We establish Talagrand’s T 2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type’s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction-Diffusion equations are provided.
In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.
In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.
This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p n q + p m q + q-4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p n q + p m q + q-3 which are represented by h 0(h m b n-1 - h n b m-1) and i *(h 0 h n h m) in the E 2-terms of the Adams spectral sequence respectively, where p ≥ 7 is a prime, n ≥ m + 2 ≥ 4; q = 2(p - 1).
This paper computes the Thom map on γ2 and proves that it is represented by 2b 2,0 h 1,2 in the ASS. The authors also compute the higher May differential of b 2,0, from which it is proved that $\widetilde{\gamma }_{s} {\left( {b_{0} h_{n} - h_{1} b_{{n - 1}} } \right)}$ for 2 ≤ s < p - 1 are permanent cycles in the ASS.
It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p 1 + p 2, p 1 ∈ P γ is solvable, with 13=15 < γ ≤ 1, where P γ = {p ∣ $p = {\left[ {m^{{\frac{1}{\gamma }}} } \right]}$; for integer m and prime p} is the set of the Piatetski-Shapiro primes.
This paper considers a family of Schrödinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of the solution outside the caustic, and near the caustic.
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, this paper verifies Sampson’s conjecture in most cases for irreducible Riemannian symmetric spaces of noncompact type.