求符号网络函数的变形双图分解分析法

引入了互补余因式对、正规双图和可行撕裂点集的概念。应用它们导出了一阶余因式Ｃ（Ｙ）的分解定理。把它与变形双图法相结合，提出了求符号网络函数的一个新的分解分析法－变形双图分解分析法。它的优点是所得符号网络函数表达式紧凑面且不含对消项，并且它的符号计算很简单。     

求符号k阶余因式的变形双图法

引入了k阶变形双图Gij和k阶变形矩阵Yij的概念。应用它们导出了图行列式C(Y)和k阶余因式Y(ij)的两个新表达式,从而提出了求符号k阶余因式Y(ij)的变形双图法。应用它可直接且高效地求得Y(ij)的一个多层展开式(没有专门的符号计算问题),而且不产生对消项,所以它优于以前的方法。     

基本电子电路

TN711.6 9402068飞M压10网络综合的状态空间方法/周湘民,荣美芝(上海交通大学)/)上海交大学报一1993,27(4).一63~72 利用多变量控制系统在频域和时域上的基木理论,提出一种新的MIMO网络综合方法,采用RC级联结构作为网络实现的基本模块,较好地解决了对电路的稳定性和灵敏度的影响.图3参13(木) 提出了网络矩阵H的一般K阶余因式H心]的拓扑分解原理和公式.应用它们求全符号网络函数,采用向下分解向上组合法可明显扩大计算机所能拓扑分析的电网络规模,更容易在计算机上实现.图4参6(木)TN711‘6 94020682大规模电网络的分层分解分析/宋玉阶,…     

网络展开图与符号网络分析

采用封闭网络模型,按照电路元件参数,采用开路、短路和着色运算,将电路图逐层分解,得到网络展开图.给出网络展开图的概念和运算规则,指出网络展开图中从根到末稍每个路径的值就是网络行列式展开式中的一个有效项,从而由网络展开图得到符号网络函数.该方法直接对电路图进行运算,不需要建立任何形式的电路方程和行列式,适用于一般的有源电路,而且能生成各种类型的网络函数.     

求一般k阶余因式的k阶缩减图法

引入了网络矩阵Ｈ的一般ｋ阶余因式的对应ｋ阶缩减图，应用它导出了一般ｋ阶余因式Ｈ的ｋ阶１因子表达式，该表达式简单、实用。     

多相开关电容网络函数计算的分类算法和符号网络函数的生成

本文通过引入增广不定导纳矩阵的概念,提出了计算多相开关电容(MSC)网络函数一阶和二阶余子式的一种快速有效分类算法。并提出了产生MSC网络符号函数的素数编码法,可以用它得到无相消项的符号或半符号网络函数。     

生成电路符号网络函数的新方法

文中给出一种生成无源电路符号网络函数的新方法，它是把符号参数抽出作为端口量，利用伴随电波法来直接建立符号网络方程。采用有效的符号行列式展开来求解此方程，从而得到所需的符号网络函数。与其他方法相比，该法具有以下特点：将数值与符号相结合；建立符号网络函数的过程简便，便于编程实现；运算量较少。     

生成有向图的所有树形图的新算法

本算法生成一个直积-直和表达式,用来表示有向图G中所有以指定结点r为根的树形图之集∑_r~ (G)。该表达式正是一种“符号网络函数”,且其形式非常适合生成树形图问题的实际应用。算法的基础是两种新的分解:图的直积分解与图的直和分解。本文还提出逆弧概念和删除逆弧算法,作为下一步改进的着眼点。复杂性:时间O(VEK),空间O(E),其中K为直和分解次数加1。     

分析线性反馈网络的新方法

本文应用回路阻抗矩阵的行列式和广义余因式导出一种分析线性反馈网络的新方法,深入系统地研究了网络函数,灵敏度、回归差、零回归差及其矩阵等,得到了规律性很强适合机辅分析的一系列公式。此法不局限于研究平面网络,特别适用于RLCM和流控电压源组成的受电压源激励的网络。     

拓展拓扑运算

求线性系统的网络函数问题,归结为求线性方程组系数矩阵行列式及其一阶代数余子式。当系数矩阵各元素或部分元素是符号,在要求符号网络函数时,通常的高斯消去法便失去了有效性。本文将从一般理论出发结合零和矩阵的伴随有向图介绍一种拓扑运算方法。本文引入矩阵拓展伴随图的概念,使计算矩阵行列式及一阶代数余子式的拓扑方法,不再需要用两种,而只需用一种拓扑运算就可以同时得到,是对W.K.Chen(陈惠开)提出的“有向图法”的补充。这不但便于计算机程序化,也使求符号网络函数的理论得到简化。     

MODIFIED DOUBLE-GRAPH DECOMPOSITION ANALYSIS FOR FINDING SYMBOLIC NETWORK FUNCTIONS

The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the modified double-graph method, a new decomposition analysis-modified double-graph decomposition analysis is presented for finding symbolic network functions. Its advantages are that the resultant symbolic expressions are compact and contain no cancellation terms, and its sign evaluation is very simple.     

