• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.749-763
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• 2022

Let C[0, T] denote an analogue of Weiner space, the space of real-valued continuous on [0, T]. In this paper, we investigate the translation of time interval [0, T] defining the analogue of Winer space C[0, T]. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on C[0, T] as the analogue of Wiener measures on C[0, s] and C[s, T] with 0 < s < T.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.587-597
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• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.303-311
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• 2017

In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.373-386
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• 2023

In this paper we have obtained various forms of (p, q)-analogue of Aleph-Function satisfying Truesdell's ascending and descending F_p,q-equation. These structures have been employed to arrive at certain generating functions for (p, q)-analogue of Aleph-Function. Some specific instances of these outcomes as far as (p, q)-analogue of I-function, H-function and G-functions have likewise been obtained.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.67-76
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• 2017

In this note, we prove the theorems in the generalized analogue of Wiener space corresponding to the second and the third arcsine laws in either concrete or analogue of Wiener space [1, 2, 7] and we show that our results are exactly same to either the concrete or the analogue of Wiener case when the initial condition gives either the Dirac measure at the origin or the probability Borel measure.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.735-742
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• 2013

In this note, we prove the translation theorem for the generalized analogue of Wiener measure space and we show some properties of the generalized analogue of Wiener measure from it.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.253-261
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• 2012

This work aims at proving the FKG inequalities for the analogue of Wiener functionals with special orders on the analogue of Wiener space.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.317-333
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• 2007

In 2002, the author and professor Ryu introduced the concept of analogue of Wiener measure. In this paper, we prove the existence theorem of Fourier-Feynman transform on analogue of Wiener measure in $L_2-norm$ sense.

• Archives of Pharmacal Research
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• v.17 no.2
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• pp.104-108
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• 1994

trans-Ethyl 1, 2, 3, 4a, 5, 6, 8a-cotahydro-2-benzyl-4-hydroxy-6-methyl-5-isoquinoline-carboxylate was prepared by intramolecular Diels-Alder reaction as a precusor of newly designed aza-analogue of mevinolin.