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  • 2005-2009  (45,721)
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  • 2005-2009  (45,721)
  • 1990-1994
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  • 1975-1979  (44,825)
  • 1950-1954  (7,259)
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  • 101
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    Bulletin of mathematical biology 40 (1978), S. 771-789 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Bifurcation theoretical and numerical analyses of one of Turing's models are performed. It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus emerge as unstable solutions. This, together with the presence of concentration-independent sink terms is responsible for the solutions becoming negative ast→∞. It is pointed out that this deficiency is an accident related to the choice of the model, and that the general idea of symmetry-breaking is perfectly compatible with the generation of regular morphogenetic patterns.
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  • 102
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    Bulletin of mathematical biology 40 (1978), S. 807-821 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Several models have been proposed to underststand the patterns of nerve impulses produced by periodic stimuli. This paper shows that for a very large class of such models there exists a pattern of phases that repeats periodically after a finite number of pulses; the actual pulses produced by the model depend on its initial condition, but in all cases they either follow such a pattern or approach it asymptotically.
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  • 103
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    Bulletin of mathematical biology 40 (1978), S. 791-805 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The global force-flow equations of nonequilibrium thermodynamics are obtained by solving the local equations of motion for a system ofn-components (n−1 solutes plus water) passing through a membrane. When viscous forces and position dependent membranepermeating species frictional interactions are considered, it becomes more difficult to obtain the result because even the stationary state problem becomes one of solving a second order linear ordinary differential equation for the barycentric velocity in a space divided inton+1 regions. Using the continuity of the boundary velocities and their gradients as well as the usual boundary conditions for the hydrodynamic problem, a set of 2n+1 linear equations in the intergration constants can be obtained and a closed form solution is possible. The resultant global description of the system does not obey Onsager reciprocity. What is more, the interpretation of global phenomenological coefficients in terms of local interactions in any simple way is next to impossible. This makes the hope of a molecular level interpretation of phenomenological membrane transport coefficients very slim. The relevance of this finding to the validity of reductionist approaches to biological transport is discussed.
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  • 104
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    Bulletin of mathematical biology 40 (1978), S. 823-837 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of transmural transport of oxygen to a metabolizing retina is presented based on the equations of fluid dynamics. The equations of oxygen transfer are derived and then solved subject to the condition that the capillaries begin to transport oxygen at an initial time. The resulting transient analysis gives us insight into how diffusive and filtrative processes lead to the oxygen distributions both inside and outside capillaries. On the other hand, the steady state solution allows us to predict the cutoff intraocular pressure above which no oxygen is transferred to retinal tissue. It also gives quantitative relationships which allow us to postulate how intracapillary hypertension counterbalances elevated intraocular pressures and how low pressure glaucoma may arise from ineffective diffusive and filtrative processes of oxygen transport.
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  • 105
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    Bulletin of mathematical biology 40 (1978), S. 839-851 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analysis of the interactions among asymptotically stable dynamical systems is formulated by making use of the dynamical system theory. Some results coming from previous mathematical analyses have been slightly modified to take into account some typical biological constraints as the boundedness properties of the solutions. In particular it has been shown that when the “coupling” among the subsystems is “loose” enough (in a sense that has to be made mathematically precise) the asymptotic behaviour of a complex system is the same of that of its individual components. The mathematical theory has been used to analyze two systems of biological significance: the coupling among chemical reactions and the stability properties of a 4-dimensional system describing the kinetics of a chemical transmitter.
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  • 106
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    Bulletin of mathematical biology 40 (1978), S. 865-872 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This note supplies missing details and corrects some mathematical errors in the recent significant paper by Auchmuty and Nicolis (1975).
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  • 107
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    The Geneva risk and insurance review 7 (1978), S. 3-15 
    ISSN: 1554-9658
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    Topics: Economics
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  • 108
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    The Geneva risk and insurance review 7 (1978), S. 16-25 
    ISSN: 1554-9658
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    Topics: Economics
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  • 109
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    The Geneva risk and insurance review 7 (1978), S. 26-34 
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    Topics: Economics
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  • 110
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    The Geneva risk and insurance review 7 (1978), S. 35-41 
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    Topics: Economics
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  • 111
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    The Geneva risk and insurance review 8 (1978), S. 3-3 
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    Topics: Economics
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  • 112
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    The Geneva risk and insurance review 7 (1978), S. 42-55 
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    Topics: Economics
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  • 113
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    The Geneva risk and insurance review 8 (1978), S. 5-19 
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    Topics: Economics
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  • 114
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    The Geneva risk and insurance review 9 (1978), S. 3-17 
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    Topics: Economics
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  • 115
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    The Geneva risk and insurance review 9 (1978), S. 18-44 
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    Topics: Economics
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  • 116
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    The Geneva risk and insurance review 9 (1978), S. 45-65 
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    Topics: Economics
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  • 117
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    Topics: Economics
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  • 118
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    European journal of wildlife research 24 (1978), S. 47-50 
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary Three cases of anomalies of the skull in a 12 month old female roe deer are described and illustrated by two photographs: 1. Retardation of the linear expansion of the ossa nasalia; 2. Hypertrophy of the tubera frontalia; 3. Malformation of the rami mandibularum and their processi coronoidei.
    Abstract: Résumé Trois cas d'irrégularités du crâne chez un Chevreuil femelle d'un an sont décrits et illustrés à l'aide de deux photos. En détail il s'agit d'une 1. retention de la croissance des ossa nasalia; 2. hypertrophie des tubera frontalia; 3. malformation des rami mandibularum et ses processi coronoidei.
    Notes: Zusammenfassung Es wird über Regelwidrigkeiten am Schädel eines 12 Monate alten Rickenkitzes berichtet. Die durch zwei Fotos belegten Anomalien sind folgende: 1. Verkürzung der Nasenbeine; 2. Hypertrophie der Stirnwülste; 3. Deformierung des Unterkieferastes, insbesondere Verbiegung des Muskelfortsatzes.
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  • 119
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    European journal of wildlife research 24 (1978), S. 155-166 
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary By “single food diet” is meant a mixture which contains all the nutritive substances, minerals and vitamins required for body mainternance and growth, with a balanced proportion of energy units. Especially for the feeding of ruminant cloven-hoofed game animals, such a food has great nutritional and physiological advantages over a conventional concentrate of other foods such as cereals, beet, hay or straw since all the components are taken simultaneously by the game animal. In this way it is possible to avoid an unbalanced food intake which, in the case of ruminants, may easily lead to damage to the rumen flora and may therefore be an important cause of illness. Silages have proved themselves to be particularly good in the feeding of ruminant cloven-hoofed game animals. In what is by now an 8-year study in three forest administrative areas of the north-west Eifel, a single food silage has been introduced and tested. Apple cores, sugar beet leaves, minerals and vitamins form the basic components along with hay or straw. Production is made easier with a power food chopper. A structured feed like this is ideal for ruminants; it is readily eaten by the animals and ad-lib intake meets maintenance needs. Costs are in the region of 90 to 100 DM per 1000 kg. In order to cut the daily production costs, 29 self-feeder troughs have so far been set up successfully; through these a permanent supply of food is available to the animals. These troughs have the advantage that failures in the food supply do not occur.
