An explicit version of Shimura's reciprocity law for Siegel modular
functions
December 29, 2011
Mathematics
Number Theory
We give an explicit version of Shimura's reciprocity law for singular values
of Siegel modular functions. We use this to construct the first examples of
class invariants of quartic CM fields that are smaller than Igusa invariants.
Our state...
The Extended UCB Policies for Frequentist Multi-armed Bandit Problems
December 8, 2011
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Computer Science
Mathematics
Statistics
Machine Learning
Probability
Statistics Theory
Statistics Theory
The multi-armed bandit (MAB) problem is a widely studied model in the field
of operations research for sequential decision making and reinforcement
learning. This paper mainly considers the classical MAB model with the
heavy-tailed reward d...
On generalized black brane solutions in the model with multicomponent
anisotropic fluid
December 7, 2011
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Physics
High Energy Physics - Theory
General Relativity and Quantum Cosmology
High Energy Physics - Theory
General Relativity and Quantum Cosmology
A family of spherically O(d0+1)-symmetric solutions in the model with
m-component anisotropic fluid is obtained. The metrics are defined on a
manifold which contains a product of n−1 Ricci-flat ``internal'' spaces. The
equation of ...
Vacuum Potentials for the Two Only Permanent Free Particles, Proton and
Electron. Appendix D: QEM Theory of IVBs, Higgs
November 14, 2011
Physics
General Physics
The two only species of isolatable, smallest, or unit charges +e and -e
present in nature interact with the universal vacuum in a polarisable
dielectric representation through two uniquely defined vacuum potential
functions. All of the non-...
Characterizing closed curves on Riemann surfaces via homology groups of
coverings
November 9, 2011
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Mathematics
Algebraic Topology
Group Theory
Let S be a hyperbolic oriented Riemann surface of finite type. The main
purpose of this paper is to show that non-trivial geometric intersection
between closed curves on S is detected by some symplectic submodules they
naturally determi...
General Lagrangian Formulation for Higher Spin Fields with Arbitrary
Index Symmetry. I. Bosonic fields
October 23, 2011
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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 construct a Lagrangian description of irreducible integer higher-spin
representations of the Poincare group with an arbitrary Young tableaux having k
rows, on a basis of the universal BRST approach. Starting with a description of
bosonic...
On the solution of the Collatz problem
October 16, 2011
Mathematics
General Mathematics
In this paper, we propose a key idea and innovation on the Collatz problem.
Let an odd Collatz's Sequence be Sc(m,t)={n0(m,t),n1(m,t),n2(m,t),…,nm(m,t),nm+1(m,t)} produced by a function $n_{i+1}(m,t)=(3n_{i}(m...
On the cactus rank of cubics forms
October 10, 2011
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Mathematics
Algebraic Geometry
Commutative Algebra
We prove that the smallest degree of an apolar 0-dimensional scheme of a
general cubic form in n+1 variables is at most 2n+2, when n≥8, and
therefore smaller than the rank of the form. For the general reducible cubic
form the smal...
The automorphism group of Mg,n
October 7, 2011
Mathematics
Algebraic Geometry
Let Mg,n be the moduli stack parametrizing
Deligne-Mumford stable n-pointed genus g curves and let
Mg,n be its coarse moduli space: the Deligne-Mumford
compactification of the moduli space of $n...
Sharp estimates for the convergence rate of Orthomin(k) for a class of
linear systems
September 12, 2011
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
In this work we show that the convergence rate of Orthomin(k) applied to
systems of the form (I+ρU)x=b, where U is a unitary operator and
0<ρ<1, is less than or equal to ρ. Moreover, we give examples of
operators U ...