article, we obtain N(m+3, 5,m) = m+11 (m ≥ 7), N(9, 5, 6) = 18, N(m+3, 6,m) = m+13 (m ≥ 8), N(10, 6, 7) = 21. Our results partly answer an open problem of Paterson et al.
We investigate boundedness and compactness of the generalized composition operators between weighted Bloch-type spaces. Some sufficient and necessary conditions for the boundedness and compactness of these operators are obtained.
