• 충청수학회지
• /
• 제24권2호
• /
• pp.187-204
• /
• 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.

• 호남수학학술지
• /
• 제43권2호
• /
• pp.183-197
• /
• 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.

• 대한수학회보
• /
• 제47권3호
• /
• pp.575-583
• /
• 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
• /
• 제40권1_2호
• /
• pp.233-242
• /
• 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.

• 한국인터넷방송통신학회논문지
• /
• 제19권2호
• /
• pp.135-141
• /
• 2019

최근 강화 학습을 통해 게임을 학습하는 인공지능 에이전트를 만드는 연구가 활발히 진행되고 있다. 게임을 에이전트에게 학습 시킬 때 어떠한 딥러닝 활성화 함수를 사용하는지에 따라 그 학습 성능이 달라진다. 본 논문은 2D 슈팅 게임 환경에서 에이전트가 강화 학습을 통해 게임을 학습할 경우 어떤 활성화 함수가 최적의 결과를 얻는지를 비교 평가 한다. 이를 위해 비교 평가에서 사용할 메트릭을 정의하고 각 활성화 함수에 따른 메트릭 값을 학습 시간에 따라 그래프로 나타내었다. 그 결과 ELU (Exponential Linear Unit) 활성화 함수에 1.0으로 파라미터 값을 설정할 경우 게임의 보상 값이 다른 활성화 함수보다 평균적으로 높은 것을 알 수 있었고, 가장 낮은 보상 값을 가졌던 활성화 함수와의 차이는 23.6%였다.

• 대한전기학회논문지:전기물성ㆍ응용부문C
• /
• 제52권4호
• /
• pp.185-191
• /
• 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.

• 대한방사선기술학회지:방사선기술과학
• /
• 제14권2호
• /
• pp.45-53
• /
• 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.

• 산업경영시스템학회지
• /
• 제38권2호
• /
• pp.40-46
• /
• 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
• /
• 제35권1호
• /
• pp.1-7
• /
• 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.

• 한국재료학회지
• /
• 제5권6호
• /
• pp.639-643
• /
• 1995

수소화된 비정질 게르마늄 (a-Ge : H)에 대해 전기전도율이 297-423K 사이에서 연구되었다. 측정된 전기전도율의 Arrhenius 구성에 의해 pre-exponential 인수 $\sigma$$_{0}$ 및 활성화에너지 $E_{c}$- $E_{F}$가 결정되었다. 튀어오름(kink) 온도의 존재로 인해 전기전도율의 arrhenius 구성이 두 exponential 함수에 의해 표현되었고, 이에 의해 결정된 페르미준위의 통계이동계수 ${\gamma}$$_{F}$는 약 8.65$\times$$10^{-3}$eV/K이었으며, $\sigma$$_{0}$는 약 2$\Omega$$^{-1}$$cm^{-1}$ /이었다. 전기전도율 데이터로부터 결함밀도가 수치해석적 방법에 의해 계산되었고, 결함밀도는 측정된 온도영역하에서 약 2배 정도 변화하였다 변화하였다화하였다