“…The results yield an algebraic understanding of first- and second-order differential operators. …”
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“…The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi’s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory. …”
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“…This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. …”
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“…We also give explicit formulas for the single-valued and clean single-valued version attached to the Nielsen polylogarithms $S_{n,2}(x)$, and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points.…”
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“…The solutions in these regions are obtained separately and matched using the necessary algebraic continuity conditions including R sub s and OMEGA. …”
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“…We find extra supersymmetry generators arising from twisted sectors, giving rise to exotic supersymmetry algebras. Among others we discover new cases with a large number of supercharges, such as $ \mathcal{N}=\left(20,8\right),\ \mathcal{N}=\left(24,8\right),\ \mathcal{N}=\left(32,0\right),\ \mathcal{N}=\left(24,24\right) $ and $ \mathcal{N}=\left(48,0\right) $ .…”
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“…The 19F(7Li,7Be)19O charge-exchange reaction at 52 MeV incident energy has been performed at INFN-LNS in Catania using the MAGNEX spectrometer. The use of an algebraic ray-reconstruction technique has allowed to extract the 19O excitation energy spectrum and the experimental angular distributions obtained with a single angular setting of the spectrometer.…”
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“…Uses modern notation and terminology in an algebraic approach to derivations. Each chapter includes examples of applications of angular momentum theory to subjects of current interest and to demonstrate the connections between various scientific fields which are provided through rotations. …”
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“…The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of fundamental algebraic and topological concepts that emerged in this theory.…”
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“…Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.…”
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“…The main topics and themes include geometric and analytic properties of infinite-dimensional Banach spaces and their convex subsets as well as some aspects of Banach spaces associated with harmonic analysis and Banach algebras.…”
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“…The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.…”
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“…It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.…”
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“…Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. …”
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“…We analyse the complete algebraic structure of the background field method for Yang--Mills theory in the Landau gauge and show several structural simplifications within this approach. …”
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“…. • Series of 3D numerical calculations, for various helium mass flows, were performed. • Algebraic formulas were proposed to evaluate the safe limit of the helium mass flow.…”
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“…Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. …”
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“…In particular, we mention the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the explora­ tion of the extraordinary enigmatic connections between Kac-Moody­ Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories.…”
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“…It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. …”
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“…Further it presents some new integration techniques for representations of Lie algebras by unbounded operators which are needed for the passage to the dual group. …”
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