• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.369-379
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• 2018

We consider a p-adic Euler L-function of two variables which interpolate the generalized Euler polynomials at nonpositive integers. We also show that the reflection formula and the functional equation for these functions.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.155-167
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• 1996

Let X be a compact Hausdorff space, C(X) denote the set of all continuous real valued functions on X and $\ell \in N$ be any natural number.

• East Asian mathematical journal
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• v.35 no.1
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• pp.77-83
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• 2019

$L^1$-weight functions are investigated to give necessary conditions on the existence of nontrivial solutions for various types of scalar equations and systems of one-dimensional Minkowski-curvature problems.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.319-339
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• 2010

In this paper, we prove that if $f^nf'\;-\;P$ and $g^ng'\;-\;P$ share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.

• Journal of Forest and Environmental Science
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• v.7 no.1
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• pp.43-61
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• 1990

The modem society has increased the needs for both public benefits of forests and the economic functions of forest products. The increased public interest and concern for forests have been resulted from rapid growth of urban population, high industrialization, deterioration of environment, and etc. It is essential to evaluate the productive and environmantal functions of forests with a scientific criteria. The purpose of this study is to introduce the scientific evaluation method of such functions of forests, and to discuss its uses and limitations.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.25-27
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• 1994

Suppose that X is a Banach space with continuous dual $X^{**}$, ($\Omega$, $\Sigma$, ${\mu}$) is a finite measure space. f : $\Omega\;{\longrightarrow}$ $X^{*}$ is a weakly measurable function such that $\chi$$^{**}$ f $\in$ $L_1$(${\mu}$) for each $\chi$$^{**}$ $\in$ $X^{**}$ and $T_{f}$ : $X^{**}$ \longrightarrow $L_1$(${\mu}$) is the operator defined by $T_{f}$($\chi$$^{**}$) = $\chi$$^{**}$f. In this paper we study the properties of bounded $X^{*}$ - valued weakly measurable functions and bounded $X^{*}$ - valued weak＊ measurable functions.(omitted)

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.231-242
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• 2004

Let $A_b(B_E)$ be the Banach algebra of all complex valued bounded continuous functions on the closed unit ball $B_E$ of a complex Banach space E, and holomorphic in the interior of $B_E$, endowed with the sup norm. We present some sufficient conditions for a set to be a boundary for $A_b(B_E)$ in case E belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in [6]. We also prove the non-existence of the Shilov boundary for $A_b(B_E)$ and give some examples of boundaries.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.95-108
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• 2023

The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined (α,h-m)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function h is bounded above by ${\frac{1}{\sqrt{2}}}$.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.4
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• pp.138-147
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• 1993

It is known that the performance of a fuzzy controller is related with fuzzification method, inference rules, defuzzification method, and linguistic variables. Among these, generally, the linguistic variables and control rules are transfered to control engineers from an expert or experts of the controlled system and other parts are designed by control engineers. However, there may be some missed infirmations or uncertainties in the transfered data. The purpose of the paper is to propose an algorithm to tune the membership functions of initially given fuzzy sets To do so, a simple shape of the membership fuction is assumed for the fuzzy sets, and the relations between the shapes of the fuzzy sets and the performance of the control system is derived. According to the relations, the shape of the membership functions are modified during operation of the whole system. The proposed algorithm will be applied to two emample plants, type 1 and type 0 systems.