36 results
Search Results
2. COUNTS DELAYED BUT NOT LOST-A NOTE ON A PAPER OF HAIGHT.
- Author
-
Anderson, J. A. and Bithell, J. F.
- Subjects
MIXTURE distributions (Probability theory) ,MARKOV processes ,STOCHASTIC processes ,DISTRIBUTION (Probability theory) ,NUMERICAL analysis ,MATHEMATICAL analysis ,PROBABILITY theory - Abstract
This paper generalizes, by the use of compound distributions, a result of HAIGHT (1966) on counts that are delayed but not lost. An application of Markov chains indicates a simple method of numerical evaluation of the distributions involved. Finally a continuous time analogue is studied. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
3. ASYMPTOTICALLY OPTIMAL TESTS OF COMPOSITE HYPOTHESIS FOR RANDOMIZED EXPERIMENTS WITH NONCONTROLLED PREDICTOR VARIABLES.
- Author
-
Neyman, Jerzy and Scott, Elizabeth L.
- Subjects
RANDOM variables ,HYPOTHESIS ,DISTRIBUTION (Probability theory) ,MATHEMATICAL analysis ,NUMERICAL analysis ,CHARACTERISTIC functions - Abstract
The paper is concerned with randomized experiments with one treatment. Two randomization schemes are considered: randomized pairs and unrestricted randomization. If effective at all, the treatment is supposed to affect the conditional distribution of the "experimental" variable Y given another variable X, called "predictor". The distribution of X is not affected by the treatment. Using the general theory published elsewhere, the paper deduces the locally asymptotically optimal test of the hypothesis that the treatment has no effect. Apart from the usual difficulties connected with asymptotic tests (how large must N be?), the theory is easily applicable in many "live" cases even though the conditional distribution of Y given X may contain nuisance parameters and be of unusual form. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
4. ON THE LOADING PROBLEM--A COMMENT.
- Author
-
Lev, Benjamin
- Subjects
ALGORITHMS ,HEURISTIC programming ,MATHEMATICAL programming ,MATHEMATICAL optimization ,RESOURCE allocation ,RESOURCE management ,MATHEMATICAL models ,MATHEMATICAL analysis ,NUMERICAL analysis ,OPERATIONS research ,PROBLEM solving - Abstract
The author responds to the paper "The Loading Problem," by Eilon and Christofides. He focuses on suggesting a solution to the problem. The recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the one proposed by Eilon and Christofides. It is suggested that the simpler algorithm offered by the author reaches mathematical optimization as often as the aforementioned algorithm. It is further proposed that the algorithm presented by Eilon and Christofides cannot be used to solve multi-dimensional programming problems. The author goes on to discuss a numerical analysis that can be used for the allocation of industrial resources. Related mathematical models are discussed in detail. A table comparing the results of the two algorithms is also presented.
- Published
- 1972
- Full Text
- View/download PDF
5. RISK-SENSITIVE MARKOV DECISION PROCESSES.
- Author
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Howard, Ronald A. and Matheson, James E.
- Subjects
MARKOV processes ,ITERATIVE methods (Mathematics) ,STOCHASTIC processes ,DECISION making ,PROBABILITY theory ,NUMERICAL analysis ,RISK ,MATHEMATICAL analysis ,MATHEMATICAL optimization ,MATHEMATICAL models - Abstract
This paper considers the maximization of certain equivalent reward generated by a Markov decision process with constant risk sensitivity. First, value iteration is used to optimize possibly time-varying processes of finite duration. Then a policy iteration procedure is developed to find the stationary policy with highest certain equivalent gain for the infinite duration case. A simple example demonstrates both procedures. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
6. THE USE OF MULTIPLE RANKING PROCEDURES TO ANALYZE SIMULATIONS OF MANAGEMENT SYSTEMS: A TUTORIAL.
- Author
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Kleijnen, Jack P. C., Naylor, Thomas H., and Seaks, Terry G.
