• Bulletin of the Korean Chemical Society
• /
• 제35권5호
• /
• pp.1523-1528
• /
• 2014

Silicon quantum dots (Si QDs) were synthesized by etching silicon nanopowder with aqueous hydrofluoric acid (HF) and nitric acid ($HNO_3$). Then, the hydride-terminated Si QDs (H-Si QDs) were functionalized by 1- octadecene (ODE). By only controlling the etching time, the maximum luminescence peak of octadecylterminated Si QDs (ODE-Si QDs) was tuned from 404 nm to 507 nm. The average optical gap was increased from 2.60 eV (ODE-Si QDs-5 min) for 5 min of etching to 3.20 eV (ODE-Si QDs-15 min) for 15 min of etching, and to 3.40 eV (ODE-Si QDs-30 min) for 30 min of etching. The electron affinities (EA), ionization potentials (IP), and quasi-particle gap (${\varepsilon}^{qp}_{gap}$) of the Si QDs were determined by cyclic voltammetry (CV). The quasi-particle gaps obtained from the CV were in good agreement with the average optical gap values from UV-vis absorption. In the case of the ODE-Si QDs-30 min sample, the difference between the quasi-particle gap and the average optical gap gives the electron-hole Coulombic interaction energy. The additional electronic levels of the ODE-Si QDs-30 min and ODE-Si QDs-15 min samples determined by the CV results are interpreted to have originated from the Si=O bond terminating Si QD.

• East Asian mathematical journal
• /
• 제35권1호
• /
• pp.91-98
• /
• 2019

This paper is concerned with the global existence of strong solution for the controlled ode-pde systems. Also, we consider the continuous dependence of solution on the control.

• East Asian mathematical journal
• /
• 제35권5호
• /
• pp.547-557
• /
• 2019

This paper is concerned with the necessary conditions for optimal control problem governed by some ODE-PDE systems. That is, we obtain the necessary conditions for optimal control by showing the differentiability of the solution with respect to the control.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2004년도 가을 학술발표논문집 Vol.31 No.2 (1)
• /
• pp.733-735
• /
• 2004

생명 현상을 시스템적으로 이해하기 위해서는 현상에 대한 수학적 모델링이 필수적이다. 여러 가지 수학적 모델 가운데 상미분 방정식(ODE) 모델은 여러 가지 생화학 반응을 모델링 하는데 널리 사용되고 있다. 본 논문에서는 신호전달 경로에 B형 간염 바이러스가 미치는 영향을 ODE로 모델링하고, 이를 시뮬레이션 한 결과를 보인다. 또한, ODE모델을 설계하는데 있어 보다 유연하고 확장 가능한 새로운 표현 방식을 제안한다.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.231-244
• /
• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Journal of Information Processing Systems
• /
• 제14권2호
• /
• pp.455-468
• /
• 2018

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.

• Journal of applied mathematics & informatics
• /
• 제7권1호
• /
• pp.183-193
• /
• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1995년도 하계학술대회 논문집 B
• /
• pp.901-903
• /
• 1995

The ordinary differential equation (ODE) method has been widely used for the convergence analysis of stochastic recursive algorithms. The principal objective of this method is to associate to a given algorithm a differential equation with continuous righthand side. Usually some assumptions should be imposed to get such a differential equation. If any of assumptions fails, then the ODE method cannot be used. Recently a new method using differential inclusions (DIs) was introduced in [3], which is useful to deal with those cases. The DI method shares the same idea with the ODE method, but it is different in that a differential inclusion is identified instead of a differential equation with continuous righthand side. In this paper, we briefly review the DI method and then analyze a Robbins and Monro (RM)-type algorithm. Our focus is placed on the projected algorithm.

• 대한수학회보
• /
• 제54권2호
• /
• pp.655-666
• /
• 2017

In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.

• Kyungpook Mathematical Journal
• /
• 제61권2호
• /
• pp.309-322
• /
• 2021

A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.