Showing papers in "Siam Review in 1982"
TL;DR: Various algorithms which have been suggested for generating full length nonlinear shift register sequences of length $2^n $ are discussed.
Abstract: Shift registers have been used to generate sequences of 0’s and 1’s for over thirty years. A wide variety of applications has been made of these sequences. Principally, communications have made use of the sequences generated.One particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences. These sequences are periodic and of length $2^n $ and all $2^n $ different binary n-tuples appear exactly one time in a periodic portion of the sequence. In this paper we discuss various algorithms which have been suggested for generating these sequences.
448 citations
204 citations
TL;DR: This paper provides a systematic review of several of the available manpower scheduling algorithms from a common framework based on the recognition that the general scheduling problem can be decomposed into five separate but related subproblems or stages.
Abstract: This paper provides a systematic review of several of the available manpower scheduling algorithms from a common framework. The five-stage framework is based on the recognition that the general scheduling problem can be decomposed into five separate but related subproblems or stages, namely, the determination of temporal manpower requirements, total manpower requirement, recreation blocks, recreation/work schedule, and shift schedule. One or more general models are developed at each stage to categorize the problem formulation(s) suggested by the various algorithms. Additionally, the algorithms are compared and their stage-specific solution methods are discussed.
188 citations
TL;DR: The purpose of this paper is to try to convince the reader that the QR algorithm is neither more nor less than a clever implementation of simultaneous iteration, which is itself a natural, easily understood extension of the power method.
Abstract: The $QR$ algorithm is currently the most popular method for finding all eigenvalues of a full matrix. While $QR$ is now well understood by specialists in eigenvalue computations, this understanding...
141 citations
TL;DR: A survey of theoretical results and numerical evidence concerning Stieltjes polynomials, Kronrod schemes and their generalizations applied to integrals with a (classical) nonnegative weight function can be found in this article.
Abstract: In this paper we present a survey of theoretical results (some of them new) and numerical evidence of others concerning Stieltjes polynomials, Kronrod schemes and their generalizations applied to integrals with a (classical) nonnegative weight function. The use of these schemes in automatic integration routines is briefly outlined.
97 citations
TL;DR: A survey of the most interesting work on nonlinear systems, together with a discussion of the major obstacles standing in the way of a comprehensive theory of nonlinear processes can be found in this paper.
Abstract: Results on controllability, observability and realization of input/output data for linear systems are well-known and extensively covered in a variety of books and papers. What is not so well-known is that substantial progress has been made in recent years on providing similarly detailed results for nonlinear processes. This paper represents a survey of the most interesting work on nonlinear systems, together with a discussion of the major obstacles standing in the way of a comprehensive theory of nonlinear systems.
67 citations
60 citations
TL;DR: A concise review of all contemporary concepts of identifiability can be found in this article, where the concepts are axiomatically defined for a specific class of linear, deterministic and stochastic systems.
Abstract: To capture a unified perspective of the identification problem, we present a concise review of all contemporary concepts of identifiability. These concepts are axiomatically defined for a specific class of linear, deterministic and stochastic systems. From a derived set of criteria we demonstrate a basic correspondence between the principal concepts in discrete time. Such an equivalence statement constitutes the motif for the future development of a global identifiability concept applicable to nonlinear problems.
55 citations
TL;DR: An asymptotic solution, valid for $\varepsilon $ small, is constructed for the time-dependent queue length probability distribution, which consists of five typical parts corresponding to five typical time periods.
Abstract: A single server queue is considered having exponentially distributed inter-arrival and service times with slowly changing time-dependent rates $\lambda (\varepsilon t)$ and $\mu (\varepsilon t)$. The parameter $\varepsilon $ is the ratio of an average inter-arrival time to the time over which the rates change appreciably, so it is small. Therefore an asymptotic solution, valid for $\varepsilon $ small, is constructed for the time-dependent queue length probability distribution. It consists of five typical parts corresponding to five typical time periods. They are the initial period, the period of light traffic when ${\lambda / \mu } < 1$, the saturation transition period when ${\lambda / \mu }$ increases through unity, the oversaturation period when ${\lambda / \mu }$ starts out greater than unity and then decreases below unity, and the transition period at the end of oversaturation, when the queue returns to the light traffic condition. By combining the solutions for these five intervals, the solution fo...
50 citations
43 citations
TL;DR: In this paper, Lagrange-like and Euler-like expansions of the perturbation parameter are considered for partial differential equations to be solved on a domain that is also perturbed.
Abstract: Expansions in powers of a perturbation parameter are considered for partial differential equations to be solved on a domain that is also perturbed. Two kinds of expansions—Lagrange-like and Euler-like—are developed and shown to be equivalent to one another under a certain transformation of dependent variables. This equivalence is used to justify the hierarchy of partial differential equations produced by the Euler-like expansion.In addition to partial differential equations, integrals extended over a perturbed domain are also considered. Such integrals suffer perturbations due to the domain perturbation. A formula for these perturbations is given that involves the domain-mapping function only at the boundary of the unperturbed domain. This contrasts with the usual change-of-domain formula, which involves the Jacobian of the domain-mapping function throughout the unperturbed domain. The formula in question is compatible with Euler-like expansions (and the usual change-of-domain formula is compatible with L...
