• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.353-362
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• 2012

In this paper decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions and appropriate for Soil-Structure Interaction problems are described and discussed. These elements can be treated as a new form of the recently proposed Elastodynamic Infinite Elements with United Shape Functions (EIEUSF) infinite elements. The formulation of 2D horizontal type infinite elements (HIE) is demonstrated, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be formulated. It is demonstrated that the application of the elastodynamical infinite elements is the easier and appropriate way to achieve an adequate simulation including basic aspects of Soil-Structure Interaction. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite Element Method is explained in brief. Finally, a numerical example shows the computational efficiency of the proposed infinite elements.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.57-68
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• 1996

In the classical analysis there are various theorems which permit us to interchange limits and infinite sums, limits and integrals, integrals and infinite sums, etc. The infinite products as well as the infinite series play an important role in different branches of mathematics.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.577-587
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• 2006

We present several properties concerning infinite maximal planar graphs. Results related to the infinite VAP-free planar graphs are also included. Finally, we extend the result of W. Goddard, who showed that every finite 4-connected maximal planar graph is 4-ordered, to infinite strong triangulations.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.779-783
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• 2004

A group G is said to satisfy the minimal condition on normal subgroups of infinite index if there does not exist an infinite properly descending chain $G_1$ > $G_2$ > ... of normal subgroups of infinite index in G. We characterize the structure of locally nilpotent groups satisfying this chain condition.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.465-472
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• 2004

A group G is said to satisfy the maximal condition on infinite normal subgroups if there does not exist an infinite properly ascending chain of infinite normal subgroups. We characterize the structure of locally nilpotent groups satisfying this chain condition. We then show how to construct locally nilpotent groups with the maximal condition on infinite normal subgroups, but not the maximal condition on subgroups.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.245-252
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• 2012

In this paper we present a necessary and sufficient conditions for an infinite VAP-free plane graph to be a 3LV-graph as well as an LV-graph. We also introduce and investigate the concept of the order and the kernel of an infinite connected graph containing no one-way infinite path.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.221-237
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• 2021

B. C. Berndt has found modular transformation formulae for a large class of functions coming from generalized Eisenstein series. Using those formulae, he established a lot of infinite series identities, some of which explain many infinite series identities given by Ramanujan. Continuing his work, the author proved a lot of new infinite series identities. Moreover, recently the author found transformation formulae for a class of functions coming from generalized non-holomorphic Eisenstein series. In this paper, using those formulae, we evaluate a few new infinite series identities which generalize the author's previous results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.11-18
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• 1998

In this paper the stochastic analysis of semi-infinite domain is presented using the weighted integral method, which is expanded to include the infinite finite elements. The semi-infinite domain can be thought as to have more uncertainties than the ordinary finite domain in material constants, which shows the needs of and the importance of the stochastic finite element analysis. The Bettess's infinite element is adopted with the theoretical decomposition of the strain matrix to calculate the deviatoric stiffness of the semi-infinite domains. The calculated value of mean and the covariance of the displacement are revealed to be larger than those given by the finite domain assumptions giving the rational results which should be considered in the design of structures on semi-infinite domains.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.521-528
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• 2005

In this paper, three dimensional dynamic infinite elements are developed for the soil-structure interaction analysis in multi-layered halfspace. For the efficient discretization of 3-D for field regions, five types of dynamic infinite elements are developed. They are the horizontal, vertical, horizontal comer, vertical comer and horizontal/vertical corner infinite elements. The shape functions of the infinite elements are based on approximate expressions of analytical solutions of propagating waves in the infinite region. Numerical example analyses are presented for compliances of rigid circular and square plates to demonstrate the effectiveness of the proposed infinite elements.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.6
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• pp.1017-1025
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• 2004

Generally generator is connected to the bus with no load. After the connection to the bus. the frequency of generator system with no load has to be increased for preventing the reverse power. But in a few case of parallel running with infinite bus system, we have to synchronize the loaded generator to the infinite bus. The frequency of generator system with load has to be lowered for prevention of load shift to the bus system. The blackout of infinite bus decreases the parallel running generator's frequency because of load increasing. In this paper we propose a method that the generator with load maintains the frequency constantly after the blackout of infinite bus. With the constant speed control and load control method of parallel running system to the infinite bus we apply the method to the industrial generating system.