Many notes deal with the existence problem of solutions for boundary value problems of the kind (1.1). Constructive statements are of a special interest. The first purpose of the following note is to show that it is p...
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Many notes deal with the existence problem of solutions for boundary value problems of the kind (1.1). Constructive statements are of a special interest. The first purpose of the following note is to show that it is possible to obtain all the iterative statements about the existence quoted below in a uniform manner. Secondly we will limit the range of convergence of those iteration processes by discussion of some characteristic eigenvalue problem.
Three enclosing circles are defined for sets that are obtained by addition, subtraction, multiplication and division of complex circles. The algebraic structures resulting from these arithmetic procedures and the radi...
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Three enclosing circles are defined for sets that are obtained by addition, subtraction, multiplication and division of complex circles. The algebraic structures resulting from these arithmetic procedures and the radii of the enclosing circles are compared. In addition to the two arithmetic procedures described by N. Krier [5], the smallest enclosing circles are defined which preserve the algebraic structure ofP(ℂ) („optimal circular arithmetic”). Calculations of an inverse matrix are made by arithmetic procedures for complex circles and axially-parallel rectangles, and the error bounds and computation times are compared.
In different approximation methods in the theory of optimization, very often the solution of the given problem is approached by solving a sequence of problems. It will be denoted, that in each single problem the cost ...
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In different approximation methods in the theory of optimization, very often the solution of the given problem is approached by solving a sequence of problems. It will be denoted, that in each single problem the cost function will not be optimized under the given, but modified constraints. The solution of the original problem is then obtained by limiting process. Typical examples are the cutting plane method and the method ofRitz. In this paper, this procedure will be described in a general way. Further, some sufficiant criteria are presented, under which the limit of the sequence of solutions is an absolute minimum, a relative minimum or a stationary point of the cost function.
A computer programming algorithm is presented which is based on Yen's principle [1] for finding the K loopless paths that have the shortest lengths from one fixed node to another in a network. Several modification...
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A computer programming algorithm is presented which is based on Yen's principle [1] for finding the K loopless paths that have the shortest lengths from one fixed node to another in a network. Several modifications and extensions permitted to construct an extremely efficient algorithm, with regard to the number of necessary memory addresses as well as to the need of operations. The computer time increases linearly with K and is mostly less than the time of Hoffman-Pavley's algorithm [2], moreover, each of the generated paths is loopless. The algorithm published in this paper may be one of the best methods available till now for the solution of the K-shortest paths problem.
Choosing a special case of a general Hermitian interpolating operator, an interpolating spline is constructed with respect to the usual transient-conditions within the knots of the spline. The resulting spline in gene...
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Choosing a special case of a general Hermitian interpolating operator, an interpolating spline is constructed with respect to the usual transient-conditions within the knots of the spline. The resulting spline in general is not a polynomial spline. The polynomial spline is contained as a special case as well as e. g. rational, trigonometrical, and exponential splines. A sufficient criterion for existence and uniqueness is given for general interpolating splines of third degree. A statement concerning convergence is added.
The present paper contains a generalization of the concept of an ordinary differential nquation of nth order with complex variables and deals with existence and uniqueness problems of such gereralized differential equ...
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The present paper contains a generalization of the concept of an ordinary differential nquation of nth order with complex variables and deals with existence and uniqueness problems of such gereralized differential equations.
A binary relation “more canonical than” can be defined for derivationsR, S of a Semi-Thue production system:R<.S. If there is a canonical (leftmost) derivationK in a class [S] of unessentially different derivatio...
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A binary relation “more canonical than” can be defined for derivationsR, S of a Semi-Thue production system:R<.S. If there is a canonical (leftmost) derivationK in a class [S] of unessentially different derivations then the transitive closure ≪. of <. is an irreflexive ordering. Furtheron, [S] is a finite lattice for which theJordan-Dedekind chain condition is fulfilled. [S] can be embedded as a sublattice into the braid group& which has a lattice structure by the relation of right divisibility.& has a weaker structure than lattice groups in the sense ofLorenzen [8] have. As an extra result we gain a further simple algorithm to solve the word problem for the braid group.
Simple methods for solving problems of nonlinear descriptive geometry inR3 by means of a computer and a plotter are suggested: automatic constructions of contours of surfaces in parallel and central projection and of ...
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Simple methods for solving problems of nonlinear descriptive geometry inR3 by means of a computer and a plotter are suggested: automatic constructions of contours of surfaces in parallel and central projection and of parallel and central projections of curves of intersection of two surfaces with hidden lines omitted or dotted. The methods are generally appl.cable to all surfaces which are given by an equation and by equations in parametric form.
In the literature the reduction of the page fault rate in a paging environment is oriented towards the analysis of reference strings of program addresses. Here we describe a method to improve the locality property in ...
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In the literature the reduction of the page fault rate in a paging environment is oriented towards the analysis of reference strings of program addresses. Here we describe a method to improve the locality property in referencing data areas, which we discuss in the actually interesting case of accessing arrays. If the programmer has a suited tool in his programming language to express the freedom in the reference sequence on data, then the compiler can fix the sequence as to minimize the paging behaviour. The details of this approach are given.
Known methods for checking graph isomorphism start with the construction of two partitions of the node sets. The partitioning is made in such a way that each set of the first partition corresponds uniquely to a set of...
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Known methods for checking graph isomorphism start with the construction of two partitions of the node sets. The partitioning is made in such a way that each set of the first partition corresponds uniquely to a set of the second partition under each possibly existing graph isomorphism. The paper deals with a generalization of this idea and describes a direct method for finding finest partitions.
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