• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-998
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• 2009

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.805-810
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• 2014

The shape invariant potentials are proved to be exactly solvable, i.e. the wave functions and energies of a particle moving under the influence of the shape invariant potentials can be algebraically determined without any approximations. It is well known that the SWKB quantization is exact for all shape invariant potentials though the SWKB quantization itself is approximate. This mystery has not been mathematically resolved yet and may not be solved in a concrete fashion even in the future. Therefore, in the present work, to understand (not prove) the mystery an attempt of deriving exactly solvable potentials directly from the SWKB quantization has been made. And it turns out that all the derived potentials are shape invariant. It implicitly explains why the SWKB quantization is exact for all known shape invariant potentials. Though any new potential has not been found in this study, this brute-force derivation of potentials helps one understand the characteristics of shape invariant potentials.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.1
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• pp.1-9
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• 1994

In general, when IIR digital filter are designed from analog filters, the bilinera transformation and the impluse invariant tramsformation are commonly used. It is known, however, that high frequency response of digital filters designed by these transformations can not be well approximated to the sampled analog signals. In this paper, the symbol pulse invariant transformation is analyzed theoretically so that the symbol pulse invariant transformation which was originally application to a rectangular pulse is newly applied to double rate pulse signals and generic shape pulse signals. Also, the relation of spectra between a transfer function of digital filter and one of analog filter is considered. Further, we apply to design the digital high pass filters using the symbol pulse invariant transformation method.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.913-931
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• 1998

Using invariant theory, new invariant cubature formulas over a unit cube are given by imposing a group structure on the formulas. Cools and Haegemans [Computing 40, 139-146 (1988)] constructed invariant cubature formulas over a unit square. Since there exists a problem in directly extending their ideas over the unit square which were obtained by using a concept of good integrity basis to some constructions of invariant cubature formulas over the unit cube, a Reynold operator will be used to obtain new invariant cubature formulas over the unit cube. In order to practically find integration nodes and weights for the cubature formulas, it is required to solve a system of nonlinear equations. With an IMSL subroutine DUNLSF which is used for solutions of the system of nonlinear equations, we shall give integration nodes for the new invariant cubature formulas over the unit cube depending on each degree of polynomial precision.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1179-1190
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• 2001

Quadratic invariant curve is one of the simplest nonlinear invariant curves and was considered by C. T. Ng and the author in order to study the one-dimensional nonlinear dynamics displayed by a second order delay differential equation with piecewise constant argument. In this paper a functional equation derived from the problem of invariant curves is discussed. Using a different method from what C. T. Ng and the author once used, we define solutions piecewisely and give results in the remaining difficult case left in C. T. Ng and the authors work. A problem of analytic extension given in their work is also answered negatively.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1207-1214
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• 2008

We give an elementary proof of one of the main results in [H.O. Kim, R.Y. Kim, J.K. Lim, The infimum cosine angle between two finitely generated shift-invariant spaces and its applications, Appl. Comput. Har-mon. Anal. 19 (2005) 253-281] concerning the existence of an oblique projection onto a finitely generated shift-invariant space along the orthogonal complement of another finitely generated shift-invariant space under the assumption that the generators generate Riesz bases.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.707-724
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• 2019

We investigate the new Clairaut conditions for anti-invariant submersions whose total manifolds are cosymplectic. In particular, we prove the fibers of a proper Clairaut Lagrangian submersion admitting horizontal Reeb vector field are one dimensional and classify such submersions. We also check the existence of the proper Clairaut anti-invariant submersions in the case of the Reeb vector field is vertical. Moreover, illustrative examples for both trivial and proper Clairaut anti-invariant submersions are given.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.100-114
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• 2021

In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.829-841
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• 2020

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.35-46
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• 2021

The purpose of this paper is to study invariant pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparallel submanifold of a para-Kenmotsu manifold and I obtained some equivalent conditions of invariant submanifolds of para-Kenmotsu manifolds under some conditions which the submanifolds are totally geodesic. Finally, a non-trivial example of invariant submanifold of paracontact metric manifold is constructed in order to illustrate our results.