    Abstract: Résumé Par aliment complet on entend un composé comprenant toutes les matières nutritives, actives et énergétiques nécessaires au maintien et aux performances d'un animal. En ce qui concerne plus particulièrement l'alimentation des Ongulés-gibier, une telle nourriture présente, par rapport aux concentrés usels ou par rapport à d'autres aliments tels que céréales, betteraves, foins ou pailles, de gros avantages sur le plan physiologique, tous les ingrédients prévus étant absorbés simultanément. On évite de la sorte une alimentation trop exclusive qui, chez les ruminants, peut causer des dommages à la flore stomacale et ètre à l'origine de maladies. Pour l'affouragement des Ongulés-gibier ruminants, l'ensilage s'est avéré particulièrement probant. Voici maintenant huit années qu'un aliment complet sous forme d'ensilage est fabriqué et fait l'objet d'essais dans trois régions forestières du Nord-Ouest de l'Eifel. Comme composants de base sont utilisés le marc de pommes, la feuille de betteraves sucrières, des vitamines, des éléments minéraux de même que de la paille ou du foin. Pour la fabrication de l'ensilage on se sert d'une hacheuse soufflante. Un tel aliment structuré est destiné à être aussitôt ruminé, est appété par les animaux et couvre, lorsqu'il est distribué ad libitum, les besoins du métabolisme de maintien. Le prix de revient se situe aux environs de 90 à 100 DM par kg. Afin de réduire les frais d'acheminement quotidien de la nourriture, 29 distributeurs automatiques ont d'ores et déjà été installés avec succès, excluant par la même occasion les déficiences liées à un approvisionnement journalier.
    Notes: Zusammenfassung Unter einem „Alleinfutter” ist eine Futtermischung zu verstehen, in der alle für die Erhaltung und Leistung erforderlichen Nähr-, Mineral- und Wirkstoffe mit einem entsprechenden Energieanteil enthalten sind. Speziell für die Fütterung des wiederkäuenden Schalenwildes bildet eine solche Äsung gegenüber einem üblichen Kraftfutter und sonstigen Futterstoffen, wie z. B. Getreide, Rüben, Heu oder Stroh große ernährungsphysiologische Vorteile, da alle vorgesehenen Inhaltstoffe gleichzeitig vom Wild aufgenommen werden. Auf diese Weise kann eine einseitige Futteraufnahme verhindert werden, die bei Wiederkäuern leicht zu Schädigungen der Pansenflora führt und damit wesentliche Ursache für das Auftreten von Erkrankungen ist. Besonders bewährt haben sich zur Verfütterung an wiederkäuendes Schalenwild Silagen. In nunmehr über 8 Jahre durchgeführten Versuchen in 3 Forstverwaltungen der nordwestlichen Eifel ist eine Alleinfutter-Silage hergestellt und erprobt worden. Als Grundkomponenten dienen Apfeltrester, Zuckerrübenblatt, Mineral- und Wirkstoffe sowie Heu oder Stroh. Die Herstellung erfolgt mit Hilfe eines Gebläsehäckslers. Ein solch strukturiertes Futter ist wiederkäuergercht, wird von den Tieren gerne aufgenommen und deckt bei ad libitum-Aufnahme den Erhaltungsbedarf. Die Kosten betragen etwa 90–100 DM/1000 kg. Um die täglichen Ausbringungskosten zu vermindern, sind bisher 29 Selbstfütterungen mit gutem Erfolg eingesetzt worden, durch die dem Wild ständige Äsung zur Verfügung steht und somit Fütterungsfehler dieser Art entfallen
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    European journal of wildlife research 24 (1978), S. 182-186 
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The paper presents the findings of a study by the district veterinary office in Kleve, which deals with geese losses on the Lower Rhine in N. Rhine Westphalia in connection with a winter thunderstorm. The report suggests lightning strikes, damage by hail, collision with aircraft (bird strikes), and the effects of pressure differences in nose diving from flying at high altitudes as possible causes of death.
    Abstract: Résumé Les pertes observées dans le Bas-Rhin (Rhénanie-Westphalie) par les services vétérinaires de Kleve en liaison avec une perturbation atmosphérique au cours de l'hiver font l'objet d'une discussion. Dans la présente communication, on fait état des causes possibles suivantes: foudre, grèle, collision avec des avions de même que l'effet de variations de pressions atmosphériques lorsque les oiseaux quittent brusquement les hautes altitudes.
    Notes: Zusammenfassung Zur Diskussion gestellt wird der Untersuchungsbefund aus dem Kreisveterinäramt Kleve, der sich mit Gänseverlusten am Niederrhein in Nordrhein-Westfalen in Zusammenhang mit einem Wintergewitter befaßt. Erörtert werden als mögliche Ursachen in der vorliegenden Mitteilung Blitzschlag, Hagelschlag, Zusammenstoß mit Flugzeugen (Vogelschlag) und die Auswirkung von Druckunterschieden bei sturzflugartigem Verlassen großer Flughöhen.
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    European journal of wildlife research 24 (1978), S. 207-211 
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Mathematical programming 15 (1978), S. 330-342 
    ISSN: 1436-4646
    Keywords: Global Optimization ; Random Search ; Convergence ; Sequential Minimization ; Lipschitz Functions ; Stochastic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A sequential random search method for the global minimization of a continuous function is proposed. The algorithm gradually concentrates the random search effort on areas neighboring the global minima. A modification is included for the case that the function cannot be exactly evaluated. The global convergence and the asymptotical optimality of the sequential sampling procedure are proved for both the stochastic and deterministic optimization problem.
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    Mathematical programming 15 (1978), S. 364-364 
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  • 124
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    Mathematical programming 15 (1978), S. 1-11 
    ISSN: 1436-4646
    Keywords: APL-Codes ; Polytope ; Point Set ; Vertices ; Faces ; Facets ; Quadratic Programming ; Distance ; Decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Methods are described and APL-codes are supplied to find vertices, edges, other faces and facets of polytopes given by point sets. The basic subroutine is a simplicial decomposition version of least distance, i.e. quadratic, programming. Computational experience indicates high efficiency.
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  • 125
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    Mathematical programming 14 (1978), S. 127-127 
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  • 126
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    Mathematical programming 14 (1978), S. 224-248 
    ISSN: 1436-4646
    Keywords: Augmented Lagrangian ; Lagrangian Function ; Nonlinear Constraints ; Nonlinear Programming ; Optimization Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Lagrangian functions are the basis of many of the more successful methods for nonlinear constraints in optimization calculations. Sometimes they are used in conjunction with linear approximations to the constraints and sometimes penalty terms are included to allow the use of algorithms for unconstrained optimization. Much has been discovered about these techniques during the last eight years and this paper gives a view of the progress and understanding that has been achieved and its relevance to practical algorithms. A particular method is recommended that seems to be more powerful than the author believed to be possible at the beginning of 1976.
