共查询到18条相似文献，搜索用时 406 毫秒
1.
In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe. 相似文献
2.
The bilinear Baecklund transformation (BT) provides a means of finding multisoliton solutions of some non-linear evolution equations, where Hirota‘s technique is used. In this paper, the bilinear BT for Toda lattice was modified and then some novel solutions of the Toda lattice was constructed through the modified BT. 相似文献
3.
HUANGDe－bin LIUZeng－rong 《上海大学学报(英文版)》2001,5(4):273-275
In this paper,the nonlinear Schrodinger(NLS)equation was analytically solved.Firstly,the stationary solutions of NLS equation were explicitly given by the elliptic functions.Then a family of exact solutions of NLS equation were botained from these stationary solutions by a method for finding new exact solutions from the stationary solutions of integrable evolution equations. 相似文献
4.
We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper. 相似文献
5.
A modified Lindstedt-Poincaré(LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equations are converted into a group of linear ordinary differential equations by introducing a set of simple transformations.An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modified method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation,and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales. 相似文献
6.
To consider the internal pressure loaded by both the cylindrical Ti-Al alloy liner and the carbon fiber resin composite （CFRC） wound layers, two models are built. The first one is a cylinder loaded with the internal pressure in the hoop direction only. In this model, the total hoop direction load is distributed over all layers under the internal pressure. The second one is a cylinder loaded with the internal pressure in the axial direction only. In this model, the total axial load is distributed over all cylinders under the internal pressure. Taking the boundary conditions of the continuous displacement between layers into account, a group of equations are built. From these equations, we get the solutions of stresses in both hoop direction and axial direction loaded by every layer under internal pressures. After the stresses are obtained, a reasonable design can be done. An example is given in the final section of this study. 相似文献
7.
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^ in Banach spaces. By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval. 相似文献
8.
We have derived a set of field equations for a Weyssenhoff spin fluid including magnetic interacton among the spinning particles prevailling in spatially homogeneous,but anisotropically cosmological models of Bianchi type V based on Einstein-Cartan theory.We analyze the field equations in three different equations of states specified by p=1(1/3)ρand p=0,The analytical solutions found are non-singular provided that the combined energy arising from matter spin and magnetic interaction among particles overcomes the anisotropy energy in the Universe,We have also deduced that the minimum particle numers for the radiation(p=(1/3)ρ) and matter(p=0) epochs are 10^88 and 10^108 respectively.the minimum particle number for the state p=ρ is 10^96,leading to the conclusion that we must consider the existence of neutrinos and other creation of particles and anti-particles under torsion and strong gravitational field in the early Universe. 相似文献
9.
《语数外学习(高中版)》2008,(30):56-57
It＇s summertime, and the living is easy. For many Americans, this is the season to travel. Why？ Because school is out. Because the weather is great. And most of all, because we all deserve a break. When Americans take a break, they often head for their favorite vacation spot. 相似文献
10.
Dingpin Wu Zhi Ping Lui 《宜宾学院学报》1998,(2)
<正> In this paper,we study a class of completely generalized strongly set-valued nonlinearquasi-complementarity problems and discuss the existence of solutions for this kind of quasi-complementariy problems without compactness and the convergence of iterative sequencesgenerated by the algorithms. 相似文献
11.
LU Li-gang YAN Li-tan XIANG Li-chi 《浙江大学学报(A卷英文版)》2007,8(1):158-163
INTRODUCTION Throughout this paper, we shall work with a filtered complete probability space (?,F,(Ft),P) sat-isfying the usual conditions. Let B=(Bt)t≥0 be a stan-dard Brownian motion with B0=0. Denote by ú the set of all non-negative real numbers. Recall that a diffusion process X starting at x≥0 is called the square of a Bessel process of dimension δ>0 if d X t = δd t 2 | X t |d Bt , X 0= x, (1) Clearly, this equation has a unique non-negative strong solution X, i.e., … 相似文献
12.
BAIYan－qin 《上海大学学报(英文版)》2001,5(1):15-19
We extend a results presented by Y.F.Hu and C.Storey(1991)^[1] on the global convergence rsult for conjugate gradient methods with different choices for the parameter βk.In this note,the conditions given on βk are milder than that used by Y.F.Huang C.Storey. 相似文献
13.
姜海益 《浙江大学学报(A卷英文版)》2004,5(7):754-758
Let k,m,n be positive integers,and k≥2,α∈(0,1],0＜r＜min {m,n} an integer,d=r (m-r)/(k α),and iff∈ Ck,α(Rm,R″),A =Cr(f)= {x ∈ Rm ,rank(Df(x))≤r},thenf(A)is d-null.Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2. 相似文献
14.
In this work, we made progress on the problem that lr(○×)lp(○×)lq is a Banach algebra under schur product. Our results extend Tonge's results. We also obtained estimates for the norm of the random quadralinear form A:lMr×lNp×lKq×lHs→ C, defined by: A(ei, ej, ek, es)=aijks, where the (aijks)'s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions lr(○×)lp(○×)lq (○×)ls is not a Banach algebra under schur product. 相似文献
15.
Shailesh A. Shirali 《Resonance》2007,12(7):27-43
For non-negative integers k, n, let P
k
(n) denote the sum {fx27-1}. We show by two different means that if k ≥ 3 and odd, then n
2(n+1)2 iss a factor of the polynomial P
k
(n); and if k ≥ 2 and even, then n (n+1) (2n+1) is a factor of the polynomial P
k
(n). We also derive a relatively unknown result first obtained by Johann Faulhaber in the 17th century.
Shailesh Shirali has been at Rishi Valley School, Andhra Pradesh (Krishnamurti Foundation India) since the 1980’s. He has
a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis
on problem solving and on historical aspects of the subject. He has been involved in the Mathematics Olympiad movement at
the national and international level for the past two decades. He is the author of several expository books and articles aimed
at interested high school students. 相似文献
16.
Zhang Hanlin 《上海大学学报(英文版)》1998,2(3):191-193
１ＩｎｔｒｏｄｕｃｔｉｏｎＤｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈｔｕｒｎｉｎｇｐｏｉｎｔｓｅｘｉｓｔｗｉｄｅｌｙｉｎｍａｎｙｐｒｏｂｌｅｍｓｏｆｍａｔｈｅｍａｔｉｃｓｐｈｙｓｉｃｓ,ｓｏｔｈｅｓｅｐｒｏｂｌｅｍｓａｒｅｖｅｒｙｉｍｐｏｒｔａ... 相似文献
17.
A new empirical correlation has been presented for the effect of entrainment on distillation tray efficiency based on the results of numerical solution given by Lockett,et al.The calculated results are in good agreement with those of the numerical solution given by Lockett,et al.The average deviation is 1.14% and the maximum deviation is 4.76% for the ranges of 0相似文献
18.
ZHAO Li-li 《浙江大学学报(A卷英文版)》2007,8(6):957-962
In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics. 相似文献