关于Thue方程的解数

设ｍ是正整数，ｆ（Ｘ，Ｙ）＝ａ０Ｘｎ＋ａ１Ｘ（ｎ－１）Ｙ＋．．．＋ａｎＹｎ∈Ｚ［Ｘ，Ｙ］是Ｑ上不可约化的叫ｎ（ｎ≥３）次齐次多项式。本文证明了：当ｇｃｄ（ｍ，ａ０）＝１，ｎ≥４００且ｍ≥１０（３５）时，方程｜ｆ（ｘ，ｙ）｜＝ｍ，ｘ，ｙ∈ｚ，ｇｃｄ（ｘ，ｙ）＝１，至多有６ｎｖ（ｍ）组解（ｘ，ｙ），其中ｖ（ｍ）是同余式Ｆ（ｚ）＝ｆ（ｚ，１）≡０（ｍｏｄｍ）的解数。特别是当ｇｃｄ（ｍ，ＤＦ）＝１时，该方程至多有６ｎ（ω（ｍ）＋１）组解（ｘ，ｙ），其中ＤＦ是多项式Ｆ的判别式，ω（ｍ）是ｍ的不同素因数的个数．     

The Coset Group and Com ove Group

§１．　ＢａｓｉｃＤｅｆｉｎｉｔｉｏｎｓＬｅｔＸａｎｄＹｂｅｓｅｔｓ，ｆｏｒａｇｉｖｉｎｇｍａｐｐｉｎｇｆ：Ｘ→Ｙ，ｘ｜→ｙ＝ｆ（ｘ），ａｍａｐｐｉｎｇｆｏｎｐｏｗｅｒｓｅｔｃａｎｂｅｃｏｎｄｕｃｔｅｄｂｙｆ：ｆ：Ｐ（Ｘ）→Ｐ（Ｙ），Ａ｜→Ｂ＝ｆ（Ａ）＝｛ｙ｜ｘ∈Ａ，ｙ＝ｆ（ｘ）｝．　　Ｎｏｔｅｔｈａｔａｂｉｎａｒｙｏｐｅｒａｔｉｏｎｉｓａｓｐｅｃｉａｌｍａｐｐｉｎｇｏｎｓｅｔｓ．ＧｉｖｅｎａｂｉｎａｒｙｏｐｅｒａｔｉｏｎｏｎｓｅｔＸｓｕｃｈｔｈａｔ：：Ｘ×Ｘ→Ｘ，　（ｘ，ｙ）｜→ｘ…     

关于集值映照优化解的稳定性

设Ｘ，Ｙ为Ｂａｎａｃｈ空间，ｆ：Ｘ０→２Ｙ（Ｘ０　Ｘ），Ｄ：Ｙ０→、２Ｙ（Ｙ０＝∪ｆ（ｘ）），对ｙ∈Ｙ０，Ｄ（ｙ））均取锥值．本文讨论集值映照ｆ（ｘ）关于控制结构Ｄ（ｙ）的优化问题，当目标函数和控制结构同时有扰动时优化解的稳定性．     

算子方程解的稠密性及半线性系统的近似可控性

本文利用Ｂａｎａｃｈ不动点定理和Ｓｃｈａｕｄｅｒ不动点定理研究如下算子方程解的稠密性：ｙ＝ｙ０＋ＬＦ（ｙ）＋ＬＨ（ｖ）（其中，Ｌ、Ｈ为线性算子，Ｆ为非线性算子），然后，利用所得结论讨论Ｂａｎａｃｈ空间内的半线性系统：ｘ＇（ｔ）＋Ａ（ｔ）ｘ（ｔ）＝ｆ（ｔ，ｘ（ｔ）＋Ｂｕ（ｔ）的近似可控性。     

关于积域上的粗糙奇异积分算子的一点注记

讨论积域上的奇异积分算子：ＴΩｆ（ｘ,ｙ） ＝ ｐ．ｖ．∫Ｒｎ×ＲｍΩ（ｕ,ｖ）｜ｕ｜ｎ｜ｖ｜ｍ ｆ（ｘ － ｕ,ｙ － ｖ）ｄｕｄｖ的Ｌｐ 有界性,及相应的Ｍａｒｃｉｎｋｉｅｗ ｉｃｚ积分的Ｌ２ 有界性． 其中Ω为类似文［４］中引进的函数类．     