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  • 127
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    Mathematical programming 14 (1978), S. 262-262 
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  • 128
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    Mathematical programming 14 (1978), S. 325-331 
    ISSN: 1436-4646
    Keywords: Integer Programming ; Formulation ; Models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Two practical problems are described, each of which can be formulated in more than one way as a mixed integer programming problem. The computational experience with two formulations of each problem is given. It is pointed out how in each case a reformulation results in the associated linear programming problem being more constrained. As a result the reformulated mixed integer problem is easier to solve. The problems are a multi-period blending problem and a mining investment problem.
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    Mathematical programming 14 (1978), S. 349-372 
    ISSN: 1436-4646
    Keywords: Indefinite Quadratic Programming ; Matrix Factorizations ; Numerical Software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Numerically stable algorithms for quadratic programming are discussed. A new algorithm is described for indefinite quadratic programming which utilizes methods for updating positivedefinite factorizations only. Consequently all the updating procedures required are common to algorithms for linearly-constrained optimization. The new algorithm can be used for the positive-definite case without loss of efficiency.
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  • 130
    ISSN: 1436-4646
    Keywords: Menu Planning ; Separation Scheduling ; Menu Scheduling ; Decomposition ; Non-linear Programming ; Binary Knapsack Problem ; Lagrangian Relaxation ; Transportation Problem ; Branch and Bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, the analytical representation of food preference is used in a separable non-linear program to yield the serving frequencies of menu items for a finite time horizon. The frequencies obtained in this way insure cost and nutritional control. Subsequently, the scheduling problem dealing with item assignments to meals and days is formulated as an integer program consisting of several transportation problems linked by weekly nutritional constraints. This problem is solved using a branch and bound algorithm which employs Lagrangian relaxation to obtain bounds and to decide on branching strategy.
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    Mathematical programming 15 (1978), S. 92-99 
    ISSN: 1436-4646
    Keywords: Network Flows ; Multicommodity Networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Several classes of multicommodity networks have been shown to have the property that they can be transformed to equivalent uncapacitated single commodity flow problems. We show that many of these networks can be further reduced to smaller, semi-capacitated flow problems using the inverse of a result of Ford and Fulkerson. This appears to be a useful computationally-oriented tool for developing practically efficient algorithms. These concepts are also used to establish a generalization of a previous result concerning multicommodity transportation problems.
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    Mathematical programming 15 (1978), S. 119-120 
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    Mathematical programming 15 (1978), S. 146-154 
    ISSN: 1436-4646
    Keywords: Linear Complementarity Problem ; Principal Pivoting Algorithm
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    Topics: Computer Science , Mathematics
    Notes: Abstract The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0,ż ≥ 0,w T ż = 0, where a dot denotes the derivative with respect to the scalar parametert ≥ 0. In this problem,q, p aren-vectors withq ≥ 0 andM is an byn P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.
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    Mathematical programming 15 (1978), S. 130-145 
    ISSN: 1436-4646
    Keywords: Minimax Problems ; Minisum Problems ; Nondifferentiable Optimization ; Subgradients ; Location Problems ; Linear Approximation Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a subgradient algorithm for minimizing the maximum of a finite collection of functions. It is assumed that each function is the sum of a finite collection of basic convex functions and that the number of different subgradient sets associated with nondifferentiable points of each basic function is finite on any bounded set. Problems belonging to this class include the linear approximation problem and both the minimax and minisum problems of location theory. Convergence of the algorithm to an epsilon-optimal solution is proven and its effectiveness is demonstrated by solving a number of location problems and linear approximation problems.
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    Mathematical programming 14 (1978), S. 73-86 
    ISSN: 1436-4646
    Keywords: Gradient ; Subdifferential ; Generalized Gradient ; Optimality Conditions ; Nondifferentiability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is devoted to necessary optimality conditions in a mathematical programming problem without differentiability or convexity assumptions on the data. The main tool of this study is the concept of generalized gradient of a locally Lipschitz function (and more generally of a lower semi-continuous function). In the first part, we consider local extremization problems in the unconstrained case for objective functions taking values in (−∞, +∞]. In the second part, the constrained case is considered by the way of the cone of adherent displacements. In the presence of inequality constraints, we derive in the third part optimality conditions in the Kuhn—Tucker form under a constraint qualification.
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    Mathematical programming 14 (1978), S. 98-107 
    ISSN: 1436-4646
    Keywords: Network Flows ; Equilibrium Trade ; Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract When supply and demand curves for a single commodity are approximately linear in each ofN regions and interregional transportation costs are linear, then equilibrium trade flows can be computed by solving a quadratic program of special structure. An equilibrium trade flow exists in which the routes carrying positive flow form a forest, and this solution can be efficiently computed by a tree growing algorithm.
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    Mathematical programming 14 (1978), S. 125-125 
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    Mathematical programming 14 (1978), S. 126-126 
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    Mathematical programming 14 (1978), S. 170-185 
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Pseudoconvexity ; Second order Characterizations ; Extended Hessians ; Bordered Determinants ; Quadratic Functions
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    Topics: Computer Science , Mathematics
    Notes: Abstract Second order characterizations for (strictly) pseudoconvex functions are derived in terms of extended Hessians and bordered determinants. Additional results are presented for quadratic functions.
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    Mathematical programming 14 (1978), S. 263-263 
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    Mathematical programming 14 (1978), S. 378-378 
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    Mathematical programming 14 (1978), S. 380-380 
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    Mathematical programming 14 (1978), S. 381-381 
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    Mathematical programming 15 (1978), S. 87-91 
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    Keywords: Lagrange Multipliers ; Constrained Convex Optimization ; Kuhn—Tucker Theorem ; Duality
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    Topics: Computer Science , Mathematics
    Notes: Abstract The duality theorem of linear programming is used to prove several results on convex optimization. This is done without using separating hyerplane theorems.
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    Mathematical programming 15 (1978), S. 110-113 
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    Keywords: Fixed Point Computation
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    Notes: Abstract Conditions are presented which are necessary for the existence of a regular fixed point of aC 1 map.
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    Mathematical programming 15 (1978), S. 122-122 
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    Mathematical programming 15 (1978), S. 162-176 
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    Keywords: Mixed Integer Programming ; Knapsack Problem ; Branch and Bound Method
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    Notes: Abstract The ordinary knapsack problem is to find the optimal combination of items to be packed in a knapsack under a single constraint on the total allowable resources, where all coefficients in the objective function and in the constraint are constant. In this paper, a generalized knapsack problem with coefficients depending on variable parameters is proposed and discussed. Developing an effective branch and bound algorithm for this problem, the concept of relaxation and the efficiency function introduced here will play important roles. Furthermore, a relation between the algorithm and the dynamic programming approach is discussed, and subsequently it will be shown that the ordinary 0–1 knapsack problem, the linear programming knapsack problem and the single constrained linear programming problem with upper-bounded variables are special cases of the interested problem. Finally, practical applications of the problem and its computational experiences will be shown.
