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  • 2010-2014
  • 1990-1994  (31)
  • 1985-1989  (16)
  • 1975-1979
  • 1890-1899
  • 1990  (31)
  • 1988  (16)
  • English  (47)
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  • 2010-2014
  • 1990-1994  (31)
  • 1985-1989  (16)
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  • 1890-1899
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  • 1
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    Fast Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. (1990)
    Details
    Publication Date: 2014-02-26
    Description: A family of secant methods based on general rank-1 updates has been revisited in view of the construction of iterative solvers for large non- Hermitian linear systems. As it turns out, both Broydens "good" and "bad" update techniques play a special role - but should be associated with two different line search principles. For Broydens "bad" update technique, a minimum residual principle is natural - thus making it theorectically comparable with a series of well-known algorithms like GMRES. Broydens "good" update technique, however, is shown to be naturally linked with a minimum "next correction" principle - which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized PDE's of convection diffusion type in 2-D with internal layers give a first impression of the possible power of the derived "good" Broyden variant. {\bf Key Words:} nonsymmetric linear system, secant method, rank-1 update, Broydens method, line search, GMRES. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 2
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    An Adaptive Multilevel Approach to Parabolic Equations I. General Theory & 1D-Implementation. (1990)
    Details
    Publication Date: 2014-02-26
    Description: A new adaptive multilevel approach for parabolic PDE's is presented. Full adaptivity of the algorithm is realized by combining multilevel time discretization, better known as extrapolation methods, and multilevel finite element space discretization. In the theoretical part of the paper the existence of asymptotic expansions in terms of time-steps for single-step methods in Hilbert space is established. Finite element approximation then leads to perturbed expansions, whose perturbations, however, can be pushed below a necessary level by means of an adaptive grid control. The theoretical presentation is independent of space dimension. In this part I of the paper details of the algorithm and numerical examples are given for the 1D case only. The numerical results clearly show the significant perspectives opened by the new algorithmic approach.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 3
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    Symplectic Difference Schemes for Perturbed Hamiltonian Systems. (1990)
    Details
    Publication Date: 2014-02-26
    Description: In this paper we consider symplectic difference schemes for perturbed Hamiltonian systems of integrable ones, which can cover many important problems. Symplectic difference schemes for general Hamiltonian systems can also be used to these problems. But the perturbation property has not been paid proper attention to, which is important in the method proposed here. Numerical simulation shows that, for this method the time step size can be taken quite large and the qualitative property , such as preserving invariant tori, is also better than usual symplectic difference schemes.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 4
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    Numerical Treatment of Countable Systems of Ordinary Differential Equations. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and medicine. They can be considered as ordinary differential equations in sequence spaces. In this work, a full adaptive algorithm for the computational treatment of such systems is developed. The method combines time discretization with extrapolation in Hilbert spaces with a discrete Galerkin approach as discretization of the stationary subproblems. The Galerkin method is based on orthogonal functions of a discrete variable , which are generated by certain weight functions. A theory of countable systems in the associated weighted sequence spaces is developed as well as a theory of the Galerkin method. The Galerkin equations can be assembled either by use of analytical properties of the orthogonal functions or numerically by a multilevel summation algorithm. The resulting algorithm CODEX is applied to many examples of technological interest, in particular from polymer chemistry.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 5
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    Uniqueness Theorems for Stiff ODE Initial Value Problems (1990)
    Details
    Publication Date: 2020-03-06
    Language: English
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  • 6
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    Fast secant methods for the iterative solution of large nonsymmetric linear systems (1990)
    Details
    Publication Date: 2021-03-16
    Language: English
    Type: article , doc-type:article
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  • 7
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    Recent Developments in Chemical Computing (1990)
    Details
    Publication Date: 2020-12-14
    Language: English
    Type: article , doc-type:article
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  • 8
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    On Identifying in Polynomial Time Violated Subtour Elimination and Precedence Forcing Constraints for the Sequential Ordering Problem (1990)
    Details
    Publication Date: 2014-02-24
    Language: English
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  • 9
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    Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints (1990)
    Details
    Publication Date: 2014-02-24
    Language: English
    Type: article , doc-type:article
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  • 10
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    Composition of facets of the clique partitioning polytope (1990)
    Details
    Publication Date: 2014-02-24
    Language: English
