The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Shen Yan - One of the best experts on this subject based on the ideXlab platform.
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A New Probe to Direct Sum Decomposition Problem for Finite Dimension of Linear Space
Journal of Nanjing Audit University, 2010Co-Authors: Shen YanAbstract:The Direct Sum Decomposition for finite dimension of linear space has a wide application in mathematics,mechanics and other applied areas.This paper provides a new theorem for the Direct Sum Decomposition,and proves a Direct Sum Decomposition theorem for finite dimension of linear space by the Cayley-Hamilton theorem.And in its application,it deduces the well-known Direct Sum Decomposition theorem.Finally,two examples are discussed to illustrate the methods of Direct Sum Decomposition.
Yutaka Yamamoto - One of the best experts on this subject based on the ideXlab platform.
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Behavioral controllability and coprimeness for pseudorational transfer functions
Systems & Control Letters, 2016Co-Authors: Yutaka YamamotoAbstract:Abstract Controllability plays various crucial roles in behavioral system theory. While there exist several characterizations of this notion, in terms of the Bezout identity, image representation, Direct Sum Decomposition, etc., its overall picture for infinite-dimensional systems still remains rather incomplete, in spite of various existing attempts. This article gives an extension of such results in a well-behaved class of infinite-dimensional systems, called pseudorational. A proper choice of an algebra makes the treatment more transparent. We establish equivalent conditions for controllability in terms of the Bezout identity, relationships with notions such as image representation and Direct Sum Decompositions.
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CDC - Behavioral controllability and coprimeness for a class of infinite-dimensional systems
2008 47th IEEE Conference on Decision and Control, 2008Co-Authors: Yutaka Yamamoto, Jan C. WillemsAbstract:Behavioral system theory has become a successful framework in providing a viewpoint that does not depend on a priori notions of inputs/outputs. In particular, this theory provides notions as controllability, without an explicit reference to the state space formalism. One also obtains several interesting consequences of controllability, for example, Direct Sum Decomposition of the signal space with a controllable behavior B as a Direct Summand. While there are some attempts to extend this theory to infinite-dimensional systems, for example, delay systems, the overall picture remains incomplete. This article extends this theory, particularly the notion of controllability, to a well-behaved class of infinite-dimensional systems, called pseudorational. A crucial notion in this context is the Bezout identity, and we relate a recent result to the context of behavioral controllability. We establish its relationships with notions as image representation and Direct Sum Decompositions.
Adriaan A. Lammertsma - One of the best experts on this subject based on the ideXlab platform.
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Linear dimension reduction of sequences of medical images: II. Direct Sum Decomposition
Physics in medicine and biology, 1995Co-Authors: Flemming Hermansen, P M Bloomfield, John Ashburner, Paolo G. Camici, Adriaan A. LammertsmaAbstract:Using unitary transformations together with a previously described statistical theory for optimal linear dimension reduction it is shown how pixels in a sequence of images can be decomposed into a Sum of variates, covariates, and residual vectors, with all covariances equal to zero. It is demonstrated that this Decomposition is optimal with respect to noise. In addition, it results in simplified and well conditioned equations for dimension reduction and elimination of covariates. The factor images are not degraded by subdivision of the time intervals. In contrast to traditional factor analysis, the factors can be measured Directly or calculated based on physiological models. This procedure not only solves the rotation problem associated with factor analysis, but also eliminates the need for calculation of the principal components altogether. Examples are given of factor images of the heart, generated from a dynamic study using oxygen-15-labelled water and positron emission tomography. As a special application of the method, it is shown that the factor images may reveal any contamination of the blood curve derived from the original dynamic images with myocardial activity.
Zainoulline Kirill - One of the best experts on this subject based on the ideXlab platform.
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Relative Equivariant Motives and Modules
'Canadian Mathematical Society', 2020Co-Authors: Calmès Baptiste, Neshitov Alexander, Zainoulline KirillAbstract:25pp; This is a substantially revised and reorganized version. Several proofs were revised and simplified. Examples addedWe introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic Decomposition type of a versal flag variety depends on the Direct Sum Decomposition type of the parabolic module. To do this we use localization techniques of Kostant-Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties
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Relative equivariant motives and modules
'Canadian Mathematical Society', 2019Co-Authors: Calmès Baptiste, Neshitov Alexander, Zainoulline KirillAbstract:We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic Decomposition type of a versal flag variety depends on the Direct Sum Decomposition type of the parabolic module. To do this we use localization techniques of Kostant-Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.Comment: 25pp; This is a substantially revised and reorganized version. Several proofs were revised and simplified. Examples adde
Jan C. Willems - One of the best experts on this subject based on the ideXlab platform.
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CDC - Behavioral controllability and coprimeness for a class of infinite-dimensional systems
2008 47th IEEE Conference on Decision and Control, 2008Co-Authors: Yutaka Yamamoto, Jan C. WillemsAbstract:Behavioral system theory has become a successful framework in providing a viewpoint that does not depend on a priori notions of inputs/outputs. In particular, this theory provides notions as controllability, without an explicit reference to the state space formalism. One also obtains several interesting consequences of controllability, for example, Direct Sum Decomposition of the signal space with a controllable behavior B as a Direct Summand. While there are some attempts to extend this theory to infinite-dimensional systems, for example, delay systems, the overall picture remains incomplete. This article extends this theory, particularly the notion of controllability, to a well-behaved class of infinite-dimensional systems, called pseudorational. A crucial notion in this context is the Bezout identity, and we relate a recent result to the context of behavioral controllability. We establish its relationships with notions as image representation and Direct Sum Decompositions.
