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 可积性条件
 integrability condition
 The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics 三维精确可解统计模型──Baxter－Bazhanov模型的可积性条件 短句来源 Owing to the connection between the nonlinear Schrodinger equation and the integrability condition for the AKNS equation or the Dirac equation, we can obtain the exact solution for elastic large deflection problem by inverse scattering method. 由于非线性Schr(?) dinger方程与AKNS方程即Dirac方程的可积性条件相联系,因此,弹性大挠度问题可以用逆散射方法求得其精确解,也就是说,它完全成了量子本征值问题。 短句来源 In this paper, locally integrability condition of plane vector field is given at first, then the main theorem of whole integrability theorem is obtained by defining the rotation number, and is proved using the rectangular closed path. 给出了平面向量场的局部可积性条件,通过定义旋转数得到了整体可积性定理,并利用直角形闭路径给出了其证明。 短句来源 By means of the generalized It's role, we proved the comparison theorem for strong solutions of one-dimensional time homogeneous It stochastic differential equations under the condition that diffusion coefficients may be degenerate and discontinuous, and some integrability condition on the coefficients. 本文用广义Ito公式,在扩散系数可退化可间断,方程系数仅仅满足某种局部可积性条件下,证明了一维时齐Ito型随机微分方程的强解比较定理。 短句来源 In this paper,we consider the solvable condition of the boundary value problem:εUtt+Ut-Uxx=f(x,t) 0integrability condition. 本文对下述边值问题εU＿（tt）＋U＿t－U＿（xx）＝f（x，t）　　　　　　　0＜X＜1，0＜t＜TU（0，t）＝U（1，t）＝0　　　　　　　　0＜t＜TU（x，0）＝S（x），Ut（x，0）＝W（x）　0＜x＜1的可解性进行了研究，认为可以放宽文［1］中对函数f、s、w所作的假定，满足一般的可积性条件即可． 短句来源 更多
 integral condition
 The problems of stability and integral condition of the origin are also solved. 由此解决了其原点的稳定性和可积性条件问题 ; 短句来源 According to the theory of the singular point value and by the calculating method, for a class of cubic system the highest singular point of the origin--6th degree is obtained and proved,and the problems of stability and integral condition of the origin are also solved. 运用奇点量理论和计算方法求出了一类三次系统原点的最高阶奇点量 ,并证明为6阶 ,解决了其原点的稳定性和可积性条件问题 . 短句来源
 integrability conditions
 The Integrability Conditions of the Higher Order Nonholonomic Constraint Equations 高阶非完整约束方程的可积性条件 短句来源 Formulas of Values of Singular Point and the Integrability Conditions for A Class of Cubic System 一类三次系统的奇点量公式与可积性条件 短句来源 Using the constructive theorem,formu- las of values of singular point and the integrability conditions of(E_2)and(E_3)have been derived. )的全部120个基本 Lie 不变量,并应用奇点量结构定理得到(E_2)和(E_(?) ~((3)))的奇点量公式及可积性条件. 短句来源 A intcgrability condition of Riccati equations was given, and it is applied to obtain some integrability conditions of two-dimensional linear deffcrential systems. 给出黎卡提方程的一个可积性条件,并由此导出二维线性微分系统的一系列可积性条件。 短句来源 Critical Point Quantities and Integrability Conditions for Complex Planar Resonant Polynomial Differential Systems 复平面多项式共振微分系统的奇点量与可积性条件 短句来源 更多
 size condition
 It is shown that the operator T b,k and the corresponding maximal operator are bounded on L p(R n) with bounded C‖b‖ k BMO(R +) when Ω satisfies certain minimum size condition. 在 Ω 具有某种最小可积性条件时 ,证明了 Tb,k及其相应的极大算子是Lp(Rn) (1 短句来源

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 integrability condition
 A new integrability condition for Riccati differential equation All results are for a system consisting of two exchange-coupled spins with biaxial exchange and single-site anisotropy, a system with a nontrivial integrability condition. Integrability Condition on an Almost Complex Structure and Its Application We obtain and apply a simple form of the integrability condition of an almost complex Owing to connection between the nonlinear Schr?dinger equation and the integrability condition for the AKNS equation or the Dirac equation, we can obtain the exact solution for elastic large deflection problem by inverse scattering method. 更多
 integral condition
 A Mixed Problem with Integral Condition for the Hyperbolic Equation In this paper, we study a mixed problem for the hyperbolic equation with a boundary Neumann condition and a nonlocal integral condition. An integral condition for the electrical resistance (nonlinearly depending on the magnetic field) under which the magnetic flux penetrates into the sample with a finite rate is found. Nonlocal problem with a first-kind integral condition for a multidimensional hyperbolic equation Economical Difference Schemes for the Solution of a Two-Dimensional Parabolic Problem with an Integral Condition 更多
