Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

PERIODIC SOLUTIONS OF PLANAR SYSTEM WITH SIX DELAYS

In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree.     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

On Two Theorems of Finite Solvable Groups

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions： （1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2： （3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.     

Tetradecanol dehydrogenation over CuO catalyst supported on BaO, CaO and MgO

Bimetallic Cu/Mg, Ca, Ba mixed oxide compounds acted as catalyst in the dehydrogenation of tetradecanol into tetradecanal, and were characterized by thermal gravimetric analysis, surface area, X-ray diffraction, temperature-programmed reduction and desorption of CO₂. Alkaline earth oxides increased the total basic site concentration in the order of Mg>Ca>Ba. A correlation was found between the total basic site concentration and initial dehydrogenation rate. This revised version was published online in June 2006 with corrections to the Cover Date.     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

正系数多项式倒数逼近的点态和整体估计

利用Ditzian-Totik光滑模对于[0,1]上定义的非角连续函数f(x)，且f(x)≠0，文中证明存在正系数多项式Pn(x)及常数C，使得|f9x)-1/Pn(x)|≤Cωψ^λ（f,n^-1/2(ψ(x) 1/√n)^1-λ)。当λ＝1时，上述结果导出已有的整体估计，而当0≤λ＜1时，得到倒数逼近一个新的点态局部估计。     

Integral Method o Reciprocity in the Spectroscopy of Laser Crystals with Impurity Centers

A new method of determining the stimulated emission cross-section spectra from the absorption cross-section spectra, which we call the integral method of reciprocity, is suggested it does not require knowledge of the structure of the impurity-center electron levels. Based on this method, formulas for calculating the radiation lifetime of impurity centers in crystals have been derived. The effectiveness of the integral method of reciprocity was demonstrated in determining the stimulated emission cross sections and radiation lifetime of an ytterbium ion in the laser crystals Yb³⁺:KYW and Yb³⁺:KGW.     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.