    Type: bookpart , doc-type:bookPart
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  • 11
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    Facets of the clique partitioning polytope (1990)
    Details
    Publication Date: 2014-02-24
    Language: English
    Type: article , doc-type:article
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  • 12
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    Symbolic Exploitation of Symmetry in Numerical Path-following. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Parameter-dependent systems of nonlinear equations with symmetry are treated by a combination of symbolic and numerical computations. In the symbolic part of the algorithm the complete analysis of the symmetry occurs, and it is here where symmetrical normal forms, symmetry reduced systems, and block diagonal Jacobians are computed. Given a particular problem, the symbolic algorithm can create and compute through the list of possible bifurcations thereby forming a so-called tree of decisions correlated to the different types of symmetry breaking bifurcation points. The remaining part of the algorithm deals with the numerical pathfollowing based on the implicit reparametrisation as suggested and worked out by Deuflhard/Fiedler/Kunkel. The symmetry preserving bifurcation points are computed using recently developed augmented systems incorporating the use of symmetry. {\bf Keywords:} pathfollowing, mixed symbolic-numeric algorithm, parameter-dependent, nonlinear systems, linear representations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 13
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    Symbolic solution of polynomial equation systems with symmetry. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Systems of polynomial equations often have symmetry. The Buchberger algorithm which may be used for the solution ignores this symmetry. It is restricted to moderate problems unless factorizing polynomials are found leading to several smaller systems. Therefore two methods are presented which use the symmetry to find factorizing polynomials, decompose the ideal and thus decrease the complexitiy of the system a lot. In a first approach projections determine factorizing polynomials as input for the solution process, if the group contains reflections with respect to a hyperplane. Two different ways are described for the symmetric group Sm and the dihedral group Dm. While for Sm subsystems are ignored if they have the same zeros modulo G as another subsystem, for the dihedral group Dm polynomials with more than two factors are generated with the help of the theory of linear representations and restrictions are used as well. These decomposition algorithms are independent of the finally used solution technique. We used the REDUCE package Groebner to solve examples from CAPRASSE, DEMARET and NOONBURG which illustrate the efficiency of our REDUCE program. A short introduction to the theory of linear representations is given. In a second approach problems of another class are transformed such that more factors are found during the computation; these transformations are based on the theory of linear representations. Examples illustrate these approaches. The range of solvable problems is enlarged significantly.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 14
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    On Symplectic Difference Schemes for Hamiltonian Systems. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Symplectic difference schemes have been shown to be a right formalism for numerical computation of Hamiltonian systems. They are suitable to long time computation and of good qualitative properties. These properties are ensured by the fact that a symplectic difference scheme approximating to a time-independent Hamiltonian system can be regarded as a perturbed time-dependent Hamiltonian system of the original one. That is, a solution of a symplectic difference scheme is a solution of a certain perturbed time dependent Hamiltonian system evaluated at discrete (time) points. This is the main result of the paper. Moreover, linear symplectic difference schemes approximating to a linear time-independent Hamiltonian system can be regarded as a perturbed time-independent Hamiltonian system. So it has all properties that a linear Hamiltonian system has. Based on these results, stochastic webs and chaos in symplectic difference schemes are also discussed. They will appear in numerical simulation for Hamiltonian systems, even with one degree of freedom.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 15
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    Self Adaptive FEM Simulation of Reverse Biased pn-Junctions. (1990)
    Details
    Publication Date: 2014-02-26
    Description: The potential distribution of reverse biased pn-junctions can be described by a double obstacle problem for the Laplacian. This problem is solved by a self adaptive Finite Element Method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse biased pn- junction with multi-step field plate and stop- electrode to illustrate its efficiency and reliability.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 16
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    Asymptotic Mesh Independence of Newton-Galerkin Methods via a Refined Mysovskii Theorem. (1990)
    Details
    Publication Date: 2020-12-15
    Description: The paper presents a theoretical characterization of the often observed asymptotic mesh independence of Newton's method, which means that Newton's method applied to discretized operator equations behaves essentially the same for all sufficiently fine discretizations. The theory does not need any uniform Lipschitz assumptions that were necessary in comparable earlier treatments. The refined Newton-Mysovskii theorem, which will be of interest in a wider context, gives both existence and uniqueness of the solution and quadratic convergence for sufficiently good starting points. Attention is restricted to Galerkin approximations even though similar results should hold for finite difference methods - but corresponding proofs would certainly be more technical. As an illustrative example, adaptive 1-D collocation methods are discussed.
