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Modern computers are primarily binary. Proposed in this paper is a new generalized computing system, by which a number system of any arbitrary radix can be manipulated directly without encoders and decoders. The feature of being able to vary the radix is achieved by pulse counting with alterable carry conditions. The architecture and the organization of the new system are also drastically different from those of existing computers. Instead of the adder being the basic functional structure, the heart of the system consists essentially of an adder, subtractor, multiplier and an accumulator integrated into one inseparable unit. Introduced in this paper is a unified system design suitable for all computing systems and also the concept of a universal building block which can be shared both by the arithmetic unit and the memory. As a memory element, the universal building block is capable of storing a digit of any given radix rather than just binary. Instead of communicating between the binary registers and the constituents of the memory or the arithmetic unit as in existing computers, variable pulse train generators and counters are made to communicate with each other. Binary logic is adopted to channel the pulses or the instructions instead of performing the arithmetic operations. A modern computer, however complex, thus becomes a special case of the generalized computing system.

The optimum price switching problem consists in determining simultaneously the optimum prices as well as the optimum decision times for switching from price to price. This paper proposes a dynamic formulation for the pricing problem faced by a firm, and provides neee9aary conditions for the optimality of both prices and price switches. Subsequently, the paper discusses the economics of price selection and the economics of decision times.

The ' phase velocity ' of the system considered in this paper depends on the past of both the states (Oguztoreli, p. 184) and the controls (Banks and Jacobs, p. 464). However the results of Oguztöreli, Banks and Jacobs do not cover the dynamics of the plant considered in this paper. It is shown in this paper that by use of a stronger topology for the class of measurable controls it is possible to prove the closure of the set of trajectories (called the ' T-set ') without requiring the ' velocity field ' to be convex. This generalizes the class of systems at the expense of generality of the control class. In fact there is a trade-off between the two and one can be improved at the expense of the other.In practical situations where the dynamical system does not satisfy the convexity condition, the strong topology hypothesis may be used.In the concluding sections of the paper the closure property of the ' T-set' is used to prove the existence of optimal controls for the system.

The aim of this paper is to identify the denumerable stochastic systems which have an optimal strategy, namely, to give general sufficient conditions of the existence of an optimal strategy for denumerable Markovian decision processes. The aim is accomplished by using Markov potential theory and showing the range of the validity of a method to find an optimal strategy called Howard's technique. Since Markov potential theory helps to characterize the properties of evaluations of strategies on such processes, it plays an important role to find the sufficient conditions mentioned aboveFor Markov potential theory, new concepts are introduced such as absorbable chains, quasi-potentials, etc., and using them, sufficient conditions for the existence of a solution of the equation x = f+Px are generalized to the one's for cyclic chains and multi-chainsThe results obtained in this paper are as follows : if a system represents a strong Markov chain for any strategy, then there exists an optimal strategy with respect to the total or the mean expected earnings, and for any stochastic system there exists an optimal strategy with respect to the discounted total expected earnings.

This paper deals with the modular realization of sequential machines using shift registers as the modules. For a given minimal machine, the minimum number of modules required for its realization has been determined. It is well known that the number of modules required to realize a given machine can sometimes be reduced by realizing a non-minimal machine equivalent to the given minimal one, i.e. by assigning multiple codes to the states of the given minimal machine. This case is dealt with in the second part of the paper.

This paper presents an application of hierarchical identification procedures of the previous paper to the identification of interconnected power system states and parameters from input - output observed data. A three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification. The adaptivity of these procedures to structural changes are also illustrated. Numerical results are obtained by conducting a digital simulation of the three-area system and using the hierarchical identification and coordination algorithms to estimate the states and unknown system parameters. Computational aspects of the hierarchical system identification solutions are discussed.

This paper presents a method of maximizing reliability of a series system subject to multiple constraints. The use of both active series parallel and standby redundancy is considered to increase the reliability of the system. A flexible tree search method has been used in this paper which is found to be an efficient method of solution, as it requires only simple mathematical computations. A three stage system is used for illustration.