一类非线性椭圆方程组正解的存在性定理

本文考虑如下的椭圆方程组△ｙ＋ｆ（ｘ,ｕ）＋Эｕ＝０,ｘ∈Ω △ｕ＋ｕ－ｖ＝０,ｘ∈Ω ｕ＝ｖ＝０,ｘ∈ЭΩ 其中,Ω∈Ｒ＾Ｎ（Ｎ≥３）是带光滑边界的有界区域,ｆ（ｘ,ｕ）＝ｈ（ｘ）ｕ＾α＋ｕ＾β＋λｕ＾ｐ,ｈ（ｘ）∈Ｃ＾ｒ（Ω）（０〈ｒ〈１）,α,β,ｐ是正常数且０〈β〈α〈１〈ｐ〈（Ｎ＋２）／（Ｎ－２）,λ,δ是正参数,由临界点理论证明了该方程组至少存在二对正解。     

A MATHEMATICAL MODEL OF A CLASS OF AUTOCATALYTIC CHEMICAL REACTION

Ｂｙｆｏｌｏｗｉｎｇｍｅｃｈａｎｉｓｍ：ＡａαＸ，ＣｃαＹ，Ｂ＋ＸｂαＹ＋Ｄ，Ｘ＋Ｙｅα３Ｙ，ＹｆαＦ，ＸλαＦ，ａｒｔｉｃｌｅ［１］ｏｂｔａｉｎｅｄｔｈｅｆｏｌｏｗｉｎｇｓｙｓｔｅｍ：ｘ＝ａ－ｂｘ－ｅｘｙ２－λｘ，ｙ＝ｂｘ＋ｅｘｙ２－ｆｙ＋ｃ．（１...     

积域上的一类粗糙奇异积分算子

本文讨论了积域Ｒｎ×Ｒｍ上一类带粗糙核的奇异积分算子Ｔｆ（ｘ，ｙ）＝ｐ．ｖ．Ｒｎ×ＲｍΩ（ｕ，ｖ）｜ｕ｜ｎ｜ｖ｜ｍｈ（｜ｕ｜，｜ｖ｜）ｆ（ｘ－ｕ，ｙ－ｖ）ｄｕｄｖ的Ｌｐ（Ｒｎ×Ｒｍ）有界性．这里，Ω为原子Ｈａｒｄｙ空间Ｈ１ａ（Ｓｎ－１×Ｓｍ－１）中的函数且ｈ为空间ｌ∞（Ｌｑ）（Ｒ＋×Ｒ＋）中的径向函数．     

交换环上幂映射的周期轨道分支的对称性

设Ｒ是个交换环，带离散拓扑，是由ｆ（ｒ）＝ｒ￣ｎ（任ｒ∈Ｒ）定义的幂映射．又设ｘ及ｙ均是ｆ的周期点，其周期分别是ｋ及ｌ．记称Ｗ＿ｘ为ｆ的含ｘ的周期轨道分支，本文证明：（１）Ｗ＿ｘ在ｆ之下具有循环对称性，即存在着周期为ｋ的周期映射ｈ＿ｘ：Ｗ＿ｘ→Ｗ＿ｘ使得ｆｈ＿ｘ＝ｈ＿ｘｆ｜Ｗ＿ｘ且ｈ＿ｘ（ｘ）＝ｆ（ｘ）；（２）当ｌ是ｋ的因数且存在ｕ∈Ｒ使得ｙ＝ｕｘ时，　存在着映射ξ＿ｕ：Ｗ＿ｘ→Ｗ＿ｙ满足；（ｉｉｉ）若还存在着ｖ∈Ｒ使得ｘ＋ｖｙ，且ｌ＝ｋ，则此ξ＿ｖ与ξ＿ｖ互逆．     

积分算子权模不等式的权分解及其应用

设（Ｋｆ）（ｘ）：∫Ｒ￣ｎＫ（ｘ，ｙ）ｆ（ｙ）ｄｙ，本文给出了满足积分算子权模不等式的非负权函数ｕ（ｘ）和ｖ（ｘ）的一种分解结构，且该结构是使上不等式成立的充要条件，作为应用，由此给出了当时，使权模不等式成立的ｕ（ｘ）和ｖ（ｘ）的一些充分条件，其中的一种相当特殊情况便是文［１］中给出的结论。     

Sviluppo delle funzioni implicitamente definite da un sistema di equazioni nel campo reale

Sunto Per la funzione reale del punto P(x, y): F[ξ(P), η(P)], ove u=ξ(P), v=η(P) sono implicitamente definite nel campo reale dal sistema delle due equazioni u−x+ϕ(u, v)=0, v−y+φ(u, v)=0 si dà uno sviluppo che estende quello ottenuto dalLevi-Civita per la funzione F[y(x)], ove y(x) è definita dalla equazione y−x+ϕ(y)=0. Ad Antonio Signorini nel suo 70^mo compleanno.     

