• Korean Journal of Mathematics
• /
• 제21권3호
• /
• pp.293-304
• /
• 2013

In this paper we analyze an error estimator for the lowest-order triangular Raviart-Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385{395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

• East Asian mathematical journal
• /
• 제26권3호
• /
• pp.337-350
• /
• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• International Journal of Control, Automation, and Systems
• /
• 제6권4호
• /
• pp.515-525
• /
• 2008

In this paper, the problem of delay-dependent stabilization for singular systems with multiple internal and external incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily test with numerical or algebraic methods. Based on Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memoryless state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free, and asymptotically stable via solving a strict linear matrix inequality (LMI) problem. An explicit expression for the desired memoryless state feedback control laws is also given. Finally, a numerical example illustrates the effectiveness and the availability for the proposed method.

• Journal of the Korean Statistical Society
• /
• 제26권1호
• /
• pp.31-46
• /
• 1997

Let $X_{t}$ = .beta. $X_{{t-1}}$ + .epsilon.$_{t}$ be an autoregressive process where $\mid$.beta.$\mid$ < 1 and {.epsilon.$_{t}$} is independent and identically distriubted with regularly varying tail probabilities. This process is called the asymptotically stationary first-order autoregressive process (AR(1)) with infinite variance. In this paper, we obtain a host of weak convergences of some point processes based on bootstrapping of { $X_{t}$}. These kinds of results can be generalized under the infinite variance assumption to ensure the asymptotic validity of the bootstrap method for various functionals of { $X_{t}$} such as partial sums, sample covariance and sample correlation functions, etc.ions, etc.

• 전기학회논문지
• /
• 제58권9호
• /
• pp.1796-1801
• /
• 2009

This paper is concerned with the problem of delay-dependent robust $H_{\infty}$ filtering for uncertain descriptor systems with time-varying delay. The considering uncertainty is convex compact set of polytoic type. The purpose is the design of a linear filter such that the resulting filtering error descriptor system is regular, impulse-free, and asymptotically stable with $H_{\infty}$ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed descriptor systems is derived. Based on the derived BRL, a robust $H_{\infty}$ filter is designed in terms of linear matrix inequaltity (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

• Bulletin of the Korean Chemical Society
• /
• 제17권2호
• /
• pp.188-192
• /
• 1996

It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.163-176
• /
• 2022

In this paper, we introduce some new classes of generalized mappings and prove some common fixed point theorems for a pair of asymptotically regular mappings. Our results extend and improve various well-known results due to Kannan, Reich, Wong, Hardy and Rogers, Ćirić, Jungck, Górnicki and many others. In addition to it, a sequential fixed point for a mapping which is the point-wise limit of a sequence of functions satisfying Ćirić-Proinov-Górnicki type mapping has been proved. Supporting examples have been given in strengthening hypotheses of our established theorems.

• 대한수학회지
• /
• 제46권6호
• /
• pp.1151-1164
• /
• 2009

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.

• 한국통신학회논문지
• /
• 제35권8C호
• /
• pp.709-712
• /
• 2010

이 논문에서는 시간상 확률 상관이 0이 아닌 약의존성 잡음 모형에서 두 표본을 쓰는 국소 최적 순위 검파기의 검정 통계량를 얻었다. 기준 관측과 보통 관측으로 이루어진 두 표본 관측 모형에서 약의존성 잡음 환경에 알맞은 국소 최적 순위 검파기의 검정 통계량을 네이먼 피어슨 정리로부터 유도하였다. 두 표본을 쓰는 국소 최적 순위 검파기는 한 표본을 쓰는 국소 최적 순위 검파기와 같은 점근 성능을 가지며 부호 통계량을 다룰 필요가 없어 얼개가 비교적 간단하다.

• 전자공학회논문지
• /
• 제49권9호
• /
• pp.67-75
• /
• 2012

높은 전송률에서 엔트로피 제한 양자화를 수행 시 최적의 양자기는 격자(lattice) 형태의 부호책을 가지는데, 규칙적인 구조로 인하여 양자화 과정이 단순하며, 격자의 형태에 따라 여러 양자화 알고리듬이 제안되어있다. 이러한 격자 벡터 양자기(vector quantizer: VQ)는 표본 적응 프로덕트 양자기(sample-adaptive product quantizer: SAPQ)를 사용하여 구현이 가능하며, 그 출력도 단순하게 엔트로피 부호화가 가능하다. 본 논문에서는 SAPQ에 기초한 엔트로피 부호화 방법을 제안하고, 무기억성(memoryless) 가우시언 분포에 대하여 여러 제안한 격자 VQ를 구현하고 양자화 에러 곡선을 엔트로피에 대하여 구하여 그 성능을 비교하였다. 실험을 통하여 전송률이 증가하면서 균등 분포에 이론적으로 얻는 이득과 비슷한 이득을 무기억성 가우시언 분포에서도 SAPQ의 출력을 엔트로피 부호화함으로 얻을 수 있음을 확인하였다.