    Keywords: ddc:000
    Language: English
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  • 17
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    Automatic Generation of Reaction Mechanisms for Description of Oxidation of Higher Hydrocarbons. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Oxidation mechanisms even for rather simple hydrocarbons like heptane consist due to the occurrence of many isomeric structures of thousands of reactions of hundreds of species. The automatic generation of these reaction mechanisms using artificial intelligence means is described. Results are presented for n-heptane-air mixtures, where a hand-written reaction mechanism tested against experimental data is available.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 18
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    Recent Developments in Chemical Computing. (1990)
    Details
    Publication Date: 2014-02-26
    Description: The paper surveys three aspects of chemical computing, which seem to play a role in recent developments. First, extrapolation methods for the numerical treatment of differential- algebraic equations are introduced. The associated extrapolation code LIMEX has reached a certain level of sophistication, which makes it a real competitor to the elsewhere widely used multi-step code DASSL of Petzold. Second, adaptive methods of lines for partial differential equations such as those arising in combustion problems are treated. Both static and dynamic regridding techniques are discussed in some detail. Finally, some new ideas about the treatment of the kinetic equations arising from polymer reactions are presented. The new feature of the suggested approach is the application of a Galerkin procedure using sets of orthogonal polynomials over a discrete variable (which, of course, in the case of polymer reactions is the polymer degree). The new approach may open the door to a new reliable low dimensional treatment of complex polymer reactions.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 19
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    Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions. (1990)
    Details
    Publication Date: 2014-02-26
    Description: The discrete Galerkin method developed by the authors has turned out to be an efficient tool for the computational treatment of very large scale ODE systems arising in polyreaction kinetics. Up to now, this approach has been worked out in detail for homogeneous polymer reactions. The present paper deals with one line of possible extensions of the method to the case of so-called heterogeneous processes, which may appear e. g. in smog reactions. The associated mathematical models involve reaction coefficients depending on the chain length of the reacting polymer. The herein suggested extension is worked out in some detail on the basis of the earlier paper. In addition, a numerical example describing polymer degradation is included.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 20
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    Global Inexact Newton Methods for Very Large Scale Nonlinear Problems. (1990)
    Details
    Publication Date: 2014-02-26
    Description: Newton methods for nonlinear problems are known to require the solution of a sequence of linear problems of the same type. For very large scale problems, as understood herein, the arising linear systems can only be solved by iterative methods. Then Newtons iteration appears as outer iteration. The question of interest will be to control the accuracy of the inner iteration such that the convergence speed of Newtons method is preserved. The purpose of the paper is to combine the concept of inexact Newton methods with the concept of the affine invariant exact Newton methods - which is important for problems with ill- conditioned Jacobian matrices (such as typical 2-D or 3-D discretized partial differential equations).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 21
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    Sparse Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. (1990)
    Details
    Publication Date: 2014-02-26
    Description: A variety of secant methods has been revisited in view of the construction of iterative solvers for large nonsymmetric linear systems $ Ax = b $ stemming from the discretization of convection diffusion equations. In the first section, we tried to approximate $ A ^{-1} $ directly. Since the sparsity structure of A- is not known, additional storage vectors are needed during the iteration. In the next section, an incomplete factorization $ LU $ of $ A $ is the starting point and we tried to improve this easy invertible approximation of $ A $. The update is constructed in such a way that the sparsity structure of $ L $ and $ U $ is maintained. Two different sparsity preserving updates are investigated from theoretical and practical point of view. Numerical experiments on discretized PDEs of convection diffusion type in 2- D with internal layers and on "arbitrary" matrices with symmetric sparsity structure are given. {\bf Key words:} nonsymmetric linear system, sparse secant method, Broyden's method, incomplete factorization.
