• Korean Journal of Mathematics
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• 제18권1호
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• pp.63-77
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• 2010

Infinite finite range inequalities relate the norm of a weighted polynomial over ${\mathbb{R}}$ to its norm over a finite interval. In this paper we extend such inequalities to generalized polynomials with the weight $W(x)={\prod}^{m}_{k=1}{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$.

• 논리연구
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• 제9권2호
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• pp.1-30
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• 2006

This paper investigates algebraic semantics for some weak Boolean (wB) logics, which may be regarded as left-continuous t-norm based logics (or monoidal t-norm based logics (MTLs)). We investigate as infinite-valued logics each of wB-LC and wB-sKD, and each corresponding first order extension $wB-LC\forall$ and $wB-sKD\forall$. We give algebraic completeness for each of them.

• 충청수학회지
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• 제27권3호
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• pp.393-401
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• 2014

In this work, we discuss the existence of mild solutions in the ${\alpha}$-norm for some partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

• 정보관리학회지
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• 제12권1호
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• pp.87-97
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• 1995

부울 검색 시스템은 구현이 용이하고 빠를 검색 시간을 제공하기 때문에, 오늘날 정보 검색 분야에서 가장 널리 사용되고 있다. 그러나 순수한 부울 검색 시스템은 문서값을 계산할 수 없기 때문에, 검색된 문서들을 질의를 만족하는 정도에 따라 정렬 할 수 없다. 부울 검색 시스템에 순위 결정 기능을 부여하기 위하여 퍼지 집합, Waller-Kraft, Paice, P-Norm, Infinite-One과 같은 확장된 부울 모델들이 개발되어 왔다. 이들 모델에서 부울 연산자 AND와 OR에 대한 계산식은 순위 결정의 성능을 결정하는 중요한 요소이다. 본 논문에서는 부울 연산자 계산식의 수학적 특성을 제시하고, 이들이 검색효과에 미치는 영향을 분석한다. 분석 결과는 P-Norm 모델이 높은 검색 효과를 얻기에 가장 적합함을 보여준다.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.45-60
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• 2015

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the results.

• Journal of Communications and Networks
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• 제9권2호
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• pp.185-191
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• 2007

Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in signal processing. This class of process has no closed form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in S$\alpha$SG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm Kalman filtering algorithm based on least p-norm of innovation process with infinite variances, and a new robust multiuser detection method based on least p-norm Kalman filtering. The simulation experiments show that the proposed new algorithm is more robust than the conventional Kalman filtering multiuser detection algorithm.

• International Journal of Control, Automation, and Systems
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• 제3권spc2호
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• pp.270-277
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• 2005

In this paper, a decentralized control problem is considered for multimachine power systems with nonlinear interconnections and disturbances. A direct feedback linearization compensator is employed to cancel most of the nonlinearities, and then a backstepping procedure is applied to deal with the interconnections and to reduce the effects of a disturbance that does not satisfy the matching condition. In this procedure, the disturbance is handled by using a smooth approximation of the signum function. Practical stability is achieved under the assumption that the infinite norm of the disturbance is known. However, even in the case where the infinite norm of the disturbance is not known precisely, the proposed control system still guarantees $L_2$ stability. Furthermore, the origin is globally uniformly asymptotically stable in the absence of the disturbance. A three-machine power system is considered as an application example.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.1051-1059
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• 1992

Two types of digital repetitive control systems are analyzed and designed to reduce the error spectrum including not only harmonic but also non-harmonic components. First, a novel gain scheduling algorithm is suggested for conventional and modified repetitive controller is scheduled to reduce the infinite norm of error in frequency domain. For this, the relative error transfer function is mewly defined as the ratio of the error spectrum for the system with a repetitive controller to the error spectrum for the system with a repetitive controller to the error spectrum for the system without a repetitive controller. Secondly, as an alternative of a repetitive control system with the gain scheduling, a repetitive control system with higher order repetitve function is analyzed and designed, where instead of equal weightings, weightings of the higher order repetitive function is determined in such a way that the infinite norm of relative error transfer function is minimized. To show the validities of proposed methods, computer simulation results are illustrated for a typical disk drive head positioning servo system.

• 대한수학회보
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• 제54권3호
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• pp.747-761
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• 2017

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.

• 대한수학회지
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• 제45권6호
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• pp.1591-1600
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• 2008

In this paper, we introduce an iterative scheme given by infinite nonexpansive mappings in Banach spaces. We prove strong convergence theorems which are connected with the problem of image recovery. Our results enrich and complement the recent many results.