• Korean Journal of Mathematics
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• v.27 no.2
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.55-60
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• 1972

In this paper two theorems on generalised Meijer transform due to Banerjee [1, p. 433] defined by $${\varphi}_1(p)=\int\limits_{0}^{\infty}(2px)^{m-{\frac{1}{2}}_e-{\frac{1}{2}}pxn}{\varphi}({{\alpha},c;\;2px)f(x)dx$$, have been proved. Some interesting integrals involving hyper-geometric functions are evaluated by the application of theorems.

• Honam Mathematical Journal
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• v.35 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-245
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• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.33-45
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• 2002

An approximation of the Fourier Sine Transform via Gr$\ddot{u}$ss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force $E_0P$(t), where P (t) is an $L_2$-integrable function, are given.

• Proceedings of the KSAR Conference
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• 2001.03a
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• pp.16-16
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• 2001

Apoptosis로 일컬어지는 예정된 세포사멸(programmed cell death)은 개별 세포의 입장에서는 곧바로 사멸을 의미하지만, 정상적인 고등 생물의 입장에서는 개체의 발생과 분화하는데 프로그램된 과정이다. 자발적 세포사멸은 다른 조직에 비해 생식 조직인 난소나 정소에서 복잡한 apoptosis 기작들을 가지리라 사료된다. 본 연구는 Bcl-2 family중 apoptotic protein인 Bax에 대해 suppression하는 유전자를 yeast system을 활용하여 돼지 정소와 난소로부터 각각 cDNA library를 구축한 후 탐색하였다. 탐색에 활용된 cDNA library는 돼지의 정소와 난소로부터 mRNA를 분리하여 yeast vector인 pAD-GAL4-2.1에 구축하였고, 마우스 bax 유전자는 gal 1 promoter의 조절 하에 glucose 배지에서는 유도되지 않고, galactose 배지에서만 선택적으로 Bax를 발현할 수 있는 효모 vector(pL19-bax)를 구축하였다. Bax에 의한 apoptosis suppressor를 탐색하기 위해 우선 효모 W303에 pL19-bax를 transform하여 glucose 배지에서 Bax의 발현을 억제하였다. pL19-bax를 가진 효모에 정소와 난소로부터 구축된 cDNA library를 transform 시키고, transform된 효모는 각각 Bax에 의한 toxicity를 저해하는 유전자를 찾기 위해 스크린되었다. 이러한 방법으로 정소 cDNA library 탐색에서는 5 $\times$ $10^{6}$ transformant중 39개, 난소cDNA library 탐색에서는 2 $\times$ $10^{6}$ transformant중 26개의 콜로니가 생존하였다. 이들 콜로니로부터 유전자를 분리하여 분석해 본 결과 여러 그룹으로 분류할 수 있었다. 각 그룹의 관련 유전자는 protein synthesis/degradation 12종, oxidation/reductation 5종, detoxin/ cell cycle promoter 3종, signal transduction/growth factor 5종, 그리고 알려지지 않은 유전자 9종이었다. 그 중, bax-toxicity inhibition에 강력한 survival phenotype을 가지는 유전자(pSEDL)를 동정하였다. 이것은 T3-4-1 콜로니로부터 분리하였는데 140개 아미노산으로 이루어진 인간 SEDL(GenBank, XM_013096) 유전자와 매우 유사한 homology를 가지며, bax와 관련된 기능은 밝혀져 있지 않다. 이외에도 분리된 유전자에는 NADH, thioreduction, 그리고 cytochrome oxidase와 같은 positive 유전자 군이 크로닝되어, Bax를 이용한 효모에서 apoptosis suppressor에 관련된 유전자를 손쉽게 스크린하는 것이 가능하고, 분리된 유전자의 기능을 예측할 수 있어 지금까지 보고된 유전자 크로닝법 보다는 강력한 수단으로 활용될 수 있다는 사실을 시사하였다. 그러나, ORF에 관계없이 Bax 발현에 저항하는 유전자군이 선발된다든지 하는 문제점은 금후 검토가 필요하리라 사료된다.

• Korean Journal of Microbiology
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• v.2 no.1
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• pp.1-11
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• 1964

Yung Nok Lee (Dept. of Biology, Korea University) : Studies on the phosphate metabolism in Chlorella, with special reference to polyphosphate. Kor. J. Microbiol., Vol.2, No.1, p1-11 (1964). 1. Uniformly $^{32}P$-labeled Chlorella cells which were irradiated with Cobalt-60 gamma-rays of about 70, 000 $\gamma$ dose, were further grown in a standard "cold" medium ("hot".rarw."cold"), and some portions of the algae were taken out at the begining of, and at intervals during the culture, and subjected to analyze the contents of $^{32}P$- and total P in various fractions of the cell materials. Results obtained were compared with those of nonirradiated normal cells. 2. Amounts of phosphate in various fractions of the nonirradiated normal Chlorella cells were measured using uniformly $^{32}P$--labeled cells. Analysis of the $^{32}P$--labeled algal cells showed that the highest value in P-content was the fraction of RNA followed by those of lipid, polyphosphate "C" polyphosphate "B", DNA, nucleotidic labile phosphate compounds, polyphosphate "A" and protein. It was observed that content of total polyphosphates in a single Chlorella cell was almost equal to RNA-P content in the cell, and the amount of RNA-P was almost equal to ten times of DNA-P content. 3. When the $^{32}P$--labeled algae which were irradiated with gamma-rays were grown in a normal "cold" medium, phosphate contents in the fraction of DNA, nucleotidic labile phosphate compounds and protein decreased markedly, while the contents of phosphate in the fractions of polyphosphate "C" and potyphosphate "B" increased in comparison with those of unirradiated normal cells. So, it was considered that the pretreatment of above mentioned dose of gamma-ray inhibited DNA and protein synthesis from polyphosphate in Chlorella cells. 4. Proceeding the culture of $^{32}P$--labeled Chlorella in a "cold" standard medium, whose synthetic activity of DNA and protein from polyphosphate was disturded by gamma-ray irradiation, the amounts of $^{32}P$-in the fraction of polyphosphate "C" increased, in contrast with those of polyphosphate "B" fraction. According to these experimental results, it was inferred that polyphosphate "B" could transform into polyphosphate "C" in normal growing Chlorella cells.sults, it was inferred that polyphosphate "B" could transform into polyphosphate "C" in normal growing Chlorella cells.ing Chlorella cells.

• Kyungpook Mathematical Journal
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• v.16 no.2
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• pp.247-258
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• 1976

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.619-630
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• 2018

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.