• Journal of applied mathematics & informatics
• /
• v.41 no.2
• /
• pp.345-362
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1589-1600
• /
• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2021.10a
• /
• pp.545-546
• /
• 2021

In this paper, we consider the morphism of inheritance in SR DEVS. The property of determination occurring in the inheritance can be non-deterministic. In this case the process can be implemented for the inheritnace determination through the morphism. The final determination of morphism might be changed as the environments. To the morphsim, it is not the appearance of new element, but the selection is processed in current elements.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.3
• /
• pp.371-374
• /
• 2009

In this paper, we introduce the concepts of effects and observable as generalizations of event and random variable, respectively. Also, we introduce the concept of $\sigma$-morphism and we investigate some results on $\sigma$-morphism as a probability measure on the set of effects.

• Journal of Science of Art and Design
• /
• v.4
• /
• pp.91-122
• /
• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.376-379
• /
• 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].

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.561-569
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1311-1327
• /
• 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
• /
• v.14 no.1
• /
• pp.13-33
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.29 no.1
• /
• pp.155-161
• /
• 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.