• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.309-318
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• 2009

We prove the homogeneous property of the norm of the new space $L\alpha(X)$ which has been developed in [3]. We also present $Poincar\acute{e}^{\prime}s$ inequality that is fitted to the function space $L\alpha(X)$ with an appropriate slope condition.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• 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.38 no.4
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• pp.719-725
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• 2001

For a p-compact group G, if G-space X is of finite S-type then we show that the localization $S^{-1}H^*(X_{hG})$is zero. By using this result, we prove the localization theorem for the pair G-space (X, A)

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.525-527
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• 2019

Let X be a completely regular space and let β(X) be the Stone-Čech compactification of X. A flow 𝜙 on X can be extended to a flow 𝚽 on β(X).

• Honam Mathematical Journal
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• v.36 no.2
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• pp.253-261
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• 2014

In this paper, we first will show that for any space X and any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$, (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is the minimal quasi-F cover of X if and only if (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is a quasi-F cover of X and $\mathcal{A}{\subseteq}\mathcal{Q}_X$. Using this, if X is a locally weakly Lindel$\ddot{o}$f space, the set {$\mathcal{A}|\mathcal{A}$ is a Wallman sublattice of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$ and ${\Phi}^{-1}_{\mathcal{A}}(X)$ is the minimal quasi-F cover of X}, when partially ordered by inclusion, has the minimal element $Z(X)^{\sharp}$ and the maximal element $\mathcal{Q}_X$. Finally, we will show that any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}{\subseteq}\mathcal{Q}_X$, ${\Phi}_{\mathcal{A}_X}:{\Phi}^{-1}_{\mathcal{A}}(X){\rightarrow}X$ is $z^{\sharp}$-irreducible if and only if $\mathcal{A}=\mathcal{Q}_X$.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.49 no.12
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• pp.997-1010
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• 2021

This study collected and analyzed flight data of SpaceX's Falcon 9 launch vehicle. All missions were classified by orbital types, such as Polar, SSO, ISS, LEO and GTO missions. In characteristic maneuvers of main engine cutoff, boostback, reentry and landing burn at each stage of 1st stage launch vehicle, changes of the physical parameters like speed, altitude, dynamic pressure and acceleration were investigated. The guidelines derived from detailed maneuver analysis were suggested, which can be used as design and evaluation references for developing reusable launch vehicle.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.37-43
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• 2014

In this paper, we show that for any ${\sigma}$-complete Boolean subalgebra $\mathcal{M}$ of $\mathcal{R}(X)$ containing $Z(X)^{\sharp}$, the Stone-space $S(\mathcal{M})$ of $\mathcal{M}$ is a basically diconnected cover of ${\beta}X$ and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed $\mathcal{M}$-ultrafilter} of the Stone-space $S(\mathcal{M})$ is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and $\mathcal{M}{\subseteq}\{\Lambda_X(A){\mid}A{\in}Z({\Lambda}X)^{\sharp}\}$.