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    Mathematical programming 15 (1978), S. 211-213 
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    Keywords: Traveling Salesman Problem ; Cardinality Constraints ; Hamiltonian Circuits ; Network Flow Problems
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    Notes: Abstract The classic traveling salesman problem is characterized in terms of continuous flows on a specially constructed non-conservative network, in 2n − 1 linear constraints and a cardinality constraint. It is shown that every solution to the network problem is a hamiltonian circuit.
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    Mathematical programming 15 (1978), S. 220-222 
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    Keywords: Dynamic Decision Model ; Monotone Optimal Decision Functions
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    Notes: Abstract The purpose of this short note is to correct some oversights in [1]. More precisely, we point out that stronger assumptions have to be imposed on the decision model (in order to use results in [2]) and present a counterexample to a comment to [1, Theorem 3.1].
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    Mathematical programming 15 (1978), S. 239-242 
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    Keywords: Minimax Optimization ; Nonlinear Programming
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    Notes: Abstract An unconstrained minimax algorithm of Charalambous and Conn is easily modified to solve the constrained case. Here we present some numerical results and find that this algorithm compares favourably to those of Dutta and Vidyasagar.
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    Mathematical programming 15 (1978), S. 247-260 
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    Keywords: Quasi-Newton Method ; Optimal Conditioning ; Rank-two Update
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    Notes: Abstract Davidon's new quasi-Newton optimization algorithm selects the new inverse Hessian approximation $$\bar H$$ at each step to be the “optimally conditioned” member of a certain one-parameter class of rank two updates to the last inverse Hessian approximationH. In this paper we show that virtually the same goals of conditioning can be achieved while restricting $$\bar H$$ to the convex class of updates, which are bounded by the popular DFP and BFGS updates. This suggests the computational testing of alternatives to the “optimal conditioning” strategy.
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    Mathematical programming 15 (1978), S. 261-267 
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    Keywords: Sensitivity Analysis in Nonlinear Programming ; Computational Aspects ; Chemical Equilibrium Problems ; Entropy Maximization Problems
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    Notes: Abstract This paper presents an implementation of some recent results of Bigelow and Shapiro [1]. These implicit function theorems are shown to provide a convenient means of performing certain types of sensitivity analysis, in particular updating the lagrange multipliers, associated with particular classes of problems. As a result we extend the usual sensitivity analysis results to include improving estimates of the effect of changing the right-hand sides of constraints. Examples of chemical equilibrium and entropy maximization models are used to illustrate the results.
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    Mathematical programming 15 (1978), S. 278-290 
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    Keywords: Constrained Optimization ; Exact Penalty Functions ; Nondifferentiable Functions
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    Notes: Abstract The purpose of this paper is to present new exact penalty functions and discuss their properties. A lower bound on the controlling parameters is given, for which above this value, the optimum of the exact penalty function coincides with the optimum of the nonlinear programming problem.
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    Mathematical programming 15 (1978), S. 291-314 
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    Keywords: Network Flow Problems ; Computational Results—Efficiency—Comparison ; Specific problems in mathematical programming ; Computational Experiments ; Pivotal Selection Methods ; Starting Strategies ; Scaling Procedure
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    Notes: Abstract This paper describes the experimental results of testing a “large-scale” program for solving minimum-cost network flow problems. With this program, general structure transshipment problems with over ten thousand nodes and thirty thousand arcs have been easily solved without resorting to auxiliary storage. The algorithm is a variant of the primal revised simplex method; the computer code is called LPNET illustrating the close connection between linear programming and network graphs. This approach substantially improves computer processing timeand core storage, especially for relatively large network problems. The results of these experiments are provided. It is emphasized that an organized experimental design and a detailed series of empirical tests are crucial for an efficient implementation.
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    Mathematical programming 15 (1978), S. 360-362 
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    Keywords: Nonlinear Decomposition ; Nonlinear Programming
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    Notes: Abstract We show that under certain conditions nonlinear programming problems can be decomposed into a series of smaller problems. A Decomposition Theorem and example are presented.
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    Mathematical programming 15 (1978), S. 363-363 
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    Mathematical programming 15 (1978), S. 365-368 
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    Mathematical programming 15 (1978), S. 26-35 
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    Keywords: Manpower Planning ; Column Generation ; Network Flows ; Shortest Path ; System Design
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    Notes: Abstract An equilibrium model of a manpower system is developed based on the notion of a career flow. Institutional constraints and measures of system performance are linear functions of the career flow. A typical optimal design problem is formulated and a solution procedure is developed. The optimization problem is a generalized linear program in which columns are generated by solving a shortest path problem. Upper and lower bounds on the optimal value function can be developed at each stage of the calculations.
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    Mathematical programming 15 (1978), S. 53-62 
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    Keywords: Convex Program ; Decomposition ; Cutting Plane Algorithm ; Stochastic Quadratic Program with Recourse
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    Notes: Abstract A piecewise convex program is a convex program such that the constraint set can be decomposed in a finite number of closed convex sets, called the cells of the decomposition, and such that on each of these cells the objective function can be described by a continuously differentiable convex function. In a first part, a cutting hyperplane method is proposed, which successively considers the various cells of the decomposition, checks whether the cell contains an optimal solution to the problem, and, if not, imposes a convexity cut which rejects the whole cell from the feasibility region. This elimination, which is basically a dual decomposition method but with an efficient use of the specific structure of the problem is shown to be finitely convergent. The second part of this paper is devoted to the study of some special cases of piecewise convex program and in particular the piecewise quadratic program having a polyhedral constraint set. Such a program arises naturally in stochastic quadratic programming with recourse, which is the subject of the last section.
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    Description / Table of Contents: Abstract We develop a new iteration scheme giving bounds for the positive eigenvector of a nonnegative and irreducible matrix and the corresponding eigenvalue and test it on some examples.
    Notes: Zusammenfassung Wir geben ein neues Iterationsverfahren an, das Schranken für den positiven Eigenvektor einer nichtnegativen, irreduziblen Matrix und des zugehörigen Eigenwerts liefert.
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    Computing 20 (1978), S. 17-26 
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    Description / Table of Contents: Abstract Due to the free parameter in the fixed-point equation of the parallel-chord-method, it is possible to reduce the Lipschitz constant of the contraction mapping. By use of this reduction, it is possible in suitable cases to generate the contraction property of the mapping. If the mapping possesses this property, then this is also true for the mapping with the parameter determined here. In addition, both an improved error estimate for the sequences of iterates and a smaller convergence factor are obtained. An example is presented.
    Notes: Zusammenfassung Mit Hilfe des freien Parameters in der Fixpunktgleichung des Parallelenverfahrens ist es möglich, die Lipschitz-Konstante der kontrahierenden Abbildung zu verkleinern. Durch diese Verkleinerung kann in geeigneten Fällen eine kontrahierende Abbildung erzeugt werden. Ist die Abbildung bereits kontrahierend, ist sie auch kontrahierend für den berechneten Wert des Parameters. Ferner ergibt sich neben einer verbesserten Fehlerabschätzung für die Iterationsfolgen auch ein kleinerer Konvergenzfaktor. Das Verfahren wird an Hand eines Beispiels erläutert.
