• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.345-362
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• 2023

Prouhet string morphism has been a well investigated morphism in different studies on combinatorics on words. In this paper we consider Prouhet array morphism for the images of binary picture arrays in terms of Parikh q-matrices. We state the formulae to calculate q-counting scattered subwords of the images of any arrays under this array morphism and also investigate the properties such as q-weak ratio property and commutative property under this array morphism in terms of Parikh q- matrices of arrays.

• 대한수학회보
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• 제56권6호
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• pp.1589-1600
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• 2019

In this paper, we apply the notion of cocyclic maps to the category of pairs proposed by Hilton and obtain more general concepts. We discuss the concept of cocyclic morphisms with respect to a morphism and find that it is a dual concept of cyclic morphisms with respect to a morphism and a generalization of the notion of cocyclic morphisms with respect to a map. Moreover, we investigate its basic properties including the preservation of cocyclic properties by morphisms and find conditions for which the set of all homotopy classes of cocyclic morphisms with respect to a morphism will have a group structure.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2021년도 추계학술대회
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• pp.545-546
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• 2021

본 논문에서는 SR DEVS 메카니즘에서 상속의 다형형에 대해 고려한다. 상속 과정에 발생하는 결정 성격은 비결정형일 수 있다. 이 경우 상속 결정을 위해 다형형을 통하여 그 과정이 진행될 수 있다. 다형형에서 예비 선택들에 최종 결정은 그 상황에 따라 달라질 수 있다. 다형형의 경우 상속 순간에 새로운 원형 요소를 생성하는 것이 아니라 기존의 원형 요소들 안에서 선택이 이루어지게 된다.

• 한국지능시스템학회논문지
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• 제19권3호
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• pp.371-374
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• 2009

이 논문에서는 사건과 확률변수를 각각 일반화한 이펙트와 옵저버블을 소개하였다. 그리고 $\sigma$-함수의 개념을 소개하고 이펙트 집합위에서의 확률측도로서의 $\sigma$-함수의 성질을 조사하였다.

• 조형예술학연구
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• 제4권
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• pp.91-122
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• 2002

`Bio morphism` are constituted in paintings where the artists try to embody the elementary properties of living creature as of growth and durability. They are the most appropriate concept of painting to harmonize human being with nature closely. The formative ways of them attach great importance to both unconsciousness and desire , as well as variations or dynamics, by noticing a flow of natural senses and feelings of human being. In other words, the formative ways are based on a recognition of nature as the intrinsic force of life, with the result that aesthetics of incompleteness is embodied in images. Therefore they are clearly distinguished from that of functional, geometric images. A tendency of painting at that time, in a word, 'return to figure and expression', means a conversion into organic images like the incomplete, atypical, and biomorphic forms, while denying the mechanical or geometric. Elizabeth Murray are analyzed, for these works are remarkable in the characteristics of 'Bio morphism'. Consequently the features of organic images, that is, 'the formative acceptance of natural figures, or an informality' and 'the force of free will, or an incompleteness', could obviously be revealed. It is a type that obtains a motif out of natural figures like an animal, a plant, or the concrete figures of human being. In conclusion, this thesis is focused on not only emphasizing that 'Bio morphism' were a major tendency among the various trends of postmodern painting in the 20th century, but also analysing both the painterly formation of organic images and the structure of them. In addition to these points, it is a central aim to evoke that Bio morphism should accurately be evaluated and positioned in postmodern painting. A new recognition of 'Bio morphism' is a peculiarity of the times that reflects a cultural aspect of the present, hence it should be recognized as another way to approach the postmodern painting.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.376-379
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• 1998

We introduce the concept of a 'fuzzy' map between sets by modifying the concept of the extension principle introduced by Dubois and Prade in [1] and study their properties. Using these we generalize Goguen's and Zadeh's extension principles in [2] and [3].

• 대한수학회논문집
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• 제33권2호
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• pp.561-569
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• 2018

In this paper, we introduce some notions of orthogonality in the setting of Finsler $C^*$-modules and investigate their relations with the Birkhoff-James orthogonality. Suppose that ($E,{\rho}$) and ($F,{\rho}^{\prime}$) are Finsler modules over $C^*$-algebras $\mathcal{A}$ and $\mathcal{B}$, respectively, and ${\varphi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a *-homomorphism. A map ${\Psi}:E{\rightarrow}F$ is said to be a ${\varphi}$-morphism of Finsler modules if ${\rho}^{\prime}({\Psi}(x))={\varphi}({\rho}(x))$ and ${\Psi}(ax)={\varphi}(a){\Psi}(x)$ for all $a{\in}{\mathcal{A}}$ and all $x{\in}E$. We show that each ${\varphi}$-morphism of Finsler $C^*$-modules preserves the Birkhoff-James orthogonality and conversely, each surjective linear map between Finsler $C^*$-modules preserving the Birkhoff-James orthogonality is a ${\varphi}$-morphism under certain conditions. In fact, we state a version of Wigner's theorem in the framework of Finsler $C^*$-modules.

• 대한수학회보
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• 제47권6호
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• pp.1311-1327
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• 2010

We introduce the concept of cyclic morphisms with respect to a morphism in the category of pairs as a generalization of the concept of cyclic maps and we use the concept to obtain certain sets of homotopy classes in the category of pairs. For these sets, we get complete or partial answers to the following questions: (1) Is the concept the most general concept in the class of all concepts of generalized Gottlieb subsets introduced by many authors until now? (2) Are they homotopy invariants in the category of pairs? (3) When do they have a group structure?.

• Korean Journal of Mathematics
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• 제14권1호
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• pp.13-33
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• 2006

In this article, we study the relations of horizontally conformal maps and harmonic morphisms with the stability of minimal fibers. Let ${\varphi}:(M^n,g){\rightarrow}(N^m,h)$ be a horizontally conformal submersion. There is a tensor T measuring minimality or totally geodesics of fibers of ${\varphi}$. We prove that if T is parallel and the horizontal distribution is integrable, then any minimal fiber of ${\varphi}$ is volume-stable. As a corollary, we obtain that any fiber of a submersive harmonic morphism whose fibers are totally geodesics and the horizontal distribution is integrable is volume-stable. As a consequence, we obtain if ${\varphi}:(M^n,g){\rightarrow}(N^2,h)$ is a submersive harmonic morphism of minimal fibers from a compact Riemannian manifold M into a surface N, T is parallel and the horizontal distribution is integrable, then ${\varphi}$ is energy-stable.

• 대한수학회논문집
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• 제29권1호
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• pp.155-161
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• 2014

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M{\geq}-\frac{4(p-1)}{p^2}{\mu}_0$ at all $x{\in}M$ and Vol(M) is infinite, where ${\mu}_0$ > 0 is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M. Then any p-harmonic map ${\phi}:M{\rightarrow}N$ of finite p-energy is constant Also, we study Liouville type theorem for p-harmonic morphism.