具有四项的指数丢番图方程(Ⅲ)

根据定理 １,２和 ３;求任何一个方程 ａ~ｘ－ｂ~ｙ＝ｎ,ａ~ｘｂ~ｙ±ａ~ｚ±ｂ~ｗ±１＝０ 或ａ~ｘ±ｂ~ｙ±ａ~ｚ±ｂ~ｗ＝０（ｘ,ｙ,ｚ,ｗ∈≥０）的解都是很简单的,此处ａ,ｂ是适合 ２ ≤５ ａ,ｂ≤５０的互素的两个整数,ｎ是适合１≤ｎ≤８００００的整数．     

具有四项的指数丢番图方程(Ⅲ)

根据定理 １,２和 ３;求任何一个方程 ａ~ｘ－ｂ~ｙ＝ｎ,ａ~ｘｂ~ｙ±ａ~ｚ±ｂ~ｗ±１＝０ 或ａ~ｘ±ｂ~ｙ±ａ~ｚ±ｂ~ｗ＝０（ｘ,ｙ,ｚ,ｗ∈≥０）的解都是很简单的,此处ａ,ｂ是适合 ２ ≤５ ａ,ｂ≤５０的互素的两个整数,ｎ是适合１≤ｎ≤８００００的整数．     

具有四项的指数丢番图方程(Ⅱ)

本文中，我们给出了丢番图方程的解ｘ，ｙ，ｚ，ｗ的上界，其中ｐ，ｑ是给定的互素的正整数，ａ，ｂ，ｃ，ｄ是给定的适合ａｂｅｄ≠０的整数，此外，我们将指出在具体情形下如何把上界降低到方程允许的实际的解．最后，我们将用这个方法来解方程１９．５ｘ·１７ｙ＝１２．５ｚ＋４１．１７ｗ＋１４， ５． ３ｘ· １３ｙ ＋ ２０＝ ７． ３ｚ ＋ １４． １３ｗ和 １３· ２ｘ＋ ５· ３ｙ＝ ２５． ２ｚ＋ １１． ３ｗ．     

具有四项的指数丢番图方程(Ⅱ)

本文中，我们给出了丢番图方程的解ｘ，ｙ，ｚ，ｗ的上界，其中ｐ，ｑ是给定的互素的正整数，ａ，ｂ，ｃ，ｄ是给定的适合ａｂｅｄ≠０的整数，此外，我们将指出在具体情形下如何把上界降低到方程允许的实际的解．最后，我们将用这个方法来解方程１９．５ｘ·１７ｙ＝１２．５ｚ＋４１．１７ｗ＋１４， ５． ３ｘ· １３ｙ ＋ ２０＝ ７． ３ｚ ＋ １４． １３ｗ和 １３· ２ｘ＋ ５· ３ｙ＝ ２５． ２ｚ＋ １１． ３ｗ．     

关于丢番图方程x^2±2^m=y^n

本文证明了：方程ｘ２＋２ｍ＝ｙｎ，ｘ，ｙ，ｍ，ｎ∈Ｎ，ｇｃｄ（ｘ，ｙ）＝１，ｎ＞２仅有有限多组解（ｘ，ｙ，ｍ，ｎ），而且当（ｘ，ｙ，ｍ，ｎ）≠（５，３，１，３），（１１，５，２，３），（７，３，５，４）时，ｎ是适合ｎ≡７（ｍｏｄ８）以及２３≤ｎ＜８．５·１０６的奇素数，ｍａｘ（ｘ，ｙ，ｍ）＜Ｃ１；方程ｘ２－２ｍ＝ｙｎ，ｘ，ｙ，ｍ，ｎ∈Ｎ，ｇｃｄ（ｘ，ｙ）＝１，ｙ＞１；ｎ＞２仅有有限多组解（ｘ，ｙ，ｍ，ｎ），而且这些解都满足ｎ＜２·１０９炉以及ｍａｘ（ｘ，ｙ，ｍ）＜Ｃ２，这里Ｃ１，Ｃ２是可有效计算的绝对常数．     