Symbolic analysis methods and applications for analog circuits: atutorial overview

This tutorial paper gives an overview of the history and present state of the art in symbolic analysis of electronic circuits at the so-called circuit level. Symbolic analysis is defined as a technique generating a closed-form analytic expression for a circuit characteristic with the circuit's elements represented by symbols. Such analytic information complements the results from numerical simulations. The paper then describes the different application areas of symbolic analysis for the design of analog circuits. Symbolic analysis is mainly used as a means to obtain insight into a circuit's behavior, to generate analytic models for automated circuit sizing, and in applications requiring the repetitive evaluation of circuit characteristics. Next, the present capabilities and limitations of symbolic analysis, both in functionality and efficiency, are discussed. The major symbolic analysis methods are presented, and algorithmic details are provided for symbolic approximation, hierarchical decomposition, and symbolic distortion analysis. Finally, existing symbolic simulators are compared, and directions for future research are pointed out     

Two methods of decomposition symbolic simulation of circuit functions

A decomposition method of total algebraic complements with “screening” and the topology transformation method have been proposed for symbolic simulation of circuit functions. They are based on decomposition of the simulated circuit and the use of index operations in calculating the model matrix determinant and algebraic complements of its elements.     

A hierarchical approach to large circuit symbolic simulation

This paper presents a new approach to symbolic analysis of large circuits. The proposed procedure is grounded on circuit decomposition by node tearing, symbolic analysis at subcircuit level and circuit function generation. Symbolic analysis is based on matrix-determinant method implemented within our original symbolic simulator. The crucial part of this procedure is circuit function generation. Opposed to classic symbolic simulation that gives final result in canonical sum-of-product form, hierarchical approach results in compact nested form. Proposed method is described in details using a simple example. The comparison with two other similar techniques is given using a benchmark example. The overall time reduction in comparison with the circuit function extraction in fully expanded form is 30 times.     

Efficient Decomposition Techniques for Symbolic Analysis of Large-Scale Analog Circuits by State Variable Method

New tearing techniques for the systematic formulation of the state equations in symbolic normal-form for linear and nonlinear time-invariant large-scale analog circuits are developed. Some examples are given to illustrate the decomposition procedure and the assignment of the connection sources. The partial symbolic state equations of the opamp A 741 are obtained using the tearing approach, while these equations cannot be written working on the whole circuit.     

Fast fault-tree evaluation for many sets of input data

It is pointed out that system unavailability and failure frequency can be found for many sets of components data via symbolic formulas with few multiplications. The derivation of such symbolic formulas is possible by binary-tree algorithms (specifically the Shannon expansion) which could run very fast on supercomputers allowing for binary-tree parallelism. The reduction factor of the number of multiplications needed in nested versus polynomial forms is roughly half the height of the decomposition tree, and the height of the tree is roughly the number of system components     

Indexing and retrieval of images by spatial constraints

Many multimedia applications require retrieval of spatially similar images against a given query image. Existing work on image retrieval and indexing either requires extensive low-level computations or elaborate human interaction. In this paper, we introduce a new symbolic image representation technique to eliminate repetitive tasks of image understanding and object processing. Our symbolic image representation scheme is based on the concept of hierarchical decomposition of image space into spatial arrangements of features while preserving the spatial relationships among the image objects. Quadtrees are used to manage the decomposition hierarchy and play an important role in defining the similarity measure. This scheme is incremental in nature, can be adopted to accommodate varying levels of details in a wide range of application domains, and provides geometric variance independence. While ensuring that there are no false negatives, our approach also discriminates against non-matching entities by eliminating them as soon as possible, during the coarser matching phases. A hierarchical indexing scheme based on the concept of image signatures and efficient quadtree matching has been devised. Each level of the hierarchy tends to reduce the search space, allowing more involved comparisons only for potentially matching candidate database images. For a given query image, a facility is provided to rank-order the retrieved spatially similar images from the image database for subsequent browsing and selection by the user.     

DECOMPOSITION THEOREM AND k-HYPERCONNECTION EXPRESSIONS FOR GENERAL k-ORDER COFACTORS

Two k-hyperconnection expressions of a general k-order cofactor Y_((i,j)) are presentedfor the indefinite parameter matrix Y of a linear system by applying directed hypergraph theory,and based on it a decomposition theorem of Y_((i,j)) is derived.By this theorem,the multi-leveltearing and analysis can be carried out easily for any linear large system.This is a new mul-tilevel topological analysis method.Using proposed method the scale of systems which can betopologically analysed by a computer will be enlarged.     

Symbolic Reliability Analysis with the Aid of Variable-Entered Karnaugh Maps

A method for finding the symbolic reliability of a moderately complex system is presented. The method uses Bayesian decomposition to reduce the system into simpler series-parallel subsystems. The successes or failures of these subsystems are found by inspection and then recast into disjoint sum-of-product forms with the aid of the Karnaugh map. Subsequently, an almost minimal disjoint expression for the system success or failure is obtained with the aid of a variable-entered Karnaugh map (VEKM). This VEKM method is illustrated by applying it to some examples recently solved in the literature. The main advantage of the method is the pictorial insight it provides to the reliability analyst.