TL;DR: In this paper, the authors give an analysis on Lie groups and their homogeneous spaces, thanks to the work of Harish-Chandra, Helgason, Selberg and many others.
Abstract: Analysis on Lie groups and their homogeneous spaces has seen a recent flowering, thanks to the work of Harish-Chandra, Helgason, Selberg and many others. The purpose of this paper is to give an ele...
TL;DR: In this paper, the derivation of flow equations which describe the behavior of a black oil reservoir is outlined, and the functional relations among the variables which result in the nonlinearity of the equations are discussed.
Abstract: The derivation of the flow equations which describe the behavior of a black oil reservoir is outlined. The functional relations among the variables which result in the nonlinearity of the equations...
TL;DR: In this article, a mathematical approach to the climate problem is presented, in which the desired statistical information would be obtained by finding and analyzing the attractors and invariant sets of the equivalent phase space flows.
Abstract: Interest in fluctuations and long-term variations of the atmosphere’s climate poses new mathematical problems demanding development of knowledge about the multiple solutions and limit properties of stable solutions to the partial differential equations of atmospheric motion. A mathematical approach to the climate problem is presented, in which the desired statistical information would be obtained by finding and analyzing the attractors and invariant sets of the equivalent phase space flows.A suitable approximate set of equations is developed. Galerkin techniques are used to obtain a finite-dimensional system, for which it is shown that a global attractor exists and that all solutions are eventually repetitive. Comparison of this system with Axiom A flows reveals important topics and questions for mathematical study.The partial differential equations are also considered, with existence and uniqueness results summarized. The presence of micro-scale turbulence necessitates introduction of a stochastic concep...
TL;DR: In this paper, it was shown that if an aircraft traverses a closed curve at a constant air speed with respect to the wind, the time taken is always less when there is no wind, than when there are any bounded irrotational wind fields.
Abstract: Problem 82-15, by M. S. KLAMKIN (University of Alberta). It is a known result (see Problem 61-4, SIAM Rev., 4 (1962), p. 155) that if an aircraft traverses a closed curve at a constant air speed with respect to the wind, the time taken is always less when there is no wind, than when there is any bounded irrotational wind field. (i) Show more generally that if the wind field is kW (W bounded and irrotational and k is a constant), then the time of traverse is a monotonic increasing function of k ( >0). (ii) Let the aircraft be subject to the bounded irrotational wind field W,., 1, 2, and let T; denote the time of flight over the same closed path. If [WI[--< [W2[ at every point of the traverse, does it follow that T _-< T2 ?
TL;DR: In this paper, a personal view of applied mathematics in a truly nonacademic setting (an operational navy command), based on the author's experiences as a field representative of the Operations Evaluation Group, is presented.
Abstract: This is a personal view of applied mathematics in a truly nonacademic setting (an operational navy command), based on the author’s experiences as a field representative of the Operations Evaluation Group. The principles that can make analysis effective in such a setting are described and explained. The intermeshing of people and personality is as important as the fields themselves. The traits that a mathematician needs to effect change by his analysis are discussed. A number of specific examples are provided to illustrate the kinds of problems that can be encountered.
TL;DR: In this article, a method for obtaining a series approximation to the general solution of a first order differential equation is presented, and an error estimate is included, showing how the method may be used in a neighborhood of a branch point.
Abstract: A method for obtaining a series approximation to the general solution of a first order differential equation is presented. An error estimate is included. An example is given which shows how the method may be used in a neighborhood of a branch point.
TL;DR: In this article, the relative significance of the stability of difference schemes that are consistent with a hyperbolic differential equation is discussed, and a scalar conservation law is singled out to emphasize the importance of establishing a meaningful extension of the notion of stability to the nonlinear case.
Abstract: The principal aim of this essay is to clarify, within the context of various $l^p $-spaces, the relative significance of the stability of difference schemes that are consistent with a hyperbolic differential equation. We also comment on the usefulness of identifying “modified equations” which model the behaviour of the difference schemes better than the original equation, even in the case of nonsmooth data. A scalar conservation law is singled out to emphasize the importance of establishing a meaningful extension of the notion of stability to the nonlinear case.
TL;DR: In this paper, the problem of mapping a portion of a spherical surface onto a plane so as to minimize distance errors (over all pairs of points) is considered; the use of a least mean square criterion, with area weighting, leads to coupled integral equations; numerical examples of their solution are given for regions bounded by parallels.
Abstract: The problem of mapping a portion of a spherical surface onto a plane so as to minimize distance errors (over all pairs of points) is considered. The use of a least mean square criterion, with area weighting, leads to coupled integral equations; numerical examples of their solution are given for regions bounded by parallels. Extensions to more general weighting functions, and to the use of nonuniform scales, are made.