- Subjects
COMPUTER simulation ,SIMULATION methods & models ,SYSTEM analysis ,RANKING (Statistics) ,DATA analysis ,NUMERICAL analysis ,MANAGEMENT science ,MATHEMATICAL models ,MATHEMATICAL analysis ,OPERATIONS research - Abstract
This paper describes the use of multiple ranking procedures to analyze data generated from computer simulation experiments with models of management systems. After outlining the rationale for the use of multiple ranking procedures with computer simulation experiments and defining some basic terminology, we examine several specific multiple ranking procedures. Careful attention is given to the assumptions underlying the different multiple ranking procedures and the extent to which these assumptions are satisfied by the data generated by simulation experiments. An example model is included to illustrate the applicability of multiple ranking procedures to simulation experiments in management science. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
7. Addendum to a Multiple-Precision Division Algorithm.
- Author
-
Mifsud, Charles J. and Bohlen, Michael J.
- Subjects
ALGORITHMS ,DIVISION algebras ,COMPUTATIONAL mathematics ,ALGEBRA ,MATHEMATICAL analysis ,NUMERICAL analysis - Abstract
Presents the author's comments on the paper "A Multiple-Precision Division Algorithm," by C.J. Mifsud, published in the November 1970 issue of the journal "Communications of the ACM." Account of difficulties that arises with the programming and implementation of the algorithm described in the paper; Avoidance of the possibility of overflow in the calculation of trial cipher; Solution to the problems the algorithm described in the paper; Suggestions for additional informative statements that should be inserted in the original algorithm.
- Published
- 1973
- Full Text
- View/download PDF
8. TABLES OF BOUNDS FOR DISTRIBUTIONS WITH MONOTONE HAZARD RATE.
- Author
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Barlow, Richard E. and Marshall, Albert W.
- Subjects
DISTRIBUTION (Probability theory) ,HYPOTHESIS ,EQUATIONS ,MATHEMATICAL analysis ,NUMERICAL analysis ,OPERATOR theory - Abstract
This paper presents in a form convenient for applications a number of bounds for distributions with monotone hazard rate. These bounds, together with their proofs and various generalizations have been obtained by Barlow and Marshall (1964). However, many of them can be characterized only through solutions of transcendental equations, and machine calculation has been necessary to make them accessible. Section 2 gives a listing of the results, and those without explicit forms are tabulated. Section 3 lists various related bounds which are of interest for purposes of comparison, and for use when the hypothesis of monotone hazard rate is not satisfied. Applications of the bounds are discussed in Section 4, together with some numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
9. AN IMPROVED STARTING ALGORITHM FOR THE FORD-FULKERSON APPROACH TO THE TRANSPORTATION PROBLEM.
- Author
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Mueller-Merbach, Heiner
- Subjects
TRANSPORTATION problems (Programming) ,ALGORITHMS ,LINEAR programming ,ASSIGNMENT problems (Programming) ,NUMERICAL analysis ,MATHEMATICAL variables ,NETWORK analysis (Planning) ,DISTRIBUTION (Economic theory) ,COST control ,MATHEMATICAL analysis ,LOCATION problems (Programming) ,EDUCATION - Abstract
This paper presents an algorithm for yielding an improved initial dual solution of the transportation problem when the network flow algorithm of Ford and Fulkerson is used. (1) The algorithm is described. (2) It is demonstrated by means of a numerical example. (3) Computational experience is reported. 400 medium-sized (30 X 80; 50 X 60; 50 X 80) test problems with three different kinds of distance matrices and two different kinds of shipment quantity vectors were evaluated. The average improvement over the usual method was about 30%. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
10. NUMERICAL SOLUTION OF THE PROBLEM OF OPTIMUM DISTRIBUTION OF EFFORT.
- Author
-
Miehle, William
- Subjects
NUMERICAL analysis ,MATHEMATICAL analysis ,COMPUTERS ,TASKS ,MATHEMATICAL optimization ,OPERATIONS research ,EQUATIONS ,ADDITIVE functions ,MATHEMATICS - Abstract
This paper is an extension of previously published work by Bernard O. Koopman to the general case of any number of tasks and any effect function. A systematic method for the numerical calculation of the maximum effect and its corresponding optimum distribution is presented in a form which is also suitable for solution on an automatic digital computer. For the special case of additive returns which saturate, a special graphical or numerical method for any number of tasks is presented with an example worked out in detail A similar method for multiplicative effects is sketched. [ABSTRACT FROM AUTHOR]
- Published
- 1954
- Full Text
- View/download PDF
11. An Algorithm for Filon Quadrature.
- Author
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Chase, Stephen M. and Fosdick, Lloyd D.