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    Computing 20 (1978), S. 75-94 
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    Description / Table of Contents: Abstract A theory of hybrid finite element approximation is developed for a class of shell problems. Though it is applied only to the special case of clamped shallow shells with regular triangularization the results may be of larger interest comparing the predicted convergence rate with the numerical outcome of some applications of the hybrid finite element method. The convergence speed can only be increased by higher degrees of the approximation and the stresses at the edges correspondingly. The use of a so-called rank condition plays a fundamental role in the study. Weak coerciveness of the under lyigg bilinear form for the derivation of hybrid elements is proved by showing the existence of a stationary point.
    Notes: Zusammenfassung Dieser Beitrag liefert eine Theorie der Finite-Element-Approximation für eine Klasse von Schalenproblemen. Obgleich diese nur für den Fall der eingespannten flachen Schale mit regulärer Triangulierung ausführlich dargestellt wird, sind die Ergebnisse darüberhinaus von Interesse, da die abgeleiteten Konvergenzordnungen das Verhalten numerischer Näherungslösungen aus anderen Anwendungen der hybriden Finite-Element-Methode erklären helfen. Die Konvergenzgeschwindigkeit kann nur verbessert werden durch gleichzeitige Erhöhung der Ansatzgrade für die Verschiebungen im Elementinnern und für die Spannungen auf den Rändern. Die Einhaltung einer sogenannten Rangbedingung hat zentrale Bedeutung. Die schwache Koerzitivität der für die Ableitung hybrider Elemente verwendeten Bilinearform ist durch den Nachweis der Existenz eines stationären Werts gesichert.
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    Computing 20 (1978), S. 153-163 
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    Description / Table of Contents: Zusammenfassung Eine verbesserte Darstellung Newtonscher Intervall-Verfahren wird diskutiert. Es wird dabei gezeigt, daß man bestimmte Intervalle in den Verfahren durch reelle Zahlen ersetzen kann. Dadurch werden die Konvergenzeigenschaften der Verfahren verbessert.
    Notes: Abstract Improved forms of some interval Newton Methods are given. It is shown that certain intervals in the methods can be replaced by real numbers. This improves the convergence properties of the methods.
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    Computing 20 (1978), S. 177-182 
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    Description / Table of Contents: Abstract The bound of Prager-Oettli for the input error of a linear system of equations is computed via a new formula which guarantees strictness of the bound in spite of roundoff errors.
    Notes: Zusammenfassung Die Schranke von Prager-Oettli für den Eingangsfehler eines linearen Gleichungssystems wird über eine neue Formel berechnet, die trotz der Rundungsfehler die Schärfe der Schranke sichert.
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    Computing 20 (1978), S. 207-228 
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    Description / Table of Contents: Zusammenfassung Die Iterierte Defektkorrektur (IDeC) ist ein Verfahren zur schrittweisen Verbesserung einer Näherungslösung eines gegebenen ProblemsFy=0. Eines der wichtigsten Anwendungsgebiete dieses Prinzips sind Differentialgleichungen. Die IDeC kann dort als Methode zur Verbesserung der Ordnung eines Diskretisierungsverfahrens, und damit zur Verbesserung der Genauigkeit eingesetzt werden. In der vorliegenden Arbeit wird ein Metaalgorithmus für die Klasse, der IDeC-Verfahren für Differential-gleichungen vorgestellt und analysiert. Für jeden “Baustein” dieses Metaalgorithmus werden Bedingungen angegeben, die es gewährleisten, daß eine bestimmte Ordnung erreicht wird. Diese Bedingungen sind von großer praktischer Bedeutung, wenn IDeC-Verfahren als Computer-Programme implementiert werden sollen.
    Notes: Abstract Iterated Defect Correction (IDeC) is a technique for improving successively an approximate solution of a given problemFy=0. One of the most important fields of application of this principle are differential equations. Here, IDeC can be used as a technique for increasing the order of a discretization method and thus for improving the accuracy. In this paper a metalgorithm for the class of IDeC-methods for differential equations is presented and analyzed. For every component of this metalgorithm conditions are given which guarantee a certain order of accuracy. These conditions are of particular importance for practical applications, as far as the implementation of IDeC-methods is concerned.
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    Computing 20 (1978), S. 257-265 
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    Description / Table of Contents: Abstract A termination criterion by Nickel (Theorem 6, [1]) for guaranteeing the numerical convergence for locally stable and consistent algorithms is generalized. The assumption |x ν+2,x ν+1|≤L|x ν+1,x ν| (0≤L〈1,L real constant) of the approximation sequence {x ν} to the solution is replaced by the convergence of the progression $$\sum\limits_{v = 1}^\infty {|x,x_{v + 1} |/Q^v (0〈 Q〈 1)} $$ . Therefore the theorem of this paper is applicable to a large number of numerical procedures, for which untill now no termination criterion has been known (for example: Rombergprocedure). In particular this weakening is important for the computation of approximation solutions for integral equations.
    Notes: Zusammenfassung Ein Abbrechkriterium von Nickel (Satz 6, [1]) zur Sicherung der numerischen Konvergenz bei lokal stabilen und konsistenten Algorithmen wird verallgemeinert. Statt der Eigenschaft |x ν+2,x ν+1|≤L|x ν+1,x ν| (0≤L〈1,L von ν ∈ ℕ unabhängig) der Näherungsfolge {x ν} zur Lösungx reicht die Konvergenz der Reihe $$\sum\limits_{v = 1}^\infty {|x,x_{v + 1} |/Q^v (0〈 Q〈 1)} $$ aus. Damit ist der Satz dieser Arbeit bei einer großen Klasse von numerischen Verfahren anwendbar, für die bisher noch kein Abbrechkriterium bekannt ist (z. B. dem Romberg-Verfahren). Insbesondere ist diese Abschwächung zur Berechnung von Näherungslösungen bei Integralgleichungen wichtig.
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    Computing 20 (1978), S. 307-324 
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    Description / Table of Contents: Zusammenfassung Ausgehend von einem Existenz- und Eindeutigkeitssatz für die Lösung einer verallgemeinerten Volterra-Integralgleichung zweiter Art wird die Existenz und Eindeutigkeit der Lösung der hier behandelten nichtlinearen, schwach singulären Volterra-Integralgleichung erster Art untersucht. Es wird ein numerisches Verfahren der Ordnung 2 bzw. 3 angegeben. Der Konvergenzbeweis basiert in beiden Fällen auf einem Lemma über die Beschränktheit einer speziellen Differenzenungleichung. An zwei numerischen Beispielen werden die theoretischen Ergebnisse demonstriert.
    Notes: Abstract Starting from an existence and uniqueness theorem for a generalized nonsingular second kind Volterra equation existence and uniqueness for the solution of the nonlinear, weakly singular first kind Volterra equation is examined. A new type of numerical method is developed. A basic lemma concerning the boundedness of a special difference inequality is given and order two or three convergence of the method is shown. Two numerical examples illustrate the theoretical results.
