• East Asian mathematical journal
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• 제8권1호
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• pp.19-24
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• 1992

• 대한수학회논문집
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• 제1권1호
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• pp.35-41
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• 1986

• 대한수학회지
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• 제9권2호
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• pp.85-89
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• 1972

• Kyungpook Mathematical Journal
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• 제6권1호
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• pp.7-20
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• 1964

• 호남수학학술지
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• 제11권1호
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• pp.7-13
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• 1989

• 한국수학교육학회지시리즈A:수학교육
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• 제22권1호
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• pp.45-47
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• 1983

• 한국수학사학회지
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• 제27권1호
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• pp.1-12
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• 2014

From the mid 17th century, Joseon mathematics had a new beginning and developed along two directions, namely the traditional mathematics and one influenced by western mathematics. A great Joseon mathematician if not the greatest, Hong JeongHa was able to complete the Song-Yuan mathematics in his book GuIlJib based on his studies of merely Suanxue Qimeng, YangHui Suanfa and Suanfa Tongzong. Although Hong JeongHa did not deal with the systems of equations of higher degrees and general systems of linear congruences, he had the more advanced theories of right triangles and equations together with the number theory. The purpose of this paper is to show that Hong was able to realize the completion through his perfect understanding of mathematical structures.

• Structural Engineering and Mechanics
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• 제5권5호
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• pp.491-505
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• 1997

This paper deals with the formulation and solution of a wide class of structures, in the presence of both geometric and material nonlinearities, as a particular mathematical programming problem. We first present key ideas for the nonholonomic (path dependent) rate formulation for a suitably discretized structural model before we develop its computationally advantageous stepwise holonomic (path independent) counterpart. A feature of the final mathematical programming problem, known as a nonlinear complementarity problem, is that the governing relations exhibit symmetry as a result of the introduction of so-called nonlinear "residuals". One advantage of this form is that it facilitates application of a particular iterative algorithm, in essence a predictor-corrector method, for the solution process. As an illustrative example, we specifically consider the simplest case of plane trusses and detail in particular the general methodology for establishing the static-kinematic relations in a dual format. Extension to other skeletal structures is conceptually transparent. Some numerical examples are presented to illustrate applicability of the procedure.

• 대한수학회지
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• 제53권2호
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• pp.315-329
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• 2016

In the setting of continuous logic, we study atomless probability spaces and atomless random variable structures. We characterize ${\kappa}$-saturated atomless probability spaces and ${\kappa}$-saturated atomless random variable structures for every infinite cardinal ${\kappa}$. Moreover, ${\kappa}$-saturated and strongly ${\kappa}$-homogeneous atomless probability spaces and ${\kappa}$-saturated and strongly ${\kappa}$-homogeneous atomless random variable structures are characterized for every infinite cardinal ${\kappa}$. For atomless probability spaces, we prove that ${\aleph}_1$-saturation is equivalent to Hoover-Keisler saturation. For atomless random variable structures whose underlying probability spaces are Hoover-Keisler saturated, we prove several equivalent conditions.

• 대한수학회지
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• 제45권3호
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• pp.859-870
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• 2008

In the present paper, we investigate the geometric structures of the Dirichlet manifold composed of the Dirichlet distribution. We show that the Dirichlet distribution is an exponential family distribution. We consider its dual structures and give its geometric metrics, and obtain the geometric structures of the lower dimension cases of the Dirichlet manifold. In particularly, the Beta distribution is a 2-dimensional Dirich-let distribution. Also, we construct an affine immersion of the Dirichlet manifold. At last, we give the e-flat hierarchical structures and the orthogonal foliations of the Dirichlet manifold. All these work will enrich the theoretical work of the Dirichlet distribution and will be great help for its further applications.