- Subjects
ALGORITHMS ,NUMERICAL analysis software ,NUMERICAL integration ,NUMERICAL analysis ,MATHEMATICAL analysis ,COMPUTER programming - Abstract
An algorithm for Filon quadrature is described. Considerable attention has been devoted to an analysis of the round-off and truncation errors. The algorithm includes an automatic error control feature. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
12. THE RELIABILITY OF DEPENDENT PARALLEL OR STANDBY N-UNIT REDUNDANCIES.
- Author
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Eiss, Joseph J.
- Subjects
NUMERICAL analysis ,CONTAGIOUS distributions ,MOMENTUM distributions ,QUANTITATIVE research ,STATISTICS ,MATHEMATICAL analysis - Abstract
This paper is concerned with evaluating the reliability of a redundant configuration, given that at any random time its surviving components are operating with failure distributions that are dependent upon the set of failed components. An expression (9) is derived for the reliability of this class of configurations and is then generalized to obtain an expression (23) for the reliability of a similar configuration whose component failure distributions are dependent also upon the time of the last such failure. These expressions are then applied to evaluating the reliability of a stand-by configuration with off-line failures, and the reliability of a parallel configuration for which at least a certain number of components must survive in order that the configuration operate satisfactorily. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
13. QUEUING PROCESSES AT COMPETING SERVICE FACILITIES.
- Author
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Sobel, Matthew J.
- Subjects
QUEUING theory ,CUSTOMER service research ,SERVICE industries research ,NUMERICAL analysis ,MATHEMATICAL analysis ,MATHEMATICAL models ,GRAPHIC methods ,DUOPOLIES ,OLIGOPOLIES - Abstract
The queuing models constructed here have the feature that a service facility tends to lose its customers if they often encounter lengthy delays. Structurally, the arrival processes are assumed to depend on past waiting times, hence on past arrival and service processes. The cases investigated include a a service facility with several competitors and a facility with very many competitors; these correspond roughly to oligopoly and to perfect competition in micro-economics. For the duopoly case, approximate analytical solutions are presented along with graphs for numerical solutions. A data sample is given that is moderately consistent with the duopoly model. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
14. THE POWER OF AN F-TEST IN THE CONTEXT OF A STRUCTURAL EQUATION.
- Author
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Revankar, Nagesh and Mallela, Parthasaradhi
- Subjects
STATISTICAL hypothesis testing ,MATHEMATICAL analysis ,MATHEMATICAL literature ,MATHEMATICAL variables ,MATHEMATICAL constants ,MATHEMATICAL statistics ,NUMERICAL analysis ,STRUCTURAL analysis (Engineering) ,MATRICES (Mathematics) ,STRUCTURAL dynamics - Abstract
The article discusses the econometric literature suggesting an exact F-test on a specific class of hypothesis in the context of a structural equation. The authors' consideration on is based on the consistency of the test which is similar to the recent asymptotic test, and the unique characteristic which is the possibility of the test to obtain an exact analytical expression for the power. Mathematical equations using different formula including that of matrices, as well as several dependent variables are also presented in the paper.
- Published
- 1972
- Full Text
- View/download PDF
15. A Precise Numerical Analysis Program.
- Author
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Aberth, Oliver and Willoughby, R.A.
- Subjects
NUMERICAL analysis ,MATHEMATICAL programming ,COMPUTER software ,MATHEMATICAL analysis ,COMPUTER science ,COMPUTER programming - Abstract
A description is given of a program for computing the solution to a small number of standard numerical analysis problems to any specified accuracy, up to a limit of 2000 correct decimal places. Each computed number is bounded in an interval with a multiple precision midpoint. Arithmetic operations involving these numbers are executed according to interval arithmetic concepts, with non-significant digits automatically discarded. Details are supplied of problem specification and problem computation. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
