ISSN 1439-8516 CN 11-2039/O1
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations. Also solutions of the classical Neumann problem converge to a translating solution.
In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman-Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.
Let u={u(t, x), t ∈[0, T], x ∈ R} be a solution to a stochastic heat equation driven by a space-time white noise. We study that the realized power variation of the process u with respect to the time, properly normalized, has Gaussian asymptotic distributions. In particular, we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.
For two analytic self-maps φ and ψ defined on the unit disk D, we characterize completely the boundedness and compactness of the difference Cφ - Cψ of the composition operators Cφ and Cψ from Bloch space B into Besov space Bν∞. Moreover, we also give a complete characterization of the compactness of the difference Cφ - Cψ on BMOA space.
We investigate the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability measures for finitely generated semigroup actions. Let (X, G) be a system, where X is a compact metric space and G is a finite family of continuous maps on X. Given a continuous function f on X, we define Pesin-Pitskel topological pressure PG(Z, f) for any subset Z ⊂ X and measure-theoretical pressure Pμ,G(X, f) for any μ ∈ M(X), where M(X) denotes the set of all Borel probability measures on X. For any non-empty compact subset Z of X, we show that
PG(Z, f)=sup{Pμ,G(X, f):μ ∈ M(X), μ(Z)=1}.
We study the Cauchy problem for the Davey-Stewartson equation
i∂tu + Δu +|u|2u + E1(|u|2)u=0, (t, x) ∈ R×R3.
The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0) above the ground state threshold M(Q)E(Q).
In this paper, we consider the following two-coupled fractional Laplacian system with two or more isolated singularities
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where s ∈ (0, 1), n > 2s and n ≥ 2. μ1, μ2 and β are all positive constants. p1, p2 > 1 and p1 + p2=.jpg){kind=small}
Λ ⊂ Rn contains finitely many isolated points. By the method of moving plane, we obtain the symmetry results for positive solutions to above system.
Let λf(n) be the normalized n-th Fourier coefficient of holomorphic eigenform f for the full modular group and Pc(x):={p ≤ x|[pc] prime}, c ∈ R+. In this paper, we show that for all 0 < c < 1 the mean value of λf(n) in Pc(x) is << x log-A x assuming the Riemann Hypothesis. Unconditionally, in the sense of Lebesgue measure, it holds for almost all c ∈ (ε, 1-ε).
Let G be a finite group, and let P be a Sylow p-subgroup of G. Under the hypothesis that NG(P) is p-nilpotent, we provide some conditions to give a p-nilpotency criterion of finite groups by Engel condition, which improves some recent results.
In this paper, we compute the derivations of the positive part of the two-parameter quantum group of type G2 by embedding it into a quantum torus. We also show that the first Hochschild cohomology group of this algebra is a two-dimensional vector space over the complex field.
