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  • Springer  (40,518)
  • 1995-1999
  • 1975-1979  (40,518)
  • 1965-1969
  • 1976  (40,518)
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Publisher
Years
  • 1995-1999
  • 1975-1979  (40,518)
  • 1965-1969
Year
  • 101
    Electronic Resource
    Electronic Resource
    Mathematical programming study 4 (1976)
    Springer
    Mathematical programming 10 (1976), S. 409-412 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580687
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  • 102
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    Convergence conditions for restarted conjugate gradient methods with inaccurate line searches (1976)
    Springer
    Mathematical programming 10 (1976), S. 32-51 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Convergence properties of restarted conjugate gradient methods are investigated for the case where the usual requirement that an exact line search be performed at each iteration is relaxed. The objective function is assumed to have continuous second derivatives and the eigenvalues of the Hessian are assumed to be bounded above and below by positive constants. It is further assumed that a Lipschitz condition on the second derivatives is satisfied at the location of the minimum. A class of descent methods is described which exhibitn-step quadratic convergence when restarted even though errors are permitted in the line search. It is then shown that two conjugate gradient methods belong to this class.
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    URL: http://dx.doi.org/10.1007/BF01580652
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  • 103
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    Feasible directions algorithms for optimization problems with equality and inequality constraints (1976)
    Springer
    Mathematical programming 11 (1976), S. 67-80 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper two algorithms, of the feasible-directions and dual feasible-directions type, are presented for optimization problems with equality and inequality constraints. An associated problem, having only inequality constraints, is defined, and shown to be equivalent to the original problem if a certain parameter is sufficiently large. The algorithms solve the associated problem, but incorporate a method for automatically increasing this parameter in order to ensure global convergence to a solution to the original problem. Any feasible directions algorithm can be similarly modified to enable it to handle equality constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580371
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  • 104
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    Superlinearly convergent variable metric algorithms for general nonlinear programming problems (1976)
    Springer
    Mathematical programming 11 (1976), S. 263-282 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper sufficient conditions for local and superlinear convergence to a Kuhn—Tucker point are established for a class of algorithms which may be broadly defined and comprise a quadratic programming algorithm for repeated solution of a subproblem and a variable metric update to develop the Hessian in the subproblem. In particular the DFP update and an update attributed to Powell are shown to provide a superlinear convergent subclass of algorithms provided a start is made sufficiently close to the solution and the initial Hessian in the subproblem is sufficiently close to the Hessian of the Lagrangian at this point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580395
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  • 105
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    The Mathematical Programming Society (1976)
    Springer
    Mathematical programming 11 (1976), S. 301-301 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580399
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  • 106
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    The 8th IFIP Conference on optimization techniques (1976)
    Springer
    Mathematical programming 11 (1976), S. 199-199 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580387
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  • 107
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    Editor's note (1976)
    Springer
    Mathematical programming 11 (1976), S. 203-203 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580390
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  • 108
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    An existence theorem for solutions tof(x) = 0 (1976)
    Springer
    Mathematical programming 11 (1976), S. 252-262 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract InR 1, if a continuous function has opposite signs at the endpoints of an interval, then the function has a zero in the interval. If the function has a nonvanishing derivative at a zero, then there is an interval such that the function has opposite signs at the endpoints. In this paper each of these results is extended toR n .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580394
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  • 109
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    Fractional programming without differentiability (1976)
    Springer
    Mathematical programming 11 (1976), S. 283-290 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The notion of quasi-differentiability is examined and related to fractional programming. Necessary and sufficient conditions are given and various other properties of quasi-differentiable functions are discussed. Differentiability is not assumed.
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    URL: http://dx.doi.org/10.1007/BF01580396
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  • 110
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    Projections in minimax algebra (1976)
    Springer
    Mathematical programming 10 (1976), S. 111-123 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An axiomatic theory of linear operators can be constructed for abstract spaces defined over (R, ⊕, ⊗), that is over the (extended) real numbersR with the binary operationsx ⊕ y = max (x,y) andx ⊗ y = x + y. Many of the features of conventional linear operator theory can be reproduced in this theory, although the proof techniques are quite different. Specialisation of the theory to spaces ofn-tuples provides techniques for analysing a number of well-known operational research problems, whilst specialisation to function spaces provides a natural formal framework for certain familiar problems of approximation, optimisation and duality.
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    URL: http://dx.doi.org/10.1007/BF01580656
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  • 111
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    Council of the Mathematical Programming Society (1976)
    Springer
    Mathematical programming 10 (1976), S. 137-137 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01580659
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  • 112
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    Editorial policy (1976)
    Springer
    Mathematical programming 10 (1976), S. 144-144 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580663
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  • 113
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    A set of geometric programming test problems and their solutions (1976)
    Springer
    Mathematical programming 10 (1976), S. 192-213 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper attempts to provide a set of standard test examples for researchers working in the area of geometric programming and general nonlinear, continuous, nonconvex programming algorithms. The examples consist partly of applications of nonlinear programming that have appeared in the literature and partly of original geometric programming applications. Solutions to all the problems are provided as well as the starting points from which these solutions were computed. Other computationally important aspects such as tolerances and degree of accuracy with which these problems were solved, are also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580667
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  • 114
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    Analytical solution of A dynamic transaction flow problem (1976)
    Springer
    Mathematical programming 10 (1976), S. 214-229 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We analyze a mathematical programming model of a fractional flow process which consists ofn sectors and all possible time-dependent streams of flow between, into and out of the sectors. Assuming specific constraints on flow, least cost policies are determined for control of the system transactions involved over a given finite time horizon and over an infinite horizon. Several applications of the model are presented and discussed.
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    URL: http://dx.doi.org/10.1007/BF01580668
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  • 115
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    Quadratic duality over convex cone domains (1976)
    Springer
    Mathematical programming 10 (1976), S. 277-283 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580673
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  • 116
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    On A characterization of optimality in convex programming (1976)
    Springer
    Mathematical programming 11 (1976), S. 81-88 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Necessary and sufficient conditions for optimality are given, for convex programming problems, without constraint qualification, in terms of a single mathematical program, which can be chosen to be bilinear.
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    URL: http://dx.doi.org/10.1007/BF01580372
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  • 117
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    A note on polyhedral sets having A least element (1976)
    Springer
    Mathematical programming 11 (1976), S. 94-96 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580374
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  • 118
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    Finding the nearest point in A polytope (1976)
    Springer
    Mathematical programming 11 (1976), S. 128-149 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A terminating algorithm is developed for the problem of finding the point of smallest Euclidean norm in the convex hull of a given finite point set in Euclideann-space, or equivalently for finding an “optimal” hyperplane separating a given point from a given finite point set. Its efficiency and accuracy are investigated, and its extension to the separation of two sets and other convex programming problems described.
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    URL: http://dx.doi.org/10.1007/BF01580381
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  • 119
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    Transversal matroid intersections and related packings (1976)
    Springer
    Mathematical programming 11 (1976), S. 164-176 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Network flow techniques are used to show that a conjecture of Fulkerson on the blocking polyhedron associated with the intersection of two matroids is true for transversal matroids. This leads to some general integral packing results for partial transversals, bipartite edge matchings, and subpermutation matrices. A computational example for bipartite edge matchings is included.