16. UNIVERSITIES.
- Subjects
UNIVERSITIES & colleges ,COMPUTER systems ,STUDENTS ,COMPUTER training ,MATHEMATICAL analysis ,MACHINE theory ,NUMERICAL analysis - Abstract
The article reports that a National Science Foundation grant of $1.2 million will be used by Purdue University for the purchase and operation of a new time sharing computer system complex and for augmenting the computer center staff. Negotiations are already under way to acquire a Control Data Corp. G500 computer, among the largest commercial computers built in the United States. The system is expected to be installed in the new Mathematical Sciences building in August 1967. The new system will allow researchers to solve much more complicated problems, and will permit Purdue students and staff members from all schools on campus to obtain results from the computer at least five times as fast as heretofore possible. A computer science program leading to a Master of Science degree has been initiated at New Mexico State University beginning with the fall semester, 1967. Both the program and the staff have an interdisciplinary nature with specialization areas including theory of algorithms, automata theory, logical design, threshold logic, numerical analysis, programming languages and systems, and information systems.
- Published
- 1967
17. Cubic Spline Solutions to Fourth-order Boundary Value Problems.
- Author
-
Hoskins, W. D. and Willoughby, R.A.
- Subjects
BOUNDARY value problems ,DIFFERENTIAL equations ,COMPLEX variables ,NUMERICAL analysis ,FINITE differences ,MATHEMATICAL analysis - Abstract
The cubic spline approximation to the fourth-order differential equation y
in + p(x)y" + q(x)y' + r(x)y = t(x) is shown to reduce to the solution of a five-term recurrence relationship. For some special cases the approximation is shown to be simply related to a finite difference representation with a local truncation error of order (1/720)δ³y)?. [ABSTRACT FROM AUTHOR]- Published
- 1973
- Full Text
- View/download PDF
18. George Forsythe and the Development of Computer Science.
- Author
-
Knuth, Donald E.
- Subjects
COMPUTER science ,COMPUTER programming ,MATHEMATICAL analysis ,CYBERNETICS ,COLLEGE teachers ,NUMERICAL analysis - Abstract
This article discusses professor George E. Forsythe's contributions to the establishment of computer science as a recognized discipline. It is generally agreed that he, more than any other man, is responsible for the rapid development of computer science in the world's colleges and universities. His foresight, combined with his untiring efforts to spread the gospel of computing, have had a significant and lasting impact; one might almost regard him as the Martin Luther of the Computer Reformation. His early training and research in numerical analysis was a good blend of theory and practice. Starting in 1948 he worked for the National Bureau of Standards' Institute for Numerical Analysis in Los Angeles, California, where he did extensive programming for the SWAC computer. In 1954 this Institute became part of U.C.L.A. and he put a great deal of energy into the teaching of mathematics and numerical analysis. He also worked on non-numerical problems, such as the tabulation of all possible semi-groups on four elements; at this time, he considered such combinatorial algorithms to be a part of numerical analysis and he regarded automatic programming as another branch. He began to foresee the less obvious implications of programming.
- Published
- 1972
- Full Text
- View/download PDF
19. A General Method of Systematic Interval Computation for Numerical Integration of Initial Value Problems.
- Author
-
Martin, W. C., Paulson, K. C., Sashkin, L., and Traub, J.F.
- Subjects
NUMERICAL solutions to initial value problems ,NUMERICAL analysis ,NUMERICAL integration ,DIFFERENTIAL equations ,BOUNDARY value problems ,MATHEMATICAL analysis - Abstract
A procedure is given for continuously computing and monitoring the step size to be used by a self-starting, pth-order numerical integration method to solve an initial value problem. The procedure uses an estimate of the truncation error to calculate the step size. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
20. Symbolic Factoring of Polynomials in Several Variables.
- Author
-
Jordan, Dale E., Kain, Richard Y., and Clapp, Lewis C.
- Subjects
POLYNOMIALS ,ALGORITHMS ,FACTORS (Algebra) ,MATHEMATICAL programming ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
An algorithm for finding the symbolic factors of multivariate polynomial with integer coefficients is presented. The algorithm is an extension of a technique used by Kronecker in a proof that the prime factoring of any polynomial may be found in a finite number of steps. The algorithm consists of factoring single-variable instances of the given polynomial by Kronecker's method and introducing the remaining variables by interpolation. Techniques for implementing the algorithm and several examples are discussed. The algorithm promises sufficient power to be used efficiently in an online system for symbolic mathematics. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
21. Finding Zeros of a Polynomial By the Q-D Algorithm.
- Author
-
Henrici, P., Watkins, Bruce O., and Downing, Jr., A. C.
