• Journal of the Korean Statistical Society
• /
• v.34 no.4
• /
• pp.281-295
• /
• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.401-407
• /
• 1995

The best constants for two distinct weak-type inequalities for martingales and their differential subordinates with values in some spaces isomorphic to a Hilbert space are shown to be the same. This extends the result of Burkholder shown in the Hilbert space setting.

• KIEAE Journal
• /
• v.16 no.6
• /
• pp.13-19
• /
• 2016

Purpose: In this study, we examined outdoor air fraction using historical data of actual Air Handling Unit (AHU) in the existing building during intermediate season and analyzed optimal outdoor air fraction by control types for economizer. Method: Control types for economizer which was used in analysis are No Economizer(NE), Differential Dry-bulb Temperature(DT), Diffrential Enthalpy(DE), Differential Dry-bulb Temperature+Differential Enthalpy(DTDE), and Differential Enthalpy+Differential Dry-bulb Temperature (DEDT). In addition, the system heating and cooling load were analyzed by calculating the outdoor air fraction through existing AHU operating method and control types for economizer. Result: Optimized outdoor air fraction through control types was the lowest in March and distribution over 50% was shown in May. In case of DE control type, outdoor air fraction was the highest of other control types and the value was average 63% in May. System heating load was shown the lowest value in NE, however, system cooling load was shown 1.7 times higher than DT control type and 5 times higher than DE control type. For system heating load, DT and DTDE is similar during intermediate season. However, system cooling load was shown 3 times higher than DE and DEDT. Accordingly, it was found as the method to save cooling energy most efficiently with DE control considering enthalpy of outdoor air and return air in intermediate season.

• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.515-536
• /
• 2012

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the $M$-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.731-742
• /
• 2007

Let X be a Banach space, $A:D(A){\subset}X{\rightarrow}X$ the generator of a compact $C_0-semigroup\;S(t):X{\rightarrow}X,\;t{\geq}0$, D a locally closed subset in X, and $f:(a,b){\times}C([-q,0];X){\rightarrow}X$ a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order that D be a viable domain of the semi linear differential equation of retarded type $$u#(t)=Au(t)+f(t,u_t),\;t{\in}[t_0,\;t_0+T],{u_t}_0={\phi}{\in}C([-q,0];X)$$ is the tangency condition $$\limits_{h{\downarrow}0}^{lim\;inf\;h^{-1}d(S(h)v(0)+hf(t,v);D)=0}$$ for almost every $t{\in}(a,b)$ and every $v{\in}C([-q,0];X)\;with\;v(0){\in}D$.

• Journal of the Korean Society for Precision Engineering
• /
• v.20 no.2
• /
• pp.199-208
• /
• 2003

Continuously variable transmission (CVT) mechanisms considered here combine the functions of a K-H-V type differential gear unit and a V-belt type continuously variable unit (CVU). As combining the functions of a K-H-V type differential gear unit and a V-belt type CVU, 24 different mechanisms are presented. Some useful theoretical formula related to speed ratio, power flow and efficiency are derived and analyzed. These mechanisms have many advantages which are the decrease of CVT size, the increase of overall efficiency, the extension of speed ratio range, and the generation of geared neutral.

• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.54-70
• /
• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.7
• /
• pp.938-947
• /
• 2003

In this paper, we derived the formula for estimating the power of the electric motors needed to operate the Decanter-type centrifuge. In the derivation of the formula the sludge-removal torque is to be supplied from the formula derived in the first paper. The intricate nature of the transmission mechanism in the planetary gear trains of the sludge-removal power and torque has been clarified in this second paper. In particular we considered two-motor system, where the main motor drives the machine while the differential-speed control motor plays the role of braking in adjusting the differential speed. Sample calculation for the specific design treated in the first paper showed that the selection criterion for the main motor depends on the lower limit of the differential speed; when the lower limit is set low, it should be selected based on the steadily operating power, while it should be selected based on the starting power when the lower limit is set high. The total power required by both the main motor and the differential-speed control motor increases as the differential speed is decreased. It is suggested that the power loss in the differential-speed control motor could be minimized by attaching an electric generator to it.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.137-154
• /
• 2007

In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.

• Journal of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.223-233
• /
• 2010

In this paper, we use q-differential operator to recover the finite Heine $_2\Phi_1$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.