“…Then, we introduce the respective algebras of functions containing quantum observables. …”
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“…The applied technique is the New extended algebraic method. By use of this approach, acquired solutions convey various types of new families containing dark, dark-singular, dark-bright, and singular solutions of Type 1 and 2. …”
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“…For a large class of shape regular but possibly non-uniform meshes including algebraically graded meshes, we prove that the inverse of the stiffness matrix can be approximated in the [Formula: see text] -matrix format at an exponential rate in the block rank. …”
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“…These coefficients may be found iteratively by solving either a quadratic or a higher degree algebraic equation. Examples are presented to illustrate the obtained results. …”
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“…Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and such exponents can increase indefinitely. …”
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“…Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. …”
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“…Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. …”
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“…Poincaré's papers are in fact the first draft of algebraic topology, introducing its main subject matter (manifolds) and basic concepts (homotopy and homology). …”
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“…We present free field realizations for the associated vertex operator algebras of a number of four-dimensional $ \mathcal{N} $ = 2 superconformal field theories. …”
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“…An important element in a model of non-singular string cosmology is a phase in which classical corrections saturate the growth of curvature in a deSitter-like phase with a linearly growing dilaton (an `algebraic fixed point'). As the form of the classical corrections is not well known, here we look for evidence, based on a suggested symmetry of the action, scale factor duality and on conformal field theory considerations, that they can produce this saturation. …”
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“…We give a general analysis of OPEs of 1/2 BPS superfield operators for the $D=3,4,5,6$ superconformal algebras OSp(8/4,R), PSU(2,2), F${}_4$ and OSp($8^*/4$) which underlie maximal AdS supergravity in $4\leq D+1\leq 7$. \\ The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. …”
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“…RESULTS: We propose a new algebraic topological framework, which obtains intrinsic information from MALDI data and transforms it to reflect topological persistence. …”
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“…An MR rate is defined and extracted algebraically from the model. MR as a specific process is not required and may be replaced with an approach from which an MR rate emerges. …”
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“…These results offer a first demonstration that techniques from algebraic topology offer a novel perspective on structural connectomics, highlighting loop-like paths as crucial features in the human brain’s structural architecture.…”
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“…It's an algebraic invariant that can capture topological details at different spatial resolutions. …”
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“…The technical tools employed are those of the algebraic approach to quantum statistical mechanics which offers a unifying view of classical and quantum dynamical systems. …”
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“…The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.Contributors: B. …”
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“…Topics covered in this volume: (a) impact of minimal nonabelian subgroups on the structure of p-groups, (b) classification of groups all of whose nonnormal subgroups have the same order, (c) degrees of irreducible characters of p-groups associated with finite algebras, (d) groups covered by few proper subgroups, (e) p-groups of element breadth 2 and subgroup breadth 1, (f) exact number of subgroups of given order in a metacyclic p-group, (g) soft subgroups, (h) p-groups with a maximal elementary abel…”
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“…Its applications to the theory of motives with complex multiplication are systematically reviewed. In particular, algebraic relations between values of the gamma function, the so-called formula of Chowla and Selberg and its generalization and Shimura's monomial relations among periods of CM abelian varieties are all presented in a unified way, namely as the analytic reflections of arithmetic identities beetween Hecke characters, with gamma values corresponding to Jacobi sums. …”
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“…These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.…”
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