- Subjects
NUMERICAL analysis ,POLYNOMIALS ,ALGEBRA ,MATHEMATICAL analysis ,MATHEMATICS ,STOCHASTIC convergence - Abstract
A method which finds simultaneously all the zeros of a polynomial, developed by H. Rutishauser, has been tested on a number of polynomials with real coefficients. This slowly converging method (the Quotient-Difference (Q-D) algorithm) provides starting values for a Newton or a Bairstow algorithm for more rapid convergence. Necessary and sufficient conditions for the existence of the Q-D scheme ore not completely known; however, failure may occur when zeros have equal, or nearly equal magnitudes. Success was achieved, in most of the cases tried, with the failures usually traceable to the equal magnitude difficulty. In some cases, computer roundoff may result in errors which spoil the scheme. Even if the Q-D algorithm does not give all the zeros, it will usually find a majority of them. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
22. Applications of Differential Equations in General Problem Solving.
- Author
-
Klopfenstein, R. W.
- Subjects
DIFFERENTIAL equations ,NUMERICAL analysis ,CALCULUS ,BESSEL functions ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
A large class of problems leading to digital computer processing can be formulated in terms of the numerical solution of systems of ordinary differential equations. Powerful methods are in existence for the solution of such systems. A good general purpose routine for the solution of such systems furnishes a powerful tool for processing many problems. This is true from the point of view of ease of programming, ease of debugging, and minimization of computer time. A number of examples are discussed in detail. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
23. Mathematical Experimentation in Time-Lag Modulation.
- Author
-
Bellman, Richard, Buell, June, Kalaba, Robert, and Traub, J. F.
- Subjects
DELAY differential equations ,FUNCTIONAL differential equations ,NUMERICAL analysis ,DIFFERENTIAL equations ,FUNCTIONAL equations ,MATHEMATICAL analysis - Abstract
Equations of the form du / di = g(u(t), u(h(t))) arise in a number of scientific contexts. The authors point out some interesting properties of the solution of u′(t) = -u(t - 1 - k sin ωt) + sin at. These properties were obtained by means of numerical solution. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
24. Starting Approximations for Square Root Calculation on IBM System/360.
- Author
-
Fike, C. T.
- Subjects
APPROXIMATION theory ,SQUARE root ,ARITHMETIC ,FUNCTIONAL analysis ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
Several starting approximations for square root calculation by Newton's method are presented in a form to facilitate their use In IBM System/360 square root routines. These approximations include several for the range [..., 1], which is the interval of primary interest on IBM System/360. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
25. THE USE OF NUMERICAL METHODS TO DESCRIBE POPULATION DIFFERENTIATION.
- Author
-
Jardine, N. and Edmonds, J. M.
- Subjects
NUMERICAL analysis ,NUMERICAL calculations ,POPULATION ,TAXONOMY ,CLASSIFICATION ,MATHEMATICAL analysis - Abstract
We discuss, with examples, the use of numerical methods to describe and compare patterns of differentiation between populations of organisms at low taxonomic levels. The role of such methods as adjuncts to the orthodox methods of experimental taxonomy is illustrated by an account of differentiation in Solanum L. Section Solanum (Maurella). [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
26. STUDIES IN THE NUMERICAL ANALYSIS OF COMPLEX RAIN-FOREST COMMUNITIES: V: A COMPARISON OF THE PROPERTIES OF FLORISTIC AND PHYSIOGNOMIC-STRUCTURAL DATA.
- Author
-
Webb, L. J., Tracey, J. G., Williams, W. T., and Lance, G. N.