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    URL: http://dx.doi.org/10.1007/BF01580384
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  • 120
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    Editorial policy (1976)
    Springer
    Mathematical programming 11 (1976), S. 201-201 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580389
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  • 121
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    A dual algorithm for the one-machine scheduling problem (1976)
    Springer
    Mathematical programming 11 (1976), S. 229-251 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A branch and bound algorithm is presented for the problem of schedulingn jobs on a single machine to minimize tardiness. The algorithm uses a dual problem to obtain a good feasible solution and an extremely sharp lower bound on the optimal objective value. To derive the dual problem we regard the single machine as imposing a constraint for each time period. A dual variable is associated with each of these constraints and used to form a Lagrangian problem in which the dualized constraints appear in the objective function. A lower bound is obtained by solving the Lagrangian problem with fixed multiplier values. The major theoretical result of the paper is an algorithm which solves the Lagrangian problem in a number of steps proportional to the product ofn 2 and the average job processing time. The search for multiplier values which maximize the lower bound leads to the formulation and optimization of the dual problem. The bounds obtained are so sharp that very little enumeration or computer time is required to solve even large problems. Computational experience with 20-, 30-, and 50-job problems is presented.
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    URL: http://dx.doi.org/10.1007/BF01580393
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  • 122
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    Bottleneck linear programming (1976)
    Springer
    Mathematical programming 11 (1976), S. 291-298 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Bottleneck Linear Programming problem (BLP) is to maximizex 0 = max j c j ,x j 〉 0 subject toAx = b, x ⩾ 0. A relationship between the BLP and a problem solvable by a “greedy” algorithm is established. Two algorithms for the BLP are developed and computational experience is reported.
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    URL: http://dx.doi.org/10.1007/BF01580397
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  • 123
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    Bicentennial conference on Mathematical Programming (1976)
    Springer
    Mathematical programming 10 (1976), S. 284-284 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01580674
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  • 124
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    Editorial policy (1976)
    Springer
    Mathematical programming 10 (1976), S. 286-286 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01580676
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  • 125
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    An algorithm for nonconvex programming problems (1976)
    Springer
    Mathematical programming 10 (1976), S. 312-321 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Branch and bound approaches for nonconvex programming problems had been given in [1] and [4]. Crucial for both are the use of rectangular partitions, convex envelopes and separable nonconvex portions of the objective function and constraints. We want to propose a similar algorithm which solves a sequence of problems in each of which the objective function is convex or even linear. The main difference between this approach and previous approaches is the use of general compact partitions instead of rectangular ones and a different refining rule such that the algorithm does not rely on the concept of convex envelopes and handles non-separable functions. First we describe a general algorithm and prove a convergence theorem under suitable regularity assumptions. Then we give as example an algorithm for concave minimization problems.
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    URL: http://dx.doi.org/10.1007/BF01580678
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  • 126
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    Quasi balanced matrices — An addendum (1976)
    Springer
    Mathematical programming 10 (1976), S. 405-407 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01580685
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  • 127
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    The Mathematical Programming Society (1976)
    Springer
    Mathematical programming 10 (1976), S. 413-413 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01580688
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  • 128
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    Optimal conditioning of self-scaling variable Metric algorithms (1976)
    Springer
    Mathematical programming 10 (1976), S. 70-90 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Variable Metric Methods are “Newton—Raphson-like” algorithms for unconstrained minimization in which the inverse Hessian is replaced by an approximation, inferred from previous gradients and updated at each iteration. During the past decade various approaches have been used to derive general classes of such algorithms having the common properties of being Conjugate Directions methods and having “quadratic termination”. Observed differences in actual performance of such methods motivated recent attempts to identify variable metric algorithms having additional properties that may be significant in practical situations (e.g. nonquadratic functions, inaccurate linesearch, etc.). The SSVM algorithms, introduced by this first author, are such methods that among their other properties, they automatically compensate for poor scaling of the objective function. This paper presents some new theoretical results identifying a subclass of SSVM algorithms that have the additional property of minimizing a sharp bound on the condition number of the inverse Hessian approximation at each iteration. Reducing this condition number is important for decreasing the roundoff error. The theoretical properties of this subclass are explored and two of its special cases are tested numerically in comparison with other SSVM algorithms.
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    URL: http://dx.doi.org/10.1007/BF01580654
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  • 129
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    A cutting plane algorithm for solving bilinear programs (1976)
    Springer
    Mathematical programming 11 (1976), S. 14-27 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper addresses itself to a special class of nonconvex quadratic program referred to as a bilinear program in the literature. We will propose here a cutting plane algorithm to solve this class of problems. The algorithm is along the lines of H. Tui and K. Ritter, but it differs in its exploitation of the special structure of the problem. Though the algorithm is not guaranteed at this stage of the research to converge to a global optimum, the preliminary results of numerical experiments are encouraging.
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    URL: http://dx.doi.org/10.1007/BF01580367
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  • 130
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    Approximate cutting planes in nonlinear programming (1976)
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    Mathematical programming 11 (1976), S. 194-198 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An approximation criterion is presented and a convergence proof is given that allows adaptation of the cutting plane algorithm when it is impractical to compute the exact cutting planes. A source application is briefly described and a class of functions is presented for which such approximate cutting planes can be conveniently computed.
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    URL: http://dx.doi.org/10.1007/BF01580386
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  • 131
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    The Mathematical Programming Society (1976)
    Springer
    Mathematical programming 11 (1976), S. 200-200 
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    URL: http://dx.doi.org/10.1007/BF01580388
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  • 132
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    Errorbounds for simple zeros of λ-matrices (1976)
    Springer
    Computing 16 (1976), S. 17-27 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir beschreiben hier eine Methode, mit der man Fehlerabschätzungen für Eigenwerte und Eigenvektoren von λ-Matrizen erhalten kann. Mit den Ergebnissen aus einer früheren Arbeit des Autors (siehe [11]) wird ein Algorithmus gefunden, der mit wenig Rechenaufwand gute Abschätzungen liefert. Der Algorithmus wird an mehreren Beispielen getestet.
    Notes: Abstract We describe a method for finding errorbounds for eigenvalues und eigenvectors of λ-matrices. Results from an earlier paper by the author (see [11]) are used to find a fast algorithm that produces good errorbounds. The algorithm is tested on several examples.
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    URL: http://dx.doi.org/10.1007/BF02241976
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  • 133
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    A-stability of Runge-Kutta methods with single and multiple nodes (1976)
    Springer
    Computing 16 (1976), S. 39-48 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Vermutung von Ehle [5], daß gewisse Klassen von Runge-Kutta-Methoden A-stabil sind, wird bewiesen. Danach werden implizite RK-Methoden mit mehrfachen Knoten („multiderivative methods” [7]) betrachtet, die den Vorteil haben, daß für höhere Ordnung das zu lösende implizite System von wesentlich geringerer Dimension ist. Es wird gezeigt, daß diese Methoden, falls sie auf Gaußscher (Turanscher) Quadratur beruhen, nur A(α)-stabil (α〈π/2) sind. Daher werden anschließend Methoden bestimmt, die auf Lobatto-Quadratur (mit mehrfachen Knoten) basieren und die sich als A-stabil erweisen; ihre Koeffizienten werden angegeben (bis zur Ordnung 22).
    Notes: Abstract This paper gives the proofs of the conjectures of Ehle [5] concerning the A-stability of classes of implicit Runge-Kutta methods. Next the attention is turned to implicit RK methods with multiple nodes (“multiderivative methods” [7]), which have the advantage that, for higher orders, the implicit system to be solved has much lower dimension. These methods, if based on Gaussian (Turan) quadrature, are shown to be A(α)-stable (α〈π/2) only. Thus, in this paper, methods based on Lobatto quadrature (with multiple nodes) are constructed, which turn out to be A-stable. The coefficients are tabulated up to order 22.
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  • 134
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    Numerical solution of the singular Ginzburg-Landau equations by multiple shooting (1976)
    Springer
    Computing 16 (1976), S. 61-67 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine handliche Methode zur Lösung singulärer Randwertprobleme gewöhnlicher Differentialgleichungen behandelt. Taylorreihenentwicklungen des Systems in einem kleinen Intervall blenden die Singularität aus, so daß die Aufgabe mit der Mehrzielmethode gelöst werden kann. Die Zuverlässigkeit dieses Verfahrens wird bei der Lösung der Ginzburg-Landau-Gleichungen der Supraleitung nachgewiesen.
