• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.211-219
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• 1997

In [6] we proved that if a nals X is reflexive, then $X = W_X + V_X$ . In this paper we show that, for a split nals $X = W_X + V_X$, X is reflecxive if and only if $V_X$ and $W_X$ are reflcxive.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.127-133
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• 1997

O. Mayer[9] introduced an almost linear space (als), a generalization of a linear space. The notion of a basis for an als was introduced by G. Godini[3]. Later, man properties of an als established by a number of authors. In this paper, we prove that the cardinality of bases for an als is unique. All spaces involved in this paper are over the real field $R$. Let us denote by $R_+$ the set ${\lambda \in R : \lambda \geq 0}$. We recall some definitions used in this paper.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.679-688
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• 2014

The notion of asymptotically negative dependence for collection of random variables is generalized to a Hilbert space and the almost sure convergence for these H-valued random variables is obtained. The result is also applied to a linear process generated by H-valued asymptotically negatively dependent random variables.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.185-192
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• 2003

It is shown that every almost linear mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,$r\;{\neq}\;1$$x{\;}{\in}{\;}X$, that every almost quadratic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a quadratic mapping when $h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$, and that every almost cubic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a cubic mapping when $h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.181-188
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• 2021

Let X be a nondegenerate reduced closed subscheme in ℙⁿ. Assume that π_q : X → Y = π_q(X) ⊂ ℙ^n-1 is a generic projection from the center q ∈ Sec(X) \ X where Sec(X) = ℙⁿ. Let Z be the singular locus of the projection π_q(X) ⊂ ℙ^n-1. Suppose that I_X has the almost minimal presentation, which is of the form R(-3)^β_2,1 ⊕ R(-4) → R(-2)^β_1,1 → I_X → 0. In this paper, we prove the followings: (a) Z is either a linear space or a quadric hypersurface in a linear subspace; (b) $H^1({\mathcal{I}_X(k)})=H^1({\mathcal{I}_Y(k)})$ for all k ∈ ℤ; (c) reg(Y) ≤ max{reg(X), 4}; (d) Y is cut out by at most quartic hypersurfaces.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1341-1364
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• 2023

This article introduces a method for estimating the conditional hazard function of a real-valued response variable based on a functional variable. The method uses local linear estimation of the conditional density and cumulative distribution function and is applied to a functional stationary ergodic process where the explanatory variable is in a semi-metric space and the response is a scalar value. We also examine the uniform almost complete convergence of this estimation technique.

• Korean Institute of Interior Design Journal
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• no.41
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• pp.163-171
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• 2003

The scope of the study involves comparison of theaters in the west and those in the east, which experienced almost no exchange between them in the past, due to diverse restrains including a geographical one. The focus was put on the two types of these theaters whose similarities are meager historically and technologically, and whose link was not verified yet. However, similarities ,if any, will be identified among characteristics of these theaters so that the links such as liberalism, nomadic and participatory nature, non-linear space, ambivalence, mobile space-which are modern characteristics- could be connected from the past to the present, and those modern characteristics can be studied as a process where they could be sensed from the past structure or from each different target.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.2_2
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• pp.271-278
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• 2022

The solar energy has been widely used to reduce the fossil fuel and prevent the environmental pollution. The renewable energy including solar heat tends to spread due to carbon neutrality for main country of the world. Targets of solar collector are usually acquisitions of hot water or hot air. Especially, air-heating collector using solar heat is known as the technology for obtaining hot air. This study aims to investigate of characteristics of thermal flow when the hot air by air-heating collector using solar heat flows inside of indoor space. The thermal flow of heating indoor space was simulated using ANSYS-CFX program and thus the behaviors of hot air in indoor space were evaluated with standard k-𝜀 turbulence model. As the results, as the inlet velocity was increased, the behaviors of hot air became simple, and temperature range of 25~75℃ had almost no effect on behavior of flow. As the inlet temperature was increased, the temperature curve of indoor space from bottom to top was changed from linear to quadratic. Furthermore, it was confirmed that inlet velocity as well as inlet temperature also should be considered to heat indoor space equally by air-heating collector using solar heat.

• Journal of the Architectural Institute of Korea Planning & Design
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• v.36 no.2
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• pp.13-24
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• 2020

This study derives the characteristics of the private external space planning in multi-family housing through the analysis of the good case built after 2000 in Europe. First, the cases were categorized into block or block perimeter, linear and point type to examine the relationship between the type of building in urban context and the location of private external space. By block or block perimeter and linear type, private external spaces are planned in the inner courtyards or open space between buildings used as common space for residents, inducing communications between neighbors. And the direction of private external space depends on the arrangement of the building mass in urban context. In the classification as point type, there are many cases, where private external spaces are arranged in all directions, connected almost all interior spaces. Second, based on the above results, the planned characteristics of the private external space are derived by dividing it into three categories: intermediated space between inside and outside, intermediate space between private and public /individual and collective space and the identity of the intermediate space. (1) In most cases, direction, size of enclosed area and location of private extern space is designed to fit the surrounding context, so residents can perceive as much of the assets of the surrounding environment as possible, and it can be used as an extended area of living space. In another cases, it is divided into various sub-areas to experience the spatial transition from inside to outside or vice versa. 2) The private external space, which is placed in a courtyard or in a collective open space, is partially enclosed and blocked, allowing interaction with the neighbors without pressure. Along the street, they are designed to allow residents to experience the vitality of the city and to be formative element of the facade, which could confidently reveal the lifestyle and taste of residents. 3) By some of point types, which facade is three-demensional layer as a habitable external space, the private external space is very flexible for use. This intermediate space is composed of diverse spaces for various needs, or it has generous size with positional conditions connected with all interior spaces to be used multi-functional.