• Nuclear Engineering and Technology
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• v.52 no.6
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• pp.1137-1147
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• 2020

The discrete ordinates method (S_N) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only -0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.455-465
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• 2016

The number of topologies on a finite set is a famous open problem. In the present paper we discuss a method of obtaining the number of generalized topologies on finite sets.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.865-870
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• 2018

We show that if two nonconstant meromorphic functions f and g on $\mathbb{C}$ sharing some finite sets IM, then there is a nonconstant rational function R(z) such that R(f) = R(g).

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.669-679
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• 2022

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

• Transactions of Materials Processing
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• v.9 no.2
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• pp.165-170
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• 2000

In this paper, a general approach to structural analysis of forging die sets is presented and the related design system, AFDEX/DIE, is introduced. Structural analysis of die sets is conducted by the finite element method considering both contact problem and shrink fit. In the approach, amount of shrink fit is controlled by thermal load, i.e., temperature difference between die insert and shrink rings. The loading conditions are extracted automatically from the simulation results obtained by a rigie-thermoviscoplatic finite element method. Typical application examples are given, which show the applicability of the approach and the related program.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.157-165
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• 2002

The fuzzification of convex sets in median algebras is considered, and some of their properties are investigated. A characterization of finite valued fuzzy convex set is given.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.741-760
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• 2021

In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions. Also, we present some uniqueness theorems which show how two meromorphic functions are uniquely determined by their two finite shared sets. Moreover, in the last section, we make some observations that help us to construct other new classes of unique range sets.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1247-1253
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• 2022

This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give an existence of unique range sets for meromorphic functions that are the zero sets of some polynomials that do not necessarily satisfy the Fujimoto's hypothesis ([6]).

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.853-867
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• 2013

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space $\mathbb{F}^d_q$ over a finite field $\mathbb{F}_q$ with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and ${\mid}E{\parallel}F{\mid}{\geq}Cq^d$ for some large C > 1, then ${\mid}{\Pi}(E,F){\mid}{\geq}cq$ for some 0 < c < 1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.83-116
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• 2020

Let G be a finite group. By a sequence over G, we mean a finite unordered sequence of terms from G, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. The large Davenport constant D(G) is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length D(G) over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.