On strong orthogonality and strictly convex normed linear spaces
November 27, 2012
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Mathematics
Functional Analysis
We introduce the notion of strongly orthogonal set relative to an element in
the sense of Birkhoff-James in a normed linear space to find a necessary and
sufficient condition for an element x of the unit sphere SX to be an
exposed...
Enhanced six operations and base change theorem for higher Artin stacks
November 26, 2012
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Mathematics
Algebraic Geometry
Algebraic Geometry
In this article, we develop a theory of Grothendieck's six operations for
derived categories in \'etale cohomology of Artin stacks, for both torsion and
adic coefficients. We prove several desired properties of the operations,
including the...
Associahedra, Multiplihedra and units in A∞ form
November 25, 2012
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Mathematics
Algebraic Topology
Algebraic Topology
The higher associativity was introduced by Jim Stasheff in [25] with the
higher coherence condition on the unit and now becomes one of the most
important higher structures on spaces and algebras. However in [25], he claims
that the higher c...
Relaxing the Differentiability Assumption in Taylor Theorem and
Optimization: Applications to the HJB PDE and Finance
November 25, 2012
Quantitative Finance
Mathematics
Portfolio Management
Analysis of PDEs
We introduce Taylor expansions that do not require the differentiability. We
also provide new solutions to partial differential equations. We apply our
methods to finance....
Anharmonic Solutions of the Riccati equation and elliptic modular
functions
November 24, 2012
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Mathematics
Differential Geometry
We study algebraic solutions of the Riccati equation over the field of
rational functions C(t), and over the elliptic function field
C(℘,℘′)....
Rational Lukasiewicz logic and DMV-algebras
November 23, 2012
Mathematics
Logic
In this paper we present some results on the variety of divisible
MV-algebras. Any free divisible MV-algebra is an algebra of continuous
piecewise linear functions with rational coefficients. Correspondingly,
Rational {\L}ukasiewicz logic i...
Dispersion law for a one-dimensional weakly interacting Bose gas with
zero boundary conditions
November 7, 2012
Physics
Quantum Gases
From the time-dependent Gross equation, we find the quasiparticle dispersion
law for a one-dimensional weakly interacting Bose gas with a non-point
interatomic potential and zero boundary conditions (BCs). The result coincides
with the disp...
General Lagrangian Formulation for Higher Spin Fields with Arbitrary
Index Symmetry. 2. Fermionic fields
November 6, 2012
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Physics
Mathematics
High Energy Physics - Theory
Mathematical Physics
Mathematical Physics
Representation Theory
High Energy Physics - Theory
Mathematical Physics
Mathematical Physics
Representation Theory
We continue the construction of a Lagrangian description of irreducible
half-integer higher-spin representations of the Poincare group with an
arbitrary Young tableaux having k rows, on a basis of the BRST--BFV approach
suggested for boso...
Non-Archimedean Analytic Singular Homology Based On Cosimplicial
Perfectoid Spaces and Integration along Cycles
November 6, 2012
Mathematics
Number Theory
Algebraic Geometry
We introduce singular homology for non-Archimedean analytic spaces using a
cosimplicial perfectoid space as a Galois representation. We define an
integration along a cycle, which gives a pairing with the singular homology and
the space of d...
Gray categories with duals and their diagrams
November 2, 2012
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Mathematics
Physics
Quantum Algebra
Mathematical Physics
Category Theory
Mathematical Physics
The geometric and algebraic properties of Gray categories with duals are
investigated by means of a diagrammatic calculus. The diagrams are
three-dimensional stratifications of a cube, with regions, surfaces, lines and
vertices labelled by ...