    Notes: Abstract A useful method for the numerical solution of singular two-point boundary value problems by multiple shooting techniques is treated. In a small interval Taylor series expansions are used in orderto kill the numerical singularity. The reliability of the method is demonstrated by solving the Ginzburg-Landau equations arising in the theory of superconductivity.
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  • 135
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    An algorithm of optimization for a special class of networks (1976)
    Springer
    Computing 16 (1976), S. 77-97 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird ein Optimierungsalgorithmus für nichtmarkowsche Netze dargestellt. Es wird die Definition des betrachteten Netzes gegeben und ein Optimierungsproblem formuliert. Es werden das allgemeine Konzept und dann das Ablaufschema des Algorithmus dargestellt. Die Realisierung des Algorithmus wird an einem einfachen Beispiel erklärt. Es werden auch die Möglichkeiten der Anwendung des Verfahrens für Allokationsprobleme und für nichtlineare Programmierung erwähnt. Das Programm ist in FORTRAN IV geschrieben. Es ermöglicht die Realisierung des Verfahrens auf einer EDV-Anlage.
    Notes: Abstract In this paper the author presents an algorithm of optimization for a special class of networks not having the Markov property. A definition of the class of networks under consideration and a formulation of the optimization problem are given. A conception of the algorithm is discussed and next the general and detailed flow diagrams of the algorithm are offered. The realization of the algorithm is illustrated with a simple example showing the process of execution of the tasks included in the algorithm. Some possibilities of applying the algorithm in allocation problems and nonlinear integer programming are presented. The computer program in FORTRAN IV for the execution of the algorithm is enclosed.
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    The secand method in banach spaces (1976)
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    Computing 16 (1976), S. 201-209 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Iterationsverfahren zur Bestimmung von Nullstellen nichtlinearer Operatoren in Banach-Räumen behandelt, die mit Steigungen erster Ordnung arbeiten. Zur Berechnung der Steigungen werden die Punkte auf einer Kugel beliebig gewählt.
    Notes: Abstract The paper concerns to solutions of the operator equationf(x)=0. Using the quotient operator the equation is solved with the iteration method. Points from a given sphere are arbitrarily chosen for quotients creating.
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    Approximation von stochastischen Differentialgleichungen auf Digital- und Hybridrechnern (1976)
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    Computing 16 (1976), S. 359-371 
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    Topics: Computer Science
    Description / Table of Contents: Abstract Continuous dynamical systems which are subject to random disturbances can often be represented by stochastic differential equations of the Itô-type. We discuss methods how to approximate the solution of such equations on digital and hybrid computers. The digital methods are stochastic versions of some simple deterministic methods. We give convergence theorems which show that stochastic methods differ in principle from their corresponding deterministic methods.
    Notes: Zusammenfassung Kontinuierliche dynamische Systeme, die zufälligen Störungen unterworfen werden, lassen sich oft als stochastische Differentialgleichungen vom Itô-Typ darstellen. Wir untersuchen Methoden, durch die die Lösung solcher Gleichungen auf Digital- und Hybridrechnern angenähert werden kann. Die digitalen Verfahren sind stochastische Versionen von einfachen deterministischen Verfahren. Konvergenzsätze zeigen, daß sich stochastische Verfahren prinzipiell von den entsprechenden deterministischen unterscheiden.
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    Untersuchungen des Zeitgewinns durch neue Algorithmen zur Matrix-Multiplikation (1976)
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    Computing 17 (1976), S. 23-36 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract This papers gives a survey of possible speed-ups of matrix-multiplication by the methods due to S. Winograd and V. Straßen. Questions of implementation of the algorithms are investigated and formulas for the required additional core-memory are given. By using a machine model which is similar to existing computers the results given are of practical importance.
    Notes: Zusammenfassung Diese Arbeit soll eine Übersicht über den möglichen Zeitgewinn geben, der durch den Einsatz der schnelleren Matrix-Multiplikationen von S. Winograd und V. Straßen erzielbar ist. Implementierungsfragen werden besprochen und der benötigte Zusatzspeicher wird ermittelt. Die Abschätzungen beruhen auf einem Rechner-Modell, welches den heutigen Rechenanlagen nachgebildet ist, und liefern daher realistische Ergebnisse.
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    Über Verfahren zur zweiseitigen Approximation inverser Elemente (1976)
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    Computing 17 (1976), S. 59-67 
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    Description / Table of Contents: Abstract In a partially ordered ring, a set of iterative methods is constructed in order to approximate the inverse of a given element, not necessarily positive or inverse-positive. Two sequences are generated both converging to the inverse. In addition the inverse is monotonously enclosed. The method of order four has the maximal efficiency index.
    Notes: Zusammenfassung Anknüpfend an Arbeiten von G. Alefeld und J. Herzberger und von J. W. Schmidt werden in einem halbgeordneten RingR Iterationsverfahren untersucht, welche geeignet sind, die Inverse eines nicht notwendig positiven oder inverspositiven Elementesa∈R zu approximieren. Es werden jeweils zwei Folgen (X n ) und (y n ) konstruiert, welche beide gegen die Inversea −1 konvergieren und diese zusätzlich im Sinne vonX n−1 ≦X n ≦a −1 ≦y n ≦y n−1 monoton einschließen. Von den betrachteten Verfahren hat das vierter Ordnung den größten Effektivitätsindex.
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    A method for calculating the reciprocal coefficients of function matrices (1976)
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    Computing 16 (1976), S. 29-37 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine allgemeine Methode für die Berechnung der reziproken Reihen zu einer gegebenen Potenzreihe mit Matrizenkoeffizienten vorgeschlagen. Eine ihrer Anwendungen ist für die Inversion einer Matrix, deren Elemente rationale Funktionen sind.
    Notes: Abstract A general method is proposed for calculating the reciprocal series of a given series with matrix coefficients. An application is to the inversion of matrices with entries in the form of rational functions.
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    Monotone switching circuits and boolean matrix product (1976)
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    Computing 16 (1976), S. 99-111 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir untersuchen den Effekt lokaler Änderungen auf das Eingabe/Ausgabe-Verhalten monotoner Netzwerke. Wir wenden die Ergebnisse auf die Multiplikation Boolescher Matrizen an und zeigen, daß die Schulmethode für die Matrizenmultiplikation den alleinigen optimalen Schaltkreis liefert.
    Notes: Abstract We explore the concept of local transformations of monotone switching circuits, i.e. what kind of local changes in a network leave the input/output behavior invariant. We obtain several general theorems in this direction. We apply these results to boolean matrix product and prove that the school-method for matrix multiplication yields the unique monotone circuit.
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    Algorithmus 27 Ein neuer Algorithmus zur Bestimmung vonk-kürzesten Wegen in einem Graphen (1976)
    Springer
    Computing 16 (1976), S. 139-151 
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    Topics: Computer Science
    Description / Table of Contents: Abstract The following algorithm for finding thek-shortest loopless paths from one node to another is a development of the algorithm published in [2]. Though memory need is less, the new algorithm is running is bout 20 times as fast on large networks (1000 nodes and more). The computer time increases linearly withk and about quadratic with the number of nodes on the generated paths.
    Notes: Zusammenfassung Der in der vorliegenden Arbeit vorgestellte Algorithmus zur Ermittlung vonk-kürzesten schleifenfreien Kantenfolgen von einem Anfangsknoten zu einem Endknoten stellt eine Weiterentwicklung des in [2] beschriebenen Verfahrens dar. Bei deutlich geringerem Speicherplatzbedarf konnte die Rechengeschwindigkeit stark gesteigert werden (bei Graphen von 1000 Knoten ungefähr um das 20fache). Die Rechenzeit wächst linear mitk und in etwa quadratisch mit der Knotenzahl der erzeugten Wege.
