1,166 research outputs found
Families of Graphs With Chromatic Zeros Lying on Circles
We define an infinite set of families of graphs, which we call -wheels and
denote , that generalize the wheel () and biwheel ()
graphs. The chromatic polynomial for is calculated, and
remarkably simple properties of the chromatic zeros are found: (i) the real
zeros occur at for even and for odd;
and (ii) the complex zeros all lie, equally spaced, on the unit circle
in the complex plane. In the limit, the zeros
on this circle merge to form a boundary curve separating two regions where the
limiting function is analytic, viz., the exterior and
interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late
Lax forms of the -Painlev\'e equations
All -Painlev\'e equations which are obtained from the -analog of the
sixth Painlev\'e equation are expressed in a Lax formalism. They are
characterized by the data of the associated linear -difference equations.
The degeneration pattern from the -Painlev\'e equation of type is also
presented.Comment: 24 page
Renormalization in general theories with inter-generation mixing
We derive general and explicit expressions for the unrenormalized and
renormalized dressed propagators of fermions in parity-nonconserving theories
with inter-generation mixing. The mass eigenvalues, the corresponding mass
counterterms, and the effect of inter-generation mixing on their determination
are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization
conditions and employing a number of very useful relations from Matrix Algebra,
we show explicitly that the renormalized dressed propagators satisfy important
physical properties.Comment: 14 pages; to appear in Phys. Rev.
Domain wall cosmology and multiple accelerations
We classify the cosmological behaviors of the domain wall under junctions
between two spacetimes in terms of various parameters: cosmological constants
of bulk spacetime, a tension of a domain wall, and mass parameters of the black
hole-type metric. Especially, we consider the false-true vacuum type junctions
and the domain wall connecting between an inner AdS space and an outer AdS
Reissner-Nordstrm black hole. We find that there exist a
solution to the junction equations with an inflation at earlier times and an
accelerating expansion at later times.Comment: corrected typos, title and sec.
Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System
We consider holomorphic deformations of Fuchsian systems parameterized by the
pole loci. It is well known that, in the case when the residue matrices are
non-resonant, such a deformation is isomonodromic if and only if the residue
matrices satisfy the Schlesinger system with respect to the parameter. Without
the non-resonance condition this result fails: there exist non-Schlesinger
isomonodromic deformations. In the present article we introduce the class of
the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal
deformation is also an isomonodromic one. In general, the class of the
isomonodromic deformations is much richer than the class of the isoprincipal
deformations, but in the non-resonant case these classes coincide. We prove
that a deformation is isoprincipal if and only if the residue matrices satisfy
the Schlesinger system. This theorem holds in the general case, without any
assumptions on the spectra of the residue matrices of the deformation. An
explicit example illustrating isomonodromic deformations, which are neither
isoprincipal nor meromorphic with respect to the parameter, is also given
Topology of energy surfaces and existence of transversal Poincar\'e sections
Two questions on the topology of compact energy surfaces of natural two
degrees of freedom Hamiltonian systems in a magnetic field are discussed. We
show that the topology of this 3-manifold (if it is not a unit tangent bundle)
is uniquely determined by the Euler characteristic of the accessible region in
configuration space. In this class of 3-manifolds for most cases there does not
exist a transverse and complete Poincar\'e section. We show that there are
topological obstacles for its existence such that only in the cases of
and such a Poincar\'e section can exist.Comment: 10 pages, LaTe
Removing black-hole singularities with nonlinear electrodynamics
We propose a way to remove black hole singularities by using a particular
nonlinear electrodynamics Lagrangian that has been recently used in various
astrophysics and cosmological frameworks. In particular, we adapt the
cosmological analysis discussed in a previous work to the black hole physics.
Such analysis will be improved by applying the Oppenheimer-Volkoff equation to
the black hole case. At the end, fixed the radius of the star, the final
density depends only on the introduced quintessential density term
and on the mass.Comment: In this last updated version we correct two typos which were present
in Eqs. (21) and (22) in the version of this letter which has been published
in Mod. Phys. Lett. A 25, 2423-2429 (2010). In the present version, both of
Eqs. (21) and (22) are dimensionally and analytically correc
A -anaolg of the sixth Painlev\'e equation
A -difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of -hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected
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