    Keywords: ddc:000
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  • 22
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    Numerical Treatment of Polyreactions - Recent Developments. (1990)
    Details
    Publication Date: 2014-02-26
    Description: The mathematical modeling of macromolecular reactions leads to countable (possibly infinite) systems of ordinary differential equations (CODE's). This paper reviews two recent developments of the so-called discrete Galerkin method, which has been developed for the numerical treatment of countable systems, which arise e.g. in polymer chemistry. The first approach can be considered as a method of lines with moving basis functions and has been implemented recently in the program package MACRON. The second type of the Galerkin method is characterized by a so-called outer time discretization of the complete problem and an appropriate and efficient solution of the arising subproblems. This method is realized in the research code CODEX.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 23
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    An Adaptive Multilevel Approach to Parabolic Equations II. (1990)
    Details
    Publication Date: 2014-02-26
    Description: In continuation of part I this paper develops a variable-order time discretization in Hilbert space based on a multiplicative error correction. Matching of time and space errors as explained in part I allows to construct an adaptive multilevel discretization of the parabolic problem. In contrast to the extrapolation method in time, which has been used in part I, the new time discretization allows to separate space and time errors and further to solve fewer elliptic subproblems with less effort, which is essential in view of the application to space dimension greater than one. Numerical examples for space dimension one are included which clearly indicate the improvement.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 24
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    Improvement of Incomplete Factorizations by a Sparse Secant Method. (1990)
    Details
    Publication Date: 2014-02-26
    Description: In the present paper, the improvement of an incomplete factorization of a non-symmetric matrix A is discussed. Starting from the ideas of sparsity preserving quasi-Newton methods, an algorithm is developed which improves the approximation of A by the incomplete factorization maintaining the sparsity structure of the matrices. No renumbering of the unknowns or the admittance of additional fill-in is necessary. The linear convergence of the algorithm is proved under the assumption, that $ L $ and $ U $* have the same sparsity structure and an incomplete factorization with some reasonable approximation property exits. In combination with this algorithm, the method of incomplete factorization and its several modifications are applicable to a wider class of problems with improved convergence qualities. This is shown by a numerical example. {\bf Key Words:} non-symmetric linear system, sparse secant method, incomplete factorization. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20, 65N30.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 25
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    MACRON - A Program Package for Macromalecular Reaction Kinetics. (1990)
    Details
    Publication Date: 2014-02-26
    Description: This paper presents the new program package MACRON for the simulation of macromolecular kinetics including standard chemical reactions. Such problems lead to countable (possibly) infinite systems of ordinary differential equations (CODE's), which are numerically treated by the so-called discrete Galerkin method here. By a chemical compiler the required analytical preprocessing is performed, such that the complete reaction system, standard kinetics as well as macromolecular reactions, can be entered in the chemical formalism. Typical macromolecular reaction steps are chain addition, termination, chain transfer and degradation (cracking). In order to ensure efficiency and reliability, high sophisticated numerical routines are built within the package. MACRON can be used without a detailed knowledge of the used numerical methods. As an illustration the application of MACRON to some realistic problems is presented.
    Keywords: ddc:000
    Language: English
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  • 26
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    Power-Law Type Solutions of Fourth-Order Gravity (1990)
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    Publication Date: 2014-02-26
    Description: We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension $ d = 3 $ , the Einsteinian Kasner metric is still the most general power-law type solution, for $ d 〉 3 $ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the $ d $-dimensional space into a ( $ d - 3 $)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when $ d = 9 $).