 integrability conditions
 We consider Pettis integrability conditions for the Stone transform off and relate this problem to the regular oscillation condition for the family of functions {x*f∶x*∈B(X*)}, whereB(X*) is the unit ball inX*. The integrability conditions for the equation are found for the partial absorption of charged particles by the probe surface. Critical point quantities and integrability conditions for a class of quintic systems By studying the integrability conditions of this automorphic system, i.e. Exact integrability conditions are found for ODE systems of generalized Lotka-Volterra type. 更多
 size condition
 Fefferman when the kernel satisfies certain size condition. In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. In our results the kernel function is merely assumed on a size condition. Variations in size of the NORs and/or heterochromatic segment correspond to a polymorphic size condition observed in the X chromosome. In the present study, the superplastic behavior of five Al-Mg-Zn alloys in coarse grain size condition has been studied. 更多
 This work is the continuation and the distillation of the discussion of Refs.[l-4], (A) From complementarity principle we build up dissipation mechanics in this paper. It is a dissipative theory of correspondence with the quantum mechanics. From this theory we can unitedly handle problems of macroscopic non-equilibrium thermo-dyna-mics and viscous hydrodynamics, and handle each dissipative and irreversible problems in the quantum mechanics. We prove the basic equations of the dissipation mechanics to eigenvalues... This work is the continuation and the distillation of the discussion of Refs.[l-4], (A) From complementarity principle we build up dissipation mechanics in this paper. It is a dissipative theory of correspondence with the quantum mechanics. From this theory we can unitedly handle problems of macroscopic non-equilibrium thermo-dyna-mics and viscous hydrodynamics, and handle each dissipative and irreversible problems in the quantum mechanics. We prove the basic equations of the dissipation mechanics to eigenvalues equations of correspondence with the Schrodinger equation or Dirac equation in this paper. 本文是文[1～4]的继续和升华。 (1)在本文中,我们根据互补性原理,建立了耗散力学。它是与量子力学相对应的一种耗散理论。可以用这种理论来统一地处理非平衡态热力学和粘滞流体动力学问题,并可以用它来处理量子力学中各种耗散和不可逆的问题。耗散力学的基本方程是与Schr(?)dinger方程或Dirac方程相对应的一类本征值方程; (2)在本文中,我们将一些基本的非线性耗散型方程,特别是作为宏观非平衡态热力学和粘滞流体动力学基本方程的Navier-Stokes方程,统一地归结为耗散力学基本方程的可积性条件,从而为利用散射反演方法求它们的精确解扫平了道路。 Let G be a bounded domain in the n dimensional Euclidean Space En . Let On G consider the following equation of elliptic type.where A and B satisfy the structural condition ( 2 ) and the growth in u of B israpider than any is the limiting exponent in the Sobolev Imbedding Theorem) .It is proved .that fhe property of the generalized solution of ( 1 ) , (G) , can be improved by adding the intcgrability conditions on the functions fi (x) appeared in ( 2 ) and in finale u is proved to be a Holder continuons function.... Let G be a bounded domain in the n dimensional Euclidean Space En . Let On G consider the following equation of elliptic type.where A and B satisfy the structural condition ( 2 ) and the growth in u of B israpider than any is the limiting exponent in the Sobolev Imbedding Theorem) .It is proved .that fhe property of the generalized solution of ( 1 ) , (G) , can be improved by adding the intcgrability conditions on the functions fi (x) appeared in ( 2 ) and in finale u is proved to be a Holder continuons function. 假定出现在(1)中的B关于u的增长快于任何,后者为嵌入的极限指数),研讨了(1)的广义解的性质。 对于拟线性方程或非线性方程,把解的存在性和解的正则性分开考虑是适宜的。一方面可以在比古典解的存在的更弱的条件下证明广义解的存在(广义解的存在较古典解更易于证明),另一方面在研讨解的正则性时,因为假定解为已知,完全可以像处理线性方程一样地来进行讨论。本文假定出现在(1)中的A,B满足结构条件(2),其中B关于u的增长比任何为快(当然还假定B关于u的增长低于q-1)。我们通过增加f;(x)的可积性条件逐步使方程(1)的广义解的性质得到改善并最终证明它是Hlder连续函数。当结构条件(2)中的(|u|)换为时,相应的结果在[1]中有详细的讨论。 设G是n维欧氏空间E~n中的有界区域,G记它的边界。(G)是通常的空间(其中的函数在意义下满足边界条件,范数为 In this paper, based on the general theories of Pfaff equation, We discuss the conditions of the integrability of the nonlinear equations of second order given in differential forms in the case of rot■≡0 and rot■■0 respectively. 本文根据Pfaff方程的一般理论,分rot■≡0和rot■0两种情况讨论以微分形式给出的二阶非线性方程的可积性条件,扩充了这类方程的求积类型。 << 更多相关文摘
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