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The Edmund Landau Minerva Center for Research in Mathematical Analysis and Related Areas


List of Publications supported by the Landau Center for research in Mathematical Analysis and Related Areas

1 October 1992 -- 30 September 1993

  1. Y. Sobolevski: Application of Boltyanskii's optimality principle for investigation of one linear optimal control problem with mixed constraints in discrete time.

  2. D. Fishelov: A convergent particle scheme for convection-diffusion equation.

    Abstract: In this paper we prove the convergence of the convolution-type vortex scheme for the convection-diffusion equation in two dimensions. This scheme approximates the convection-diffusion 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 time-discretized scheme and prove its convergence.

  3. A. Eizenberg, Y. Kifer and B. Weiss: Large deviations for Zd-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 hard-care lattice-gas models which are outside of the scope of [FO], [C], [O] and [B].

  4. A. Ermenko, G. Levin and M. Sodin: On the distribution of Zeros of a Ruelle Zeta-function.

    Abstract: We study the limit distribution of Zeros of a Ruelle ζ-function for the dynamical system z → z2 + c when c is real and c → -2 -0 and apply the results to the correlation functions of this dynamical system.

  5. G. Levin: A property of Scalar differential equations.

    Abstract: For one-dimensional differential equation the explicit condition is given which guarantees the good property of the shift transformations.

  6. S.R. Foguel: Markov matrices.

  7. 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.

  8. A.G. Reznikov: Harmonic maps, hyperbolic cohomology and higher Milnor inequalities.

  9. E. de Shalit: Kronecker's polynomial, supersingular elliptic curves, and p-adic periods of modular curves.

  10. A.G. Reznikov: Determinant inequalities with applications to Isoperimetrical inequalities.

  11. B. Rubin: On fractional integration of generalized functions on a half-line.

  12. A.G. Reznikov: the weak Blaschke conjecture for CPn.

  13. H.M. Farkas, J. Kopeliovich: New Theta constant identities II.

  14. H.M. Farkas, J. Kopeliovich: New Theta constant identities I.

  15. H.M. Farkas, Irwin Kra: Automorphic forms for subgroups of the modular group.

  16. A.G. Reznikov: Yamabe spectra.

  17. M. Goldstern, M. Repicky, S. Shelah, O. Spinas: On tree ideals.

    Abstract: Let l0 and m0 the ideals associated with Laver and Miller forcing, respectively. We show that add (l0) < cov (l0) and add (m0) < cov (m0) are constistent. We also show that both Laver and Miller forcing collapse the continuum to a cardinal ≤ η .

  18. D. Fishelov: Simulation of three-dimensional turbulent flow in non-Cartesian geometry.

    Abstract: A three-dimensional 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 grid-free vortex method with a derterministic approximation to the viscous term. The results indicate constant growth in time of the L2 norm of the vorticity and concentration of the vorticity field in small portions of the region.

  19. A. Devinatz: Lectures on a "spectral calculus".

  20. G. Grabarnik: Rotation sets.

  21. B. Rubin, R. Gorenflo: Regularized inversion of fractional integrals by means of truncated hypersingular integrals.

  22. A.G. Reznikov: Quadratic equations in groups through variational calculus.

  23. B. Kashin, L. Tzafriri: On random sets of uniform convergence.

  24. G. Levin, F. Frzytycki: External rays to periodic points.

  25. M. Weinstein: Lecture notes on the dynamics of nonlinear dispersive waves.

  26. 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 Chern-Simons invariant of compact arithmetic hyperbolic three-manifolds. We give the sharp higher-dimensional Milnor inequality for the volume regulator of all representations to P S O(1,n) of fundamental groups of compact n-dimensional hyperbolic manifolds, announced in our earlier paper.

  27. C. Boldrighini, M. Soloveitchik: On "large deviation" in a mechanical system.

  28. A. Dold, E. Dror Farjoun: On the cellular structures of symmetric products.

  29. 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 bi-universal 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.

  30. M. Ben Artzi, J. Falcovitz: Recent development of the GRP method.

  31. 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,Sn)| of actions of a finite group G on an n-set in terms of the order |G| = m and the number sG(d) of subgroups of index d of G for d|m. 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.

  32. 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 n} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter 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 one-parameter subgroup of G.

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