• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.457-473
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• 2005

In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary to decide whether to construct the Lanczos vectors $v_{n+l}\;and\;w{n+l}$ as regular or inner vectors. For a regular step it is necessary that $D_k\;=\;W^{T}_{k}V_{k}$ is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix $D_k$, ${\sigma}_min(D_k)$, is computed and an inner step is performed if $\sigma_{min}(D_k)<{\epsilon}$, where $\epsilon$ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance $\epsilon$. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.

• 충청수학회지
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• 제30권4호
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• pp.445-447
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• 2017

We investigate congruence properties of Fourier coefficients of modular forms for ${\Gamma}^+_0(2)$.

• Structural Engineering and Mechanics
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• 제29권5호
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• pp.469-488
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• 2008

Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

• 대한전자공학회논문지
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• 제27권6호
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• pp.910-920
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• 1990

This paper presents a method of constructing an Arithmetic Operation Unit Systems (A.O.U.S.) over Galois Field GF(2**m) for the purpose of the four arithmetical operation(addition, subtraction, multiplication and division between two elements in GF(2**mm). The proposed A.O.U.S. is constructed by following procedure. First of all, we obtained each four arithmetical operation algorithms for performing the four arithmetical operations using by mathematical properties over GF(2**m). Next, for the purpose of realizing the four arithmetical unit module (adder module, subtracter module, multiplier module and divider module), we constructed basic cells using the four arithmetical operation algorithms. Then, we realized the four Arithmetical Operation Unit Modules(A.O.U.M.) using basic cells and we constructd distributor modules for the purpose of merging A.O.U.M. with distributor modules. Finally, we constructed the A.O.U.S. over GF(2**m) by synthesizing A.O.U.M. with distributor modules. We prospect that we are able to construct an Arithmetic & Logical Operation Unit Systems (A.L.O.U.S.) if we will merge the proposed A.O.U.S. in this paper with Logical Operation Unit Systems (L.O.U.S.).

• 호남수학학술지
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• 제35권4호
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• pp.739-746
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• 2013

There are several ways to normalize a Haar measure on the orders in a quaternion algebra. In order to understand the arithmetic properties of orders, we study the volumes of orders and compute them for some cases.

• 대한수학회논문집
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• 제20권2호
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• pp.231-238
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• 2005

In this paper, we study the arithmetic properties of orders in a quaternion algebra over a dyadic local field and we find the mass formula of orders.

• Korean Journal of Mathematics
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• 제26권2호
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• pp.167-174
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• 2018

By acting the dihedral group $D_k$ on the set of k-tuple multi-partitions, we introduce k-gonal partitions for all positive integers k. We give generating functions for these new partition functions and investigate their arithmetic properties.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권1호
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• pp.79-92
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• 2000

We investigate numerical properties of Newton's algorithm for improving an eigenpair of a real matrix A using only fixed precision arithmetic. We show that under natural assumptions it produces an eigenpair of a componentwise small relative perturbation of the data matrix A.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.209-216
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• 2002

In this paper, we introduce a concept of (H)-property which generalize that of increasing(decreasing) property of binary operation. We also treat some works related to operations on fuzzy numbers and generalize earlier results of Kawaguchi and Da-te(1994).

• 대한수학회논문집
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• 제22권4호
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• pp.493-502
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• 2007

We prove that certain square functions of Littlewood-Paley type satisfy certain mapping properties on $L^q(\mathbb{Q}_p^d)$.