The Semi-global Isometric Imbedding in R3 of Two Dimensional Riemannian Manifolds with Gaussian Curvature Changing Sign Cleanly

An abstract Riemannian metric ds²= Edu² + 2Fdudv + Gdv² is given in (u, v) ∈ [0, 2&Pi] × [-&delta, &delta] where E, F, G are smooth functions of (u, v) and periodic in u with period 2&Pi. Moneover K|_{v=0} = 0. K_r|_{v=0} ≠ 0. when> K is the Gaussian curvature. We imbed it semiglobally as the graph of a smooth surface x = x(u, v ), y = y(u, v), z = z(u, v) of R³ in the neighborhood of v = 0. In this paper we show that, if [K_rΓ²_{11}]_{v=0}, and three compatibility conditions are satisified, then there exists such an isometric imbedding.     

INVERSE THEOREMS IN Lp FOR SOME MULTIDIMENSIONAL POSITIVE LINEAR OPERATORS

Let {L_n}_(n∈s) be positive linear operators in L_(I), I=[0, 1] or [0, ∞). This paper considers their variants in L_p(I×I)L_(n,m)(F; x, y)=L_n(L_m(F(u, v); y); x)=L_m(L_n(F(u, v); x); y), n, m∈N.The characterization problem for these operators is solved which gives the inverse theorems in L_p for multidimensional Bernstein type operators.     

The Chebyshev Spectral Method for Burgers-Like Equations

The Chebyshev polynomials have good approximation properties which are not affected by boundary values. They have higher resolution near the boundary than in the interior and are suitable for problems in which the solution changes rapidly near the boundary. Also, they can be calculated by FFT. Thus they are used mostly for initial-boundary value problems for P.D.E.'s (see [1, 3-4, 6, 8-11]). Maday and Quarterom discussed the convergence of Legendre and Chebyshev spectral approximations to the steady Burgers equation. In this paper we consider Burgers-like equations.$$\begin{cases}∂_iu+F(u)_x-vu_{zx}=0, & -1≤x≤1, 0＜t≤T \\ u (-1,t) =u (1,t) =0, & 0≤t≤T & (0.1)\\ u (x,0) =u_0(x), & -1≤x≤1\end{cases}$$ where $F\in C(R)$ and there exists a positive function $A\in C(R)$ and a constant $p＞1$ such that $$|F(z+y)-F(z)|\leq A(z)(|y|+|y|^p).$$ We develop a Chebyshev spectral scheme and a pseudospectral scheme for solving (0.1) and establish their generalized stability and convergence.     

一类二阶变系数常微分方程的可积条件

给出了一类二阶变系数常微分方程y″+[pu(x)-v(x)]y′+[qu2(x)+r(u(x)v(x)-u(′x))]y=f(x)及y″+[pu(x)-v(x)]y′+[qu2(x)+r(u(x)v(x)-u(′x))]y=f(x)[y-′ru(x)y]n可积的充分条件及其通解表达式,并举例说明它的应用.     

Symmetry and regularity of solutions to a system with three-component integral equations

Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < n,n is a positive constant,p,q and r satisfy some suitable conditions.It is shown that every positive regular solution(u(x),v(x),w(x)) is radially symmetric and monotonic about some point by developing the moving plane method in an integral form.In addition,the regularity of the solutions is also proved by the contraction mapping principle.The conformal invariant property of the system is also investigated.     

Lpboundednessofsingularintegralsonproductdomains

This paper proves that for Ω∈L(log+L)2(Sn-1×Sm-1), ∫Sn-1　Ω(x′,y′)dσ(x′)=0(y′∈Sm-1),∫Sm-1　　Ω(x′,y′)dσ(y′)=0(x′∈Sn-1), the singular integral operator T with kernel K(u,v)=Ω(u′,v′)｜u｜-n｜v｜-m is bounded on Lp(Rn×Rm) for 1相似文献   

變敍的項的共同分佈的極限

<正> 合X為一隨機变數,其分佈律為F(x).今對X作n次相互獨立的觀察,便得n個值,把這n個值依其大小順序排列為     

Invariant sets and solutions to the generalized thin film equation

The invariant sets and the solutions of the 1 2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set E0 = {u : ux = vxF(u), uy = vyF(u)}, where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the l l-dimensional nonlinear evolution equations.     

三角代数上的交换零点ξ-Lie可导映射

设u是数域F上的一个三角代数,δ是u上的一个线性映射,ξ∈F且ξ≠1证明了:如果对任意的x,y∈u且xy=yx=0有δ([x,y]_ξ)=[δ(x),y]_ξ+[x,δ(y)]_ξ,则在u上存在一个导子Φ和一个中心元λ使得对任意的x∈u,有δ(x)=Φ(x)+λx.