• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.873-882
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• 2022

In this paper, we construct the multiple (h, p, q)-Hurwitz-Euler eta function by generalizing the multiple Hurwitz-Euler eta function. We get some explicit formulas and properties of the higher-order (h, p, q)-Euler numbers and polynomials.

• 대한수학회보
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• 제51권2호
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• pp.401-408
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• 2014

We establish a new approach for the sums of products of the Euler numbers by using the relation of values at non-positive integers of the representation of the multiple Hurwitz-Euler eta function in terms of the Hurwitz-Euler eta function.

• 호남수학학술지
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• 제20권1호
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• pp.57-65
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• 1998

In this paper, we consider properties of Dedekind eta-function, modular discrimiant, thata-series and Weierstrass ${\wp}$-function. We prove the integrablities of ${\Delta}({\tau})$ and ${\eta}({\tau})$. Also, we give explicit formulae about ${\Delta}({\tau})$ and ${\tau}(n)$.

• 대한기계학회논문집
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• 제12권3호
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• pp.561-565
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• 1988

본 연구에서는 제어함수를 수식으로부터 유도하여 자동적인 격자간격제어가 가능한 "근사직교 경계고정곡선좌표계"를 생성하는 새로운 방법을 제시하여 2차원영역 에 대한 그 적용을 논의하고자 한다. 논의하고자 한다.

• 대한수학회논문집
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• 제32권2호
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• pp.361-373
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• 2017

In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of $Br{\ddot{u}}ck$ conjecture. In other words, we consider ${\Delta}_{\eta}f(z)=f(z+{\eta})-f(z)$ and f'(z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where ${\eta}{\in}{\mathbb{C}}{\backslash}\{0\}$ is a constant such that $f(z+{\eta})-f(z){\not\equiv}0$.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• East Asian mathematical journal
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• 제33권1호
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• 한국수정란이식학회지
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• 제29권2호
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• pp.195-200
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• 2014

Endothelin 2 (EDN2) induces follicular rupture by constricting periovulatory follicles. In this study, it was investigated the mechanisms of EDN2 action on follicular rupture with respect of receptor using the conditionally granulosa cell specific EDN2 receptor type A (ETa) KO mice (gcETaKO; $ETa^{flox/-}{\cdot}Amhr2^{Cre}$). It was generated the gcETaKO mice by breeding with $ETa^{flox/-}$ mice after mono-alleic ETa knockout by $ZP3^{Cre}$ and $Amhr2^{Cre}$ mice. Fertility, ovulation and maturation rates of ovulated oocytes after super ovulation were investigated in the gcETaKO mice compared with wild-type mice ($ETa^{flox/flox}$ and $ETa^{flox/-}$) as a control group. In the gcETaKO mice, normal fertility after breeding with male mice was shown compared with wild-type mice. And, there was no significant differences in ovulation rates after super ovulation, however its maturation rates was lower than that of wild type mice. These findings show that EDN2 in follicular rupture for ovulation is related with an other ETa not in granulosa cells. Further studies are needed to investigate how EDN2 is acted in ovarian follicular rupture for ovulation.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.67-70
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• 1998

Let ${\eta}(\tau)=q^{1/24}\prod_{n=1}^{\infty}(1-q^n)$, where $q=e^{2{\pi}i{\tau}}$ and ${\tau}{\in}\mathbb{C}$. Then the transformation $$g(\tau)={\rho}\frac{\{\eta(\frac{\tau+1}{2})\eta(\frac{\tau+2}{2})\}^{16}}{\eta(\tau)^{24}}({\bar{{\rho}}{\eta}}(\frac{\tau+1}{2})^8+{\eta}(\frac{\tau+2}{2})^8)^2$$ is holomorphic for Im ${\tau}$ > 0, and has the property $$g(\tau+1)=g(\tau),\;g(-\frac{1}{\tau})={\tau}^{12}g(\tau)$$. (Theorem)

• Structural Engineering and Mechanics
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• 제17권5호
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• pp.691-706
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• 2004

The paper presents shear lag parameters for beam-to-column connections in steel box piers. Previous researches have analyzed beam-to-column connections in steel piers using a shear lag parameter ${\eta}_o$ obtained from a simple beam model, which is not based on a reasonable design assumption. Instead, the current paper proposes a cantilever beam model and has proved the effectiveness through theoretical and experimental studies. The paper examines the inaccuracy of the previous researches by estimating the effective width, the width-span length ratio L/b, and the sectional area ratio S of a cantilever beam. Two different shear lag parameters are defined using the cantilever model and the results are compared each other. The first type of shear lag parameter ${\eta}_c$ of a cantilever beam is derived using additional moments from various stress distribution functions while the other shear lag parameter ${\eta}_{eff}$ of a cantilever beam is defined based on the concept of the effective width. An evaluation method for shear lag stresses has been investigated by comparing analytical stresses with test results. Through the study, it could be observed that the shear lag parameter ${\eta}_{eff}$ agrees with ${\eta}_c$ obtained from the $2^{nd}$ order stress distribution function. Also, it could be observed that the shear lag parameter ${\eta}_c$ using the $4^{th}$ order stress distribution function almost converges to the upper bound of test results.