• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.339-345
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• 2016

The set of priors in the representation of Choquet expectation is expressed as the one of equivalent martingale measures under some conditions. We show that the set of priors, $\mathcal{Q}_c$ in (1.1) is the same set of $\mathcal{Q}^{\theta}$ in (1.3).

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1059-1079
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• 2021

We show that given any chain transitive set of a C¹ generic diffeomorphism f, if a diffeomorphism f has the eventual shadowing property on the locally maximal chain transitive set, then it is hyperbolic. Moreover, given any chain transitive set of a C¹ generic vector field X, if a vector field X has the eventual shadowing property on the locally maximal chain transitive set, then the chain transitive set does not contain a singular point and it is hyperbolic. We apply our results to conservative systems (volume-preserving diffeomorphisms and divergence-free vector fields).

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.71-85
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• 2017

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.29-35
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• 2016

In this paper, we consider a convex optimization problem with a convex integrable objective function and a geometric constraint set. We characterize the solution set of the problem when we know its one solution.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.237-245
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• 2006

The set S of distinct scores (outdegrees) of the vertices of a k-partite tournament T($X_l,\;X_2, ..., X_k$) is called its score set. In this paper, we prove that every set of n non-negative integers, except {0} and {0, 1}, is a score set of some 3-partite tournament. We also prove that every set of n non-negative integers is a score set of some k-partite tournament for every $n{\ge}k{\ge}2$.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.1-5
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• 2007

We study the topological magnitude of a special subset from the distribution subsets in a self-similar Cantor set. The special subset whose every element has no accumulation point of a frequency sequence as some number related to the similarity dimension of the self-similar Cantor set is of the first category in the self-similar Cantor set.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.2
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• pp.484-493
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• 2004

A new lightwave locking technique which can be used in tuning the wavelength of a local laser diode to the reference wavelength is presented in this paper. The optical frequency from the reference laser source and the optical frequency from the local slave VCO laser are heterodyned on a optical receiver, resulting in the 1.5GHz RF signal corresponding to the difference frequency between two input optical signals. The difference frequency is locked to the reference 1.5GHz oscillator source in off-set frequency locking loop. Using the commercialized microwave components, frequency difference detector can be easily established to lock the lightwave. The optical frequency of 1.55um laser diode which keeps the frequency off-set of 1.5GHz is locked to the input reference optical signal with the locking range of 320MHz.

• Journal of the Korean Dietetic Association
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• v.13 no.1
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• pp.1-14
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• 2007

The purpose of this study was to assess students’ preference on set menus served in school foodservice. Questionnaires were distributed to 4,050 students enrolled in 34 middle and high schools located in Seoul, Gyeonggi, and Gyeongnam provinces. The students were asked to assess their preferences on 78 set menus using a 5-point Likert-type scale(1 : very dislike - 5 : very like). Excluding responses with significant missing data, usable responses were 3,433. Data were analyzed with descriptive analysis, t-test, and one-way analysis of variance. There was no difference between middle and high school students in terms of set menu preferences. On the other hand, there was significant difference between boys' and girls' set menu preferences. Among the seven given set menu groups(rice and soup with side dishes, tangs, rice with toppings, fried rice, western foods, noodles.ddeokguk.dumpling soups, and bibimbaps), boys had higher preference scores for the rice and soup with side dishes, tangs, rice with toppings, and fried rice than that of girls. Fried rice set menus were chosen to be boys’ favorite menus while western food set menus were most preferred by the girls. Rice and soup with side dishes set menus were least preferred by both boys and girls.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.687-700
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• 1994

Throughout this paper we will let H denote the complete Heyting algebra ($H, \vee, \wedge, *$) with order reversing involution *. 0 and 1 denote the supermum and the infimum of $\emptyset$, respectively. Given any set X, any element of $H^X$ is called H-fuzzy set (or, simply f.set) in X and will be denoted by small Greek letters, such as $\mu, \nu, \rho, \sigma$. $H^X$ inherits a structure of H with order reversing involution in natural way, by definding $\vee, \wedge, *$ pointwise (sam notations of H are usual). If $f$ is a map from a set X to a set Y and $\mu \in H^Y$, then $f^{-1}(\mu)$ is the f.set in X defined by f^{-1}(\mu)(x) = \mu(f(x))$. Also for $\sigma \in H^X, f(\sigma)$ is the f.set in Y defined by $f(\sigma)(y) = sup{\sigma(x) : f(x) = y}$ ([4]). A preorder R on a set X is reflexive and transitive relation on X, the pair (X,R) is called preordered set. A map $f$ from a preordered set (X, R) to another one (Y,T) is said to be preorder preserving (inverting) if for $x,y \in X, xRy$ implies $f(x)T f(y) (resp. f(y)Tf(x))$. For the terminology and notation, we refer to [10, 11, 13] for category theory and [7] for H-fuzzy semitopogenous spaces.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.743-753
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• 2000

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.