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MATHEMATICAL CONSTANTS ASSOCIATED WITH THE MULTIPLE GAMMA FUNCTIONS
Jung, Myung-Ho,Cho, Young-Joon,Choi, June-Sang The Youngnam Mathematical Society Korea 2005 East Asian mathematical journal Vol.21 No.1
The theory of multiple Gamma functions was studied in about 1900 and has, recently, been revived in the study of determinants of Laplacians. There is a class of mathematical constants involved naturally in the multiple Gamma functions. Here we summarize those mathematical constants associated with the Gamma and multiple Gamma functions and will show how they are involved, if possible.
Avdeenko, T.V.,Je, Hai-Gon The Youngnam Mathematical Society Korea 2000 East Asian mathematical journal Vol.16 No.2
The problem of solution uniqueness to the task of determining unknown parameters of mathematical models from input-output observations is studied. This problem is known as structural identifiability problem. We offer a new approach for testing structural identifiability of linear state space models. The approach compares favorably with numerous methods proposed by other authors for two main reasons. First, it is formulated in obvious mathematical form. Secondly, the method does not involve unfeasible symbolic computations and thus allows to test identifiability of large-scale models. In case of non-identifiability, when there is a set of solutions to the task, we offer a method of computing functions of the unknown parameters which can be determined uniquely from input-output observations and later used as new parameters of the model. Such functions are called parametric functions capable of estimation. To develop the method of computation of these functions we use Lie group transformation theory. Illustrative example is given to demonstrate applicability of presented methods.
NONLINEAR SEMIGROUPS AND DIFFERENTIAL INCLUSIONS IN PROBABILISTIC NORMED SPACES
Chang, S.S.,Ha, K.S.,Cho, Y.J.,Lee, B.S.,Chen, Y.Q. The Youngnam Mathematical Society Korea 1998 East Asian mathematical journal Vol.14 No.1
The purpose of this paper is to introduce and study the semigroups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, we utilize these results to study the Cauchy problem for a kind of differential inclusions with accertive mappings in probabilistic normed spaces.