- Subjects
ECOLOGICAL research ,NUMERICAL analysis ,PHYSIOGNOMY ,VEGETATION classification ,PLANT classification ,MATHEMATICAL analysis - Abstract
This article compares the properties of floristic and physiognomic-structural data in the numerical analysis of complex rain-forest communities. The article discusses previous work on the use of physiognomic-structural characters for the classification of vegetation and environmental types. It analyzes the data by both agglomerative polythetic and divisive monothetic methods. It notes that an analysis of the relative efficiency of recovery of environmental information for descending hierarchical levels provided no support for the familiar suggestion that structural characters are less efficient at lower levels.
- Published
- 1970
- Full Text
- View/download PDF
27. THE RELATION BETWEEN MEAN SQUARE AND BLOCK SIZE IN THE ANALYSIS OF SIMILAR PATTERNS.
- Author
-
Usher, M. B.
- Subjects
PLANT pattern formation ,NUMERICAL analysis ,PATTERN formation (Biology) ,MATHEMATICAL analysis ,PLANT development ,BIOLOGY - Abstract
This article presents a study which investigated the relation between mean square and block size in the analysis of similar plant patterns. Models of basic patterns have been prepared and the analysis of these suggests that the starting point for sampling is of importance. If the series starts towards the centre of a clump there is a strong possibility that the indicated peak mean square will be one block size smaller than the actual. A new method of field sampling is suggested which involves taking a slightly larger series of samples, and performing a number of analyses.
- Published
- 1969
- Full Text
- View/download PDF
28. EXTENDED TABLES OF THE WILCOXON MATCHED PAIR SIGNED RANK STATISTIC.
- Author
-
McCornack, Robert L.
- Subjects
STATISTICS ,STATISTICAL correlation ,PROBABILITY theory ,APPROXIMATION theory ,MATHEMATICAL analysis ,NUMERICAL analysis - Abstract
A table of critical values of the Wilcoxon Signed Rank Statistic is presented for N = 4(1)100 pairs of observations at one-tail probability levels of .00005, .0005, .0025, .005(.005).025, .050(.025).150, and .20(.05).45. Probabilities were computed accurately to at least 6 digits, regardless of the location of the decimal point. Therefore, all critical values are correct as tabled. Normal approximation probabilities were found to be biased, too small at the .05 level but too large at the .005 and .0005 probability levels. Approximation errors were less than 10% for all N >35 for the .05, .025, and .005 one-tail probability levels; but this degree of accuracy was not achieved at the .0005 level for N = 100. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
29. ON AN EXTREME RANK SUM TEST WITH EARLY DECISION.
- Author
-
Chun, D.
- Subjects
MATHEMATICAL analysis ,HYPOTHESIS ,STATISTICS ,NUMERICAL analysis ,MATHEMATICAL sequences ,MATHEMATICS - Abstract
Where Youden's extreme rank sum test is used, an early decision is often possible by performing the trials in sequence with the following method. After each trial is completed, the greatest lower bound and least upper bound of both extreme rank sums are calculated for all remaining trials. If the critical regions cover either or both intervals of the statistics or the intervals lie completely outside the critical regions, the round-robin test is terminated with the acceptance of the proper hypothesis. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
30. AN INTERACTIVE APPROACH FOR MULTI-CRITERION OPTIMIZATION WITH AN APPLICATION TO THE OPERATION OF AN ACADEMIC DEPARTMENT.
- Author
-
Geoffrion, A. M., Dyer, J. S., and Feinberg, A.
- Subjects
DECISION making ,HUMAN-machine systems ,MATHEMATICAL optimization ,MATHEMATICAL programming ,MULTIVARIATE analysis ,MATHEMATICAL analysis ,ACADEMIC departments ,NUMERICAL analysis ,MANAGEMENT science - Abstract
An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
31. RELAXATION METHODS FOR PURE AND MIXED INTEGER PROGRAMMING PROBLEMS.
- Author
-
Gorry, G. Anthony, Shapiro, Jeremy F., and Wolsey, Laurence A.
- Subjects
MATHEMATICAL programming ,RELAXATION methods (Mathematics) ,INTEGER programming ,LINEAR programming ,MATHEMATICAL optimization ,MANAGEMENT science ,NUMERICAL analysis ,MATHEMATICAL models ,DETERMINANTS (Mathematics) ,ALGORITHMS ,MATHEMATICAL analysis ,OPERATIONS research - Abstract
The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby reducing the size of the group induced by the basis. An adaption of Benders' mixed IP algorithm is given which uses these methods. Some limited computational experience is given. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
32. COMPUTATION FOR THE REDISTRIBUTION MODEL WITH SET-UP CHARGE.
- Author
-
Allen, S. G.
