• 대한수학회보
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• 제50권4호
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• pp.1243-1259
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• 2013

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$. We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.

• Structural Engineering and Mechanics
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• 제45권4호
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

• 한국실내디자인학회논문집
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• 제23권5호
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• pp.104-111
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• 2014

This study puts its purpose on presenting an integral system of representative urban landscapes, public design and colors, in practicing urban design in the context of local identity. An integral design of public design that successfully plans and executes local identity, and changes recognition of integral management of urban design, is suggested as followings. Firstly, when the catchment area is divided in metropolitan area, it should be reset according to the natural environment condition regardless of administrative area system like city and county. It is the method to classify the metropolitan area by researching and analyzing geographical condition, weather condition, soil and vegetation in detail and subclassify it by the visual commonness of natural environment. Secondly, it is necessary to access the urban landscape, public design and urban color from the overall aspect emphasizing the plan for each field and local identity. They should be practiced by the role and category of each field on the basis of consistent design strategy and instruction but the cooperation system is required as a process to reinforce and specify the mutual limit. Thirdly, the artificial structure is constructed through artificial adjustment depending on the urban formation process and the development time point. Therefore, it is necessary to pay attention to the rapid urban development, the change speed and the landscape formation of each age. It is necessary to classify the type of artificial landscape by age and form similarity and separate the area that should be generalized and controlled by entire metropolitan area form the area that should be specialized by basic local government.

• 대한전자공학회논문지
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• 제23권4호
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• pp.445-449
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• 1986

This paper presents a direct adaptive control scheme for nonminimum phase systems of which controller parameters are estimated from the least-squares algorithm, and some additional auxiliadry parameters are obtianed from the proposed polynomial identity equation. Integral action is incorporated into the adaptive controller to eliminate the steady-state error, and to satisfy a condition of the unique solution for the polynomial identity as well.

• 호남수학학술지
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• 제29권4호
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.781-795
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• 2020

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

• East Asian mathematical journal
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• 제19권2호
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• pp.221-232
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• 2003

An identity for n-time differentiable functions of a real variable in terms of multiple integrals and applications for Ostrowski type inequalities are given.

• 대한수학회보
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• 제50권4호
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• pp.1261-1275
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• 2013

We establish an integral formula for the first Chern number of a compact almost Hermitian surface and derive curvature identities from the integral formula. Further, we provide some results as applications of the identities.

• 아태비즈니스연구
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• 제1권1호
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• pp.73-95
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• 2010

European integration is characterized by the development of a transnational European identity, which is considered an integral part of the process. Northeast Asia has no similar projects to address the common identity issue, although cooperation is highly valued there as well. Identity and cooperation both require interdisciplinary approaches combining social psychology, international relations theory and international economics. This article considers the problems of applying existing studies on cooperation and identity as well as the European experience (with the Baltic Sea example) to the case of Northeast Asia. Transnational identities promote cooperation beyond the limits of rationalistic game theory, if countries of the region can define their identities and interests, commit to common goals, create shared discourses and reach a balance between nationalism and internationalism. In view of proposed negotiations on the free trade area between China, Korea and Japan and ongoing discussions about a possibility of introducing a common currency (ACU) it can be crucial to consider the importance of identity building as early as possible, before regional integration meets a stumbling block of egoistic rationality that is a problem in any model of cooperation.

• 호남수학학술지
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• 제43권3호
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• pp.441-452
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• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.