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  • 27
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    BOXES - a Program to Generate Triangulations from a Rectangular Domain Description. (1990)
    Details
    Publication Date: 2014-02-26
    Description: BOXES computes a triangulation from a 2D domain description which consists of an arbitrary set of rectangles. Each rectangle may have attributes to control the triangulating process, define subdomain classes, or specify boundary conditions. The output of the program can be used as a coarse grid for KASKADE or one of its variants. Additional features are extensive checking of the user input, graphical display, and simple editing.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 28
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    GIANT - A Software Package for the Numerical Solution of Very Large Systems of Highly Nonlinear Equations. (1990)
    Details
    Publication Date: 2014-02-26
    Description: This report presents the final realization and implementation of a global inexact Newton method proposed by Deuflhard. In order to create a complete piece of software, a recently developed iterative solver (program GBIT) due to Deuflhard, Freund, Walter is adapted and serves as the standard iterative linear solver. Alternative linear iterative solvers may be adapted as well, e.g. the widely distributed code GMRES. The new software package GIANT (Global Inexact Affine Invariant Newton Techniques) allows an efficient and robust numerical solution of very large scale highly nonlinear systems. Due to the user friendly interface and its modular design, the software package is open for an easy adaptation to specific problems. Numerical experiments for some selected problems illustrate performance and usage of the package.
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    Language: English
    Type: reportzib , doc-type:preprint
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  • 29
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    Simulation und Herstellung von Faserschleifkopplern (1990)
    Details
    Publication Date: 2022-07-07
    Language: English
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  • 30
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    Vectorization and Parallelization of Irregular Problems via Graph coloring. (1990)
    Details
    Publication Date: 2022-07-19
    Description: Efficient implementations of irregular problems on vector and parallel architectures are generally hard to realize. An important class of problems are Gauß-Seidel iteration schemes applied to irregular data sets. The unstructured data dependences arising there prevent restructuring compilers from generating efficient code for vector or parallel machines. It is shown, how to structure the data dependences by decomposing the underlying data set using graph coloring techniques and by specifying a particular execution order already on the algorithm level. Methods to master the irregularities originating from different types of tasks are proposed. An application is given and some open issues and future developments are discussed.
    Keywords: ddc:000
    Language: English
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  • 31
    Book
    Book
    Linear programming and network flows / (1990)
    New York :Wiley,
    Details
    Title: Linear programming and network flows /
    Author: Bazaraa, Mokhtar S.
    Contributer: Jarvis, John J. , Sherali, Hanif D.
    Edition: 2. ed.
    Publisher: New York :Wiley,
    Year of publication: 1990
    Pages: XIV, 684 S.
    ISBN: 0-471-63681-9
    Type of Medium: Book
    Language: English
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 32
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    Implementation of the LISP-Arbitrary Precision Arithmetic for a Vector Processor. (1988)
    Details
    Publication Date: 2018-12-06
    Description: Portable Standard LISP (PSL, Version 3.4) and REDUCE 3 were implemented for CRAY1 and Cray X- MP computers at the Konrad-Zuse-Zentrum Berlin in 1986. As an special aspect of the implementation of PSL, an interface to the vector hardware of CRAY processors was defined. With that interface and mostly driven by the needs of REDUCE applications (e.g. extensive calculations of Gröbner bases), the arbitrary precision integer arithmetic of PSL was rebuild using full power of the vector hardware. A modular arithmetic using vector hardware was also constructed.
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  • 33
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    Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs. (1988)
    Details
    Publication Date: 2014-02-26
    Description: Induction heating of large steel slabs can be described by a coupled system of nonlinear evolution equations of Stefan type representing the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi-grid algorithms are given which combined with a nested iteration type continuation strategy to proceed in time result in computationally highly efficient schemes for the numerical simulation of the induction heating process. {\bf Keywords:} induction heating, system of two coupled Stefan equations, multi-grid algorithms. {\bf Subject Classification:} AMS(MOS): 35K60, 35R35, 65H10, 65N05, 65N20, 78A25, 78A55.