关于指数型丢番图方程的整数解

本文简要地介绍了有关Ｓ－单位方程、Ｒａｍａｎｕｊａｎ－Ｎａｇｅｌｌ方程、Ｔｈｕｅ－Ｍａｈｌｅｒ方程、ＬｅＶｅｑｕｅ方程、Ｃａｔａｌａｎ方程、Ｐｉｌｌａｉ方程等指数型丢番图方程整数解的最新结果。这些结果大多是用Ｔｈｕｅ－Ｓｉｅｇｌｅ－Ｒｏｔｈ－Ｓｃｈｍｉｄｔ方法和Ｇｅｌ’ｆｏｎｄ－Ｂａｋｅｒ方法得到的。     

关于丢番图方程(x~m-1)/(x-1)=y~n

设 IP 是一切素数及其方幂的集合.本文证明了:方程(x~m-1)/(x-1)=y~n,x>1,y>1,m>2,n>1适合 x∈IP 以及 y≡1(mod x)的整数解(x,y,m,n)都满足 x~m相似文献   

指数丢番图方程的有关解

本文运用计算机论证了指数丢番图方程x3-1/x-1-yn-1/y-1的例外解(x,y,n),满足n≥27,y<2n-3,x<2n2-4n 6/2,n≠2k,k∈N.     

丢番图方程(m2+1)x+(cm2-1)y=(am)z

设m,a,c均是大于1的正整数.当am≡1(mod 4)或am≡3(mod 8),3■m或2■a,2|m,3■m时,得到了丢番图方程(m²+1)^x+(cm²-1)^y=(am)^z,1+c=a²,m≥2只有正整数解(x,y,z)=(1,1,2).特别地,当a≡1,3,5 (mod 8),a≠3或a≡7 (mod 8),a≡2(mod 3)时,方程2^x+(a²-2)^y=(a)^z只有正整数解(x,y,z)=(1,1,2).     

Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms

This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy a...     

具相互作用项的非线性Schr(o)dinger方程的散射

In this paper,we give a simplified proof on the energy scattering for the nonlinear Schr(o)dinger equations with interaction terems by u8e of the interaction Morawetz estimate,which is originally introduced in[4].     

Hamilton-Jacobi Equations with Discontinuous Source Terms

We study the initial-value problem for a Hamilton-Jacobi equation whose Hamiltonian is discontinuous with respect to state variables. Our motivation comes from a model describing the two dimensional nucleation in crystal growth phenomena. A typical equation has a semicontinuous source term. We introduce a new notion of viscosity solutions and prove among other results that the initial-value problem admits a unique global-in-time uniformly continuous solution for any bounded uniformly continuous initial data. We also give a representation formula of the solution as a value function by the optimal control theory with a semicontinuous running cost function.     

Homotopy Analysis Method for Solving(2+1)-dimensional Navier-Stokes Equations with Perturbation Terms

In this paper Homotopy Analysis Method (HAM) is implemented for obtaining approximate solutions of (2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations;by the iterations formula of HAM,the first approxima-tion solutions and the second approximation solutions are successively obtained and Homotopy Perturbation Method(HPM)is also used to solve these equations;finally, approximate solutions by HAM of (2+1)-dimensional Navier-Stokes equations with-out perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM,the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equa-tions;due to the effects of perturbation terms,the 3rd-order approximation solutions by HAM and HPM have great fluctuation.     

微分方程的指数稳定性

比较系统地研究了It方程解的指数稳定性.给出了随机指数稳定性、指数P-稳定性、几乎必然指数稳定性的比较准则,这些比较准则推广了Nevel’son和Has’minskiǐ的相应结果.     

On Some Exponential Diophantine Equations

 We apply a new, deep result of Bilu, Hanrot and Voutier to solve completely some exponential Diophantine equations of the type , where are given coprime positive integers, , and are unknown. (Received 29 May 2000; in revised form 21 September 2000)     

Ginzburg-Landau-BBM方程的指数吸引子

本文利用挤压性质和算子分解方法证明了Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－ＢＢＭ耦合方程组周期初边值问题指数吸引子的存在性．     

Exponential Stability in Non-linear Difference Equations

Non-negative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee exponential stability of the zero solution of a non-linear discrete system. The theory is illustrated with several examples.