- Subjects
INVENTORY accounting ,INVENTORY control ,USER charges ,SHIPMENT of goods ,NUMERICAL analysis ,INDUSTRIAL costs ,MATHEMATICAL models ,DISTRIBUTION (Economic theory) ,MATHEMATICAL analysis ,MARITIME shipping ,DECISION making ,PRODUCT management ,EDUCATION - Abstract
A systematic computation procedure is given for determining redistribution of stock among several user activities when set-up charges are involved. The procedure is divided into two phases, the first of which determines whether any redistributions should be made at all. Then the second phase determines the total amount to be shipped or received at each activity. [ABSTRACT FROM AUTHOR]
- Published
- 1962
- Full Text
- View/download PDF
33. Truncated Version of a Play-the-Winner Rule for Choosing the Better of Two Binomial Populations.
- Author
-
Kiefer, James E. and Weiss, George H.
- Subjects
NUMERICAL analysis ,PROBABILITY theory ,BINOMIAL distribution ,BINOMIAL theorem ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
Results are developed for play-the-winner sampling for choosing the better of two binomial populations when the maximum number of tests is specified. It is shown that for a fixed number of tests the probability of correct selection with alternating assignment exceeds that for play- the-winner sampling. However, when the probability of correct selection is fixed, neither sampling method is uniformly better than the other as measured by the expected number of tests on the poorer population, or on the total expected number of tests. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
34. Mathematics for Biology Majors.
- Author
-
Chorbajian, Torcom
- Subjects
CURRICULUM ,CURRICULUM-based assessment ,LIFE sciences ,BIOLOGY ,SET theory ,EXPERIMENTAL mathematics ,MATHEMATICAL analysis ,NUMERICAL analysis ,LINEAR algebra ,MATHEMATICAL models - Abstract
The article discusses the significance of mathematics in biomedical and biological research. It states that the implications of the instrumentation, computers, and modeling, has become increasingly important for the biology major to include mathematics as an integral part of his undergraduate studies. It suggests to design a one-year mathematics sequence for the biology major. The course will involve integration of basic ideas on set theory, algebraic systems, and analytic geometry. The course aims to help students learn useful mathematical techniques, gain appreciation for the role of mathematics in biology, and let them acquire a feeling for the mathematical way of thinking.
- Published
- 1970
- Full Text
- View/download PDF
35. Finite element solution of nonlinear heat conduction problems with special reference to phase change
- Author
-
O. C. Zienkiewicz, G. Comini, Roland W. Lewis, and S. Del Guidice
- Subjects
Numerical Analysis ,Mathematical optimization ,Applied Mathematics ,Mathematical analysis ,General Engineering ,Relativistic heat conduction ,Thermal conduction ,Heat capacity ,Nonlinear system ,Latent heat ,Transient (oscillation) ,Boundary value problem ,Heat kernel ,Mathematics - Abstract
The paper presents a generally applicable approach to transient heat conduction problems with non-linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration. Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non-linear radiation boundary conditions are given which show very good accuracy. Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.
- Published
- 1974
36. Physical approximation of color-mixture functions
- Author
-
W. E. R. Davies and G. Wyszecki
- Subjects
Series (mathematics) ,business.industry ,Numerical analysis ,Mathematical analysis ,General Engineering ,Function (mathematics) ,Fresnel equations ,Photoelectric effect ,Set (abstract data type) ,Optics ,Transmittance ,Light beam ,business ,Mathematics - Abstract
One of the most important problems in photoelectric colorimetry is the duplication, by physical means, of a given set of color-mixture functions. Several methods are outlined in this paper for the numerical derivation of close approximations to given color-mixture functions using the relative spectral-sensitivity function of a photoelectric receiver and the spectral transmittances of glass filters. The filters are placed either in series or side by side between the source and the receiver. Numerical examples illustrate the methods.
- Published
- 1962
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