关于群的方次数的若干结果

群的方次数是群论中的一个基本概念,它反映了群的元素阶的性质特征.通过对群的方次数的初步探讨,得到结论:若群G的元素阶均有限,且sup|a|a∈G=sup|a|a∈C(G),则群G的方次数expG=sup|a|a∈C(G).并进一步用方次数刻划了群的结构.

几何级数中奇素因子的方次数

本文应用初等数论理论讨论了几何级数前n项和中的奇素因子p的方次数,得到了一个计算公式。

几何级数中因子2的方次数之探讨

当n=2r+1 -1时,几何级数可以表示为:∑ni=0xi=∏rj=0(1+x2j).断定,当n=2r+1 -1时,若{x+1}2 =m,那么对于s(x) =∑ni=0xi就有{s(x)2 } =m+r成立,此处r是非负整数,x≠±1;当n=2r+1h-1时,若{x+1}2 =m,那么对于s(x) =∑nxi就有{s(x) } =m+r成立,此处r是非负整数,h,x为奇数,且h>0.

八阶二次数方的演变

提出匹配有两组对角线的八阶二次数方（幻方）．将此方作全对称行列搬动时，有８２／２＝３２种演变，图示９种；如作不全对称行列搬动时，则得强（Ｑｉǎｎｇ）体，图示１种．

一类特殊的有限3-群

主要研究了方次数是3的3-群,证明了:如果方次数是3的3-群G的幂零类是3,那么|G|≥37.进一步,设d(G)=3,则cl(G)=3当且仅当|G|=37.

有限p-反阿贝尔群的一种刻画

相对于p-阿贝尔群,引进了p-反阿贝尔群的概念,借助p-阿贝尔群的已知结果,研究了p-反阿贝尔群的性质,得到了一个有限群为p-反阿贝尔群的充要条件是它为p-阿贝尔群.

特征为0域上线性群的有限子群的界定

将Schur的线性群GL(n,Q)上扭子群必为有限群这一性质推广到Q的一般有限扩域F上,证明了GL(n,F)中方次数有限的子群的阶仅与n和[F:Q]有关.

Numerical simulation of seismic low-frequency shadows and its application

Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-frequency shadow is still unclear. To stud） the mechanism, we performed seismic numerical simulation of geological models with a hydrocarbon-bearing zone using the 2-D diffusive-viscous wave equation which car effectively model the characteristics of velocity dispersion and transform the seismic dat~ centered in a target layer slice within a time window to the time-frequency domain by usinl time-frequency signal analysis and sort the frequency gathers to common frequency cubes. Then, we observe the characteristics of the seismic low-frequency shadow in the common frequency cubes. The numerical simulations reveal that the main mechanism of seismic lowfrequency shadows is attributed to high attenuation of the medium to high seismic frequency components caused by absorption in the hydrocarbon-filled reservoir. Results from a practical example of seismic low-frequency shadows show that it is possible to identify the reservoir by the low-frequency shadow with high S/N seismic data.

On the First-degree Algebraic Equation of the Generalized Quaternion

In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.

On the Sum of a Prime and the k-th Power of a Prime

In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 and any 0【ε【14,E k(x+H)-E k(x)≤H(log x) -Aholds for x 12-14k+ε≤H≤x, here the implies constant depends at most on A and ε.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION

Quadratic Discrimination Function （QDF） is commonly used in speech emotion recognition, which proceeds on the premise that the input data is normal distribution. In this paper, we propose a transformation to normalize the emotional features, emotion recognition. Features based on prosody then derivate a Modified QDF （MQDF） to speech and voice quality are extracted and Principal Component Analysis Neural Network （PCANN） is used to reduce dimension of the feature vectors. The results show that voice quality features are effective supplement for recognition, and the method in this paper could improve the recognition ratio effectively.

Exact Solutions to Nonlinear Schr(?)dinger Equation and Higher-Order Nonlinear Schr(?)dinger Equation

We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.

A New Alpha-function for the Peng-Robinson Equation of State： Application to Natural Gas

Cubic equations of state(EOSs) are simple and easy at calculation. One way of improving the accuracy of a cubic EOS is through the modification of temperature-dependent energy parameter by using alpha-function.The industrial applications of natural gas are very wide and as a result, prediction of thermodynamic properties and phase behavior of natural gas is an important part of design for such processes. In this work we develop a newα-function for the Peng-Robinson(PR) EOS with the parameters optimized especially for natural gas components.The parameters are generalized as a linear function of acentric factor. The results are compared to the predictions from original PR EOS and other α-functions in literature. It is shown that the new α-function presents a good accuracy with the average deviation of 1.42% for natural gas components.

Three New Integrable Hierarchies of Equations

A general Lie algebra Vs and the corresponding loop algebra Vx are constructed, from which the linear isospectral Lax pairs are established, whose compatibility presents the zero curvature equation. As its application, a new Lax integrable hierarchy containing two parameters is worked out. It is not Liouville-integrable, however, its two reduced systems are Liouville-integrable, whose Hamiltonian structures are derived by making use of the quadratic-form identity and the γ formula （i.e. the computational formula on the constant γ appeared in the trace identity and the quadratic-form identity）.

Artificial perturbation for solving the Korteweg-de Vries equation

A perturbation method is introduced in the context of dynamical system for solving the nonlinear Korteweg-de Vries (KdV) equation. Best efficiency is obtained for few perturbative corrections. It is shown that, the question of convergence of this approach is completely guaranteed here, because a limited number of term included in the series can describe a sufficient exact solution. Comparisons with the solutions of the quintic spline, and finite difference are presented.

Integrable Coupling System of JM Equations Hierarchy with Self-Consistent Sources

We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/（4）. The JM equations hierarchy with self-consistent sources is derived. Furthermore, an integrable couplings of the JM soliton hierarchy with self-consistent sources is presented by using of the loop algebra sl（4）.

Lie Algebras for Constructing Nonlinear Integrable Couplings

Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.

Self-Similar Solutions of Variable-Coefficient Cubic-Quintic Nonlinear Schr(o|¨)dinger Equation with an External Potential

An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.