“…Among other things, for large classes of random fractals they establish (a) very strong versions of the Marstrand-Mattila projection and slicing results, as well as dimension conservation, (b) slicing results with respect to algebraic curves and self-similar sets, (c) smoothness of convolutions of measures, including self-convolutions, and nonempty interior for sumsets, and (d) rapid Fourier decay. …”
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“…Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. …”
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“…The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.…”
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“…The results of his in-depth theoretical investigations lead to promising new extensions and modifications of existing algebraic flux correction schemes. The main focus is on new limiting techniques designed to control the range of solution values for advected scalar quantities or the eigenvalue range of symmetric tensors. …”
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“…The author gives a number of applications to algebraic systems, parametrized systems, and to some classical examples. …”
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“…Building on results in algebraic geometry, we address the problem of deforming it away from the orbifold point from the viewpoint of topological strings. …”
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“…These include: (i) support for multiple beam-lines simultaneously, facilitating, for example, matching constraints that couple the two rings of a two-ring collider, (ii) much improved Lie-algebraic map calculations, (iii) a uniform method and format for exchanging many kinds of structured data with other programs, (iv) an improved and more consistent input language. …”
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“…The latter was derived using purely algebraic methods to reduce the initial large system of linear equations arising from separate fits of tracks and alignment parameters. …”
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“…In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.…”
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“…The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the L² extension of holomorphic functions. …”
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“…The first part is about Geometric Analysis and Conformal Geometry; this modern field lies at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical world, since many natural phenomena posses an intrinsic geometric content. …”
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“…Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: · Nicolas Addington · Benjamin Antieau · Kenneth Ascher · Asher Auel · Fedor Bogomolov · Jean-Louis Colliot-Thélène · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Martí Lahoz · Emanuele Macrì · Kelly McKinnie · Andrew Obus · Ekin Ozman · Raman Parimala · Alexander Perry · Alena Pirutka · Justin Sawon · Alexei N. …”
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“…This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. …”
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“…Of all portable vectorization techniques, explicit vectorization, using wrapper-class libraries, is proven to achieve the fastest performance, however it does not exploit optimization opportunities outside the simplest algebraic primitives. A more advanced language is therefore required, but the design of a new independent language is not feasible due to its high costs. …”
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“…It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. …”
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“…In general, we propose a purely algebraic construction of Picard--Fuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the Seiberg--Witten curve, encompassing non-simply-laced cases as well. …”
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“…The resulting theory provides algebraic expressions for BNS damping, tune shifts, transverse off-sets and emittance dilution. …”
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“…As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theories. …”
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“…We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). …”
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“…The spectrum is analyzed to determine a possibly smaller number of principal components. A Lie-algebraic point of view is used to explore the use of the machine to emulate the dynamics of other quantum systems. …”
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