• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.723-732
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• 2016

We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifold. Moreover, we determine 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds which admit a certain kind of proper biharmonic foliation.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1061-1078
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• 2020

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.121-134
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• 1999

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski type inequalities corresponding to weights W\ulcorner(x)=exp(-｜x｜\ulcorner), $\alpha$>0, to those for generalized nonnegative polynomials.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.303-311
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• 2010

Recently, some authors [3, 4, 11, 12, 15] adopted the concept of the so-called generalized R-KKM maps which are used to rewrite known results in the KKM theory. In the present paper, we show that those maps are simply KKM maps on G-convex spaces. Consequently, results on generalized R-KKM maps follow the corresponding previous ones on G-convex spaces.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.167-182
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• 2018

In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.273-281
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• 1996

It is derived that conditions of counting process ($\{N(t){\mid}t\;{\geq}\;0\}$) in which the number of events in time interval [0, t] has a (n, n+1)-generalized Poisson distribution with parameters (${\theta}t,\;{\lambda}$) and a generalized inflated Poisson distribution with parameters (${\{\lambda}t,\;{\omega}\}$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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• pp.351-354
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• 2004

Using the idea of generalized intuitionistic fuzzy set, we study the notion of generalized intuitionistic fuzzy matrices as a generalization of fuzzy matrices, We show that some properties of a square generalized intuitionistic fuzzy matrix such as reflexivity, transitivity and circularity are carried over to the adjoint generalized intuitionistic fuzzy matrix.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.335-354
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• 2007

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (${\hat}It{o}$ type) stochastic integrals with respect to the generalized Wiener process and prove the ${\hat}It{o}$ formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.385-387
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• 2016

$Fo{\check{s}}ner$ [4] defined a generalized module left (m, n)-derivation and proved the Hyers-Ulam stability of generalized module left (m, n)-derivations. In this note, we prove that every generalized module left (m, n)-derivation is trival if the algebra is unital and $m{\neq}n$.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.923-931
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• 2005

The two parameter generalized exponential distribution was recently introduced by Gupta and Kundu (1999). It is observed that the generalized exponential distribution can be used quite effectively to analyze skewed data set. This paper develops the accelerated life test model using generalized exponential distribution and considers maximum likelihood estimation of parameters under the tampered random variable model. To show the performance of proposed maximum likelihood estimates, some simulation will be performed. Using a real data set, an example will be given.