Algorithms for the numerical computation of definite integrals have been proposed for more than 300 years, but practical considerations have led to problems of ever-increasing complexity, so that , even with current computing speeds, numerical integration may be a difficult task. High dimension and complicated structure of the region of integration and singularities of the integrand are the main sources of difficulties. This volume contains 27 papers presented at the fourth conference on numerical integration held at the Mathematical Research Institute, Oberwolfach, in November 1992. The contributions give a survey of the latest results in quadrature and cubature. Since the subject matter lies somewhere between practical mathematics and analysis, a wide spectrum of topics is discussed. One main theme is the construction of rules, especially for integrands with singularities. Further focal points are error estimation in various classes of functions, structure of general rules of interpolatory type, lattice rules, and the many facets of the Gaussian rule. Many open problems were discussed in Oberwolfach, showing a liveliness and actuality of the theory. Nine of these problems could be given precise formulations; they are collected at the end of this volume. (source: Nielsen Book Data) 9783764329228 20160528
Part 1 Theoretical aspects: Helgason's support for Radon transforms - a new proof and a generalization, J. Boman-- singular value decompositions for Radon transforms, P. Maass-- image reconstruction in Hilbert space, W.R. Madych-- a problem of integral geometry for a family of rays with multiple reflections, R.G. Mukhometov-- inversion formulas for the three-dimensional ray transform, V.P. Palamodov.
Part 2 Medical imaging techniques: back-scattered photons - near tomography, V. Friedrich-- mathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transform, P. Grangeat-- diffraction tomography - some applications and extension to 3D ultrasound imaging, P. Grassin et al-- diffuse tomography - a refined model, F.A. Grunbaum-- three dimensional reconstructions in inverse obstacle scattering, R. Kress and A. Zinn-- mathematical questions of a biomagnetic imaging problem, A.K. Louis.
Part 3 Inverse problems and optimization: on variable block algebraic reconstruction techniques, Y. Censor-- on Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems, P.P. Eggermont.
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This conference was devoted to the discussion of present and future techniques in medical imaging, including 3D X-ray CT, ultrasound and diffraction tomography, and biomagnetic imaging. The mathematical models, their theoretical aspects and the development of algorithms were explored. The proceedings contain surveys on the reconstruction of inverse obstacle scattering, inversion in 3D, and constrained least squares problems. Research papers include presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam reconstruction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applications in non-medical fields. (source: Nielsen Book Data) 9783540549703 20160528
Providence, R.I. : American Mathematical Society, c1987.
Book — ix, 118 p. ; 26 cm.
The Goldie rank of a module by J. T. Stafford Noetherian group rings: An exercise in creating folklore and intuition by D. R. Farkas Primitive ideals in the enveloping algebra of a semisimple Lie algebra by J. C. Jantzen Representation theory of semisimple Lie algebras by T. J. Enright Filtered Noetherian rings by J.-E. Bjork Primitive ideals in enveloping algebras by R. Rentschler.
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Researchers in ring theory or allied topics, such as the representation theory of finite dimensional Lie algebras, will appreciate this collection of expository lectures on advances in ring theory and their applications to other areas. Five of the lectures were delivered at a conference on Noetherian rings at the Mathematisches Forschungsinstitut, Oberwolfach, in January 1983, and the sixth was delivered at a London Mathematical Society Durham conference in July 1983. The study of the prime and primitive ideal spectra of various classes of rings forms a common theme in the lectures, and they touch on such topics as the structure of group rings of polycyclic-by-finite groups, localization in non commutative rings, and rings of differential operators. The lectures require the background of an advanced graduate student in ring theory and may be used in seminars in ring theory at this level. (source: Nielsen Book Data) 9780821815250 20160528