• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.187-204
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• 2011

B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.575-583
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• 2010

In this paper, new q-analogs of Genocchi numbers and polynomials are defined. Some important arithmetic and combinatoric relations are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.2
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• pp.135-141
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• 2019

Recently, there has been active researches about building an artificial intelligence agent that can learn how to play a game by using re-enforcement learning. The performance of the learning can be diverse according to what kinds of deep learning activation functions they used when they train the agent. This paper compares the activation functions when we train our agent for learning how to play a 2D shooting game by using re-enforcement learning. We defined performance metrics to analyze the results and plotted them along a training time. As a result, we found ELU (Exponential Linear Unit) with a parameter 1.0 achieved best rewards than other activation functions. There was 23.6% gap between the best activation function and the worst activation function.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.4
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• pp.185-191
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• 2003

In this Paper, we propose an accurate and stable solution of the transient electromagnetic response from three-dimensional arbitrarily shaped conducting objects by using a time domain magnetic field integral equation. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of temporal expansion functions with decaying exponential functions and Laguerre·polynomials. Since these temporal expansion functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation and converges to zero unconditionally. To show the validity of the proposed method, we solve a time domain magnetic field integral equation for three closed conducting objects and compare the results of Mie solution and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• Journal of radiological science and technology
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• v.14 no.2
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• pp.45-53
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• 1991

SPECT 영상에서 콤프톤 산란 광자는 공간분해능의 감소와 그 양을 측정하는데 있어 정확성과 정밀성을 감소시킨다. 이와같은 콤프톤 산란의 영향을 감소시키기 위하여 사용하는 대부분의 보정방법은 선원의 위치로부터 거리의 단일지수함수로 대칭인 산란분포함수를 고려하게 된다. 본 연구는 균등 및 불균등 산란에 대한 산란분포함수를 얻기 위하여 보다 현실적인 접근방법을 시도하였다. 산란 및 비산란광자의 공간분포와 에너지분포를 얻기 위하여 뼈, 폐, 물의 균등 및 불균등 분포로 된 원통형의 팬톰 속에 $^{99m}Tc$의 선선원 및 점선원을 놓고 Monte Carlo Simulation을 하였으며, 깊이의 함수, media의 접촉영역으로부터 선원거리 및 산란체의 밀도의 변화로 표현한 산란분포함수(SDF)를 얻었다. 산란분포함수는 균등한 뼈, 폐, 물에서는 선원위치로부터 거리의 단일지수함수(single exponential functions)로 대칭으로 나타났으며, 두 물체의 조합에서는 2중지수함수(dual exponential functions)로 비대칭으로 나타났다. 산란분율은 20% window photopeak에서 총 계수의 8%에서 53%까지 다양한 변화가 있었으며, 지수함수의 기울기는 $0.1{\sim}0.9\;cm^{-1}$의 범위로 나타났다. 불균등 산란체에서 얻은 산란분포함수는 SPECT 영상에 있어 콤프톤 산란의 감소에 대한 보다 정확한 보정방법의 개발에 필요한 정보를 제공할 것이다.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.2
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• pp.40-46
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• 2015

The modular assembly system can make it possible for the variety of products to be assembled in a short lead time. In this system, necessary components are assembled to optional components tailor to customers' orders. Budget for inventory investments composed of inventory and purchasing costs are practically limited and the purchasing cost is often paid when an order is arrived. Service cost is assumed to be proportional to service level and it is included in budget constraint. We develop a heuristic procedure to find a good solution for a continuous review inventory system of the modular assembly system with a budget constraint. A regression analysis using a quadratic function based on the exponential function is applied to the cumulative density function of a normal distribution. With the regression result, an efficient heuristics is proposed by using an approximation for some complex functions that are composed of exponential functions only. A simple problem is introduced to illustrate the proposed heuristics.

• Journal of Ecology and Environment
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• v.35 no.1
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• pp.1-7
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• 2012

To calculate and predict soil carbon budget and cycle, it is important to understand the complex interrelationships involved in soil respiration rate (Rs). We attempted to reveal relationships between Rs and key environmental factors, such as soil temperature, using a laboratory incubation method. Soil samples were collected from mature deciduous (MD), mature coniferous (MC), immature deciduous (ID), and immature coniferous (IC) forests. Prior to measure, soils were pre-incubated for 3 days at $25^{\circ}C$ and 60% of maximum water holding capacity (WHC). Samples of gasses were collected with 0, 2, and 4 h interval after the beginning of the measurement at soil temperatures of 5, 15, 25, and $35^{\circ}C$ (at 60% WHC). Air samples were collected using a syringe attached to the cap of closed bottles that contained the soil samples. The $CO_2$ concentration of each gas sample was measured by gas chromatography. Rs was strongly correlated with soil temperature (r, 0.93 to 0.96; P < 0.001). For MD, MC, ID, and IC soils taken from 0-5 cm below the surface, exponential functions explained 90%, 82%, 92%, and 86% of the respective data plots. The temperature and Rs data for soil taken from 5-10 cm beneath the surface at MD, MC, ID, and IC sites also closely fit exponential functions, with 83%, 95%, 87%, and 89% of the data points, respectively, fitting an exponential curve. The soil organic content in mature forests was significantly higher than in soils from immature forests (P < 0.001 at 0-5 cm and P < 0.005 at 5-10 cm) and surface layer (P = 0.04 at 0-5 cm and P = 0.12). High soil organic matter content is clearly associated with high Rs, especially in the surface layer. We determined that the incubation method used in this study have the possibility for comprehending complex characteristic of Rs.

• Korean Journal of Materials Research
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• v.5 no.6
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• pp.639-643
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• 1995

The temperature dependence of the dark conductivity was studied on undoped hydrogenated amorphous germanium (a-Ge : H) over the range from 297 to 423 K. The pre-exponential factor $\sigma$$\_$0/ and activation energy E$\_$C/-E$\_$F/ are determined by an Arrhenius plot. The Arrhenius plot of the electrical conductivity shows a kink around the kink temperature and then is composed of two exponential functions. The obtained statistical shift ${\gamma}$$\_$F/ was about 8.65${\times}$10$\^$-3/eV/K and the pre-exponential factor $\sigma$$\_$0/ was about 2$\Omega$$\^$-1/cm$\^$-1/. A temperature dependent defect density is numerically calculated from the conductivity data. A change of the defect density is observed in the factor of about two in the range of the experimental temperature.