A paradox on the spectral representation of stationary random processes
December 27, 2012
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Statistics
Other Statistics
Other Statistics
In this note our aim is to show a paradox in the spectral representation of
stationary random processes....
A note on strong edge-colorings of 2-degenerate graphs
December 25, 2012
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Mathematics
Combinatorics
We show that every 2-degenerate graph with maximum degree Δ has a
strong edge-coloring with at most 8Δ−4 colors....
Modeling and performance evaluation of computer systems security
operation
December 20, 2012
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Computer Science
Mathematics
Cryptography and Security
Systems and Control
Optimization and Control
A model of computer system security operation is developed based on the
fork-join queueing network formalism. We introduce a security operation
performance measure, and show how it may be used to performance evaluation of
actual systems....
Koszul complexes and spectra of projective hypersurfaces with isolated
singularities
December 5, 2012
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Mathematics
Algebraic Geometry
For a projective hypersurface Z with isolated singularities, we generalize
some well-known assertions in the nonsingular case due to Griffiths, Scherk,
Steenbrink, Varchenko, and others about the relations between the Steenbrink
spectrum,...
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
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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
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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
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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....