• Honam Mathematical Journal
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• v.38 no.1
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• pp.17-23
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• 2016

This paper deals with the study of newly defined special function known as k-Bessel's function due to Gehlot [2]. Certain integral representations of k-Bessel's function are investigated. Known integrals of classical Bessel's function are seen to follow as special cases of our main results.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.321-332
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• 2017

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.749-762
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• 2017

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.741-753
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• 1998

Let G(*) be a Borel function applied to a stationary long memory sequence {X$_{i}$} of standard Gaussian random variables. Focusing on the process {G(X$_{i}$)}, the present paper establishes the almost sure representation for the empirical quantile process, that is, Bahadur's representation, and for the empirical process with respect to sample mean. Statistical applications of the representations are also addressed.sed.

• Korean Journal of Logic
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• v.10 no.1
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• pp.1-23
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• 2007

Dunn investigated algebras and semantics for negations in non-classical logics. This paper extends his investigation to dual negations, more exactly to duals to the negations in Dunn [3, 5]. I first survey and systematize the algebras of dual negations, i.e., (self-dual) subminimal negation, dual Galois negations, dual minimal negation, wB (or dual intuitionistic) negation, (self-dual) De Morgan negation, and (self-dual) ortho negation, based on partially ordered sets. I next provide dual-perp semantics for these (dual) negations. I finally give representations for them by using dual-perp semantics.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.1-16
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• 2010

By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities involving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric $_4F_3$ function are then given. Furthermore, the integral representations associated with generalized hypergeometric functions are also presented.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.735-745
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• 1996

This is the sequel to our paper "On projective representations of a group and its subgroups I" [4]. In Section 4[4] we proved some global properties on regularity condition. The purpose of this paper is to study local properties, that is, we shall ask how the regularity condition on subgroups is related to that on group. Throughout the paper we use the same notations as in [4].as in [4].

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.325-337
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• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.591-604
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• 2018

We consider a family of ribbon 2-knots with trivial Alexander polynomial. We give nonabelian SL(2, C)-representations from the groups of these knots, and then calculate the twisted Alexander polynomials associated to these representations, which allows us to classify this family of knots.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.209-224
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• 2015

Computing square, cube and n-th roots in general, in finite fields, are important computational problems with significant applications to cryptography. One interesting approach to computational problems is by using polynomial representations. Agou, Del$\acute{e}$eglise and Nicolas proved results concerning the lower bounds for the length of polynomials representing square roots modulo a prime p. We generalize the results by considering n-th roots over finite fields for arbitrary n > 2.