• Title/Summary/Keyword: infinite norm

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INFINITE FINITE RANGE INEQUALITIES

  • Joung, Haewon
    • Korean Journal of Mathematics
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    • v.18 no.1
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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 $W(x)={\prod}^{m}_{k=1}{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$.

Algebraic semantics for some weak Boolean logics

  • Yang, Eun-Suk
    • Korean Journal of Logic
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    • v.9 no.2
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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.

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EXISTENCE OF MILD SOLUTIONS IN THE α-NORM FOR SOME PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

  • Jang, Hyun Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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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.

Mathematical Properties of the Formulas Evaluating Boolean Operators in Information Retrieval (정보검색에서 부울연산자를 연산하는 식의 수학적 특성)

  • 이준호;이기호;조영화
    • Journal of the Korean Society for information Management
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    • v.12 no.1
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    • pp.87-97
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    • 1995
  • Boolean retrieval systems have been most widely used in the area of information retrieval due to easy implementation and efficient retrieval. Conventional Boolean retrieval systems. however, cannot rank retrieved documents in decreasing order of query-document similarities because they cannot compute similarity coefficients between queries and documents. Extended Boolean models such as fuzzy set. Waller-Kraft, Paice, P-Norm and Infinite-One have been developed to provide the document ranking facility. In extended Boolean models, the formulas evaluating Boolean operators AND and OR are an important component to affect the quality of document ranking. In this paper we present mathematical properties of the formulas, and analyse their effect on retrieval effectiveness. Our analyses show that P-Norm is the most suitable for achieving high retrieval effectiveness.

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EXISTENCE RESULTS FOR NEUTRAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN BANACH SPACES

  • Chandrasekaran, S.;Karunanithi, S.
    • Journal of applied mathematics & informatics
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    • v.33 no.1_2
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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.

Robust Multiuser Detection Based on Least p-Norm State Space Filtering Model

  • Zha, Daifeng
    • Journal of Communications and Networks
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    • v.9 no.2
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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.

Decentralized Control for Multimachine Power Systems, with Nonlinear Interconnections and Disturbances

  • Jung Kyu-Il;Kim Kwang-Youn;Yoon Tae-Woong;Jang Gilsoo
    • International Journal of Control, Automation, and Systems
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    • v.3 no.spc2
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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.

Analysis and design of two types of digital repetitive control systems (두가지 이산 반복제어 시스템의 해석 및 설계)

  • 장우석;김군진;김준동;서일홍
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10a
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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.

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MULTIPLICATION OPERATORS ON WEIGHTED BANACH SPACES OF A TREE

  • Allen, Robert F.;Craig, Isaac M.
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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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.

STRONG CONVERGENCE THEOREMS FOR INFINITE COUNTABLE NONEXPANSIVE MAPPINGS AND IMAGE RECOVERY PROBLEM

  • Yao, Yonghong;Liou, Yeong-Cheng
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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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.