1,590 research outputs found
Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev
We give a simplified proof and an improvement of a recent theorem by A.
Grigoriev, placing an upper bound for the number of roots of linear
combinations of solutions to systems of linear equations with polynomial or
rational coefficients.Comment: 16 page
Modules of Abelian integrals and Picard-Fuchs systems
We give a simple proof of an isomorphism between the two
-modules: the module of relative cohomologies and the module of Abelian integrals corresponding to a regular at
infinity polynomial in two variables. Using this isomorphism, we prove
existence and deduce some properties of the corresponding Picard-Fuchs system.Comment: A separate section discusses Fuchsian properties of the Picard-Fuchs
system, Morse condition exterminated. Few errors were correcte
Twist-3 distribution amplitudes of scalar mesons from QCD sum rules
We study the twist-3 distribution amplitudes for scalar mesons made up of two
valence quarks based on QCD sum rules.
By choosing the proper correlation functions, we derive the moments of the
scalar mesons up to the first two order. Making use of these moments, we then
calculate the first two Gegenbauer coefficients for twist-3 distribution
amplitudes of scalar mesons. It is found that the second Gegenbauer
coefficients of scalar density twist-3 distribution amplitudes for
and mesons are quite close to that for , which indicates that the
SU(3) symmetry breaking effect is tiny here. However, this effect could not be
neglected for the forth Gegenbauer coefficients of scalar twist-3 distribution
amplitudes between and . Besides, we also observe that the first two
Gegenbauer coefficients corresponding to the tensor current twist-3
distribution amplitudes for all the , and are very small.
The renormalization group evolution of condensates, quark masses, decay
constants and moments are considered in our calculations. As a byproduct, it is
found that the masses for isospin I=1, scalar mesons are around
GeV and GeV respectively, while the mass for
isospin state composed of is GeV.Comment: replaced with revised version, to be published in Phys. Rev.
On problem of polarization tomography, I
The polarization tomography problem consists of recovering a matrix function
f from the fundamental matrix of the equation
known for every geodesic of a given Riemannian metric. Here
is the orthogonal projection onto the hyperplan
. The problem arises in optical tomography of slightly
anisotropic media. The local uniqueness theorem is proved: a - small
function f can be recovered from the data uniquely up to a natural obstruction.
A partial global result is obtained in the case of the Euclidean metric on
Quantum geometrodynamics for black holes and wormholes
The geometrodynamics of the spherical gravity with a selfgravitating thin
dust shell as a source is constructed. The shell Hamiltonian constraint is
derived and the corresponding Schroedinger equation is obtained. This equation
appeared to be a finite differences equation. Its solutions are required to be
analytic functions on the relevant Riemannian surface. The method of finding
discrete spectra is suggested based on the analytic properties of the
solutions. The large black hole approximation is considered and the discrete
spectra for bound states of quantum black holes and wormholes are found. They
depend on two quantum numbers and are, in fact, quasicontinuous.Comment: Latex, 32 pages, 5 fig
Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
For the Schrodinger equation at fixed energy with a potential supported in a
bounded domain we give formulas and equations for finding scattering data from
the Dirichlet-to-Neumann map with nonzero background potential. For the case of
zero background potential these results were obtained in [R.G.Novikov,
Multidimensional inverse spectral problem for the equation
-\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22,
(1988)]
Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows
G-equations are well-known front propagation models in turbulent combustion
and describe the front motion law in the form of local normal velocity equal to
a constant (laminar speed) plus the normal projection of fluid velocity. In
level set formulation, G-equations are Hamilton-Jacobi equations with convex
( type) but non-coercive Hamiltonians. Viscous G-equations arise from
either numerical approximations or regularizations by small diffusion. The
nonlinear eigenvalue from the cell problem of the viscous G-equation
can be viewed as an approximation of the inviscid turbulent flame speed .
An important problem in turbulent combustion theory is to study properties of
, in particular how depends on the flow amplitude . In this
paper, we will study the behavior of as at
any fixed diffusion constant . For the cellular flow, we show that
Compared with the inviscid G-equation (), the diffusion dramatically slows
down the front propagation. For the shear flow, the limit
\nit where
is strictly decreasing in , and has zero derivative at .
The linear growth law is also valid for of the curvature dependent
G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square
root of log growt
On the multiplicity of the hyperelliptic integrals
Let be an Abelian integral, where
is a hyperelliptic polynomial of Morse type, a
horizontal family of cycles in the curves , and a polynomial
1-form in the variables and . We provide an upper bound on the
multiplicity of , away from the critical values of . Namely: $ord\
I(t) \leq n-1+\frac{n(n-1)}{2}\deg \omega <\deg H=n+1\delta(t)nHHI(t)\gamma(t)\textbf C^ n\gamma(t)\omegaHI(t)\{H=t\}
\subseteq \textbf C^2\omega\gamma(t)\textbf C^{n+1}ord I(t)\deg \omega$.Comment: 18 page
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