Most modern computers with very few exceptions operate on the binary number system, This paper suggests a new generation of computer systems capable of performing computations in many number systems. At the present, a modern computer handles numbers other than binary through encoding prior to performing the arithmetic operations. The converting processes of encoding and decoding are both wasteful and time consuming. The proposed system is able to carry out computations in a given radix without conversions. In order to operate on a specific number system a radix control can be preset to the desired value, the computer is then converted instantly to be of that radix. In general, a number system is formed basically from counting with proper carry or carries to be generated when a desired radix is reached. High speed pulse counting with a controllable and variable carry producing mechanism is thus the most direct and efficient approach for the implementation of a variable radix computer system. In essence, a high speed electronic variable radix computer is a counterpart of a mechanical calculator which would consist of essentially wheels with number of teeth variable. This paper attempts to lay the basic and the most essential foundation necessary for such a versatile system. Similar to the conventional systems, the addition of numhers in an arbitrary radix can be performed by the use of a variable radix adder ; and the subtraction by the addition of the (R -l)'s complement, where R is the radix. Multiplication can be carried out by repeated additions and the division by the cyclic subtractions. The chosen number representation will be presented in the paper first and then the formuli, which are given either in simple expressions or in the compact series forms, for the basic arithmetic operations. In addition, numerical examples in various radices are given for the readers to ponder and enjoy.

This paper is aimed at the development of a stochastic model for an academic institution. It is argued that many of the parameters of such an institute can only be effectively modelled in a probabilistic sense. It is proposed that all such parameters which cause a deterministic model of the institute to be erroneous can be lumped together as a white noise term in the state variable model. It is shown that the covariance of the noise term as well as the parameters of the deterministic part of the model can be recursively estimated on the basis of the known performance of the institute over a period of post several years. Once the model is identified it is shown that a prediction of the future performance of the institute is possible. The various concepts are illustrated in the paper on the basis of data collected from an existing institute.

The paper presents a new approach to the problem of identification of non-stationary model parameters. It is shown that a recursive algorithm for the smoothed parameter estimates can be obtained through an application of the Kalman filtering algorithm to an augmented system. As an illustration of the versatility of this approach, estimates of non stationary model parameters of a system with non-white process noise are also derived in the paper. Finally, formal solutions of the problem of identification of non-stationary parameters of a continuous time system are presented.

The pipeline system with which this paper is concerned transports a act of various oil products produced by a number of gas plants located along the main pipeline. Each gas plant has a storage tank for each product it produces. The problem is to determine a feasible sequence in which the various products are pumped within each schedule period such that the interface loss is minimized. This paper proposes an algorithmic approach in which suitable dispatching rules are developed. The functions of this algorithm are to : (1) determine the sequence and batch size of products flowing in the pipeline ; (2) update the storage tanks and pipeline status after each pumping ; and (3) identify the type, identify the number, and compute the volume of interfaces created during the schedule period. A comparative evaluation of both existing and proposed procedures are conducted for seven consecutive production periods (600 hours). The criterion considered is the ratio of interface volume created to the total volume of products pumped. The average improvement is 44-5% over the results obtained by the existing procedure.

This paper analyses dynamic core allocation for a real-time system. The buffer allocation and release is administered by sub-routine BUFAL. This programme allocates, on request, one or more buffer storage areas in eight distinct sizes. It also releases these areas for subsequent re-allocation. On initialization the available storage is divided into 2048 byte bins. When smaller sizes are initially requested BUFAL forms the additional chains by dividing some of the 2048 byte bins. In this paper a general model is obtained and the special case of two types of devices (TTY, CRT) each requesting a different size bin is treated in detail. The expected waiting time is obtained as a function of the available core size.

The purpose of this paper is to investigate the existence and asymptotic mean square behaviour of random solutions of non-linear stochastic integral equations of the form[image omitted]fort≥o.A random solution of the equation is defined to he a second-order stochastic process x(t;ω) on {0, ∞) which satisfies the equation almost certainly. Conditions are given such that a unique random solution exists which is G-stable hi mean square. Finally, an application of the results to stochastic differential systems is presented. This paper extends the results of Tsokos and Hamdan (1972) to a more general class of stochastic integral equations and a more general concept of stability.

In addition to classical networks this paper introduces the concept of S-type networks. While in the case of the former only complementary variable pairs may be associated with the branches of the graph, in the latter case intensive variables without complement are also involved. The paper offer an axiomatic definition of the S-network theory and, by deriving the equations of a linear S-network, it presents some guidelines for practical application purposes. Finally, the possibilities of using the S-network concept for the digital modelling of large systems are explained.

In an earlier paper (Gupta 1971), an iterative hyperpower method of any finite- order for computing generalized inverse A+ and the associated projections AA+ and A+ A for any complex matrix A was developed. In this paper, hyperpower methods of different orders are compared and it is shown that there exists an optimum hyperpower method of order three.