Anisotropy and asymptotic degeneracy of the physical-Hilbert-space
inner-product metrics in an exactly solvable crypto-unitary quantum model
December 4, 2012
Physics
Mathematics
Quantum Physics
Mathematical Physics
Mathematical Physics
In quantum mechanics (formulated, say, in Schr\"{o}dinger picture) only the
knowledge of a complete set of observables Λj enables us to declare
the related physical inner product (i.e., the Hilbert-space metric Θ
such that $...
Unlinking and unknottedness of monotone Lagrangian submanifolds
November 28, 2012
|
Mathematics
Symplectic Geometry
Differential Geometry
Under certain topological assumptions, we show that two monotone Lagrangian
submanifolds embedded in the standard symplectic vector space with the same
monotonicity constant cannot link one another and that, individually, their
smooth knot ...
Algebraic and geometric aspects of bipartite planar graphs
November 28, 2012
|
Mathematics
Commutative Algebra
Let B_{2t} be a bipartite planar graph with an even number of regions. We are
able to find bounds for the graded Betti numbers and the projective dimension
of the quotient ring associated to the graph. We also will investigate the
minimal v...
On strong orthogonality and strictly convex normed linear spaces
November 27, 2012
| |
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
| | |
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
|
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
|
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...