• The Pure and Applied Mathematics
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• v.31 no.3
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• pp.311-324
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• 2024

This article presents the above and below bounds for Midpoint and Trapezoid types inequalities for 𝜓-Hilfer fractional integrals with the assistance of the functions whose second derivatives are bounded. We also possess some extensions and generalizations of Hermite-Hadamard inequalities via 𝜓-Hilfer fractional integrals with the aid of the functions that have the conditions that will said.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.341-348
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• 1994

Some extensions of the law of the iterated logarithm via self-normalization are obtained for seuences of sign-invariant random variables.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.7-9
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• 1999

In this paper, we introduce the regularity, the hyperexactness and the hyperregularity, and we study on the extensions of regularity and the holomorphical regularity of the bounded linear operators.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.285-294
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• 1996

In this paper, we show relations between injective covers and direct sums, some commutative properties, and composition properties in the injective covers.

• Korean Journal of Mathematics
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• v.3 no.1
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• pp.131-133
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• 1995

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2004.07a
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• pp.450-450
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• 2004

• East Asian mathematical journal
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• v.8 no.1
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• pp.91-102
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• 1992

• IE interfaces
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• v.1 no.2
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• pp.13-24
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• 1988

Various models usable for finding desired configuration of FMSs are presented. Extensions on reported models are made and new models are also introduced. Usages and solution algorithms of each model are discussed.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.735-741
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• 1998

In this paper we will derive some new properties of q-extensions of p-adic gamma functions and p-adic Euler constants.

• Journal of KIISE:Databases
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• v.33 no.5
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• pp.453-462
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• 2006

Discovering sequential patterns is an important problem for many applications. Existing algorithms find sequential patterns in the sense that only items are included in the patterns. However, for many applications, such as business and scientific applications, quantitative attributes are often recorded in the data, which are ignored by existing algorithms but can provide useful insight to the users. In this paper, we consider the problem of mining sequential patterns with quantities. We demonstrate that naive extensions to existing algorithms for sequential patterns are inefficient, as they may enumerate the search space blindly. Thus, we propose hash filtering and quantity sampling techniques that significantly improve the performance of the naive extensions. Experimental results confirm that compared with the naive extensions, these schemes not only improve the execution time substantially but also show better scalability for sequential patterns with quantities.