• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.951-962
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• 2013

We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.443-457
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• 2012

In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of $R_2^9$.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.852-856
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• 2004

The present paper establishes a necessary and sufficient condition for weak convergence for weighted sums of compactly uniformly integrable level-continuous fuzzy random variables as a generalization of weak laws of large numbers for sums of fuzzy random variables.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.273-277
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• 1999

In this paper we will consider interval-valued martin-gales. We obtain several results parallel to the case of real-valued martingales. For example an $L_1$-bounded interval-valued martingale converges a.e. An interval-valued martingale ${{F_n}^\infty}_{n=1}$ is uniformly in-tegrable if and only if there is an interval-valued random variable F with $\parallel F \parallel _1<\infty$ such that $F_n=E(F\mid A_n)$, for all $n\geq 1$

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.383-399
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• 2013

In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.297-308
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• 2003

Hypersurfaces of a Riemannian manifold equipped with a hypercosymplectic 3-structure are studied. Integrability conditions for certain distributions on the hypersurface are investigated. Geometry of leaves of certain distribution are also studied.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.667-676
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• 2014

In this article, we study slant and semi-slant submanifolds of $(LCS)_n$-manifolds. Integrability conditions of distributions involved in definition of semi-slant submanifolds of a $(LCS)_n$-manifold have been obtained.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.233-237
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• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.177-182
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• 2004

In this paper, we establish some results on almost sure convergence for sums and weighted sums of uniformly integrable fuzzy random sets taking values in the space of upper-semicontinuous fuzzy sets in $R^{p}$.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.27-40
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• 2017

In this paper, we construct exact traveling wave solutions of various kind of partial differential equations arising in mathematical science by the system technique. Further, the $Painlev{\acute{e}}$ test is employed to investigate the integrability of the considered equations. In particular, we describe the behaviors of the obtained solutions under certain constraints.