• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.47-53
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• 2017

Generalized integral formulas involving the generalized modified k-Bessel function $J^{b,c,{\gamma},{\lambda}}_{k,{\upsilon}}(z)$ of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.441-450
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• 1999

In this paper we first evaluate the conditional Wiener integral of certain functionals using a Park and Skoug's formula. and we also evaluate the conditional wiener integral E(F│$X_\alpha$) of functional F on C[0, T] given by $F(x)=exp\{{\int_0}^T s^kx(s)ds\}$ for a general conditioning function $X_\alpha$ on C[0,T].

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.999-1018
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• 1998

In this paper, we prove stability theorems for the operator-valued Feynman integral of certain functionals involving some Borel measures on (0, t) as a bounded linear operator from L$_1$(R) to $C_{0}$(R).

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.63-72
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• 1999

We introduce a concept of fuzzy linearity: A function $F:L^0(X){\rightarrow}\mathbb{R}$ is fuzzy linear if $F[({\alpha}{\wedge}f){\vee}(b{\wedge}g)]=[a{\wedge}F(f)]{\vee}[b{\wedge}F(g)]$ for $f,g{\in}L^0(X)$ and a, b > 0. We show that a fuzzy integral is fuzzy linear if the measure is fuzzy c-additive.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.1
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• pp.77-86
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• 1989

A modified $C^{*}$ integral as load parameter in creep fracture is proposed considering the effect of crack growth. It is shown that the parameter does not depend on crack velocity. By performing experiment using STS 304 stainless steel at 600.deg.C the validity of the parameter is investigated. The results show that the parameter is a good measure as a load parameter in creep fracture and the rate of crack tip opening displacement can also be a creep load parameter for STS 304 at 600.deg. C.C.

• Proceedings of the Korean Biophysical Society Conference
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• 1998.06a
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• pp.28-28
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• 1998

RbsC of Escherichia coli is the integral membrane component of the high-affinity ribose transport system classified as the AraH family. To understand the function and structure of RbsC, the topology of RbsC was investigated by alkaline phosphatase fusion. Characterization of a total of 64 RbsC-PhoA fusions revealed that RbsC is composed of six transmembrane helixes and has three periplasmic and two cytoplasmic loops.(omitted)

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.709-723
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• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.

• 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.

• Journal of Korean Society on Water Environment
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• v.21 no.4
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• pp.410-415
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• 2005

The main purpose of this study is to evaluate the characteristics of three sets of traditional control methods (proportional, integral, and proportional - integral controls) through lab-scale biological reactor experiments. An increase in proportional gain ($K_c$) resulted in reduced dissolved oxygen (DO) offset under proportional control. An increase in integral time ($T_i$) resulted in a slower response in DO concentration with less oscillation, but took longer to get to the set point. P-I control showed more stable and efficient control of DO and airflow rates compared to either proportional control or integral control. Developed P-I control system was successfully applied to lab-scale Sequencing Batch Reactor (SBR) for treating industrial wastewater with high organic strength.