“…Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. …”
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“…Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin–Schelter regular algebras, and the noncommutative Zariski cancellation problem. …”
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“…The prerequisites are a good course in advanced calculus, some preparation in linear algebra, and a reasonable acquaintance with elementary complex analysis. …”
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“…The authors survey the literature on all of this material, including a discussion of the multipliers of ell^p_A and a discussion of the Wiener algebra ell^1_A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. …”
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“…This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories, semantic search and intelligent textbooks.…”
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“…Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bilinears. …”
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“…They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmannians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed. …”
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“…The first two talks (2 May at 11.00 hrs and 11 May* at 14.00 hrs) will be by way of mathematical introduction for those whose matrix algebra and solution of differential equations may need refreshing. …”
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“…When fluxes are turned on one can construct new gaugings of N=4 supergravity, where the twelve bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice of fluxes.…”
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“…The theory of D-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. …”
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“…The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra.…”
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“…We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. …”
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“…Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. …”
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“…At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library.…”
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“…We prove the existence of series [Formula: see text] , whose coefficients [Formula: see text] are in [Formula: see text] and whose terms [Formula: see text] are translates by rational vectors in [Formula: see text] of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener’s algebra [Formula: see text] , [Formula: see text] , [Formula: see text] , [Formula: see text] , for every [Formula: see text] , and the space of measurable functions. …”
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“…It is proved that the new inclusion sets are tighter than the Geršgorin-type sets (Qi in Linear Algebra Appl. 56:105-119, 1984) and the Brauer-type sets (Li in Comput. …”
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“…For an algebra [Formula: see text] belonging to a quasivariety [Formula: see text] , the quotient [Formula: see text] need not belong to [Formula: see text] for every [Formula: see text] . …”
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“…Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. …”
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“…A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. …”
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“…In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.…”
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