• The Mathematical Education
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• v.18 no.1
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• pp.21-23
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• 1980

In [3], an extension of B. Brosowski s T-invariant Point Theorem is given where the linearity of the function and the convexity of the set are relaxed. In this paper, our main purpose is to generalize S. P. Singh's T-invariant Point Theorem to Approximation Theory.

• Korean Institute of Interior Design Journal
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• v.14 no.3 s.50
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• pp.64-72
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• 2005

The purpose of this study is to propose a topological design principles and to analyze the space of digital architecture applying topological invariant expressive characteristics. As this study is based on topology as a science of true world's pattern, we intented to explain the concepts and provide some methods of low-level and hyperspace topological invariant Properties. Four major aspects are discussed. Those are connection theory, boundary concept, homotopy group, knot Pattern theory as topological invariant properties. Then we intented to make understand topological characteristics of the Algorithms, luring machine, cellular automata, string theory, membrane, DNA and supramolecular chemistry. In fine, the topological invariant properties of the digital architecture as genetic algorithms based on self-organization and heterogeneous networks of interacting actors can be analyzed and used as a critical tool. Therefore topology can be provided endless possibilities for architecture, designers and scientists intended in expressing the more complex and organic patterns of nature as life.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.821-833
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• 2017

We get a result that shows the existence of infinitely many solutions for a class of the elliptic systems involving subcritical Sobolev exponents nonlinear terms with even functionals on the bounded domain with smooth boundary. We get this result by variational method and critical point theory induced from invariant subspaces and invariant functional.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.263-271
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• 2012

We investigate the number of the solutions for the biharmonic boundary value problem with a variable coefficient nonlinear term. We get a theorem which shows the existence of $m$ weak solutions for the biharmonic problem with variable coefficient. We obtain this result by using the critical point theory induced from the invariant function and invariant linear subspace.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.507-519
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• 2009

We give a theorem of the existence of the multiple solutions of the Hamiltonian system with the square growth nonlinearity. We show the existence of m solutions of the Hamiltonian system when the square growth nonlinearity satisfies some given conditions. We use critical point theory induced from the invariant function and invariant linear subspace.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.667-680
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• 2016

We get a theorem which shows the multiple weak solutions for the bifurcation problem of the superquadratic nonlinear Hamiltonian system. We obtain this result by using the variational method, the critical point theory in terms of the $S^1$-invariant functions and the $S^1$-invariant linear subspaces.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.333-341
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• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.349-357
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• 1995

In the theory of elliptic curves over a complete field with bad reduction (i.e. with nonintegral j-invariant) Tate elliptic curves play an important role. Likewise, in the theory of Drinfeld modules, Tate-Drinfeld modules replace Tate elliptic curves.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.6
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• pp.946-961
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• 2004

A new adaptive controller which combines a model reference adaptive controller (MRAC) and a fuzzy controller is developed for unstable nonlinear time-invariant systems. The fuzzy controller is used to analyze and to compensate the nonlinear time-invariant characteristics of the plant. The MRAC is applied to control the linear time-invariant subsystem of the unknown plant, where the nonlinear time-invariant plant is supposed to comprise a nonlinear time-invariant subsystem and a linear time-invariant subsystem. The stability analysis for the overall system is discussed in view of global asymptotic stability. In conclusion. the unknown nonlinear time-invariant plant can be controlled by the new adaptive control theory such that the output error of the given plant converges to zero asymptotically.