• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.5
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• pp.11-16
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• 1998

We analyze the software reliability growth models for the specified period from the viewpoint of theory of differential equations. we defien a genralized form of reliability growth models as follws: dN(t)/dt = b(t)f(N(t)), Where N(t) is the number of remaining faults and b(t) is the failure rate per software fault at time t. We show that the well-known three software reliability growth models - Goel - Okumoto, s-shaped, and Musa-Okumoto model- are special cases of the generalized form. We, also, extend the generalized form into an extended form being dN(t)/dt = b(t, .gamma.)f(N(t)), The genneralized form can be obtained if the distribution of failures is given. The extended form can be used to describe a software reliabilit growth model having weibull density function as a fault exposure rate. As an application of the generalized form, we classify three mentioned models according to the forms of b(t) and f(N(t)). Also, we present a case study applying the generalized form.

• 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.

• Journal of Photoscience
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• v.1 no.2
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• pp.113-117
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• 1994

The quantum yields of fluorescence ($\Phi$$_f$) and trans $\to$ cis photoisomerization ($\Phi$$_{t$\to$ c}$), trans-4-(2-(9-anthryl)vinyl)pyridine, an aza analogue of 1-(9-anthryl)-2-phenylethylene, were measured in several solvents at room temperature. $\Phi$$_f$ and $\Phi$$_{t$\to$ c}$ are 0.38 and < 0.01 in hexane and 0.02 and 0.38 in acetonitrile, respectively. As solvent polarity decreases, $\Phi$$_{t$\to$ c}$ strongly reduced, whereas $\Phi$$_f$ strongly increased. A singlet mechanism of trans $\to$ cis photoisomerization is suggested since $\Phi$$_{t$\to$ c}$ and $\Phi$$_f$ change in opposite direction.

• Computers and Concrete
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• v.2 no.1
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• pp.55-77
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• 2005

The closed form solution of the equilibrium equations in the ultimate design of reinforced concrete sections under biaxial bending is presented. The stresses in the materials are described by the Model Code 1990 equations. Computation of the integral equations is performed generally in terms of all variables. The deformed shape of the section in the ultimate conditions is defined by Heaviside functions. The procedure is convenient for the use of mathematical manipulation programs and the results are easily included into nonlinear analysis codes. The equations developed for rectangular sections can be applied for other sections, such as T, L, I for instance, by decomposition into rectangles. Numerical examples of the developed model for rectangular sections and composed sections are included.

• Asian Pacific Journal of Cancer Prevention
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• v.17 no.7
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• pp.3569-3573
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• 2016

Purpose: The aim of this study was to compare C-11 choline and F-18 FDG PET/CT, gadoxetic-enhanced 3-T MRI and contrast-enhanced CT for diagnosis of hepatocellular carcinoma (HCC). Materials and Methods: Twelve chronic hepatitis B patients suspected of having HCC by abdominal ultrasonography received all diagnostic modalities performed within a one-week timeslot. PET/CT results were analyzed visually by two independent nuclear medicine physicians and quantitatively by tumor to background ratio (T/B). Nine patients then had histopathological confirmation. Results: Six patients had well differentiated HCC, while two and one patient(s) were noted with moderately and poorly differentiated HCC, respectively. All were detected by both CT and MRI with an average tumor size of $5.7{\pm}3.8cm$. Five patients had positive C-11 choline and F-18 FDG uptake. Of the remaining four patients, three with well differentiated HCC showed negative F-FDG uptake (one of which showed negative results by both tracers) and one patient with moderately differentiated HCC demonstrated no C-11 choline uptake despite intense F-18 FDG avidity. The overall HCC detection rates with C-11 choline and F-18 FDG were 78% and 67%, respectively, while the sensitivity of F-18 FDG for non-well differentiated HCC was 100%, compared with 83% of C-11 choline. The average T/B of C-11 choline in well-differentiated HCC patients was higher than in moderately and poorly differentiated cases (p=0.5) and vice versa with statistical significance for T/B of F-18 FDG (p = 0.02). Conclusions: Our results suggested better detection rate in C-11 choline for well differentiated HCC than F-18 FDG PET. However, the overall detection rate of PET/CT with both tracers could not compare with contrast-enhanced CT and MRI.

• Journal of Korean Ophthalmic Optics Society
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• v.7 no.2
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• pp.169-174
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• 2002

Make Photochromic lens Photochromism estimation method, and gouge photochromic lens and investigated UV light source to apply. UV light source irradiation ago and after wavelength dependence of photo-transmittance (T%) of darkening and fading state by do optical equipment which is consisted of spectrophotometer, light source, power meter and detecter. Use relative ratio value of maximum $T%{\times}{\lambda}$ area and saturated state area in light off. Dependences estimation introduced darkening efficiency $(K_d)=(1-C_1/A_1)/t_{on}$ relationship value course fading efficiency$(K_f)=(C_2/A_2)/t_{on}$ value during Photochromism's irradiation time in Photochromic lens. Wavelength dependence of transmittance (T%) has form of $T_m+T_1{\exp}[-(x_0-t)/a]$ in Darkening course fading state. Can receive each estimation parameter value as result that apply Photochromism's estimation parameter Z, $K_d$, $K_f$ in Photochromic lens.

• 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].

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.359-366
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• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.365-371
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• 2016

Let f be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and a be a nonzero constant. We give a quantitative estimate of the characteristic function T(r, f) in terms of $N(r,1/(f^2(f^{\prime})^n-a))$, which states as following inequality, for positive integers $n{\geq}2$, $$T(r,f){\leq}\(3+{\frac{6}{n-1}}\)N\(r,{\frac{1}{af^2(f^{\prime})^n-1}}\)+S(r,f)$$.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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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.