• 대한수학회지
• /
• 제45권6호
• /
• pp.1635-1646
• /
• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• 제어로봇시스템학회논문지
• /
• 제11권1호
• /
• pp.9-12
• /
• 2005

This paper presents an LMI-based method to design sliding mode observers for a class of uncertain systems. Using LIs we derive an existence condition of a sliding mode observer guaranteeing a stable sliding motion. And we give explicit formulas of the observer gain matrices. We also consider sliding mode observer design problems under an α-stability constraint or an LQ performance bound constraint. Finally, we give a numerical design example.

• 대한수학회보
• /
• 제60권4호
• /
• pp.933-955
• /
• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• 응용통계연구
• /
• 제22권3호
• /
• pp.541-551
• /
• 2009

Generalized processor sharing(GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. In a queueing system with single-class traffic, the stationary queue length becomes larger stochastically when the bandwidth (i.e. the service rate) of the system decreases. For a given GPS server, we consider the similar problem to this. We define the monotonicity for the head of the line processor sharing(HLPS) servers in which the units in the heads of the queues are served simultaneously and the bandwidth allocated to each queue are determined by the numbers of units in the queues. GPS is a type of monotonic HLPS. We obtain the HLPS server whose queue length of a class stochastically bounds upper that of corresponding class in the given monotonic HLPS server for all classes. The queue lengths process of all classes in the obtained HLPS server has the stationary distribution of product form. When the given monotonic HLPS server is GPS server, we obtain the explicit form of the stationary queue lengths distribution of the bounding HLPS server. Numerical result shows how tight the stochastic bound is.

• 경영정보학연구
• /
• 제13권1호
• /
• pp.97-114
• /
• 2011

본 연구는 IT 거버넌스 개념을 설정하는데 있어서 제기되는 두 개의 개념적 난제를 다루었다. 먼저 엔터프라이즈 IT 활동의 내용을 살펴서 이를 토대로 거버넌스와 비 거버넌스를 나누고자 하는 전통적 IT 거버넌스 개념 설정이 가진 자의성과 비논리성 문제를 지적하고, 이를 해결하는 방안으로서 목적기반 거버넌스 개념을 제시하였다. 다음으로 이러한 목적 기반 거버넌스 개념이 기존 엔터프라이즈 IT 활동과 가지는 개념적 충돌 문제를 지적하고, 이를 해결하기 위하여 IT 거버넌스 개념을 엔터프라이즈 IT 활동에 내재된 효과성 투명성 책임성 요소를 명시적으로 드러내고 이를 공식화, 외부화 하는 노력으로 새롭게 정의할 것을 제안하였다. 본 연구는 상기 논의를 전개하는데 있어서 IT 활동축이라는 개념적 장치를 도입하여 이를 일관되게 적용함으로써 IT 거버넌스 개념이 개념적 통일성과 논리적 일관성을 가지고 전개될 수 있음을 제시하였다. 끝으로 본 연구가 제시한 IT 거버넌스 개념이 가진 시사점과 향후 과제를 논의하였다.

• 한국통신학회논문지
• /
• 제25권4A호
• /
• pp.489-495
• /
• 2000

In this paper we propose an approximate method to estimate the cell loss probability(CLP) due to buffer overflow in ATM networks. The main idea is to relate the buffer capacity with the CLP target in explicit formula by using the approximate upper bound for the tail distribution of a queue. The significance of the proposition lies in the fact that we can obtain the expected CLP by using only the source traffic data represented by mean rate and its variance. To that purpose we consider the problem of estimating the cell loss measures form the statistical viewpoint such that the probability of cell loss due to buffer overflow does not exceed a target value. In obtaining the exact solution we use a typical matrix analytic method for GI/D/1B queue where B is the queue size. Finally, in order to investigate the accuracy of the result, we present both the approximate and exact results of the numerical computation and give some discussion.

• International Journal of Control, Automation, and Systems
• /
• 제4권6호
• /
• pp.697-704
• /
• 2006

The paper is concerned with $H_{\infty}$ filtering for descriptor systems. A necessary and sufficient condition is established in terms of linear matrix inequalities(LMIs) for the existence of normal filters such that the error systems are admissible and the transfer function from the disturbance to the filtering error output satisfies a prescribed $H_{\infty}$-norm bound constraint. When these LMIs are feasible, an explicit parameterization expression of all desired normal filter is given. All these results are yielded without decomposing the original descriptor systems, which makes the filter design procedure simple and direct. Finally, a numerical example is derived to demonstrate the applicability of the proposed approach.

• ETRI Journal
• /
• 제15권3_4호
• /
• pp.1-26
• /
• 1994

Simulated annealing is an attractive, but expensive, heuristic method for approximating the solution to combinatorial optimization problems. Attempts to parallel simulated annealing, particularly on distributed memory multicomputers, are hampered by the algorithm's requirement of a globally consistent system state. In a multicomputer, maintaining the global state S involves explicit message traffic and is a critical performance bottleneck. To mitigate this bottleneck, it becomes necessary to amortize the overhead of these state updates over as many parallel state changes as possible. By using this technique, errors in the actual cost C(S) of a particular state S will be introduced into the annealing process. This paper places analytically derived bounds on this error in order to assure convergence to the correct optimal result. The resulting parallel simulated annealing algorithm dynamically changes the frequency of global updates as a function of the annealing control parameter, i.e. temperature. Implementation results on an Intel iPSC/2 are reported.

• 제어로봇시스템학회논문지
• /
• 제11권9호
• /
• pp.750-754
• /
• 2005

This paper deals with the design problem of multivariable PID controllers guaranteeing the closed-loop system stability and a prescribed $H_\infty$ norm bound constraint. We reduce the problem to the static output feedback stabilization problem. We derive a necessary and sufficient condition f3r the existence of PID controllers and we give an explicit formula of PID controllers. We also give an existence condition of PID controllers guaranteeing a prescribed decay rate. Finally, we give an LMI-based design algorithm, together with a numerical design example.

• 제어로봇시스템학회논문지
• /
• 제9권11호
• /
• pp.861-867
• /
• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.