• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.429-443
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• 2004

In this paper, using Zhang, Guo and Liu's comments in [17], we define interval-valued functionals and investigate their properties. Furthermore, we discuss some applications of interval-valued Choquet expectations.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.745-751
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• 2014

In this paper we introduce the interval-valued Henstock integral on time scales and investigate some properties of these integrals.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.97-109
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• 1998

We first obtain the white noise calculus to the computation of Feynman integral for a generalized function, according to the definition of Feynman integrals by T. Hida and L. Streit. We next give the translation theorem for Feynman integral of a generalized function.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.143-146
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• 2005

In this paper, we define correlation coeeficients of interval-valued fuzzy numbers by utilizing Choquet integrals. Also we discuss some properties of them.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.409-420
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• 2001

In this paper we establish a Fubini theorem for various analytic Wiener and Feynman integrals. We then proceed to obtain several integration formulas as corollaries.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.635-658
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• 2006

This paper is concerned with giving some rather weak size conditions implying the $L^P$ boundedness of the multiple Marcin-kiewicz integrals for some fixed $1\;<\;p\;<\;{\infty}$, which essentially improve and extend some known results.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.191-202
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• 2022

In this paper, we obtain the quantitative weighted bounds of oscillatory singular integral with rough kernel. Moreover, the quantitative weighted bounds of maximally truncated oscillatory singular integral with rough kernel are also obtained.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.682-688
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• 2023

The main object of this paper is to establish twenty definite integrals involving Struve functions and modified Srtuve functions associated with hypergeometric functions, which are presumably new and not present in the scientific literature.

• ETRI Journal
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• v.35 no.1
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• pp.131-141
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• 2013

Integral cryptanalysis, which is based on the existence of (higher-order) integral distinguishers, is a powerful cryptographic method that can be used to evaluate the security of modern block ciphers. In this paper, we focus on substitution-permutation network (SPN) ciphers and propose a criterion to characterize how an r-round integral distinguisher can be extended to an (r+1)-round higher-order integral distinguisher. This criterion, which builds a link between integrals and higher-order integrals of SPN ciphers, is in fact based on the theory of direct decomposition of a linear space defined by the linear mapping of the cipher. It can be directly utilized to unify the procedure for finding 4-round higher-order integral distinguishers of AES and ARIA and can be further extended to analyze higher-order integral distinguishers of various block cipher structures. We hope that the criterion presented in this paper will benefit the cryptanalysts and may thus lead to better cryptanalytic results.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.