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    Buchbesprechungen (1976)
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    Computing 16 (1976), S. 169-185 
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    Monotone Einschließung von Inversen positiver Elemente durch Verfahren vom Schulz-Typ (1976)
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    Computing 16 (1976), S. 211-219 
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    Description / Table of Contents: Abstract The conditional iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n−1 =inf (y n ,x n +y n (e−ax n )) generating sequences (x n ) and (y n ) is considered in partially ordered spaces. Under certain conditions it is shown, that the inversea −1 of a positive elementa≧0 is monotonously enclosed in the sensex n ≦x n+1 ≦a −1 ≦y n+1 ≦y n and that (x n ) and (y n ) converge toa −1 quadratically.
    Notes: Zusammenfassung Es wird gezeigt, daß die bedingte Iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n+1 =inf (y n ,x n +y n (e−ax n )) unter bestimmten Voraussetzungen die Inversea −1 eines positiven Elementsa≧0 gemäßx n ≦x n+1 ≦a −1 ≦y n+1 ≦y n monoton einschließt und daß die Folgen (x n ) und (y n ) quadratisch gegena −1 konvergieren.
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    Boundary flux estimates for elliptic problems by the perturbed variational method (1976)
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    Computing 16 (1976), S. 339-347 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird gezeigt, daß man scharfe Schranken für die Normalableitung durch die Anwendung eines Extrapolationsprozesses im gestörten Variationsprinzip erhalten kann. QuasioptimaleL 2-Schranken für den Fehler werden angegeben, sowie numerische Resultate in einem Modellproblem.
    Notes: Abstract In this note we show that high order accurate approximations to the boundary flux are readily obtained by use of certain extrapolation process in the perturbed variational principle. QuasioptimalL 2 estimates for the error are obtained. Numerical results are presented for a model problem.
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    On an approach to the automatic evaluation of the subjects' verbal behavior in Roemer's inkblot tests (1976)
    Springer
    Computing 16 (1976), S. 373-378 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Roemer, ein Mitarbeiter von Roschach, entwickelte eine „Symboltestserie”, die als eine der projektiven Methoden bei psycho-diagnostischen Tests verwendet wird. (Fragen nach der Verläßlichkeit solcher Methoden stehen hier nicht zur Debatte.) Ein in der Entwicklung stehendes, lernendes Programm wird beschrieben, das Versuchspersonen auf Grund ihres verbalen Verhaltens klassifizieren könnte. Wird das vom Computer gelieferte Persönlichkeitsprofil mit der Diagnose des Psychologen, die als „objektive Wahrheit” angenommen wird, verglichen, so läßt sich seine Qualität laufend verbessern.
    Notes: Abstract Roemer, a collaborator of Rorschach's, devised a “symbol test series” that is used as one of the projective methods of psychodiagnostic testing. We refrain from getting involved in the controversy related to the reliability of such technique. A learning program under development is described that would be able to classify the subjects on the basis of their verbal behavior. By comparing the diagnosis of the psychologist, accepted as “objective truth”, with the profile provided by the computer, the quality of the latter can be made to improve continuously.
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    Ein intergriertes Hardware-Software-System zur Steuerung der Ein/Ausgabe (1976)
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    Computing 17 (1976), S. 1-21 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The input/output components in contemporary operating systems are frequently “grown” parts which have individually and specifiquely been designed and amended in the course of new technical developments. However, a rigid analysis reveals the possibility for a unique control system which is mainly built upon the means for interprocess communication. The system is easily continuated into the technical elements. Also, inhomogeneities within the peripheral attachment scheme as well as unconventional service strategies are smoothly incorporated.
    Notes: Zusammenfassung In heutigen realen Betriebssystemen sind die Ein/Ausgabekomponenten häufig „gewachsene” Teile, die im Zuge neuer technischer Ausbauten individuell und spezifisch entworfen und aufgenommen wurden. Bei genauer Analyse ergibt sich die Möglichkeit, ein einheitliches Steuerungssystem zu entwerfen, das im wesentlichen auf die Interprozeßkommunikationsmittel zurückgreift. Dieses System setzt sich zwanglos in die technischen Elemente hinein fort. Es zeigt sich, daß auch Inhomogenitäten im Anschlußschema und besondere Abfertigungsstrategien leicht zu berücksichtigen sind.
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    On the numerical solution of some algebraic integral equations (1976)
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    Computing 17 (1976), S. 69-77 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir behandeln die numerische Lösung einiger algebraischer Integralgleichungen und Integralgleichungen vom Lichtenstein-Typ mit Hilfe einer Variationsmethode und unter Verwendung des Unterraumes derL-Splinefunktionen. Für diese Näherungslösungen werden die Beweise der Existenz, Eindeutigkeit und Konvergenz sowie Fehlerabschätzungen gegeben.
    Notes: Abstract We discuss the numerical solution of some algebraic integral equations and integral equations of Lichtenstein type by means of a variational method and by using the subspace ofL-splines. For these approximate solutions the proofs of existence, uniqueness, and convergence as well as error estimates are given.
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    Parameterdarstellung kubischer und bikubischer Splines (1976)
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    Computing 17 (1976), S. 87-92 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The known representation of curves and surfaces by P. Bezier is applied to cubic and bicubic splines. In this form spline-conditions are particularly vivid and along easily manageable. A parametric representation naturally connected with spline-conditions allows moreover a most simple and clear correction of splines and bisplines.
    Notes: Zusammenfassung Die bekannte Darstellung von Kurven und Flächen nach Pierre Bezier wird auf kubische und bikubische Splines angewendet. In dieser Darstellung sind die Spline-Bedingungen besonders anschaulich und daher leicht zu handhaben. Eine mit den Spline-Bedingungen auf natürliche Weise verbundene Parameterdarstellung gestattet außerdem eine höchst einfache und übersichtliche Korrektur der Splines und Bisplines.
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    On maximally distant spanning trees of a graph (1976)
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    Computing 17 (1976), S. 115-119 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eine Menge vonk Gerüsten eines GraphenG heißtmaximal entfernt, falls ihre Vereinigung eine maximale Anzahl von Kanten des Graphen enthält. Es wird eine notwendige und hinreichende Bedingung angegeben, die gewährleistet, daß eine Menge von Gerüsten maximal entfernt ist. Dann wird ein effizienter Algorithmus beschrieben, der in einem gegebenen Graphenk maximal entfernte Gerüste findet.
    Notes: Abstract A set ofk spanning trees of a graphG is calledmaximally distant if their union contains the maximum number of edges ofG. We present a necessary and sufficient condition for a set of spanning trees to be maximally distant. We also give an efficient algorithm which actually findsk maximally distant spanning trees in a given graph.
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    Numerische Erfahrungen bei der Lösung des dreidimensionalen Transportproblems (1976)
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    Computing 17 (1976), S. 129-145 
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    Topics: Computer Science
    Description / Table of Contents: Abstract To find an initial basic feasible solution is a special problem on solving the three dimensional transportation problem. It is not possible to do this work in a similar simple way as it can be done in the usual transportation problem. In [3] Haley proposes to solve a new problem that is essentionally the old one with the addition of a set of artificial variables. However, numerical investigations have shown that this procedure enlarges the amount of computing very much. This paper now gives another procedure for finding an initial basic solution for the three dimensional transportation problem. A great number of examples is discussed which demonstrate the efficiency of this procedure.
