• 호남수학학술지
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• 제32권3호
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• pp.441-451
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• 2010

In this paper we evaluate the analogue of Wiener integral ${\int\limits}_{C[0,t]}x(t_1){\cdots}x(t_n)d\omega_\rho(x)$ where 0 = $t_0$ < $t_1$ $\cdots$ < $t_n$ $\leq$ t and the Paley-Wiener-Zygmund integral ${\int\limits}_{C[0,t]}$ exp $({\int\limits}_0^t h(s)\tilde{d}x(s))d\omega_\rho(x)$ is the analogue of Wiener measure space.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• 대한기계학회논문집
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• 제18권10호
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• pp.2543-2553
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• 1994

Caustics method has been applied successfully to determine the fracture parameters such as stress intensity factor and the J-integral for elastic and/or elastic-plastic stress field around the crack tip. For stress fields at the vicinity of crack tip in the creep domain, no experimental report concerning fracture mechanics parameters by using the caustics method has been published up to date. This study investigated creep behavior at the vicinity of crack tips at high temperature($175^{\circ}C$) and attempted to determine of proper fracture parameters for A1 5086 H24 specimens by using the caustics method. The results obtained from the limited experimental investigation are as follows; $J_{th}/J_{caus}$ is found to approach to 1 more rapidly than $K_{th}/K_{caus}$ does during incipient period(within 80 minutes). It is confirmed that experimental $K_{caus}$ approached to theoretical $K_{th}$ after 80 minutes by analyzing the ratio of $K_{th}$ to $K_{caus}$. Unlike the case of room temperature, it is confirmed experimentally that caustics diameter enlarged gradually even the distance between specimen and screen keeps constant. It showed that initial curve of the caustics was initially located in the plastic zone, but it grew out rapidly into the elastic zone for Al 5086 H24 at $175^{\circ}C$. It is confirmed that caustics is a function of time, temperature and distance between specimen and screen at high temperature.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.1-28
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• 2014

We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type $B_2$. We prove in this paper that these operators are positivity preserving and allow positive integral representations. In particular we deduce that the product formulas of the Opdam-Cherednik and the Heckman-Opdam kernels are positive integral transforms, and we obtain best estimates of these kernels. The method used to obtain the previous results shows that these results are also true in the case of the root system of type $C_2$.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회B
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• pp.1953-1958
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• 2007

This paper presents the results of a series of performance tests for the integral Stirling cryocooler. Infrared sensor systems incorporating cryocoolers are required to be qualified to the appropriate environmental specification. Integral Stirling cryocooler for thermal imaging system have matured to the stage of undergoing formal qualification test program. The thermal environmental test of the Stirling cryocooler is presented in this paper. We performed that low and high temperature keeping test from $-40^{\circ}C$ to $+71^{\circ}C$ and operating test at high and low temperature cyclic range with acceptance tests performed at scheduled intervals. Cooldown time to 80K and steady state input power at 80K were determined as a function of cooler components temperatures at the compressor, hot end and cold tip. Tests performed on this cooler have been successful with a measured cooldown time to 80K of less than 5 minutes 24seconds for $71^{\circ}C$ ambient temperature with input power of 11W

• Korean Journal of Mathematics
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• 제30권2호
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• pp.239-247
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• 2022

Let C₀[0, T] denote the Wiener space, the space of continuous functions x(t) on [0, T] such that x(0) = 0. Define a random vector $Z_{\vec{e},k}:C_0[0,\;T] {\rightarrow}{\mathbb{R}}^k$ by $$Z_{\vec{e},k}(x)=({\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;e_1(t)dx(t),\;{\ldots},\;{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;ek(t)dx(t))$$ where e_j ∈ L₂[0, T] with e_j ≠ 0 a.e., j = 1, …, k. In this paper we study the conditional Fourier-Feynman transform and a conditional convolution product for a cylinder type functionals defined on C0[0, T] with a general vector valued conditioning functions $Z_{\vec{e},k}$ above which need not depend upon the values of x at only finitely many points in (0, T] rather than a conditioning function X(x) = (x(t₁), …, x(t_n)) where 0 < t₁ < … < t_n = T. In particular we show that the conditional Fourier-Feynman transform of the conditional convolution product is the product of conditional Fourier-Feynman transforms.

• 대한수학회논문집
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• 제36권4호
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• pp.685-704
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• 2021

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C²_a,b[0, T]. The function space C_a,b[0, T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C²_a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C²_a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.

• 충청수학회지
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• 제24권3호
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• pp.417-426
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• 2011

Let ${\mu}$ be a finite positive Borel measure on the unit ball $B{\subset}{\mathbb{C}}^n$ and ${\nu}$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, ${\sigma}$ is the rotation-invariant measure on S such that ${\sigma}(S) =1$. Let ${\mathcal{P}}[f]$ be the Poisson-$Szeg{\ddot{o}}$ integral of f and $\tilde{\mu}$ be the Berezin transform of ${\mu}$. In this paper, we show that if there is a constant M > 0 such that ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}M{\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\nu}(z)$ for all $f{\in}L^p(\sigma)$, then ${\parallel}{\tilde{\mu}}{\parallel}_{\infty}{\equiv}{\sup}_{z{\in}B}{\mid}{\tilde{\mu}}(z){\mid}<{\infty}$, and we show that if ${\parallel}{\tilde{\mu}{\parallel}_{\infty}<{\infty}$, then ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}C{\mid}{\mid}{\tilde{\mu}}{\mid}{\mid}_{\infty}{\int_S}{\mid}f(\zeta){\mid}^pd{\sigma}(\zeta)$ for some constant C.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권2호
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• pp.71-75
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• 2009

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$\Phi((C)\;{\int}\;fd{\mu})\;{\leq}\;(C)\;\int\;\Phi(f)d{\mu},$$ where f is Choquet integrable, ${\Phi}\;:\;[0,\;\infty)\;\rightarrow\;[0,\;\infty)$ is convex, $\Phi(\alpha)\;\leq\;\alpha$ for all $\alpha\;{\in}\;[0,\;{\infty})$ and ${\mu}_f(\alpha)\;{\leq}\;{\mu}_{\Phi(f)}(\alpha)$ for all ${\alpha}\;{\in}\;[0,\;{\infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

• 호남수학학술지
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• 제35권2호
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• pp.179-200
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.