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    Computing 20 (1978), S. 343-350 
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    Description / Table of Contents: Abstract For each α ε (0, π/2), the existence ofA (α)-stable linear multistep methods with arbitrary order of consistency is shown by an explicit construction. Some characteristic data of the methods and numerical results are given.
    Notes: Zusammenfassung Es wird in einer expliziten Konstruktion gezeigt, daß für jedes α ε (0, π/2)A (α)-stabile lineare Mehrschrittverfahren beliebiger Konsistenzordnung existieren. Einige charakteristische Daten der Verfahren und numerische Rechnungen werden angegeben.
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    Computing 21 (1978), S. 17-35 
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    Description / Table of Contents: Zusammenfassung Der Ansatz, Strings, die zusammengemischt werden, auf Magnetplatten vorzuplanen, wird unter Leistungsgesichtspunkten untersucht. Konzepte für die interne Pufferzuordnung, für die Erzeugung der anfänglichen Strings durch ein internes Sortierverfahren, und für die Stringverteilung auf Magnetplatten werden ausgewertet. Ein Algorithmus beschreibt die Konstruktion von suboptimalen Mischbäumen, die planbare Mischbäume genannt werden. Ein Kostenmodell, das auf detaillierte Annahmen der Zuordnung vonk Eingabeplatten und der Planung einesr-Wege-Mischens beruht, wird für das exakte Vorplanen aufgestellt. Zeitbetrachtungen für Sortieren und Mischen, die Hardware-Eigenschaften von Magnetplatten einschließen, zeigen signifikante Zeitgewinne verglichen mit weitverbreiteten Sortier- und Mischverfahren.
    Notes: Abstract The idea of preplanning strings on disks which are merged together is investigated from a performance point of view. Schemes of internal buffer allocation, initial string creation by an internal sort, and string distribution on disks are evaluated. An algorithm is given for the construction of suboptimal merge trees called plannable merge trees. A cost model is presented for accurate preplanning which consists of detailed assumptions on disk allocation fork input disks andr-way merge planning. Timing considerations for sort and merge including hardware characteristics of moveable head disks show a significant gain of time compared to widely used sort/merge applications.
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    Computing 21 (1978), S. 53-69 
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    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden mehrere effiziente Methoden zur Berechnung von Funktionen, die durch Potenzenreihen definiert sind, präsentiert. Einfache Computerprogramme für zwei schnelle Algorithmen werden in einem eigenen Beitrag ([9]) angegeben. Die Konvergenzgeschwindigkeiten der vorgeschlagenen Verfahren werden theoretisch untersucht und die erhaltenen Ergebnisse werden an numerischen Beispielen erläutert.
    Notes: Abstract In this paper we present several efficient methods for evaluating functions defined by power series expansions. Simple computer codes for two rapid algorithms are given in a companion paper. The convergence rates of the proposed computational schemes are investigated theoretically and the results are illustrated by numerical examples.
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    Computing 21 (1978), S. 71-79 
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    Description / Table of Contents: Zusammenfassung Mit Hilfe der Pseudoinversen eines beschränkten linearen Operators von ℝ n inl 2 wird eine Methode zur Konstruktion von Quadraturformeln für die Integration über einem beliebigen beschränktenm-dimensionalen GebietB⊂ℝ m hergeleitet, mit der Eigenschaft, daß der mittlere Fehler in einer vorgeschriebenen FamilieF sowie die Varianz der Rundungsfehler gemäß Sard [8] minimal werden. Sodann wählen wirF als gewichtete Monome und behandeln als Beispiel Integration auf der Oberfläche derm-Kugel.
    Notes: Abstract Using the concept of the generalized inverse of a bounded linear transformation between ℝ n andl 2, a method is given for constructing quadrature rules for integration over an arbitrary boundedm-dimensional regionB⊂ℝ m with the property that the average error over the prescribed familyF of the functions continuous inB as well as the variance of the rounding errors according to Sard [8] are minimal. Then we specializeF to the weighted monomials and treat as an example integration on the surface of them-sphere.
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    Computing 21 (1978), S. 87-91 
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    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden zwei Computerprogramme für die Berechnung der Summe einer Potenzenreihe, die einer allgemeinen Klasse zugehört, beschrieben. Die Verwendung der Programme ist mit einem Beispiel erläutert.
    Notes: Abstract This paper describes two computer codes for calculating the sum of power series, belonging to a certain general class. The use of the codes for an illustrative test example is explained.
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    Computing 20 (1978), S. 1-16 
    ISSN: 1436-5057
    Keywords: Integration ; Runge-Kutta integration ; truncation error ; error estimates ; accumulated error ; accumulated error estimates ; accumulated truncation error ; true error
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Methode für die Entwicklung von Runge-Kutta-Integrationsalgorithmen angegeben, die die Schätzung des globalen Verfahrensfehlers ermöglichen. Mehrere neue Algorithmen 2., 3. und 4. Ordnung werden angeführt. Die Rechenarbeit pro Schritt ist identisch für die neuen Algorithmen und für Algorithmen, die nur eine Schätzung des lokalen Verfahrensfehlers ermöglichen. Numerische Versuche mit den neuen Algorithmen ergeben, daß der geschätzte Fehler den wahren akkumulierten Fehler gut wiedergibt. Außerdem ist der Fehler von derselben Ordnung wie bei gewöhnlichen Runge-Kutta-Algorithmen.
    Notes: Abstract A method is presented for developing Runge-Kutta integration algorithms with built-in estimates of the accumulated truncation error. Several new 2-nd, 3-rd, and 4-th order algorithms are given. The computation per step of the new algorithms is identical to that of algorithms which provide only an estimate of the local truncation error. Numerical experimentation with the new algorithms shows that the estimated error compares very well with the true accumulated error. Further, the error is of the same order as that incurred using traditional Runge-Kutta algorithms.
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    Computing 20 (1978), S. 47-60 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Anfangsrandwertproblem für die hyperbolische Differentialgleichunga(t,x,u)u tt +2b(t,x,u)u tx +c(t,x,u)u xx =d(t,x,u,u t ,u x ) zweiter Ordnung wird mit Hilfe eines Charakteristikenverfahrens gelöst, das keine Differenzengleichungen füru t undu x benutzt. Die Lösung des diskretisierten Problems besitzt eine asymptotische Entwicklung nach geraden Potenzen der Schrittweite. Daher können die numerischen Ergebnisse durch Extrapolation verbessert werden.
    Notes: Abstract The hyperbolic initial-boundary value problem for the second order equationa(t,x,u)u tt +2b(t,x,u)u tx +c(t,x,u)u xx =d(t,x,u,u t ,u x ) is solved by a special method of characteristics involving no difference equations foru t andu x . The discrete solution has an asymptotic expansion in even powers of the step size. Therefore, the numerical results can be improved by extrapolation to the limit.
