Showing papers on "Network topology published in 1972"

Wave Sensitivities of Networks

Abstract: A theoretical foundation is presented for the efficient computation of first- and second-order sensitivities of networks with respect to network parameters in terms of wave variables. The concept of the adjoint network is used. First-order sensitivity formulas for a wide variety of elements are presented, including lumped and uniformly distributed elements, active and passive elements, and reciprocal and nonreciprocal elements. Parameters include electrical quantities, geometrical dimensions, and frequency. It is shown how gradients related to wave-based least pth and minimax objective functions can be computed. A comparison with a method which avoids the need for analysis of adjoint networks is made. Applications in the computer-aided design of networks using efficient gradient minimization methods are envisaged.

Computer-Aided Reliability Analysis of Complicated Networks

Abstract: A computer-aided procedure is described for analyzing the reliability of complicated networks. This procedure breaks down a network into small subnetworks whose reliability can be more readily calculated. The subnetworks which are searched for are those with only two nodes; this allows the original network to be considerably simplified.

Optimizing the Reliability in Centralized Computer Networks

Abstract: This paper deals with a heuristic procedure for optimizing the reliability of computer networks consisting of clusters of terminals connected to remote concentrators that are connected to a data-processing center. The expected percentage of terminals connected to the processing center is used as a measure of network reliability. It is shown that configurations other than the frequently used star are often considerably more reliable and less expensive.

Design of a diode function generator using the diode equation and iteration

Abstract: A resistor-diode network topology is described which permits a simple iterative solution for the network resistors in order to satisfy a given nonlinear input-output specification. The diodes are modeled by the diode equation giving excellent accuracy over a wide range of diode operation. Combining operational amplifiers with the basic resistor-diode topology permits the realization of a general single-valued continuous nonlinear function.

Class of communication networks with optimal connectivity

Abstract: A network has optimal connectivity if the number of alternative paths between any pair of vertices is the greatest possible with the given number of lines and vertices. A new class of optimal configurations is described, which is sufficiently extensive to enable networks to be devised with almost any required connectivity, provided that the number of vertices is factorisable. Some implications for communication networks are discussed.

Order of complexity of linear active networks and a common tree in the 2-graph method

Abstract: An upper bound on the order of complexity of a linear active network is the sum of the numbers of tree capacitances and link inductances, defined by a common tree of the voltage and current graph that contains a maximum number of capacitances and a minimum number of inductances. It is valid as far as a common tree exists, and is the lowest possible upper bound if only the network topology is known.

Bipartite communication networks with optimal connectivity

Abstract: A network configuration is described which offers a maximal number of alternative paths between pairs of vertices for a given number of links. A trunking scheme for switched networks, based on this configuration, offers a better ratio of alternative paths to crosspoints than is given by simple link trunking.

Planning of a Digital Hierarchy

Abstract: The choice of the fundamental parameters of a pulsecode modulation (PCM) system hierarchy depends on many factors, such as transmission media characteristics, time division switching and multiplexing plant requirements, traffic demand and network topology, etc. This paper deals with the problem of clarifying these interdependences and gives the general design criteria for planning a digital hierarchy. In accordance with these criteria, the main characteristics of a digital hierarchy, starting from the 2.048-Mbit/s primary PCM system, are derived and proposed. At present, systems in accordance with this proposal are being developed in Italy.

