• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.507-516
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• 2017

Real Bott manifolds is a class of flat manifolds with holonomy group $\mathbb{Z}^k_2$ of diagonal type. In this paper we formulate necessary and sufficient conditions of the existence of a Spin-structure on real Bott manifolds. It extends results of [9].

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.473-486
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• 2021

We prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the k-th generalized Tanaka-Webster connection.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.57-79
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• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.

• East Asian mathematical journal
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• v.32 no.5
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• pp.621-633
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• 2016

We establish the existence of positive solutions to nonlocal boundary value problems with integral boundary condition and non-negative real boundary parameter by mainly using the Schauder-Fixed point theorem.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.779-796
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• 2024

In this paper, under the ABC-conjecture, we show that there exist infinitely many real quadratic fields with odd period of minimal type.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.10
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• pp.982-990
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• 2010

In a target tracking system using image information from a CCD (Charged Couple Device) or an IIR (Imaging Infra-red) sensor, occluded targets can result in track losses. If the target is occlued by background objects such as buildings or trees, probability of track existence will be reduced sharply and track will be terminated due to track maintenance algorithms. This paper proposes data association algorithm based on target existence for the robust tracking performance. we suggest the HPDA (Highest Probability Data Association) algorithm based on target existence and the tracking performance is compared with the established method based on target perceivability. Image tracking simulation that utilizes virtual 3D images and real IR images is employed to evaluate the robustness of the proposed tracking algorithm.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2089-2101
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• 2013

The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.993-1002
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• 2016

In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.