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    Computing 20 (1978), S. 165-176 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das folgende Problem wird behandelt: gegeben sei eine Menge vonm rechteckigen Gebieten in der Ebene, man finde ein Intervall-Polynom vom Gradn〉m durch diese Gebiete. Dies ist eine Verallgemeinerung des diskreten Problems der kleinsten Quadrate. Drei Verallgemeinerungen der gewöhnlichen Methode der kleinsten Quadrate für Polynome werden betrachtet und an numerischen Beispielen verglichen. Eine dieser Methoden wird empfohlen, da sie in allen Testbeispielen bessere Ergebnisse gibt.
    Notes: Abstract The following problem is treated: given a set ofm rectangular regions in the plane, fit an interval polynomial of degreen〉m through the regions. This is a generalization of the discrete polynomial least squares problem. Three generalizations of the standard methods for the discrete polynomial least squares are considered and compared on numerical examples. One of the methods is recommended since it gives superior results in all cases tested.
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    Computing 20 (1978), S. 189-205 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eines der am besten beschriebenen Modelle kombinatorischer Optimierung ist das Scheduling Problem, bei dem eine endliche Anzahl von Tätigkeiten auf einer festen Anzahl von Maschinen so ausgeführt werden muß, daß eine gegebene Zielfunktion minimiert wird. Jede Tätigkeit benötigt charakteristische Daten wie Bearbeitungszeit, Fertigsteillungstermin, Strafkosten und technologische Nachfolgebeziehungen. Ein algebraischer Ansatz für die Zielfunktion führt zu einem allgemeinen Problem, das alle in der Literatur bekannten klassischen Fälle von Summen und Maximum Zielfunktionen einschließt. Durch die Lösung eines algebraischen Transportproblems wird eine untere Schranke für den Zielfunktionswert bestimmt. Um eine Optimallösung zu erhalten, verwenden wir ein Branch and Bound Verfahren. Weiterhin betrachten wir das allgemeine Job Shop Scheduling Problem mit algebraischer Zielfunktion.
    Notes: Abstract One of the well-studied models of combinatorial optimization is the scheduling problem dealing with a finite set of tasks, which have to be executed on a fixed number of machines so that a given objective is minimized. Each task requires a set of characteristic data like operating time, due date, penalty cost and technological requirements. An algebraic approach to the objective leads to a general problem which includes all classical cases of sum and bottleneck objectives known in literature. By solving an algebraic transportation problem a lower bound for the objective value can be determined. To obtain an optimal solution we employ a branch and bound procedure. Furthermore we consider the general job shop scheduling problem with algebraic objective function.
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    Computing 20 (1978), S. 325-331 
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    Topics: Computer Science
    Description / Table of Contents: Abstract The result of this paper is the economizing of cpu-time by identical guaranteed precision of the approximate solution. This is possible by an optimal selection ofn j in every iteration stepj, wheren j is the number of subintervals for the numerical integration. The determination ofn 1,n 2, ... is reduced to the solution of a solvable convex optimization job.
    Notes: Zusammenfassung Es wird die Einsparung von Rechenzeit bei gleicher garantierter Genauigkeit der Näherungslösung ermöglicht. Dies wird erreicht durch eine optimale Wahl vonn j bei jedem Iterationsschrittj, wobein j die Zahl der Teilintervalle für die Quadratur ist. Die Bestimmung vonn 1,n 2,... wird auf die Lösung einer lösbaren konvexen Optimierungsaufgabe zurückgeführt.
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    Computing 20 (1978), S. 279-290 
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    Topics: Computer Science
    Description / Table of Contents: Abstract It is one of the basic questions in designing a database system to determine which attributes to invert. The literature presents a variety of models to solve this question. This paper attempts to give a guideline, under which conditions a primitive model considering only retrieve operations, suffices to determine an optimal solution. The relevance of that question lies in the smaller costs of simpler models.
    Notes: Zusammenfassung Eine wesentliche Fragestellung beim Aufbau eines Datenbanksystems ist die Auswahl der Schlüsselattribute. Bei Inverted-File Systemen ist dies äquivalent zur Auswahl der zu invertierenden Attribute. In diesem Aufsatz wird versucht darzustellen, unter welchen Bedingungen Modelle, die lediglich das Retrieve-Verhalten des Benutzers berücksichtigen, zuverlässige Resultate liefern können. Die Relevanz dieser Fragestellung liegt vor allem in den durch das einfachere Modell verminderten Kosten der Datenbeschaffung und Datenanalyse im DB-Designprozeß.
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    Computing 20 (1978), S. 351-361 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein allgemeines, quasilineares, nichtstationäresk-Schrittverfahren für die Lösung des Cauchy-Problems für gewöhnliche Differentialgleichungen untersucht. Ein Konvergenzsatz mit ziemlich schwachen Bedingungen wird angegeben. Die Inkrementfunktion muß nicht Lipschitz-stetig sein; es genügt, wenn diese Funktion die Perron-Bedingung aus der Eindeutigkeitstheorie für das Cauchy-Problem mit nichtabnehmender Vergleichfunktion erfüllt. Das Ergebnis ist eine Erweiterung der Theorie von G. Dahlquist und des letzten Resultats von K. Taubert.
    Notes: Abstract The general form of a quasilinear nonstationaryk-step method for solving of the Cauchy problem for ordinary differential equations is discussed. The convergence theorem is stated under rather weak conditions. It is not assumed that the increment function is Lipschitz-continuous but only that it satisfies the Perron type condition appearing in the uniqueness theory for the Cauchy problem with a nondecreasing comparison function. The result established in the paper is an extension of the theory given by G. Dahlquist and the recent result of K. Taubert.
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    Computing 20 (1978), S. 363-375 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Hier wird ein neuer selbsteichender Algorithmus für die Integration der analytischen Funktionen dargestellt. Der Algorithmus wirkt auf das Integrationsintervall indem er örtliche Unterintervalle hervorruft, deren Länge durch ein neues System überwacht wird. Die Überwachung ergibt sich aus einer Formel, die von einer analytischen Basis abgeleitet wird und für jede beliebige Integrationsregel gilt: mit zwei verschiedenen Annäherungen eines Integrals wird die Intervallänge berechnet, die notwendig ist, um eine Integralannäherung mit der innerhalb zugelassener Fehlergrenzen notwendigen Genauigkeit zu erreichen. Die daraus entstehende Methode für die Erzeugung der Unterintervalle und eine wirksame Auswahl der Fehlerverteilung unter die Unterintervalle bringen einen selbstanpassenden Algorithmus hervor, der über einen genauen und höchst günstigen Integrationsprozeß verfügt. Darauf wird der besondere Algorithmus betrachtet, der sich mit Hilfe der 6-Punkte-Gauß-Legendre-Integrationsregel ergibt. Außerdem wird er mit den besten unter den anderen Integrationsalgorithmen verglichen.
