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Electromagnetic model of a hidden object. We model propagation of electromagnetic waves in a medium, which is inhomogeneous with a rough layer, and which hides an object. We first get an effective med...
This paper present an overview of some of the applications of the martingale transform inequalities of D.L. Burkholder to Lp-bounds for singular integrals concentrating on Lp-bounds for the Hilbert, R...
Our purpose is to prove the uniqueness of the representation for G-martingales with finite variation.
There is a curious relation between two kinds of phase space distributions associated to Laplace-eigenfunctions ϕk on a compact hyperbolic manifold Y .
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore,we show that convergence rate to equilibrium is expon...
Let S be a minimal surface of general type with pg = q = 1,K2S = 7.We prove that the degree of the bicanonical map is 1 or 2. Furthermore, if the degree is 2, we describe S by a double cover.
The condition of plane polynomial curve to be a line in well-known Abhyankar-Moh Theorem is replaced by weaker ones. A criterion of embedded line is obtained from this strong theorem.
In the third paper in this series, we examine the Reshetikhin-Turaev and Turaev-Viro TQFTs at the level of surfaces. In particular, we show that for a closed surface , ZTV,C() = ZRT,Z(C)(), thus e...
For a compact minimal hypersurface M in Sn+1 with the squared length of the second fundamental form S we confirm that there exists a positive constant (n) depending only on n, such that if n ≤ S ≤ n ...
Abstract. If G is a group of permutations of a set , then the suborbits of G are the orbits of point-stabilisers G acting on .The cardinalities of these suborbits are the subdegrees of G. Every infin...
It is proven that, for any affine supermanifold M equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck-Teichm¨uller Lie algebra grt on t...
Describing the combinatorial structure of the tropical complex C of a tropical ma-troid polytope, we obtain a formula for the coarse types of the maximal cells of C. Due to the connection between trop...
The Gowers uniformity norms kfkUk(G) of a function f : G → C on a finite additive group G, together with the slight variant kfkUk([N]) defined for functions on a discrete interval [N] := {1, . . . ,N}...
In this note, we first classify all topological torus knots lying on the Heegaard torus in Lens spaces, and then we classify Legendrian representatives of torus knots. We show that all Legendrian toru...
A family of random models for bosonic quasi-particle excitations, e.g. the vibrations of a disordered solid, is introduced. The generator of the linearized phase space dynamics of these models is the ...

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