    Notes: Zusammenfassung Bei der Lösung eines dreidimensionalen Transportproblems bereitet die Ermittlung einer ersten zulässigen Basislösung Schwierigkeiten, da man nicht mehr so einfach vorgehen kann wie beim gewöhnlichen Transportproblem. In [3] schlägt Haley vor, hierfür ein geeignetes Hilfsproblem zu lösen, das ebenfalls die Form eines dreidimensionalen Transportproblems hat. Nuemrische Untersuchungen haben aber gezeigt, daß dieses Vorgehen einen hohen Rechenaufwand erfordert. In dieser Arbeit wird deshalb eine Alternative zur Ermittlung einer ersten zulässigen Basislösung beim dreidimensionalen Transportproblem angegeben und anhand zahlreicher durchgerechneter Beispiele die größere Effizienz dieses Verfahrens aufgezeigt.
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    Sampling from the poisson distribution on a computer (1976)
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    Computing 17 (1976), S. 147-156 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit beschreibt eine Methode zur Erzeugung von Poissonverteilten Zufallszahlen mit einem Computer, die schneller zu sein scheint als eine in [1] angegebene Methode. Die empfohlene Methode beruht für nichtganzzahlige μ〈7 auf einem konventionellen Suchalgorithmus nach Verwendung der Umkehrtransformation, für ganzzahlige μ auf einer Modifikation davon, wobei die Suche beim Modus beginnt und auf einer Kombination dieser beiden Methoden für nichtganzzahlige μ〉7. Für große μ ist die Rechenzeit proportional zu $$\sqrt \mu $$ . In der Arbeit wird auch gezeigt, daß für μ≥15 bei Verwendung von max (0, [μ + $$Y\sqrt \mu $$ + 0.5]), wobeiY nachN(0, 1) verteilt ist, derselbe Fehler auftritt. Da die Rechenzeit fürY eine Konstante ist, liefert diese Methode eine obere Schranke für die Rechenzeit zur Erzeugung nach Poisson verteilter Zufallszahlen.
    Notes: Abstract This paper describes a method of sampling from the Poisson distribution on a computer that appears to be less costly than a recently suggested method in [1]. The proposed method relies on a conventional search using the inverse transform approach for nonintegral μ〈7, on a modification of the inverse transform approach that begins the search at the mode for integral μ, and on a combination of these two approaches for nonintegral μ〉7. For large μ the sampling cost is proportional to μ1/2. The paper also shows that for μ≥15 an incidental error occurs by using max (0, [μ+Yμ1/2+0.5]) whereY is fromN(0,1). Since the sampling cost ofY is a constant, this approach places an upper bound on the cost of generating a Poisson variate.
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    An integral equation method for the numerical calculation of ion drift and diffusion in evaporated dielectrics (1976)
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    Computing 17 (1976), S. 169-176 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Methode vorgelegt, um die partielle Differentialgleichung für einen zeitabhängigen Strömungs-Diffusionsprozeß in einem eindimensionalen endlichen Raum zu lösen. Die Methode beruht auf einer Integralgleichungstechnik, die leicht mit Hilfe von Ziffernrechenanlagen durchgeführt werden kann. Die Technik wurde dazu verwendet, den Transport von beweglichen Ionen in evakuierten Dielectrica unter dem Einfluß eines elektrischen Feldes zu studieren.
    Notes: Abstract A method is presented to solve the partial differential equation for a time dependent drift — diffusion process in a one dimensional finite space. The method is based on an integral equation technique, which is easily solved numerically on a digital computer. This technique has been used to study the transport phenomenon of mobile ions in evaporated dielectrics under influence of an electric field.
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    Zur numerischen Behandlung inkorrekt gestellter aufgaben (1976)
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    Computing 17 (1976), S. 193-206 
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    Topics: Computer Science
    Description / Table of Contents: Abstract For the numerical solution of improperly posed problems a regularization by linear inqualities is proposed. In order to avoid difficulties with ill-conditioned matrices, the problem is solved by computing certain correct functionals and by singular value decomposition of the matrices.
    Notes: Zusammenfassung Zur numerischen Behandlung von inkorrekt gestellten Problemen wird eine Regularisierung durch Ungleichungen vorgeschlagen. Schweirigkeiten mit schlecht konditionierten Matrizen kann man durch Zurückführen des Problems auf die Berechnung von geeigneten korrekten Funktionalen und durch Zerlegung der Matrizen nach singulären Werten vermeiden.
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    Zur Diskretisierung quasilinearer elliptischer Differentialgleichungen vierter Ordnung (1976)
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    Computing 17 (1976), S. 231-246 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Abstrakt The present paper is concerned with the numerical solution of quasilinear elliptic differential equations of the fourth order by the method of finite differences. A discrete analogue of the corresponding variational problem is constructed. Existence and uniqueness of the solution of the discrete problem and, in connection with the convergence to the exact solution, consistence and stability are treated.
    Notes: Zusammenfassung Quasilineare elliptische Differentialgleichungen vierter Ordnung werden numerisch behandelt mit dem Differenzenverfahren, indem das zugehörige Variationsproblem diskretisiert wird. Existenz und Eindeutigkeit der diskreten Lösung und Konvergenz dieser gegen die exakte Lösung werden bewiesen. In diesem Zusammenhang werden Untersuchungen über Konsistenz und Stabilität angestellt.
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    Zum Fettsäuremuster der Serumlipide (1976)
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    European journal of nutrition 15 (1976), S. 305-310 
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    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The standard distribution of the fatty acids in the total lipids of serum was gaschromatographically defined in the respective umbilical cord blood of 24 mothers and their newborn babies, as well as in 20 placentas. The same examinations were made with 30 newborn babies on the day of birth, 14 children in the newborn stage, 22 young babies between 3 and 10 weeks old and 16 older babies between 4 and 12 months old. In the umbilical cord mixed blood of another collective (n=10) the separation of the total serum lipids in the individual fatty fractions (neutral lipids, phospholipids, cholesterol esters) was also undertaken. The results were compared and existing differences were discussed. It was further established that an advance towards the adult's fatty acid pattern already takes place at an age between 4 and 12 months.
    Notes: Zusammenfassung Bei 24 Gebärenden, dem zugehörigen Nabelschnurmischblut der Neugeborenen und 20 Plazenten wurde die Normverteilung der Fettsäuren in den Gesamtlipiden des Serums gaschromatographisch bestimmt. Die gleichen Untersuchungen wurden an 30 Neugeborenen am 1. Lebenstag, 14 Kindern im Neugeborenenalter, 22 jungen Säuglingen zwischen 3 und 10 Wochen alt und 16 älteren Säuglingen zwischen 4 und 12 Monaten alt durchgeführt. Außerdem wurde im Nabelschnurmischblut eines anderen Kollektivs (n=10) die Auftrennung der Serumgesamtlipide in die einzelnen Fettfraktionen (Neutralfett, Phosphatide, Cholesterinester) vorgenommen. Die gewonnenen Ergebnisse wurden miteinander verglichen und bestehende Unterschiede diskutiert. Es wurde außerdem festgestellt, daß eine Annäherung an das Fettsäuremuster des Erwachsenen schon im Alter von 4 bis 12 Monaten stattfindet.
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    Buchbesprechungen (1976)
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    European journal of nutrition 15 (1976), S. 313-326 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    Intestinal absorption of iron alone and in combination with authentic or natural vitamin C and carotene (1976)
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    European journal of nutrition 15 (1976), S. 327-332 
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    ISSN: 1436-6215
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Es wurde die Wirkungsweise von echtem bzw. natürlichem Vitamin C und Carotin auf die Eisenresorption im Darm untersucht. Vitamin C bewirkte eine leichte Steigerung der Eisenresorption, während Carotin diese behinderte. Orangen-, Petersilien- und Pfeffersaft, sämtlich reich an beiden Vitaminen, behinderten in verschiedenem Maße die Eisenresorption im Darm. Es wird daher empfohlen, Patienten mit Eisenmangel nicht mit carotinreicher Nahrung zu versorgen, besonders nicht während der Eisentherapie.
