The method of Shannon and Lupanov to estimate the minimal size of a logical net for the representation of a typical truth function is generalized to computations in partial algebras of finite type. appl.cations are gi...
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The method of Shannon and Lupanov to estimate the minimal size of a logical net for the representation of a typical truth function is generalized to computations in partial algebras of finite type. appl.cations are given to free groups, polynomial rings over finite fields, Boolean rings and to the approximate computation of real numbers.
作者：
BROMBEER, RFachbereich Mathematik
Universität Kaiserslautern Pfaffenbergstraße 95 D-6750 Kaiserslautern Bundesrepublik Deutschland
A linear discretisation formula (1) for the approximation of a given linear functionalF over a Hilbert spaceH is called a ρ-optimal formula for ρ≧0, if it minimizes\(\left\| {F - \tilde F} \right\|_{H*} \) under th...
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A linear discretisation formula (1) for the approximation of a given linear functionalF over a Hilbert spaceH is called a ρ-optimal formula for ρ≧0, if it minimizes\(\left\| {F - \tilde F} \right\|_{H*} \) under the sidecondition\(r(\tilde F) \leqq \rho \) among all formulas\(\tilde F\) of type (1). Herein\(r(\tilde F)\), is a suitably chosen parameter of the numerical instability of\(\tilde F\) (see (3)).\(\tilde F\) is called relative-optimal if\(\tilde F\) is ρ-optimal for\(r(\tilde F) \leqq \rho \). For very general classes of HilbertspacesHε, ε>0, of analytic functions (whose regions of regularity cover, the hole complex plane for ε→0) we investigate asymptotic properties of relative-optimal formulas: as a main result it is shown that they converge (for ε→0) to the well-known least-square approximate formulas of to a generalized type of least square formulas.
In this paper the well-known multilevel processor-sharing algorithm for M/G/1 systems without priorities is extended to M/G/1 systems with priority classes. The average response timeT j (x) and the average waiting tim...
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In this paper the well-known multilevel processor-sharing algorithm for M/G/1 systems without priorities is extended to M/G/1 systems with priority classes. The average response timeT j (x) and the average waiting timeW j (x) for aj-class job, which requires a total service ofx sec, is analytically calculated. Some figures demonstrate, how the priority classes and the total number of the different levels affect the behavior of the functionsT j (x) andW j (x). In addition, the foreground-background algorithm with priorities, which is in the literature not yet covered, is treated as a special case of the multilevel processor-sharing algorithm.
The mathematical background of some recently proposed cryptographic systems is investigated. The analysis of the mathematics behind these systems, leads to extensions and shows how to avoid insecurity.
The mathematical background of some recently proposed cryptographic systems is investigated. The analysis of the mathematics behind these systems, leads to extensions and shows how to avoid insecurity.
A new model of a Turing Machine, called “Tabulator Turing Machine”, is defined. It can shift its head over several squares of the tape and is therefore more similar to a real computer than a normal Turing Machine. T...
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A new model of a Turing Machine, called “Tabulator Turing Machine”, is defined. It can shift its head over several squares of the tape and is therefore more similar to a real computer than a normal Turing Machine. The complexity classes defined by this machine are different from those defined by a normal multitape Turing Machine. This device is appl.ed to measure the complexity of several recognition procedures for context free languages.
There are well known methods to investigate the mappings-properties of Analytic Functions on Analog computers. In the present paper these methoextended to a more general Function Theory and illustrated by examples.
There are well known methods to investigate the mappings-properties of Analytic Functions on Analog computers. In the present paper these methoextended to a more general Function Theory and illustrated by examples.
A description of the out-of-kilter-algorithm is given which uses only combinatorial means instead of linear programming concepts. The antisymmetry of the system allows a data organization with minimal storage demands....
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A description of the out-of-kilter-algorithm is given which uses only combinatorial means instead of linear programming concepts. The antisymmetry of the system allows a data organization with minimal storage demands. An ALGOL-procedure is given.
We consider boundary-value problems for differential equations, which are the Euler-Lagrange-equation of a variational problem that contains an additional integral along the boundary of the plane domain. For a discret...
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We consider boundary-value problems for differential equations, which are the Euler-Lagrange-equation of a variational problem that contains an additional integral along the boundary of the plane domain. For a discrete analogue of the variational problem we prove the existence of a unique solution and the discrete convergence of this solution to the solution of the continuous problem if the width of the mesh is refined. The shape of a capillary surface is computed using the given discretization and the SOR-Newton-algorithm.
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.
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.
In this paper an iteration method for computing all real roots off (x)=0 in a given interval is proposed. The algorithm can be described very easy by a rekursive procedure. Intervalanalysis is used to solve the proble...
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In this paper an iteration method for computing all real roots off (x)=0 in a given interval is proposed. The algorithm can be described very easy by a rekursive procedure. Intervalanalysis is used to solve the problem. The results are intervals, the union of these intervals contains all roots. Some known methods are special cases of the described algorithm.
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