Institute for Systems Research

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Author: search.filters.author.Berenstein, Carlos A.Subject: search.filters.subject.Intelligent Control Systems

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Now showing 1 - 10 of 13
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    On the Converse to Pompeiu's Problem
    (1997) Berenstein, Carlos A.; ISR
    This is a reprint of a 1976 paper that appears in an inaccessible Brazilian journal and has become very looked after. It deals with the problem of determining a convex plane domain from the existence of infinitely many over determined Neumann eigenvalues. Recent related work in magneto hydrodynamics of Vogelius and other applications are closely related to this result. The more general result appears in J. Analyse Math 1980 and Crelle l987. See Zalcmain's bibliographic survey of pompeiu problem for other references.
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    Radon Transform, Wavelets, and Applications
    (1996) Berenstein, Carlos A.; ISR
    Notes of a graduate course given in Venice, Italy, during June 1996 organized by CIME, directed to graduate students to show the interplay of different kinds of Radon transforms and medical and material science problems
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    Residue Calculus and Effective Nullstellensatz
    (1996) Berenstein, Carlos A.; Yger, A.; ISR
    We provide new tools to compute multidimensional residues for rational functions, even over fields of positive characteristic. As a corollary one obtains solutions of the Betout equation for polynomials over a ring with a site that have almost optimal estimates for degree and size.
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    Approximation by Spherical Waves in Lp-Space
    (1996) Agranovsky, Mark; Berenstein, Carlos A.; Kuchment, Peter; ISR
    We prove that functions of the form f(1x-a1), a in a closed surface, are dense in the space of all functions in Lp, for zn/(n+1). This property fails for 1zn/(n+1). By letting f be a Gsussian, we obtain a result about approximation by wavelets generated by the Gaussian.
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    Do Solid Tori Have the Pompeiu Property?
    (1996) Berenstein, Carlos A.; Khavinson, Dmitry; ISR
    We show that solid tori in Rn satisfy the Pompeiu property: This problem remains open for dimensions n ﺠ4.
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    A 2D Nondestructive Inspection Method to Detect a Through Crack by, Electrostatic Boundary Measurements
    (1996) Berenstein, Carlos A.; Chang, Der-Chen; Wang, Emei; ISR
    A detailed procedure is proposed to find the position and length of a linear crack originating at the boundary of a 2-d object by means of electrostatic boundary measurements.
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    The Pompeiu Problem, What's New?
    (1995) Berenstein, Carlos A.; ISR
    Survey of recent developments on the Pompeiu problem and the Schiffer problem. This problem has surprising interactions with inverse scattering, image processing and other applied problems.
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    Monodromic differential equations
    (1995) Berenstein, Carlos A.; ISR
    Lecture presented at Taniguchi Symposium, Katata, June 1995. Deals with new kind of differential equations for multivalued functions. The monodromy operator is allowed to enter into the equation. Related to resurgence and complex dynamics.
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    D-Module and Exponential Polynomials
    (1995) Berenstein, Carlos A.; ISR
    Lecture delivered at Research Institute for Mathematical Sciences, Kyoto University, Symposium on Algebraic Analysis, July 1995. Explains the relationship between new kinds of D-modules and ideals of exponential polynomials.
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    Wavelet-Based Multiresolution Local Tomography
    (1995) Rashid-Farrokhi, F.; Liu, K.J. Ray; Berenstein, Carlos A.; Walnut, D.; ISR
    We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data which significantly reduces the amount of exposure and computations in X-ray tomography. This property which distinguishes our algorithm from the previous algorithms is based on the observation that for some wavelet basis with sufficiently many vanishing moments, the ramp-filtered version of the scaling function as well as the wavelet function has extremely rapid decay. We show that the variance of the elements of the null- space is negligible in the locally reconstructed image. Also we find an upper bound for the reconstruction error in terms of the amount of data used in the algorithm. To reconstruct a local region 20 pixels in radius in a 256 X 256 image we require 12.5% of full exposure data while the previous methods can reduce the amount of exposure only to 40% for the same case.