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    Language: English
    Type: reportzib , doc-type:preprint
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  • 34
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    On Gröbner Bases Computation on a Supercomputer Using REDUCE. (1988)
    Details
    Publication Date: 2018-12-06
    Description: Gröbner bases are the main tool for solving systems of algebraic equations and some other problems in connection with polynomial ideals using Computer Algebra Systems. The procedure for the computation of Gröbner bases in REDUCE 3.3 has been modified in order to solve more complicated algebraic systems of equations by some general improvements and by some tools based on the specific resources of the CRAY X-MP. We present this modification and illustrate it by examples.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 35
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    Concepts of an Adaptive Hierarchical Finite Element Code. (1988)
    Details
    Publication Date: 2014-02-26
    Description: The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this approach permits a flexible balance between iterative solver, local error estimator, and local mesh refinement device - which are the main components of an adaptive PDE code. Without use of standard multigrid techniques, the same kind of computational complexity is achieved - independent of any uniformity restrictions on the applied meshes. In addition, the method is extremely simple and all computations are purely local - making the method particularly attractive in view of parallel computing. The algorithmic approach is illustrated by a well-known critical test problem. {\bf Keywords:} finite elements, hierarchical basis, adaptive mesh refinement, preconditioned conjugate gradient methods.
    Keywords: ddc:000
    Language: English
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  • 36
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    REDUCE User s Guide for the CRAY 1 / CRAY X-MP Series Running UNICOS. Version 3.3. (1988)
    Details
    Publication Date: 2018-12-06
    Description: This document describes operating procedures for running REDUCE specific to the CRAY 1 and CRAY X-MP computers running the Operating System UNICOS. The document was derived from the corresponding document for Vax/UNIX prepared by A. C. Hearn and L. R. Seward, The Rand Corporation, Santa Monica, (CP85).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 37
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    Thermal recovery after passage of the pulmonary circulation assessed by deconvolution (1988)
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    Publication Date: 2020-03-06
    Language: English
    Type: article , doc-type:article
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  • 38
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    Evaluation of monoexponential extrapolation of transpulmonary thermal-dye kinetics by use of a new model-free deconvolution algorithm (1988)
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    Publication Date: 2020-03-06
    Language: English
    Type: article , doc-type:article
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  • 39
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    An application of combinatorial optimization to statistical physics and circuit layout design (1988)
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    Publication Date: 2014-02-24
    Language: English
    Type: article , doc-type:article
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  • 40
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    Geometric Algorithms and Combinatorial Optimization (1988)
    Details
    Publication Date: 2020-11-16
    Language: English
    Type: book , doc-type:book
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  • 41
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    Computational Treatment of Polyreaction Kinetics by Orthogonal Polynomials of a Discrete Variable. (1988)
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    Publication Date: 2014-02-26
    Description: The paper presents a new approach to the computational treatment of polyreaction kinetics. This approach is characterized by a Galerkin method based on orthogonal polynomials of a discrete variable, the polymer degree (or chain length). In comparison with the known competing approaches (statistical moment treatment, Galerkin methods for continuous polymer models), the suggested method is shown to avoid the disadvantages and preserve the adventages of either of them. The basic idea of the method is the construction of a discrete inner product associated with a reasonably chosen probability density function. For the so-called Schulz-Flory distribution one thus obtains the discrete Laguerre polynomials, whereas the Poisson distribution leads to the Charlier polynomials. Numerical experiments for selected polyreaction mechanisms illustrate the efficiency of the proposed method.
