• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.537-547
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• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.233-242
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• 2022

The purpose of this paper is to find some properties and identities for (p, q)-cosine Genocchi polynomials. This polynomials which is one of Appell polynomials, have multifarious relations of (p, q)-other polynomials.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.219-234
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• 2019

We use the definition of Euler polynomials of the second kind with (p, q)-numbers to identify some identities and properties of these polynomials. We also investigate some relationships between (p, q)-Euler polynomials of the second kind, (p, q)-Bernoulli polynomials, and (p, q)-tangent polynomials by using the properties of (p, q)-exponential function.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.331-357
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• 2020

Let p be an analytic function defined on the open unit disk 𝔻. We obtain certain differential subordination implications such as ψ(p) := p^λ(z)(α+βp(z)+γ/p(z)+δzp'(z)/p^j(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to 𝒫, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy |log(zf'(z)/f(z))| < 1, |(zf'(z)/f(z))² - 1| < 1 and zf'(z)/f(z) lying in the parabolic region v² < 2u - 1.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.12 no.4
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• pp.1-10
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• 2013

This study was conducted to investigate that bus information was used as an information of travel speed. To determine the travel speed on the road, bus information and the information collected from the point detector and the interval detection installed were compared. If bus information has the function of traffic information detector, can provide the travel speed information to road users. To this end, the model of recognizing the traffic patterns is necessary. This study used simple moving-average method, simple exponential smoothing method, Double moving average method, Double exponential smoothing method, ARIMA(Autoregressive integrated moving average model) as the existing methods rather than new approach methods. This study suggested the possibility to replace bus information system into other information collection system.

• Journal of Ecology and Environment
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• v.34 no.4
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• pp.411-423
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• 2011

This study was conducted to quantify soil $CO_2$ efflux using the continuous measurement method and to examine the applicability of an automatic continuous measurement system in a Korean deciduous broad-leaved forest. Soil respiration rate (Rs) was assessed through continuous measurements during the 2004-2005 full growing seasons using an automatic opening/closing chamber system in sections of a Gwangneung temperate deciduous forest, Korea. The study site was an old-growth natural mixed deciduous forest approximately 80 years old. For each full growth season, the annual Rs, which had a gap that was filled with data using an exponential function derived from soil temperature (Ts) at 5-cm depth, and Rs values collected in each season were 2,738.1 g $CO_2$ $m^{-2}y^{-1}$ in 2004 and 3,355.1 g $CO_2$ $m^{-2}y^{-1}$ in 2005. However, the diurnal variation in Rs showed stronger correlations with Ts (r = 0.91, P < 0.001 in 2004, r = 0.87, P < 0.001 in 2005) and air temperature (Ta) (r = 0.84, P < 0.001 in 2004, r = 0.79, P < 0.001 in 2005) than with deep Ts during the spring season. However, the temperature functions derived from the Ts at various depths of 0, -2, -5, -10, and -20 cm revealed that the correlation coefficient decreased with increasing soil depth in the spring season, whereas it increased in the summer. Rs showed a weak correlation with precipitation (r = 0.25, P < 0.01) and soil water content (r = 0.28, P < 0.05). Additionally, the diurnal change in Rs revealed a higher correlation with Ta than that of Ts. The $Q_{10}$ values from spring to winter were calculated from each season's dataset and were 3.2, 1.5, 7.4, and 2.7 in 2004 and 6.0, 3.1, 3.0, and 2.6 in 2005; thus, showing high fluctuation within each season. The applicability of an automatic continuous system was demonstrated for collecting a high resolution soil $CO_2$ efflux dataset under various environmental conditions.