查询词典 generalized Boolean algebra

The relationships among Boolean algebra, set algebra, logic, and binary arithmetic have given Boolean algebras a central role in the development of electronic digital computers.

由于布尔代数，集合代数，逻辑学和二进制算术之间的内在联系，使得布尔代数的理论在电子计算机的发展中起到举足轻重的作用。

Like ordinary algebra, Boolean algebra has its own unique identities based on the bivalent states of Boolean variables.

象普通代数，布尔代数具有基于布尔变量的二价规定的独特的特性。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Another part of our work begins with definition of multioutput generalized bent functions. We show their spectral characteristics and give equivalence definition using generalized first order Chrestenson cyclic spectrum. Also we calculate rate of accordance between multioutput generalized bent functions and multioutput m-valued affine functions. Then we define multioutput m-valued perfect nonlinear functions and show relationship between them and multioutput generalized bent functions. Finally we give two ways of constructions of multioutput generalized bent functions.

第三章中首先给出了剩余类环上的多输出广义Bent函数的定义，得到了多输出广义Bent函数的广义一阶Chrestenson谱特征，然后计算了多输出广义Bent函数与多输出m值仿射函数的符合率；接着定义了多输出m值完全非线性函数，讨论了多输出m值完全非线性函数与多输出广义Bent函数之间的关系；最后给出了两种构造多输出广义Bent函数的方法。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

The preface gave the definition and introduced history, background of development and significance of generalized inverse matrix. The first chapter, from the development process of generalized inverse, discussed all kinds of definition of generalized inverse determined by the Moore - Penrose equations. The second chapter discussed the definition and nature of dashes inverse A in generalized inverse as well as its application in compatible linear equations. The third chapter discussed the definition and calculation of the minimum norm inverse A in generalized inverse, as well as the Minimal Norm Solution of its compatible linear equations Ax = b.

前言从引进广义逆矩阵的定义着手，介绍了它的历史概况以及发展的背景及其意义；第一章从广义逆的发展历程讨论由Moore-Penrose方程确定的各种广义逆的定义；第二章讨论广义逆中的减号逆A 的定义及性质以及在相容线性方程组的应用；第三章讨论广义逆中的最小范数逆A 的定义及计算以及它与相容线性方程组Ax=b的极小范数解。

In a method and an arrangement for processing a skin print image, and particularly a fingerprint image, which image exists as a gray-level image, provision is made for the gray-level image to be convolved in the direction of two axes by generalized gradient filters, for the generalized gradients obtained in this way to be normalized, for the normalized, generalized gradients each to be convolved with generalized gradient filters, and for the sum of the two results of the convolution of the normalized, generalized gradients to be converted to binary form.

在处理皮肤印迹图像的方法和设备中，具体来说，处理指纹图像的方法和设备中，指纹图像是作为灰度级图像存在的，对于灰度级图像进行如下的规定：通过通用梯度滤波器沿两个轴的方向卷积灰度级图像，归一化以这种方式获得的通用梯度，利用通用梯度滤波器卷积每一个归一化的、通用梯度，并且转换归一化的、通用梯度的卷积的两个结果之和为二进制形式。

At first, setting up the arith relation between the signal input and the signal output of the generalized multi-carrier system of the Discrete Fourier Test spread-spectrum; then setting equilibria parameters of the frequency field equilibria subcarrier of the generalized multi-carrier system of the DFT spread-spectrum according to channel frequency response, channel noise variance and equilibria method; then calculating average power of useful signal, interferential average power between signals as well as noise variance of the generalized multi-carrier system receiving terminal of the DFT spread-spectrum according to the arith relation as well as the frequency field equilibria parameter, and recomputing available signal information noise ratio, so as to calculate the available signal information noise ratio of the generalized multi-carrier transmission system accurately, the method for estimating the available signal information noise ratio can be used for link self-adapting transmission solution of the generalized multi-carrier system based on Discrete Fourier Test spread-spectrum and radio material management.

一种DFT扩频的广义多载波系统的SINR估计方法，其通过首先建立所述离散傅立叶变换扩频的广义多载波传输系统的信号输入输出之间的数学关系，然后根据信道频率响应、信道噪声方差和均衡方法，设定所述DFT扩频的广义多载波传输系统的频域均衡子载波的均衡系数，再根据所述数学关系及所述频域均衡系数分别计算所述DFT扩频的广义多载波传输系统接收端有用信号的平均功率、信号间干扰的平均功率以及噪声方差，再计算有效信干噪比，如此以实现对广义多载波传输系统的有效信干噪比的准确计算，该有效信干噪比估计方法可用于基于离散傅立叶变换扩频的广义多载波传输系统的链路自适应传输方案和无线资源管理方面。

Specify what status the spatial operator algebra locates at in many methods of multibody systems dynamics formulations and what the relations are between the spatial operator algebra and other dynamics formulations.We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition, substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

A special kind of prime dual ideals are defined in a lattice implication algebra, then their structures and properties are discussed. It is proved that the implication operation on this lattice implication algebra is determined by these prime dual ideals, and all of these prime dual ideals compose a lattice implication algebra which is lattice implication isomorphic to the former lattice implication algebra.

在格蕴涵代数中定义了一类特殊的素对偶理想，讨论了它们的结构和性质，证明了该格蕴涵代数中的蕴涵运算可以由这些特殊的素对偶理想所确定，并且这些特殊的素对偶理想全体自然地构成一个格蕴涵代数，它和原格蕴涵代数具有格蕴涵代数同构关系。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。