    Keywords: ddc:000
    Language: English
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  • 42
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    Symbolic Solution of Large Stationary Chemical Kinetics Problems. (1988)
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    Publication Date: 2018-12-06
    Description: The paper presents a new application of computer algebra to the treatment of steady states of reaction systems. The method is based on the Buchberger algorithm. This algorithm was modified such that it can exploit the special structure of the equations derived from reaction systems, so even large systems can be handled. In contrast to numerical approximation techniques, the algebraic solution gives a complete and definite overview of the solution space and it is even applicable when parameter values are unknown or undetermined. The algorithm, its adaptation to the problem class and its application to selected examples are presented.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 43
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    REDUCE Installation Guide for CRAY 1 / X-MP Systems Running UNICOS. Version 3.3. (1988)
    Details
    Publication Date: 2018-12-06
    Description: This guide describes the CRAY/UNICOS REDUCE distribution tape and the procedures for installing, testing and maintaining REDUCE on a CRAY 1 or CRAY X-MP running UNICOS. This document was derived from the corresponding document for Vax/UNIX prepared by A. C. Hearn and L.R. Seward, The Rand Corporation, Santa Monica, publication CP84.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 44
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    Global Decoupling of Coupled Symmetric Oscillators. (1988)
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    Publication Date: 2014-02-26
    Description: We model a symmetric system of coupled oscillators as a graph with symmetry group $\gamma$. Each vertex of the graph represents an "oscillator" or a "cell" of reactants. The magnitude (concentration) of the reactants in the $ i $ th cell is represented by a vector $ x^i $. The edges represent the coupling of the cells. The cells are assumed to evolve by identical reaction-diffusion equation which depends on the sum of the reactants in the nearest neighbors. Thus the dynamics of the system is described by a nonlinear differential system \begin{flushleft} \[ \mbox {(*) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \dot{x}^i = f (x^i,\sum_{j \in N_i} x^j), \mbox { \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \] \end{flushleft} where the sum ranges over the set $ N_i $ of neighbors of cell $ i $ . If $ f $ also has a symmetry (e.g., oddness), there are geometric conditions on the graph such that the nonlinear system $ (*) $ decouples globally into a product flow on certain sums of isotropy subspaces. Thus we may detect higher-dimensional tori of solutions of $ (*) $ which are not amenable to other types of analysis. We present a number of examples, such as bipartite graphs, complete graphs, the square, the octahedron, and a 6-dimensional cube.
    Keywords: ddc:000
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  • 45
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    Parallel Polynomial Operations in the Buchberger Algorithm. (1988)
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    Publication Date: 2018-12-06
    Description: The Buchberger algorithm is a basic tool for the solution of systems of polynomial equations in an environment of computer algebra applications. A model for overlapped processing of different steps of the algorithm is presented, which uses the data structure of the polynomials (distributive representation) for synchronization. The model can be applied for multi processors with fast access to shared data. It is tested with Cray X-MP multi processors based on a parallel version of Portable Standard Lisp (PSL 3.4).
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    Language: English
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  • 46
    Book
    Book
    Flames /; Part 1 (1988)
    Details
    Title: Flames /; Part 1
    Author: Kuhl, A. L.
    Year of publication: 1988
    Pages: XIX, 439 S.
    Series Statement: Dynamics of reactive systems Part 1
    ISBN: 0-930403-46-0
    Type of Medium: Book
    Language: English
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  • 47
    Book
    Book
    Global bifurcation of periodic solutions with symmetry /; 1309 (1988)
    Berlin [u.a.] :Springer,
    Details
    Title: Global bifurcation of periodic solutions with symmetry /; 1309
    Author: Fiedler, Bernold
    Publisher: Berlin [u.a.] :Springer,
    Year of publication: 1988
    Pages: VIII, 144 S. : , Ill., graph. Darst.
    Series Statement: Lecture notes in mathematics 1309
    ISBN: 3-540-19234-4 , 0-387-19234-4
    Type of Medium: Book
    Language: English
    Parallel Title: obal bifurcation of periodic solutions with symmetry
    URL: http://www.zentralblatt-math.org/zmath/en/search/?an=0644.34038
    URL: http://www.gbv.de/dms/hbz/toc/ht003121723.pdf
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