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1.
Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. This work was supported by the National Natural Science Foundation of China (Grant No. 11671179) and the Natural Science Foundation of Yunnan Province (Grant No. 2005A0092M).  相似文献   

2.
Abstract In this paper, we investigate the value distribution properties for the solution w(z) of higher-order Painlevé equations. We prove that the Nevanlinna’s second main inequality for w(z) is reduced to an asymptotic equality. Supported by the Mathematical Tianyuan Foundation of China (No.10426007) and the National Natural Science Foundation of China (No.10272017, No.10471028)  相似文献   

3.
In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.  相似文献   

4.
LetΔ_1(x;φ) be the error term of the first Riesz mean of the Rankin-Selberg problem. We study the higher power moments ofΔ_1(x;φ) and derive an asymptotic formula for the 3-rd, 4-th and 5-th power moments by using Ivic's large value arguments and other techniques.  相似文献   

5.
This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution.  相似文献   

6.
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation u_t f(u)_x=u_(xx) u_(xx) on the half line with the conditions u(0, t)=, u-, u(∞,t)=u_ and, u_-相似文献   

7.
The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).  相似文献   

8.
The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^*,γ(R^n), with 1〈p〈∞and A = n-(2α-1)p, and for a small external force in a time-weighted weak Morrey space.  相似文献   

9.
By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^+ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.  相似文献   

10.
The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.  相似文献   

11.
Abstract This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value prob-lem for scalar viscous conservations laws u_t+f(u)_x=u_(xx) on[0,1],with the boundary condition u(0,t) =u_,u(1,t)=u_+ and the initial data u(x,0)=u_0(x,0)=u_0(x),where u_≠u_+ and f is a given function satisfyingf'(u)>0 for u under consideration.By means of energy estimates method and under some more regular condi-tions on the initial data,both the global existence and the asymptotic behavior are obtained.When u_u_+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shockwaves,which means that │u_-u_+│is small.Moreover,exponential decay rates are both given.  相似文献   

12.
Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 + b^2 = c^3 and b is an odd prime, then the equation a^x + b^y = c^z has only the positive integer solution (x, y, z) = (2,2,3).  相似文献   

13.
Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators. This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10 th five year plan of 211 Project for Shanghai University of Finance and Economics (the 3 rd phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444)  相似文献   

14.
§ 1 IntroductionIn this paperwe shall study successively the equationsgiven in [1 ,2 ] .Underthe sameconditions(i.e.the initial boundary value and other conditions) as in[1 ,2 ] ,the upperbound of the dimension of their global attractor will be obtained respectively.Theexistence of the global attractors have been proved in[1 ,2 ] .This paper is organized as follows:In§ 2 ,we derive the Frechet differential of the solution operator s(t) for theperturbed system.In§ 3 ,we show the finite di…  相似文献   

15.
The Bott generator of the homotopy group π2k-1U(∞) is used to construct an almost complex structure on S6, which is integrable except a small neighborhood.  相似文献   

16.
The structure of the groupoidG associated with the ToeplitzC *-algebraC *(Ω) of the L-shaped domain is discussed. The detailed characterization ofM by the classification of the closed subgroup of the Euclidean space is presented. Project supported partially by the National Natural Science Foundation of China, Fok Yingtung Educational Foundation and the Foundation of the State Education Commission of China.  相似文献   

17.
Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.  相似文献   

18.
The main aim of this paper is to investigate the effects of the impulse and time delay on a typeof parabolic equations.In view of the characteristics of the equation,a particular iteration scheme is adopted.The results show that Under certain conditions on the coefficients of the equation and the impulse,the solutionoscillates in a particular manner—called"asymptotic weighted-periodicity".  相似文献   

19.
In this paper, we derive a lattice model for a single speciesin a one-dimensional patchy environment with infinite numberof patches connected locally by diffusion. Under the assumptionthat the death and diffusion rates of the mature populationare age independent, we show that the dynamics of the maturepopulation is governed by a lattice delay differential equationwith global interactions. We study the well-posedness of theinitial-value problem and obtain the existence of monotone travellingwaves for wave speeds c > c*. We show that the minimal wavespeed c* is also the asymptotic speed of propagation, whichdepends on the maturation period and the diffusion rate of maturepopulation monotonically.  相似文献   

20.
We prove that if G is a finite group in which the elements of the same order outside the center are conjugate,then either G is abelian or G(?)S_3.  相似文献   

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