Semirings of functions determine finite ₒ topologies

Abstract: An analogue of the Stone-Gelfand-Kolmogoroff theorem for compact Hausdorff spaces is proven for finite T0 topological spaces. Let C(X) be the semiring of continuous functions from finite T0 X into Z, the nonnegative integers with open sets of the form {0, 1, 2, • • • , m}. Products and sums in C(X) are defined pointwise. Denote the set of nonzero semiring homomorphisms of C(X) into Z by H(X) and give it the compact-open topology where C(X) is considered discrete. Then (1) Xand H(X) are homeomorphic. (2) C(X) is semiring isomorphic to C( Y) iff X is homeomorphic to Y. (3) The topology of X can be completely recovered from the inclusion relations among the ideals of C{X) which are kernels of the elements in H{X). The study of finite topological spaces may at first seem somewhat contrived. However finite spaces do naturally occur and they can be useful for something other than nice counterexamples. For instance, recently in [1] they were used in a metrization problem. Since computers (and perhaps even the entire universe) are finite, some finite spaces may have application to practical physical problems. A natural question is the extent to which maps on a space determine its topology. For example, the classical result for compact Hausdorff spaces is that the topology is determined by the algebraic structure of the ring of real valued continuous functions. In this paper it is shown that the semiring C(X) of continuous functions from a finite T0 space X into the nonnegative integers Z with an order induced ,4-space topology characterizes the topology of A. The method of proof is to first show Ais homeomorphic to the set H(X) of nontrivial semiring homomorphisms from C(X) to Z. Here C(X) is considered discrete and H(X) has the compact open topology. It then follows that C(X) and C( Y) are semiring isomorphic if and only if X and Y are homeomorphic. The following facts about finite spaces and ^-spaces will be used. Good references are [3] and [4]. A partial order on a set A determines a topology on X by defining the minimal open set containing i to be those/ withy'—;'. Presented to the Society, September 27, 1971; received by the editors October 11, 1971. AMS 1970 subject classifications. Primary 54C35; Secondary 54C40.

Approximate Identities and Strict Topologies.

Abstract: I n t h i s p a p e r we i n v e s t i g a t e c e r t a i n g e n e r a l i z a t i o n s o f t h e s t r i c t to p o lo g y and o f t o p o l o g i c a l m e asu re th e o r y . A lth o u g h we a r e p r i m a r i l y i n t e r e s t e d i n non co m m u ta tiv e C * a lg e b r a s , we do d e v o te some a t t e n t i o n t o l i n e a r s p a c e s o f v e c to r v a lu e d f u n c t io n s . I n C h a p te r I n o t a t i o n and te rm in o lo g y a r e e s t a b l i s h e d . I n C h a p te r I I , we s tu d y a p p ro x im a te i d e n t i t i e s ( i n B anach a l g e b r a s ) w h ich a r e i n t e r e s t i n g i n th e m s e lv e s and a l s o p ro v id e a u s e f u l t o o l f o r s tu d y in g s t r i c t t o p o lo g ie s and to p o l o g i c a l m e asu re t h e o r y . Our m ain r e s u l t s i n Chap­ t e r I I h a v e to do w i th w e ll -b e h a v e d and P t o t a l l y bounded ap p ro x im a te i d e n t i t i e s i n t h e f u n c t io n a l g e b r a Cq ( S ) . We show t h a t Cq (S ) h a s a 0 t o t a l l y bounded a p p ro x im a te i d e n t i t y i f and o n ly i f S i s p a ra c o m p a c t and t h a t i f S i s c o n n e c te d o r l o c a l l y c o n n e c te d and CQ(S ) h a s a w e l l b eh av ed a p p ro x im a te i d e n t i t y , th e n S i s p a ra c o m p a c t. We a l s o d e f i n e s e v e r a l o th e r ty p e s o f a p p ro x im a te i d e n t i t i e s and g iv e c o n d i t i o n s on B anach a l g e b r a s n e c e s s a r y a n d /o r s u f f i c i e n t t h a t th e y p o s s e s s one o r m ore o f th e s e t y p e s . C h a p te r I I I i s th e c e n t r a l c h a p te r i n o u r p a p e r . I n

Alternative generalised equilibrium equations in active-linear-network analysis

Abstract: An alternative simple matrix form of generalised equilibrium equations for an active linear network is formulated from a network graph by considering ideal sources, as well as RLC elements, as branches. No source transformation is required in the formulation. Solutions obtained give element currents and element voltages for the network.