    Notes: Summary The effect of vitamin C and carotene derived from authentic or natural sources on intestinal iron absorption was studied. Vitamin C caused slight enhancement to iron absorption, while carotene hindered it. The three juices tested, namely orange, parsley and pepper, which were found to be rich in these two vitamins, hindered intestinal iron absorption to different extents. It was recommended that patients suffering from iron deficiency are not supplied with nutrients rich in carotene particulary during iron therapy.
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    Die Lupine, ein Beitrag zur Nahrungsversorgung in den Anden 4. Die Akzeptabilität des Mehles von Lupinus albus (1976)
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    European journal of nutrition 15 (1976), S. 396-402 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary 48 different dishes enriched withlupinus albus flour have been tested by 20 persons. The test duration has been 4 weeks. Meals and products with lupine admixtures have been judged equally with concern to corresponding conventional dishes. Farinaceous products had the best test results. Therefore, it is recommended for Peru to add lupine flour when producing bread, biscuits, sauces, soups, and noodles (maccaronis etc.). The test time had no influence to the test results.
    Notes: Zusammenfassung 20 Prüfpersonen beurteilten über vier Wochen 48 verschiedene Speisen, die mit dem Mehl vonLupinus albus angereichert wurden. Die Speisen und Produkte mit Lupinenzusatz wurden mit der korrespondierenden konventionellen Speise geschmacklich gleich bewertet. Besonders günstig liegen die Teigwaren in der Beurteilung. Es empfiehlt sich zukünftig in Peru, einen Lupinenzusatz in Brot, Kekse, Soßen, Suppen und Nudeln einzuarbeiten. Ein zeitlicher Einfluß auf die Beurteilung fand nicht statt.
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    Buchbesprechungen (1976)
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    European journal of nutrition 15 (1976), S. 403-405 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    Mitteilungen (1976)
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    European journal of nutrition 15 (1976), S. 406-406 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    Die Lupine, ein Beitrag zur Nahrungsversorgung in den Anden 3. Ernährungsphysiologische Untersuchung mit dem Mehl der Süßlupine (Lupinus albus) (1976)
    Springer
    European journal of nutrition 15 (1976), S. 391-395 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary Lupinus albus flour doses of 58.9±9.6 g have been given to 20 persons. This sweet lupine flour has been digestible without complications in all cases. There have been no significant changes of hemoglobine, hematocrite, total protein, urea, bilirubine, and SGOT in the blood. So the lupine may be used for improvement of protein supply in men under the criteria that (1) the alkaloid content of the seed does not exceed 0.02%, (2) the seed itself contains no secondary fungi which may cause a lupinosis.
    Notes: Zusammenfassung 20 Personen erhielten über vier Wochen 58,9±9,6 g Mehl vonLupinus albus. Alle Personen vertrugen das Süßlupinenmehl gut. Es konnten keine nennenswerten Veränderungen von Hämoglobin, Hämatokrit, Gesamtprotein, Harnstoff, Bilirubin und SGOT im Blut festgestellt werden. Die Lupine kann mit zur Eiweißversorgung in der menschlichen Ernährung beitragen, wenn sichergestellt ist, daß 1. der Alkaloidgehalt im Samen nicht über 0,02 % liegt und 2. der Samen frei von Sekundärpilzen ist, die eine Lupinose bewirken können.
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    Ein Distributivitätskriterium für Verbände (1976)
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    Monatshefte für Mathematik 81 (1976), S. 1-3 
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    Notes: Abstract Those one-place functions on a latticeL with values inL which can be obtained from the identityx and the constant functions by means of the fundamental operations ofL in a finite number of steps are called one-place polynomial functions. —It is shown that a latticeL is distributive iff all its one-place polynomial functions can be represented by words such that in every word the indeterminatex occurs at most once.
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    Just two total graphs are complementary (1976)
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    Monatshefte für Mathematik 81 (1976), S. 5-13 
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    Notes: Abstract It is proved that there are just two non-trivial total graphs which are complementary, namely the triangle and its complement.
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    Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 15-40 
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    Notes: Abstract In this paper we study the class $$\mathfrak{A}$$ of all locally compact groupsG with the property that for each closed subgroupH ofG there exists a pair of homomorphisms into a compact group withH as coincidence set, and the class $$\mathfrak{D}$$ of all locally compact groupG with the property that finite dimensional unitary representations of subgroups ofG can be extended to finite dimensional representations ofG. It is shown that [MOORE]-groups (every irreducible unitary representation is finite dimensional) have these two properties. A solvable group in $$\mathfrak{D}$$ is a [MOORE]-group. Moreover, we prove a structure theorem for Lie groups in the class [MOORE], and show that compactly generated Lie groups in [MOORE] have faithful finite dimensional unitary representations.
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    Euler-Summierbarkeit konform-äquivalenter Reihen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 63-68 
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    Notes: Abstract Let Φ be a conformal one to one mapping of the unit disc with Φ (1)=1. Given the convergent series Σa n putf(z):=Σa n zn, |z|〈1, and leta n (Φ) be defined by the relation $$f(\Phi (w)) = \sum\limits_{n = 0}^\infty {a_n } (\Phi )w^n ,\left| w \right|〈 1.$$ The series Σa n (Φ) is called the conformal equivalent of Σa n with respect to Φ and need not converge as was discovered byTurán. We prove that it is nevertheless summable (E;q),q〉0.
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    Approximation properties of Jacobi's algorithm (1976)
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    Monatshefte für Mathematik 81 (1976), S. 59-61 
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    Notes: Abstract The paper improves a previous result which is a generalization of Hurwitz' theorem for Jacobi's algorithm.
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    Kurepa's Hypothesis and a problem of Ulam on families of measures (1976)
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    Monatshefte für Mathematik 81 (1976), S. 41-57 
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    Notes: Abstract We prove that if Kurepa's Hypothesis holds, then on a set of cardinality ℵ1, there does not exist a family of ℵ1 non-trivial measures such that each subset is measurable with respect to at least one of them. We also strengthen a theorem ofErdös andAlaoglu on the non-existence of enumerable families of measures.
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    Die algebraischen Konoide mit ebener Striktionslinie (1976)
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    Monatshefte für Mathematik 81 (1976), S. 69-81 
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    Notes: Abstract Among the algebraic ruled surfaces a theorem ofH. Brauner characterizes certain helicoids of projective screw motions by the property to possess continuous sets of plane shadow curves. Making use of this theorem all algebraic conoids with a plane striction curve are determined in euclidean 3-space and some properties of these curves are discussed.
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    Buchbesprechungen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 83-88 
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    On the lower Markov spectrum (1976)
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    Monatshefte für Mathematik 81 (1976), S. 95-107 
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    Notes: Abstract C. Hightower found two infinite sequences of gaps in the Markov spectrum, (α n , β n ) and (γ n , δ n ) with β n and γ n both Markov elements, converging to $$1 + \sqrt 5 $$ . This paper exhibits Markov elements α n * and δ n * such that, for alln ⩾ 1, (α n * , β n ) and (γ n δ n * ) are gaps in the Markov spectrum. Other results include showing that, for alln ⩾ 1, β n is completely isolated, while the other endpoints of the gaps are limit points in the Markov spectrum.
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    A note on log (f(z)/z) forf inS (1976)
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    Monatshefte für Mathematik 81 (1976), S. 89-93 
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    Notes: Abstract We prove that forf a normalized schlicht function in the disk the boundary values of log |f(z)/z| satisfy a growth condition on subarcs of the unit circle Г.
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    Zum Einbettungsproblem für Markoff-Prozesse (1976)
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    Monatshefte für Mathematik 81 (1976), S. 119-129 
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    Notes: Abstract Every elementary Markov process with a polish state space and with a discrete set of time parameter dense in ℝ+, whose finite dimensional distributions are derived from a semigroup (K t) of Markov kernels continuous in 0 ∈ ℝ+ and whose initial distribution μ satisfies μK t≪μ, can be imbedded in an elementary Markov process with the same state space and with parameter set ℝ+ so that the corresponding finite dimensional distributions are equal.
