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...
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...
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 ...
The eta invariant on two-step nilmanifolds
October 30, 2012
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Mathematics
Differential Geometry
K-Theory and Homology
Spectral Theory
The eta invariant appears regularly in index theorems but is known to be
directly computable from the spectrum only in certain examples of locally
symmetric spaces of compact type. In this work, we derive some general formulas
useful for ca...
On the Betti numbers and gracefulness of some planar graphs
October 30, 2012
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Mathematics
Commutative Algebra
In this article bipartite planar graphs St_r are investigated, r the number
of their plane regions. Bounds for the graded Betti numbers and the projective
dimension of the quotient ring associated to such graphs are discussed. We
prove that...