Preprints
List of Publications supported by the Landau Center for research in
Mathematical Analysis and Related Areas
1 October 1992  30 September 1993
 Y. Sobolevski: Application of Boltyanskii's optimality principle
for investigation of one linear optimal control problem with mixed
constraints in discrete time.
 D. Fishelov: A convergent particle scheme for convectiondiffusion
equation.
[pdf]
 Abstract:
In this paper we prove the convergence of the convolutiontype vortex
scheme for the convectiondiffusion equation in two dimensions. This scheme
approximates the convectiondiffusion equation by first formulating it along
particle trajectories and then approximating the viscous term via a discrete
convolution of the vorticity with the Laplacian of the cutoff function. We also
derive stability condition for the timediscretized scheme and prove its
convergence.
 A. Eizenberg, Y. Kifer and B. Weiss: Large deviations for
Z^{d}actions.
 Abstract:
We exstablish large deviations bounds for translation invariant Gibbs measures
of multidimensional subshifts of finite type. This generalizes [FO] and
partially [C], [O] and [B] where only full shifts where considered. Our
framework includes, in particular, the hardcare latticegas models which are
outside of the scope of [FO], [C], [O] and [B].
 A. Ermenko, G. Levin and M. Sodin: On the distribution of Zeros of
a Ruelle Zetafunction.
 Abstract:
We study the limit distribution of Zeros of a Ruelle ζfunction for the
dynamical system z → z^{2} + c when c is real and
c → 2 0
and apply the results to the correlation functions of this dynamical system.
 G. Levin: A property of Scalar differential equations.
 Abstract:
For onedimensional differential equation the explicit condition is given which
guarantees the good property of the shift transformations.
 S.R. Foguel: Markov matrices.
 B. Rubin: Hypersingular integrals of Marchaud's type and the
inversion problem for potentials.
 Abstract:
In 1927 A. Marchaud defined a fractional derivative of a function of one
variable in the form of the integral containing the finite difference of this
function. The purpose of the paper is to show that this idea can be generalized
to become a foundation of the general method which enables to invert and to
characterize a wide class of potential type operators with a semigroup property
arising in analysis and in mathematical physics. This method leads to
hypersingular integrals (HSI's), by means of which one can construct both
explicit and stable approximate inverses to potentials. The paper contains the
description and the justification of the method as well as its applications to
various important one and multidimensional potentials.
 A.G. Reznikov: Harmonic maps, hyperbolic cohomology and higher
Milnor inequalities.
 E. de Shalit: Kronecker's polynomial, supersingular elliptic curves,
and padic periods of modular curves.
 A.G. Reznikov: Determinant inequalities with applications to
Isoperimetrical inequalities.
 B. Rubin: On fractional integration of generalized functions on a
halfline.
 A.G. Reznikov: the weak Blaschke conjecture for
CP^{n}.
 H.M. Farkas, J. Kopeliovich: New Theta constant identities II.
 H.M. Farkas, J. Kopeliovich: New Theta constant identities I.
 H.M. Farkas, Irwin Kra: Automorphic forms for subgroups of the
modular group.
 A.G. Reznikov: Yamabe spectra.
 M. Goldstern, M. Repicky, S. Shelah, O. Spinas: On tree ideals.
 Abstract:
Let l^{0} and m^{0} the ideals associated with
Laver and Miller
forcing, respectively. We show that add (l^{0}) < cov
(l^{0}) and add (m^{0}) < cov (m^{0})
are constistent. We also show that both Laver and Miller
forcing collapse the continuum to a cardinal ≤ η .
 D. Fishelov: Simulation of threedimensional turbulent flow in
nonCartesian geometry.
 Abstract:
A threedimensional simulation of turbulent (high Reynolds numbers) flow
over a sphere was performed. We have applied vortex schemes by decomposing the
pysical region into two. The first is a thin layer near the sphere, where we
have used a spherical coordinate system. The second is the rest of the
physical domain, where we have applied the gridfree vortex method with a
derterministic approximation to the viscous term. The results indicate
constant growth in time of the L_{2} norm of the vorticity and
concentration of the vorticity field in small portions of the region.
 A. Devinatz: Lectures on a "spectral calculus".
 G. Grabarnik: Rotation sets.
 B. Rubin, R. Gorenflo: Regularized inversion of fractional
integrals by means of truncated hypersingular integrals.
 A.G. Reznikov: Quadratic equations in groups through variational
calculus.
 B. Kashin, L. Tzafriri: On random sets of uniform convergence.
 G. Levin, F. Frzytycki: External rays to periodic points.
 M. Weinstein: Lecture notes on the dynamics of nonlinear
dispersive waves.
 A.G. Reznikov: Rationality of secondary classes.
 Abstract:
We prove the Bloch conjecture on rationality of the Beilinson characteristic
classes for flat rank two vector bundles over complex projective varieties. We
prove also the rationality of the ChernSimons invariant of compact arithmetic
hyperbolic threemanifolds. We give the sharp higherdimensional Milnor
inequality for the volume regulator of all representations to P S O(1,n)
of fundamental groups of compact ndimensional hyperbolic manifolds,
announced in our earlier paper.
 C. Boldrighini, M. Soloveitchik: On "large deviation" in a
mechanical system.
 A. Dold, E. Dror Farjoun: On the cellular structures of symmetric
products.
 M. Kojman, S. Shelah: Embedding homogeneous families.
 Abstract:
A homogeneous family of subsets over a given set is one with a very "rich"
automorphism group. We prove the existence of a biuniversal element in the
class of homogeneous families over a given infinite set and give an explicit
construction of 2 isomorphism types of homogeneous families over a countable
set. The results are meaningful to model theorists and graph theorists as well
as set theorists.
 M. Ben Artzi, J. Falcovitz: Recent development of the GRP
method.
 Th. Muller: Finite group actions, subgroups of finite index in free
products and asymptotic expansion of e^{(P(z)}.
 Abstract:
We establish an asymptotic expansion for the number
 Hom(G,S_{n}) of
actions of a finite group G on an nset in terms of the order G
= m and the number s_{G}(d) of subgroups of index
d of G
for dm. This expansion follows from a more general asymptotic expansion
for the coefficients of entire functions of the form
e^{(P(z)}, P(z)
a real polynomial, which is explicit in the degree and the coefficients of
P(z). The asymptotic behavior and the asymptotics of the number
sΓ(n) of subgroups of index n in a free product [gamma] of
finite groups.
 S. Mozes, N. Shah: On the space of ergodic invariant measures of
unipotent flows.
 Abstract:
Let G be a Lie group and Γ be a discrete subgroup. We show that if
{μ_{n}} is a convergent sequence of probability measures on
G/Γ which are invariant and ergodic under actions of unipotent
oneparameter subgroups, then the limit μ of such a sequence is
supported on a closed orbit of the subgroup preserving is, and is invariant
and ergodic for the action of a uunipotent oneparameter subgroup of G.
