查询词典 generalized function

We establish the relation of inversion formulas among generalized Radon transform with known weight functions, the exponential Radon transform and classical Radon transform, furthermore obtain approximate inversion formula of the exponential Radon transform, the idea of approach above is applied to contour reconstruction and is generalized to n-dimentional euclidean space case. We discuss the support theorem, range condition of the exponential Radon transform.

本文建立了带权广义Radon变换、指数型Radon变换与古典Radon变换反演公式的关系，从而得到指数型Radon变换的近似反演公式，并且应用这种思想方法于轮廓重构，并将这一结果推广到任意维欧氏空间的情形；讨论了指数型Radon变换的支集定理及值域条件。

It is proved by this commutable diagram that the invertibility of a generalized symmetric system is equivalent to that of the quotient system, which makes the verification of the invertibility of generalized symmetric systems much easier.

利用这个交换图证明了广义对称系统的可逆性等价于其商系统的可逆性，从而使可逆性的检验大为简单。

WT9.BZ: Theory of generalized tautology in logic system , W and W k is generalized and applied to Lukasiewicz logic system. The main results are as follows: congruence about on set of logic formulas F has been obtained in the system; it is proved that in this system, for any irrational number α, there does not exist accessible α-tautology; and for any real number α, there does not exist accessible α+-tautology; and the relation theorems have been given between categori...

将逻辑系统 W ，W ，Wk 中的广义重言式理论进行推广并应用到Lukasiewicz逻辑系统中，主要结果是：得到了逻辑公式集F在该系统中关于﹁同余的分划；证明了在该逻辑系统中对每个无理数α而言，不存在可达α重言式，且对每个实数α而言，不存在可达α+重言式；给出了广义重言式、广义矛盾式各类之间的关系定理。

An optimal algorithm of the generalized Jacobi method is developed to solve the generalized eigen-problems in the finite element analysis of structural problems.

针对有限单元法结构分析中的对称方阵广义特征值问题，提出广义 Jacobi方法的一种优化算法。

Chapter 4In this chapter,we applied the generalized Laguerre polynomial as the basis functions and introduced the linear combination technique into WBEPM theory.He atom ground-state energy is studied by using double generalized Laguerre polynomial.The result obtained from this method is at the same level with the other theoretical methods.

第四章本章用广义拉盖尔函数作为基函数，将线性组合技术引入到WBEPM理论中，对He原子的基态能量做了双广义拉盖尔函数的研究，得到可与现有理论方法相比照的结果。

OD estimation was divided into fixed steps, with every step containing a bi-level programming. The upper-level problem was a generalized least squares estimator, while the lower level problem was a stochastic user equilibrium model. Namely, based on generalized least squares estimator and stochastic user equilibrium, a new estimator of the OD matrix was proposed by target matrix and traffic counts updating.

将OD估计分为固定的步数，每一步都是一个双层规划，上层为广义最小二乘估计，下层为随机用户均衡分配模型，即以广义最小二乘估计和随机用户均衡分配模型为基础，通过更新估计模型中目标矩阵和实测路段上的流量来估计OD矩阵。

This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems.

本文主要研究了大型线性方程组的交替迭代法及迭代法的各种变形，给出了当系数矩阵为Hermitian正定矩阵时各类迭代法的收敛原理及其相应的比较理论。

In chapter two,we consider a lumped mass generalized difference scheme for linear integro-differential equation in two dimensions.Lp and error estimates of the generalized Ritz-Volterra projection u ? V and and -norm error estimates of Dk = 1,2 are made,then we obtain and -norm error estimates of u?

第二章考虑二维线性积分微分方程的广义差分集中质量法，建立了广义Ritz-Volterra投影，得到u-V_h~*u的W~(1，p)和L~p(2≤p≤∞)模误差估计和D_t~k，k=1，2的V~p和W~(1，p)(2≤p≤∞)模误差估计，从而得到u-u_h的最优W~(1，p)和L~p(2≤p≤∞)模误差估计。

Under certain donditions ,the existence of generalized synchronization can be turned to the problem of compression fixed point in the family of Lipschitz functions.Theoretical proofs are proposed to the Lipschitz smooth,H lder continuity and exponential attractive property of generalized synchronization manifold.

若满足一定条件，广义同步流形的存在性问题可转化为Lipschitz函数族压缩不动点问题，并且理论上证明了两类广义同步流形的Lipschitz光滑性、H lder连续性和指数吸引性。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。