• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권3호
• /
• pp.147-163
• /
• 2014

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions $$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

• 한국통신학회논문지
• /
• 제36권6C호
• /
• pp.384-390
• /
• 2011

The paper derives formulas for the mean-squared error distortion and resulting signal-to-noise (SNR) ratio of a fixed-rate scalar quantizer designed optimally in the minimum mean-squared error sense for a Gaussian density with the standard deviation ${\sigma}_q$ when it is mismatched to a Laplacian density with the standard deviation ${\sigma}_q$. The SNR formulas, based on the key parameter and Bennett's integral, are found accurate for a wide range of $p\({\equiv}\frac{\sigma_p}{\sigma_q}\){\geqq}0.25$. Also an upper bound to the SNR is derived, which becomes tighter with increasing rate R and indicates that the SNR behaves asymptotically as $\frac{20\sqrt{3{\ln}2}}{{\rho}{\ln}10}\;{\sqrt{R}}$ dB.

• Kyungpook Mathematical Journal
• /
• 제50권1호
• /
• pp.1-5
• /
• 2010

Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = ${\alpha}$>, the upper to P with respect to ${\alpha}$. Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$; and is R-isomorphic to an overring of D if and only if deg(${\alpha}$) = 1.

• 대한수학회지
• /
• 제50권1호
• /
• pp.189-202
• /
• 2013

On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${\omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.

• 대한수학회보
• /
• 제50권5호
• /
• pp.1673-1681
• /
• 2013

The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao [6]. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao [6] follow as special cases of our main results.

• 대한수학회논문집
• /
• 제22권4호
• /
• pp.509-512
• /
• 2007

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

• Structural Engineering and Mechanics
• /
• 제37권3호
• /
• pp.285-296
• /
• 2011

The plane crack-contact problem for an infinite elastic layer with two symmetric rectangular rigid stamps on its upper and lower surfaces is considered. The elastic layer having an internal crack parallel to its surfaces is subjected to two concentrated loads p on its upper and lower surfaces trough the rigid rectangular stamps and a pair of uniform compressive stress $p_0$ along the crack surface. It is assumed that the contact between the elastic layer and the rigid stamps is frictionless and the effect of the gravity force is neglected. The problem is reduced to a system of singular integral equations in which the derivative of the crack surface displacement and the contact pressures are unknown functions. The system of singular integral equations is solved numerically by making use of an appropriate Gauss-Chebyshev integration formula. Numerical results for stress-intensity factor, critical load factor, $\mathcal{Q}_c$, causing initial closure of the crack tip, the crack surface displacements and the contact stress distribution are presented and shown graphically for various dimensionless quantities.

• 한국통신학회논문지
• /
• 제12권6호
• /
• pp.563-570
• /
• 1987

本 硏究에서는 從來의 RSA 公開키이 暗號方式을 擴張한 새로운 RSA 公開키이 暗號方式을 提案한다. 暗號化의 根本이 되는 法 파라메터 p, q를 擴張하여 秉算回數를 增加시켰다. 그 結果 暗號解讀에 要求되는 計算量이 增加되었으며, 整數論에 基礎를 둔 證明을 通하여 RSA公開키이 暗號의 强度를 改善할 수 있었다.

• Structural Engineering and Mechanics
• /
• 제25권4호
• /
• pp.383-403
• /
• 2007

The contact problem for an elastic layer resting on an elastic half plane is considered according to the theory of elasticity with integral transformation technique. External loads P and Q are transmitted to the layer by means of two dissimilar rigid flat punches. Widths of punches are different and the thickness of the layer is h. All surfaces are frictionless and it is assumed that the layer is subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane will be continuous, if the value of load factor, ${\lambda}$, is less than a critical value, ${\lambda}_{cr}$. However, if tensile tractions are not allowed on the interface, for ${\lambda}$ > ${\lambda}_{cr}$ the layer separates from the interface along a certain finite region. First the continuous contact problem is reduced to singular integral equations and solved numerically using appropriate Gauss-Chebyshev integration formulas. Initial separation loads, ${\lambda}_{cr}$, initial separation points, $x_{cr}$, are determined. Also the required distance between the punches to avoid any separation between the punches and the layer is studied and the limit distance between punches that ends interaction of punches, is investigated. Then discontinuous contact problem is formulated in terms of singular integral equations. The numerical results for initial and end points of the separation region, displacements of the region and the contact stress distribution along the interface between elastic layer and half plane is determined for various dimensionless quantities.

• 대한수학회보
• /
• 제55권1호
• /
• pp.187-204
• /
• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.