    Notes: Abstract A new adaptive algorithm for the integration of analytic functions is presented. The algorithm processes the integration interval by generating local subintervals whose length is controlled through a feedback loop. Control is performed by means of a relation derived on an analytical basis and valid for an arbitrary integration rule: two different estimates of an integral are used to compute the interval length necessary to obtain an integral estimate with accuracy within the assigned error bounds. The implied method for local generation of subintervals and an effective assumption of error partition among subintervals give rise to an adaptive algorithm provided with an accurate and very efficient integration process. The particular algorithm obtained by choosing the 6-point Gauß-Legendre integration rule is considered and extensive comparisons are made with other outstanding integration algorithms.
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    Computing 21 (1978), S. 37-52 
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    Description / Table of Contents: Abstract Direct methods for the solution of linear approximation problems tend to fail in practice because of numerical instabilities. Difficulties arise from an undesired accumulation of round-off errors. In [3] and in chapter 2 of this paper effective and inexpensive tests are developed to recognize numerical difficulties and stabilize numerical methods by iterative refinement and restart procedures, if necessary. On the ground of this, a stabilized version of a modified revised dual simplex algorithm can be developed capable of solving the approximation problems under consideration. The technical details of this method and a FORTRAN implementation are given in [4]. Numerical examples are discussed to illustrate that the developed method is superior to commonly used algorithms not only by a broader range of applications and more stability, but also by considerably less storage requirement (for large problems), while the execution times are comparable or less.
    Notes: Zusammenfassung Anhäufungen von Rundungsfehlern führen in der Praxis häufig dazu, daß direkte simplexartige Methoden zur Lösung linearer Approximationsprobleme in der Maximumsnorm versagen. Vor dem approximationstheoretischen Hintergrund des Problems werden in der vorliegenden Arbeit einfach durchzuführende Tests entwickelt, die numerische Schwierigkeitenim voraus anzeigen und so Gegenmaßnahmen ermöglichen. Anhand einer Reihe von Beispielen werden Stabilität, Anwendungsbereich und Grenzen darauf aufbauender Algorithmen diskutiert.
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    Computing 21 (1978), S. 81-86 
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    Description / Table of Contents: Zusammenfassung Für das „0–1 single Knapsack Problem” wird eine FORTRAN-Implementierung eines wirkungsvollen Lösungsverfahrens angegeben. Die angeführten Rechenergebnisse zeigen, daß die vorgeschlagene Methode den derzeit besten bekannten Algorithmen überlegen ist.
    Notes: Abstract The FORTRAN implementation of an efficient algorithm which solves the 0–1 single knapsack problem is given. Computational results are presented, showing the proposed method to be generally superior to the best known algorithms.
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    Meteorology and atmospheric physics 5 (1952), S. 1-4 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Die Bedeutung der hydrodynamischen Instabilität für die Bildung antizyklonaler Wirbel direkt südlich des westlichen Freistrahlstromes in mittleren Breiten wird dargelegt. Ferner macht der Verfasser auf seine früheren Untersuchungen von 1941 über dynamische Instabilität aufmerksam.
    Abstract: Résumé L'auteur montre l'importance de l'instabilité hydrodynamique pour la formation de tourbillons anticycloniques immédiatement au Sud du courant d'Ouest (jet stream) aux latitudes moyennes. Il rappelle ensuite ses précédentes recherches de 1941 sur l'instabilité dynamique.
    Notes: Summary The importance of the hydrodynamic instability for the formation of anticyclonic eddies just south of westerly jet stream in the middle latitudes is pointed out. Finally, the author would like to call attention for his earlier works on dynamic instability in 1941.
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    Meteorology and atmospheric physics 5 (1952), S. 5-16 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Durch die Grenzfläche jedes Luftteilchens, das sich in der Atmosphäre bewegt, strömt ständig Energie in die benachbarte Atmosphäre hinein und aus ihr hinaus. Die Energie, die das Luftteilchen aus der benachbarten Atmosphäre aufnimmt, wird aus der Gradientkraft und aus den Druckkräften durch Gl. (4′) bestimmt. Ein Teil dieser Energie bedingt eine Änderung der potentiellen Energie des barischen Feldes des Luftteilchens, der andere Teil dagegen eine Änderung seiner inneren Energie. Die potentielle Energie des Druckfeldes kann durch die Enthalpie definiert werden. Jedes Luftteilchen besitzt neben anderen Energiearten noch eine äußere Energie, die ihren Sitz nicht im Luftteilchen selbst, sondern außerhalb desselben in der umgebenden Atmosphäre hat; diese Energie ist gleich der Differenz zwischen der Enthalpie und der inneren Energie des Luftteilchens.
    Abstract: Summary Through the boundary surface of any air particle moving in the atmosphere a permanent flow of energy is outgoing and incoming to and from the atmosphere. The energy absorbed by the air particle from the neightbouring atmosphere is defined from the gradient force and the pressure force by the equation (4′). One part of this energy induces a modification of the potential energy of the field of pressure of the air particle, and the other part a variation of the internal energy. The potential energy of the field of pressure can be defined by the enthalpy. In addition to other kinds of energy each air particle holds and external energy, the place of which is not in the air particle itself but in the surrounding atmosphere. This energy is equal to the difference between the enthalpy and the internal energy of the air particle.
    Notes: Résumé De la surface limite de n'importe quelle particule d'air qui se meut dans l'atmosphère sort perpétuellement une énergie dans l'atmosphère ambiante et inversement. En raison de la présence de la force du gradient et de la force de pression, l'énergie que reçoit la particule de l'atmosphère ambiante est établie par l'équation (4′). Une partie de cette énergie détermine une modification de l'énergie potentielle du champ barique de la particule, et l'autre une modification de son énergie interne. L'énergie potentielle du champ barique peut être définie par l'enthalpie. Chaque particule d'air possède, outre les autres énergies, encore une énergie externe qui diffère de l'énergie interne en ce qu'elle ne réside pas dans la particule mais en dehors d'elle, dans l'atmosphère ambiante. Cette énergie est égale à la différence entre l'enthalpie et l'énergie interne de la particule.
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    Monatshefte für Mathematik 56 (1952), S. 1-15 
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    Monatshefte für Mathematik 56 (1952), S. 16-37 
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    Monatshefte für Mathematik 56 (1952), S. 49-60 
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    Monatshefte für Mathematik 56 (1952), S. 38-48 
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    Monatshefte für Mathematik 56 (1952), S. 61-74 
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    Monatshefte für Mathematik 56 (1952), S. 75-88 
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    Monatshefte für Mathematik 56 (1952), S. 89-95 
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    Monatshefte für Mathematik 56 (1952), S. 96-100 
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    Monatshefte für Mathematik 56 (1952), S. 101-104 
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    Monatshefte für Mathematik 56 (1952), S. 105-125 
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    Monatshefte für Mathematik 56 (1952), S. 137-143 
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    Monatshefte für Mathematik 56 (1952), S. 126-136 
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    Monatshefte für Mathematik 56 (1952), S. 144-149 
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    Monatshefte für Mathematik 56 (1952), S. 150-163 
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    Monatshefte für Mathematik 56 (1952), S. 180-180 
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    Monatshefte für Mathematik 56 (1952), S. 164-179 
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