• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1101-1111
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• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.407-415
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• 2011

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.

• Kyungpook Mathematical Journal
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• v.19 no.2
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• pp.257-260
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• 1979

We show that the condition S of Sidon is sufficient for the integrability of the limit of Rees-$Stanojevi{\acute{c}$ cosine sums $g_n(x)={\frac{1}{2}}{\limits\sum^{n}_{k=0}}{\Delta}a_k+{\limits\sum^{n}_{k=1}}{\limits\sum^{n}_{j=k}}{\Delta}a_j\;cos\;kx$.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.791-803
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• 2021

Earlier investigators have made detailed studies of geometric properties such as integrability, partial integrability, and invariants, such as the fundamental 2-form, of some canonical f-structures, such as f³ ± f = 0, on the frame bundle FM. Our aim is to study metallic structures on the frame bundle: polynomial structures of degree 2 satisfying F² = pF +qI where p, q are positive integers. We introduce a tensor field F_α, α = 1, 2…, n on FM show that it is a metallic structure. Theorems on Nijenhuis tensor and integrability of metallic structure F_α on FM are also proved. Furthermore, the diagonal lifts g^D and the fundamental 2-form Ω_α of a metallic structure F_α on FM are established. Moreover, the integrability condition for horizontal lift F_α^H of a metallic structure F_α on FM is determined as an application. Finally, the golden structure that is a particular case of a metallic structure on FM is discussed as an example.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.289-300
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• 2008

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.1-7
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• 1996

Since the invention of the Pettis integral over half century ago, the problem of recognizing the Pettis integrability of a function against an individual condition has been much studied [1,6,7,8,12]. In spite of the R.F. Geitz (1982) and M. Talagrand's (1984) characterization of Pettis integrability, there is often trouble in recognizing when a function is or is not Pettis integrable.(omitted)

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.299-303
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• 1998

In this paper weak laws of large numbers are obtained for random variables in $L^{1}(R)$ which satisfy a compact uniform integrability condition.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.477-489
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• 2016

The purpose of this paper is to establish the complete moment convergence and the integrability of supremum for weighted sums of pairwise negatively quadrant dependent random variables satisfying stochastically dominating condition.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.427-435
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• 2006

In this paper, we are to study the generic submanifold M of a Kenmotsu manifold and consider the integrability condition of the almost complex structure induced on the even-dimensional product manifold $M{\times}R^p{\times}R^1$ where p is the codimension.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1331-1339
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• 2018

In this paper the decomposition of basic equations of $(LCS)_n$-manifolds is carried out into horizontal and vertical projections. Further, we study the integrability of the distributions $D,D{\oplus}[{\xi}]$ and $D^{\perp}$ totally geodesic of semi-invariant submanifolds of $(LCS)_n$-manifold.