• Korean Journal of Mathematics
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• v.31 no.4
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• pp.445-463
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• 2023

The paper introduces the concept of direct product and discusses some basic facts about distant ideals. We also introduce the definition of directly indecomposable in an autometrized algebra. Furthermore, we present the concept of a subdirect product and simple autometrized algebra and its behavior. We also introduce the definition of subdirectly irreducible in an autometrized algebras. In particular, we prove that every subdirectly irreducible monoid autometrized algebra is directly indecomposable. Finally, we discuss different properties of chain autometrized algebras and introduce the representability in the autometrized algebra. We also prove that if a weak chain monoid normal autometrized l-algebra is nilradical, then it is representable.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.847-853
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• 1999

The purpose of this paper is to develop the theory of coassociated primes and to investigate Melkersson's question [8].

• The Journal of the Korea Contents Association
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• v.13 no.1
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• pp.127-136
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• 2013

This report is aimed to be used as the basic research resource about the various form expression about the picture books, based upon the analysis whether male and female children are different from their preferences to illustrations and whether the expression form between male and female children are different from the other. The objects of study are one hundred and sixteen's of 6 to 7 years old children (male 58 vs. female 58) who are able to understand the illustration. The two times of response surveys were done with one hand is to interview an individual child and the other hand is to fill out by children. The methods used in this study are composed of the representable, simple, exaggerated, and distorted form of expression in order to draw the detail and precise reactions of male and female children In the case of preference analysis of male and female about the illustration, both male and female prefer the distorted form which express contradictively rather than the real, representable, simple, and exaggerate form of expression or which expresses the distorted and the changed by the binding of different things. In the respect of the responses, the various responses were seen to the simple and the exaggerated form in comparative with the representable form. In the respect of the analysis of language response, the individual response was highly marked to the representable form, and the informational response, the heuristic response, and the imaginative response.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1017-1030
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• 2005

In this paper, we study averaging properties in Banach spaces using the Brunel-Sucheston's spreading model. We show that the Schlumprecht space S does not have the Banach­Saks property and II is finitely representable in the Schlumprecht space S using the spreading model properties.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.215-219
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• 1995

The most fundamental examples of (combinatorial) geometries are projective geometries PG(n - 1,q) of dimension n - 1, representable over GF(q), where q is a prime power. Every upper interval of a projective geometry is a projective geometry. The Whitney numbers of the second kind are Gaussian coefficients. Every flat of a projective geometry is modular, so the projective geometry is supersolvable in the sense of Stanley [6].

• Korean Security Journal
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• no.2
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• pp.125-159
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• 1999

The Police is the provider of the Police Service that is the most evident and active. This paper centers on the crime prevention activity of New york City Police Department that is most large and representable in America on account of the enormity of the scale and the material selection. I examine the duty and organization of the City Police Department the Crime Prevention activity of the city police and I research a conclusion.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.167-177
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• 2020

Let I be an ideal of Noetherian local ring (R, m) and M an artinian R-module. In this paper, we study colocalization of local homology modules. In fact we give Colocal-global Principle for the artinianness and minimaxness of local homology modules, which is a dual case of Local-global Principle for the finiteness of local cohomology modules. We define the representation dimension r^I (M) of M and the artinianness dimension a^I (M) of M relative to I by r^I (M) = inf{i ∈ ℕ₀ : H^I_i (M) is not representable}, and a^I (M) = inf{i ∈ ℕ₀ : H^I_i (M) is not artinian} and we will prove that i) a^I (M) = r^I (M) = inf{r^IR_𝖕 (_𝖕M) : 𝖕 ∈ Spec(R)} ≥ inf{a^IR_𝖕 (_𝖕M) : 𝖕 ∈ Spec(R)}, ii) inf{i ∈ ℕ₀ : H^I_i (M) is not minimax} = inf{r^IR_𝖕 (_𝖕M) : 𝖕 ∈ Spec(R) ∖ {𝔪}}. Also, we define the upper representation dimension R^I (M) of M relative to I by R^I (M) = sup{i ∈ ℕ₀ : H^I_i (M) is not representable}, and we will show that i) sup{i ∈ ℕ₀ : H^I_i (M) ≠ 0} = sup{i ∈ ℕ₀ : H^I_i (M) is not artinian} = sup{R^IR_𝖕 (_𝖕M) : 𝖕 ∈ Spec(R)}, ii) sup{i ∈ ℕ₀ : H^I_i (M) is not finitely generated} = sup{i ∈ ℕ₀ : H^I_i (M) is not minimax} = sup{R^IR_𝖕 (_𝖕M) : 𝖕 ∈ Spec(R) ∖ {𝔪}}.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.187-205
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• 2015

We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.241-256
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• 2006

We generalize the $Cram{\acute{e}}r$-von Mises Statistic to test multivariate normality using Roy's union-intersection principle. We show the limit distribution of the suggested statistic is representable as the integral of a suitable Gaussian process. We also consider the computational aspects of the proposed statistic. Power performance is assessed in a Monte Carlo study.

• Korean Institute of Interior Design Journal
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• v.14 no.5 s.52
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• pp.193-204
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• 2005

Design took a radical turn in the 1980's, deconstructing the rigid ideology of the Modernism, often with great humor. Contemporary representable Avant-garde designers, Philippe Starck and Ron Arad brazenly borrowed from the 'historical elements' of previous styles and created bio-morphic forms with whimsical names of furniture. This study is proposed to understand the diversity of contemporary design, by comparing these two furniture designers. It also covers the common factors in contemporary furniture design, and analyzes their individual differences and similarities in design. It helps to plan the foundation of design methods for 21C, and predict and respond to the future as a reference point. Philippe Starck links Romantic Rationalism within Minimal style and Ron Arad links Deconstructivism within High-tech style but both of them pursue of Organic concept design in their furniture through the concept of humanism. They are able to establish a base of contemporary furniture design by adapting new conceptual form, and design process for the general public.