• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권4호
• /
• pp.281-296
• /
• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Computers and Concrete
• /
• 제29권3호
• /
• pp.201-207
• /
• 2022

The evaluation of velocity profile for large values of buoyancy parameter and Bioconvected Rayleigh number is examined. The non-linear problem has been tackled numerically by shooting technique. Nanofluid temperature and nanoparticle concentration slightly elevates for increasing values of thermophoresis coefficient. Thickness of thermal boundary layer is significantly increased with thermophoresis coefficient whereas thickness of concentration boundary layer is more slightly enhanced. The response of temperature and nanoparticles concentration is observed due to change in Brownian motion parameter. As Brownian motion parameter increased temperature distribution is slightly enhanced. The reverse behavior is observed in case of nanoparticles concentration. Comparison of numerical technique with the extant literature is made and an acceptable agreement is attained.

• 호남수학학술지
• /
• 제45권3호
• /
• pp.433-456
• /
• 2023

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝⁿ) of bounded continuous ℝⁿ-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛_BC (ℝⁿ) of linear bounded operators from BC ([-r, 0] ; ℝⁿ) to ℝⁿ. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

• Journal of Applied and Pure Mathematics
• /
• 제5권1_2호
• /
• pp.23-40
• /
• 2023

This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.

• 대한수학회지
• /
• 제27권2호
• /
• pp.239-244
• /
• 1990

• 한국항만경제학회지
• /
• 제34권1호
• /
• pp.99-110
• /
• 2018

본 연구는 해운기업의 주요 비용요인 벙커 가격과 환율의 불확실성으로 인한 재무적 리스크를 수치화하는 방법론을 2010년 1월 1일부터 2018년 1월 31일까지의 일별자료를 대상으로 적용한다. 기하브라운 운동 (Geometric Brownian Motion 이하 GBM)과 이를 확장한 조건부 이분산성(heteroskedasticity) 및 점프 확산 프로세스(jump diffusion process)에 의존하는 모형으로부터 추정한 현금 흐름 리스크 추정치는 다음 세 가지 학술적 기여로 요약할 수 있다. 첫째, 운임수익률과 같은 단일 변수에 의존한 리스크 분석을 벙커가격과 환율 수익률 변동성과 같이 복합요인으로부터 발생하는 영향으로 분석을 확장하였다. 둘째, 개별기업 수준에서 벙커가격과 환율 리크스 관리의 필요성을 민감도 분석을 통해 현금흐름수준으로 제시하였다. 마지막으로 분석결과가 제시하는 리스크 규모를 근거로 해운기업은 리스크 관리를 위한 수단으로 무엇이 적절한가를 고민해야 할 필요성이 있음을 제기한다.

• Advances in concrete construction
• /
• 제14권2호
• /
• pp.103-113
• /
• 2022

On the basis of fabrication, the utilization of nano material in numerous industrial and technological system, obtained the utmost significance in current decade. Therefore, the current investigation presents a theoretical disposition regarding the flow of electric conducting Williamson nanoliquid over a stretchable surface in the presence of the motile microorganism. The impact of thermal radiation and magnetic parameter are incorporated in the energy equation. The concentration field is modified by adding the influence of chemical reaction. Moreover, the splendid features of nanofluid are displayed by utilizing the thermophoresis and Brownian motion aspects. Compatible similarity transformation is imposed on the equations governing the problem to derive the dimensionless ordinary differential equations. The Homotopy analysis method has been implemented to find the analytic solution of the obtained differential equations. The implications of specific parameters on profiles of velocity, temperature, concentration and motile microorganism density are investigated graphically. Moreover, coefficient of skin friction, Nusselt number, Sherwood number and density of motile number are clarified in tabular forms. It is revealed that thermal radiation, thermophoresis and Brownian motion parameters are very effective for improvement of heat transfer. The reported investigation can be used in improving the heat transfer appliances and systems of solar energy.

• 한국입자에어로졸학회지
• /
• 제8권1호
• /
• pp.29-35
• /
• 2012

The Faraday cup electrode of different size has been developed and evaluated to investigate the diffusion effect of particles by Brownian motion in a particle beam mass spectrometer(PBMS). Particles which focused and accelerated by aerodynamic lens are charged to saturation in an electron beam, and then deflected electrostatically into a Faraday cup detector for measurement of the particle current. The concentration of particles is converted from currents detected by Faraday cup. Measurements of particle current as a function of deflection voltage are combined with measured relationships between particle velocity and diameter, charge and diameter, and mass and diameter, to determine the particle size distribution. The particle currents were measured using 5, 10, 20, 40 mm sized Faraday cup that can be move to one direction by motion shaft. The current difference for each sizes as a function of position was compared to figure out diffusion effect during transport. Polystyrene latex(PSL) 100, 200 nm sized standard particles were used for evaluation. The measurement using 5 mm sized Faraday cup has the highest resolution in a diffusion distance and the smaller particles had widely diffused.

• 센서학회지
• /
• 제31권3호
• /
• pp.175-179
• /
• 2022

The physical properties of biomaterials are important for their isolation and separation from body fluids. In particular, the precise evaluation of the multi-physical properties of single biomolecules is essential in that the correlation between physical and biological properties of specific biomolecule. However, the majority of scientific equipment, can only determine specific-physical properties of single nanoparticles, making the evaluation of the multi-physical properties difficult. The improvement of analytical techniques for the evaluation of multi-physical properties is therefore required in various research fields. In this study, we developed a motion-tracking algorithm to evaluate the multi-physical properties of single-nanoparticles by analyzing their behavior. We observed the Brownian motion and electric-field-induced drift of fluorescent nanoparticles injected in a microfluidic chip with two electrodes using confocal microscopy. The proposed algorithm is able to determine the size of the nanoparticles by i) removing the background noise from images, ii) tracking the motion of nanoparticles using the circular-Hough transform, iii) extracting the mean squared displacement (MSD) of the tracked nanoparticles, and iv) applying the MSD to the Stokes-Einstein equation. We compared the evaluated size of the nanoparticles with the size measured by SEM. We also determined the zeta-potential and surface-charge density of the nanoparticles using the extracted electrophoretic velocity and the Helmholtz-Smoluchowski equation. The proposed motion-tracking algorithm could be employed in various fields related to biomaterial analysis, such as exosome analysis.

• 대한수학회지
• /
• 제38권3호
• /
• pp.657-667
• /
• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.