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    Die Polynomlösungen spezieller partieller Differentialgleichungen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 109-117 
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    Notes: Abstract One of the main problems in the theory of orthogonal polynomials in several variables is the determination of partial differential equations which have the given polynomials as their solutions. In this note, we consider partial differential equations which are two-dimensional generalizations of the classical differential equation for the Chebyshev polynomials in one variable and we will give conditions for its polynomial solutions. In addition, we will be able to determine all polynomials of a given class which are solutions of the partial differential equation under consideration. In the last section, we establish a connection between the different polynomial solutions.
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    Zur Möbiusgeometrie der Kurventheorie (1976)
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    Monatshefte für Mathematik 81 (1976), S. 141-148 
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    Notes: Abstract Using the derivational formulas for stripes we derive in section 1 the derivational formulas for spacecurves in three-dimensional conformal spaceM 3. With a curve we associate locally a one-parameter family of so calledQ 4-surfaces having contact of order 5. AQ 4-surface is generated by two special parabolic pencils of spheres. We investigate alsoQ 4-surfaces having contact of orderk(k=7,8). Section 2 deals with isogonal-trajectories on the surface of the principal circles of the given spacecurve. We avoid invariant parameters as used in projective geometry for getting results of conformal geometry.
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    Prime ideal decomposition in $$F({}^m\sqrt \mu )$$ (1976)
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    Monatshefte für Mathematik 81 (1976), S. 131-139 
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    Notes: Abstract LetF be an algebraic number field and μ∈F such thatx m−μ is irreducible, wherem is an integer. Let $$\mathfrak{p}$$ be a prime ideal inF with $$N (\mathfrak{p}) = pf$$ . The prime decomposition of $$\mathfrak{p}$$ in $$F({}^m\sqrt \mu )$$ is explicitly obtained in the following cases. Case 1: $$\mu \mathop \equiv \limits^8 0 (\bmod \mathfrak{p}^a )$$ , (a,m) = 1 (where $$\mu \mathop \equiv \limits^8 0 (\bmod \mathfrak{p}^a )$$ means $$\mu \equiv 0 (\bmod \mathfrak{p}^a )$$ ,ς ≢ 0 $$(\bmod \mathfrak{p}^a + 1)$$ ). Case 2:m ≡lt, wherel is a prime andl ≢ 0 $$(\bmod \mathfrak{p})$$ . Case 3:m ≢ 0 $$(\bmod \mathfrak{p})$$ and every prime that dividesm also dividespf−1. It is not assumed that thev th roots of unity are inF for anyv ≠ 2.
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    The bilinear field of values (1976)
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    Monatshefte für Mathematik 81 (1976), S. 153-167 
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    Notes: Abstract A complete characterization is given of a bilinear field of values involving orthonormal sets of vectors.
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    On Mercer's theorem for (C,2)-means (1976)
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    Monatshefte für Mathematik 81 (1976), S. 149-152 
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    Notes: Abstract A direct proof is given for the following theorem, contained as a special case in a more general result ofPolniakowski:Theorem. Denote σ n the Cesaro-means of order 2 of the sequenceS 1, S2, ... ,α any real number satisfying 0〈α〈=1. Then $$\mathop { \lim }\limits_{n \to \infty } (\alpha S_n + ((1 - \alpha )\sigma _n ) = S$$ implies $$\mathop { \lim }\limits_{n \to \infty } S_n = S$$
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    Buchbesprechungen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 169-176 
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    Near integral domains on nonabelian groups (1976)
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    Monatshefte für Mathematik 81 (1976), S. 177-183 
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    Notes: Abstract In this paper the concept of a special automorphism is introduced and used to analyze near integral domains having nonabelian addtive groups. We show that there are finite and infinite near integral domains having additive groups with arbitrary class of nilpotency. We also give another example of a non-nilpotent group which is the additive group of a near integral domain. Finally, nonabelian groups of order less than 1000 are examined to determine which can be the additive group of a near integral domain.
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    Limit circle results for second order equations (1976)
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    Monatshefte für Mathematik 81 (1976), S. 185-194 
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    Notes: Abstract It is known that for second order linear equations the assumption of limit circle (all solutions being square integrable) is not sufficient to imply boundedness of solutions. We investigate what additional hypotheses are needed to insure that all solutions are bounded. Also, we prove certain limit circle results using Liapunov functions.
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    The fractional parts of a sum of polynomials (1976)
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    Monatshefte für Mathematik 81 (1976), S. 195-202 
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    Notes: Abstract LetX=(x 1,...,x s ) be a vector ofs real components and $$f(X) = \sum\limits_{j = 1}^8 {Pj(xj)} $$ , whereP j (x j ) are polynomials of exact degree k with real coefficients and without constant terms. The authors extend a result of Davenport and obtain an approximation on ‖f(X)‖ where ‖t‖ means the distance fromt to the nearest integer.
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    Über die Lösungsanzahl der Gleichungf(n)=ϰ·n für gewisse Klassen multiplikativer Funktionen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 213-216 
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    Notes: Abstract Denote byV æ (f,x) the number of solutionsn≦x of the equationf(n)=æ·n. Then there are multiplicative functions , such that the lower estimate holds for infinitely many pairs (æ,x),x→∞.
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    The expected number of parts in a partition ofn (1976)
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    Monatshefte für Mathematik 81 (1976), S. 203-212 
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    Notes: Abstract Forn a positive integer letp(n) denote the number of partitions ofn into positive integers and letp(n,k) denote the number of partitions ofn into exactlyk parts. Let $$P(n) = \sum\limits_{k = 1}^\infty {kp(n,k)} $$ , thenP(n) represents the total number of parts in all the partitions ofn. In this paper we obtain the following asymptotic formula for $${{P(n)} \mathord{\left/ {\vphantom {{P(n)} {p(n)}}} \right. \kern-\nulldelimiterspace} {p(n)}}:{{P(n)} \mathord{\left/ {\vphantom {{P(n)} {p(n)}}} \right. \kern-\nulldelimiterspace} {p(n)}} = \sqrt {{{3n} \mathord{\left/ {\vphantom {{3n} {2\pi }}} \right. \kern-\nulldelimiterspace} {2\pi }}} (\log n + 2\gamma - \log {\pi \mathord{\left/ {\vphantom {\pi 6}} \right. \kern-\nulldelimiterspace} 6}) + 0(\log ^3 n).$$ .
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    ε-Invarianten bei verallgemeinerten Carlesonmengen (1976)
    Springer
    Monatshefte für Mathematik 81 (1976), S. 217-224 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Generalized Carleson-sets with modulus of continuity ω(δ) and sets of uniqueness for the classA ω ={f(z): f regular inD={z: |z|〈1} and continuous with modulus of continuity ω(δ) in $$\bar D$$ } are described by the behavior of their ε-entropy and ε-capacity (in the sense of Kolmogorov).
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    Zum Cauchy-Problem bei der verallgemeinerten Wärmeleitungsgleichung (1976)
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    Monatshefte für Mathematik 81 (1976), S. 225-233 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Cauchy's problem for the equationu xx +λx −1 u x =u t (λ real) was discussed byD. Colton if λ≠−1,−2,−3, ... Now existence and uniqueness theorems and representations of the solutions are given for the cases λ=−1,−2, −3,... The methods ofD. Colton and of this paper are different but the results are similar.
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    Almost locally univalent functions (1976)
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    Monatshefte für Mathematik 81 (1976), S. 235-240 
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    Topics: Mathematics
    Notes: Abstract We study ALU holomorphic functions defined in the introduction, and prove two criteria for a function holomorphic in the unit disk to be ALU.
