设 S 是 n 项可图序列, σ(S) 是 S 中的所有项之和, 设 H 是一个简单图, σ(H,n)是使得任意 n 项可图序列满足 σ(S) ≥ m , 则 S 有一个实现包含 H 作为子图的 m 的最小值, 本文给出了 σ(K p,1,1,...,1,n) 的...设 S 是 n 项可图序列, σ(S) 是 S 中的所有项之和, 设 H 是一个简单图, σ(H,n)是使得任意 n 项可图序列满足 σ(S) ≥ m , 则 S 有一个实现包含 H 作为子图的 m 的最小值, 本文给出了 σ(K p,1,1,...,1,n) 的下界并猜测对于所有的 n ≥ (t2 ) + 3p 此下界是可达到的.展开更多
The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratica...The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect.展开更多
A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer ...A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer sequence π=(d 1,d 2,...,d n) is said to be graphic if it is the degree sequence of a simple graph G of order n and such a graph G is referred to as a realization of π . A graphic sequence π is said to be potentially P k graphic if it has a realization G having property P k . The problem: determine the smallest positive even number σ(k,n) such that every n term graphic sequence π=(d 1,d 2,...,d n) without zero terms and with degree sum σ(π)=d 1+d 2+...+d n at least σ(k,n) is potentially P k graphic has been proved positive.展开更多
文摘设 S 是 n 项可图序列, σ(S) 是 S 中的所有项之和, 设 H 是一个简单图, σ(H,n)是使得任意 n 项可图序列满足 σ(S) ≥ m , 则 S 有一个实现包含 H 作为子图的 m 的最小值, 本文给出了 σ(K p,1,1,...,1,n) 的下界并猜测对于所有的 n ≥ (t2 ) + 3p 此下界是可达到的.
基金supported by the Research Fellow of Indian School of Mines in Dhanbad (No. 2010DR0016)
文摘The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect.
文摘A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer sequence π=(d 1,d 2,...,d n) is said to be graphic if it is the degree sequence of a simple graph G of order n and such a graph G is referred to as a realization of π . A graphic sequence π is said to be potentially P k graphic if it has a realization G having property P k . The problem: determine the smallest positive even number σ(k,n) such that every n term graphic sequence π=(d 1,d 2,...,d n) without zero terms and with degree sum σ(π)=d 1+d 2+...+d n at least σ(k,n) is potentially P k graphic has been proved positive.
