Nonexistence of time-periodic solutions of the Dirac equation in
nonextreme Kerr-Newman-AdS spacetime
August 18, 2016
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Physics
Mathematics
General Relativity and Quantum Cosmology
Classical Analysis and ODEs
In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no
nontrivial Dirac particle which is Lp for 0<p≤34 with
arbitrary eigenvalue λ, and for 34<p≤3−2q4,
0<q<23 with eig...
The high type quadratic Siegel disks are Jordan domains
August 14, 2016
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Mathematics
Dynamical Systems
Let α be an irrational number of sufficiently high type and suppose
Pα(z)=e2πiαz+z2 has a Siegel disk Δα centered
at the origin. We prove that the boundary of Δα is a Jordan curve,
and th...
We consider rough differential equations whose coefficients contain
path-dependent bounded variation terms and prove the existence and a priori
estimate of solutions. These equations include classical path-dependent SDEs
containing running ...
Border Ranks of Monomials
August 8, 2016
Mathematics
Computer Science
Algebraic Geometry
Computational Complexity
Young flattenings, introduced by Landsberg and Ottaviani, give determinantal
equations for secant varieties and their non-vanishing provides lower bounds
for border ranks of tensors and in particular polynomials. We study
monomial-optimal s...
The rightness of the Riemann Hypothesis
August 8, 2016
Mathematics
General Mathematics
The properties of several functions are employed to investigate the zeros of
the Riemann zeta function ζ(a+bi)(0<a<1,b=0). If the zeros of the
zeta function have not the form 21+ib where i=−1, we derive
a c...
Towards Grand Unification
August 8, 2016
Physics
General Physics
Sidharth had shown that gravitation can be reconciled with electromagnetic
and other forces if we start from a Landau-Ginzburg phase transition. This is
further remarked upon and a unification of all forces of nature is proposed....
Physics on the adiabatically changed Finslerian manifold and cosmology
August 5, 2016
Physics
General Physics
In present paper we confirm our previous result [5] that the Planck constant
is adiabatic invariant of electromagnetic field propagating on the
adiabatically changed Finslerian manifold. Direct calculation from cosmological
parameters gives...
Superconducting instability in non-Fermi liquids
August 3, 2016
Physics
High Energy Physics - Theory
Superconductivity
Strongly Correlated Electrons
We use renormalization group (RG) analysis and dimensional regularization
techniques to study potential superconductivity-inducing four-fermion
interactions in systems with critical Fermi surfaces of general dimensions
(m) and co-dimensio...
A study on partial dynamic equation on time scales involving derivatives
of polynomials
August 2, 2016
Mathematics
Classical Analysis and ODEs
Analysis of PDEs
Let P(m,b,x) be a 2m+1-degree polynomial in x,b. Let be a
two-dimensional timescale Λ2=T1×T2={t=(x,b):x∈T1,b∈T2} such that
T1=T2...
m-Modular Wythoff
August 2, 2016
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Mathematics
Combinatorics
We introduce a variant of Wythoff's Game that we call m-Modular Wythoff's
Game. In the original Wythoff's Game, players can take a positive number of
tokens from one pile, or they can take a positive number of tokens from both
piles if th...