Two classes of high-performance neural networks for solving linear and quadratic programming problems are given. We prove that the new system converges globally to the solutions of the linear and quadratic programming problems. In a neural network, network parameters are usually not specified. The proposed models can overcome numerical difficulty caused by neural networks with network parameters and obtain desired approximate solutions of the linear and quadratic programming problems.

The paper presents explicit formulas for the reflection coefficient of a broadband matching Chebyshev equalizer, satisfying Youla's coefficient constraints. The results are very important in that they provide the missing links permitting computation of element values for Chebyshev equalizers of any order.

It is shown that the return difference matrix possesses the same functions and plays the same important role in stability analysis and design of a multivariable feedback network as it does in control theory. The generalized Nyquist criterion, characteristic loci and other methods of stability analysis and design for multivariable feedback systems in control theory are applicable directly to multivariable feedback networks. In particular, a general frequency stability criterion for a multivariable lumped and distributed-parameter feedback network is presented.

In this paper, we propose a new approach to solve a general floorplan area optimization problem. By using the analogy between a floorplan and a resistive network, we have shown that a class of zero wasted area floorplan can be achieved under the shape constraint of continuous aspect ratio. However, in many practical designs, each module may have constraints on its dimensions such as minimum length or width. In this paper, we define the floorplan area minimization problem under the constrained aspect ratio and give necessary conditions for the realization of zero wasted area floorplan under the shape constraints. A set of optimization methods is developed to minimize the wasted area if no zero wasted area floorplan is achievable. Examples are given to demonstrate the approach.

In this paper a set of coefficient constraints on the realizability of an optimum lossless equalizer between a non-Foster positive-real load impedance and a resistive generator is given. The equivalency between this set and Youla's coefficient constraints is proved. A realization procedure is given.>

It is demonstrated that sufficient and reasonable utilization of the constrained horizontal and vertical routing resources is the key to achieving a high completion rate in this one-and-one-half layer routing approach. By using the minimum intersection graph to order the nets, the number of intersections among the nets is minimum, the number of intersection columns is as small as possible, and the total length of poly-bars used in wiring is as short as possible. From this the requirements for the horizontal and vertical routing resources are as few as possible. A reasonable assignment of the horizontal routing resources can be achieved by operating the active track matrices of the nets at the predicted columns, while the optimal assignment of the vertical routing resources is obtained by using the cluster assignment algorithm of the incidence intersection columns. Guided by the wiring tracks in the predicted columns and using the poly-bars assigned, the channel routing can be implemented with high performance by scanning the channel from left to right and column by column.>

It is shown that based on the indefinite-impedance matrix formulation, the sum of the reciprocals of the return differences with respect to all network elements of a planar network equals the rank of the network. Some consequences of this theorem in relation to the summation of driving-point and transfer network admittances are discussed.