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    Remarks on maximal left ideals in semigroups (1976)
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    Monatshefte für Mathematik 81 (1976), S. 257-260 
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    Topics: Mathematics
    Notes: Abstract Some similar results to those for maximal (two-sided) ideals in a compact semigroupS are obtained for maximal left ideals inS, with one exception i.e. the intersection of all maximal left ideals inS may be empty. The maximal left ideals in the convolution semigroup of measures onS are also considered.
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    Mellin's formula and some combinatorial identities (1976)
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    Monatshefte für Mathematik 81 (1976), S. 261-265 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Mellin's formula is applied to expandt/e ande/t in powers of log logt, and to obtain certain identities for the Stirling and Bell numbers.
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    Buchbesprechungen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 241-256 
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    Topics: Mathematics
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    Eine gemeinsame Basis für die Theorie der Eulerschen Graphen und den Satz von Petersen (1976)
    Springer
    Monatshefte für Mathematik 81 (1976), S. 267-278 
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    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract The main result states: Lete 1,e 2,e 3 be three lines incident to the pointv (degv≥4) of the connected bridgeless graphG such thate 1 ande 3 belong to different blocks ifv is a cutpoint. “Split the pointv” in two ways: Lete 1,e j ,j=2, 3, be incident to a new pointv 1j and leave the remainder ofG unchanged, thus obtainingG 1j . Then at least one of the two graphsG 12,G 13 is connected and bridgeless. — A classical result ofFrink follows from this theorem which is the key to a simple proof of Petersen's theorem. Moreover, the above result can be used to prove practically all classical results on Eulerian graphs, including best upper and lower bounds for the number of Eulerian trails in a connected Eulerian graph. In the theory of Eulerian graphs, it can be viewed as the basis for good algorithms checking on several properties of this class of graphs.
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    Periodische und multiplikative zahlentheoretische Funktionen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 279-289 
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    Topics: Mathematics
    Notes: Abstract Letf: N→C be a multiplicative, periodic, arithmetical function with period α〉0. In the case of irrational α it is shown: Iff is the restriction of a continuous functionF: R+→C, thenf(N)={1} orf(N)={0}. (Much weaker conditions supply the same result). If α is integral, thenf is completely characterized. In particular, the connection with Dirichlet characters is discribed. The argument is elementary in the second case. For the first case exponential sums with primes and Weyl's criterion for uniform distribution are used.
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    Isomorphisms ofp-adic group rings (1976)
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    Monatshefte für Mathematik 81 (1976), S. 305-309 
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    Topics: Mathematics
    Notes: Abstract SupposeP is the ring ofp-adic integers,G is a finite group of orderp n , andPG is the group ring ofG overP. IfV p (G) denotes the elements ofPG with coefficient sum one which are of order a power ofp, it is shown that the elements of any subgroupH ofV p (G) are linearly independent overP, and if in additionH is of orderp n , thenPG≅PH. As a consequence, the lattice of normal subgroups ofG and the abelianization of the normal subgroups ofG are determined byPG.
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    Strongly self-complementary and hereditarily isomorphic tournaments (1976)
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    Monatshefte für Mathematik 81 (1976), S. 291-304 
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    Topics: Mathematics
    Notes: Abstract A tournament is strongly self-complementary if every subtournament is self-complementary. TournamentsR, B defined on the same vertex setV are hereditarily isomorphic if for every subsetA ofV, the induced subtournamentsR(A) andB(A) are isomorphic. We determine all strongly self-complementary tournaments and apply this result to characterize the paris of hereditarily isomorphic tournaments.
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    Die Verteilung der schlichten Funktionen in einem Funktionenraum (1976)
    Springer
    Monatshefte für Mathematik 81 (1976), S. 311-314 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the set of regular functions $$H = \{ f:f = z + \sum\limits_{n = 2}^\infty {nb_n z^n ,|b_n |{\mathbf{ }} \leqslant 1\} {\mathbf{ }}} on{\mathbf{ }}|z|{\mathbf{ }}〈 {\mathbf{ }}1$$ . We construct a Borel measure μ and a class of outer measures μ h onH. With these μ and μ h we show that: μ(H∩S)=0 and μ h (H∩S)=0, (S is the set of normed univalent functions). From μ h (H∩S)=0 follows—forh=t α—that the Hausdorff—Billingsley-dimension ofH∩S is zero.
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    Buchbesprechungen (1976)
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    Monatshefte für Mathematik 81 (1976), S. 325-336 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
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    Invariant density estimation (1976)
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    Monatshefte für Mathematik 81 (1976), S. 315-324 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the existence of optimal estimators for the unknown density function, based on a finite number of independent observations. If the statistical problem given is invariant with respect to a certain transformation group, then the invariant density estimators form an essentially complete class of decision functions. If, in particular, the sample space is an Euclidean space and if the densities in question are with respect to Lebesgue measure, an optimal density estimator exists, which is symmetric in the observations and invariant under isometric transformations. If a sufficient sub-σ-algebra ℭ exists, under additional conditions, only ℭ-measurable density estimators are to be considered.
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    Über nullstellenfreie Gebiete von ζ(itk) (s) (1976)
    Springer
    Monatshefte für Mathematik 82 (1976), S. 17-26 
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    Topics: Mathematics
    Notes: Abstract Let ζ(itk) (s) denote thek-th derivative of the Riemann Zeta-function,s=σ+it, σ,t real numbers,k≥1 rational integers. Using ideas fromT. C. Titchmarsh and from a paper ofR. Spira, lower bounds are derived for |ζ(itk)(s)|, |ζ(itk)(1-s) for σ〉1 and some infinitely many, sufficiently large values oft. Further let σ be an algebraic number of degreen and heightH; then a lower bound for |ζ(itk)(its)|, dependent onn, H, k is established for alln,H≥1,k≥3, σ≥2+7k/4 and all realt.
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    Über Funktional-Differentialgleichungen mit voreilendem Argument (1976)
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    Monatshefte für Mathematik 82 (1976), S. 1-16 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a functional differential equation (1)u′(t)=F(t,u) for )≤t≤∞ together with a generalized initial condition (2)u(t)=ϕ(t) forr≤t≤0 or a generalized Nicoletti condition (3)N u=η. Here,N is a linear operator; in the case of a system ofn equations the classical Nicoletti operator is given byN u=(u 1(t 1),...,u n(t n)), with givent i. The functionsu, F ϕ are Banach space valued, the functionF(t, z) is defined fort≥0 andz∈C 0[r,∞). The main point is that the value ofF(t, z) may depend on the values ofz(s) forr≤s≤t+σ(t), where σ(t)〉0. Simple examples show that without a restriction on the magnitude of the advancement σ(t) there is neither existence nor uniqueness. Our results show that when σ(t) is properly bounded and when the solution is to satisfy a certain growth condition which depends on σ(t), then there exists exactly one solution, and it depends continuously on the given data. In the case of the Nicoletti problem (1), (3) there is convergence to the solution satisfyingu(0)=η if 0≤t i≤T andT→0 (this holds in infinite-dimensional spaces, too). These results are true ifF satisfies a Lipschitz condition of the form $$\left| {F(t,z) - F(t,y)} \right| \leqslant h(t)\max \left\{ {\left| {z(s) - y(s)} \right|:r \leqslant s \leqslant t + \delta (t)} \right\}.$$ . In the case where (1) is a finite system andF is only continuous, an existence theory is developped based onSchauder's fixed point theorem. Again, growth conditions play an essential role here.
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    Zur Verteilung der schlichten Funktionen (1976)
    Springer
    Monatshefte für Mathematik 82 (1976), S. 27-29 
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    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The functions that are holomorphic in the unit disk and do not assume the value zero there, are considered. By means of a product representation of these functions, a metric space is formed with them. It is shown that every component of this space contains at most one bounded schlicht function.
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