The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Arup Bose - One of the best experts on this subject based on the ideXlab platform.
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ESTIMATION OF AUTOCOVARIANCE MATRICES FOR INFINITE Dimensional Vector LINEAR PROCESS
Journal of Time Series Analysis, 2014Co-Authors: Monika Bhattacharjee, Arup BoseAbstract:type="main" xml:id="jtsa12063-abs-0001"> Consider an infinite Dimensional Vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-Dimensional Vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large Dimensional variance–covariance matrix has the same convergence rate as that in case of i.i.d. samples.
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Estimation of Autocovariance matrices for Infinite Dimensional Vector Linear Process
Journal of Time Series Analysis, 2014Co-Authors: Monika Bhattacharjee, Arup BoseAbstract:Consider an infinite Dimensional Vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-Dimensional Vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large Dimensional variance–covariance matrix has the same convergence rate as that in case of i.i.d. samples.
Clément De Seguins Pazzis - One of the best experts on this subject based on the ideXlab platform.
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Products of Involutions of an Infinite-Dimensional Vector Space
Canadian Journal of Mathematics, 2019Co-Authors: Clément De Seguins PazzisAbstract:AbstractWe prove that every automorphism of an infinite-Dimensional Vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are the product of three involutions. More generally, we study decompositions of automorphisms into three or four factors with prescribed split annihilating polynomials of degree $2$.
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Sums of Quadratic Endomorphisms of an Infinite-Dimensional Vector Space
Proceedings of the Edinburgh Mathematical Society, 2018Co-Authors: Clément De Seguins PazzisAbstract:We prove that every endomorphism of an infinite-Dimensional Vector space over a field splits into the sum of four idempotents and into the sum of four square-zero endomorphisms, a result that is optimal in general.
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Sums of quadratic endomorphisms of an infinite-Dimensional Vector space
arXiv: Rings and Algebras, 2016Co-Authors: Clément De Seguins PazzisAbstract:We prove that every endomorphism of an infinite-Dimensional Vector space splits as the sum of four idempotents and as the sum of four square-zero endomorphisms, a result that is optimal in general.
Monika Bhattacharjee - One of the best experts on this subject based on the ideXlab platform.
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ESTIMATION OF AUTOCOVARIANCE MATRICES FOR INFINITE Dimensional Vector LINEAR PROCESS
Journal of Time Series Analysis, 2014Co-Authors: Monika Bhattacharjee, Arup BoseAbstract:type="main" xml:id="jtsa12063-abs-0001"> Consider an infinite Dimensional Vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-Dimensional Vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large Dimensional variance–covariance matrix has the same convergence rate as that in case of i.i.d. samples.
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Estimation of Autocovariance matrices for Infinite Dimensional Vector Linear Process
Journal of Time Series Analysis, 2014Co-Authors: Monika Bhattacharjee, Arup BoseAbstract:Consider an infinite Dimensional Vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-Dimensional Vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large Dimensional variance–covariance matrix has the same convergence rate as that in case of i.i.d. samples.
Nobuhiro Kawatsuki - One of the best experts on this subject based on the ideXlab platform.
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Effects of recording wavelength on three-Dimensional Vector holograms in photoreactive liquid crystal composites
Optics Communications, 2010Co-Authors: Tomoyuki Sasaki, Nobuhiro Kawatsuki, Osamu Hanaizumi, Takanori Iwato, Akira Emoto, Hiroshi OnoAbstract:Effects of recording wavelength on the recently proposed (Sasaki, 2008) three-Dimensional Vector holograms, in which the optical anisotropy is three-Dimensionally modulated, are presented experimentally and theoretically. The polarization states of the interference light are three-Dimensionally modulated due to both the polarization interference and optical anisotropy in the recording medium. These spatial distributions of the polarization states and the resulting diffraction properties in the three-Dimensional Vector holograms are strongly dependent on the recording wavelength. Theoretical consideration based on the finite-difference time-domain (FDTD) method reveals the mechanism of the optical characteristics of the three-Dimensional Vector holograms recorded by various kinds of light sources with different wavelengths.
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Reconstruction of polarized optical images in two- and three-Dimensional Vector holograms
Journal of Applied Physics, 2009Co-Authors: Hiroshi Ono, Tomoyuki Sasaki, Takanori Iwato, Akira Emoto, Kakeru Suzuki, Tatsutoshi Shioda, Nobuhiro KawatsukiAbstract:In the present paper, we extensively study the optical diffraction in two- and three-Dimensional Vector holograms and demonstrate the reconstruction of polarized optical images recorded in azobenzene-containing amorphous polymers (AP) and polymer-dissolved liquid-crystalline composites (PDLCC). The polarization states of the interference light are not modulated in the isotropic AP films, while modulated in the anisotropic PDLCC films. The information of the polarized optical image is recorded as the polarization induced anisotropy in the AP and PDLCC medium and is reconstructed as the polarized optical images. The theoretical consideration well explained the characteristics of the reconstructed polarized optical images from both two- and three-Dimensional Vector holograms.
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Anisotropic photonic structures induced by three-Dimensional Vector holography in dye-doped liquid crystals
Journal of Applied Physics, 2008Co-Authors: Tomoyuki Sasaki, Hiroshi Ono, Nobuhiro KawatsukiAbstract:Periodic anisotropic structures were induced by means of a three-Dimensional Vector holographic technique in an azo-dye-doped liquid crystal composite with uniaxial alignment. The three-Dimensional Vector hologram was fabricated by both the polarization interference and the polarization propagation in the anisotropic recording medium. In order to obtain clear insight into the optical properties of three-Dimensional Vector holograms, various types of structures were induced by changing the polarization states and incident angles of the recording beams. The diffraction properties of various types of three-Dimensional Vector holograms were calculated by the finite-difference time-domain method, and the theoretical explanations were in good agreement with the experimental results.
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Three-Dimensional Vector holograms in anisotropic photoreactive liquid-crystal composites.
Applied optics, 2008Co-Authors: Tomoyuki Sasaki, Hiroshi Ono, Nobuhiro KawatsukiAbstract:In this paper, we describe the principle of the three-Dimensional Vector holograms formed in anisotropic recording medium. The polarization states of the interference light are three-Dimensionally modulated due to both the polarization interference and optical anisotropy in the recording medium. The electric field of the polarized light reorients the director and forms the three-Dimensional Vector hologram in anisotropic photoreactive liquid-crystal composites. The theoretical consideration reveals the formation mechanism and optical characteristics of the resultant three-Dimensional Vector holograms.
A. Kasapi - One of the best experts on this subject based on the ideXlab platform.
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Three-Dimensional Vector model for a three-state system
Journal of the Optical Society of America B, 1996Co-Authors: A. KasapiAbstract:A three-Dimensional Vector model for the three-state system interacting with a bichromatic electromagnetic field is presented. The model is used to relate and provide a visual representation for two topics of current interest, electromagnetically induced transparency and adiabatic population transfer.
