• East Asian mathematical journal
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• v.16 no.2
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• pp.251-266
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• 2000

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.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.197-197
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• 1986

• Journal of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-173
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• 1986

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.145-151
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• 1992

• Communications of the Korean Mathematical Society
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• v.1 no.1
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• pp.11-13
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• 1986

• The Mathematical Education
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• v.25 no.1
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• pp.33-37
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• 1986

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.101-110
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• 2006

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green's functions and contraction mapping principle.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.419-431
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• 2008

In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain some uniqueness theorems which improve those given by N. Terglane, Hong-Xun Yi & Xiao-Min Li, and others. Some examples are provided to show that the results in this paper are best possible.

• East Asian mathematical journal
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• v.24 no.1
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• pp.111-123
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• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.139-146
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• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.