Random version of Dvoretzky’s theorem in ℓpn

We study the dependence on $\epsilon$ in the critical dimension $k(n,p,\epsilon )$ for which one can find random sections of the ${?}_p^n$-ball which are $(1+\epsilon )$-spherical. We give lower (and upper) estimates for $k(n,p,\epsilon )$ for all eligible values $p$ and $\epsilon$ as $n\to \infty$, which agree with the sharp estimates for the extreme values $p=1$ and $p=\infty$. Toward this end, we provide tight bounds for the Gaussian concentration of the ${?}_p$-norm.     

Berezin–Toeplitz quantization for lower energy forms

Let M be an arbitrary complex manifold and let L be a Hermitian holomorphic line bundle over M. We introduce the Berezin–Toeplitz quantization of the open set of M where the curvature on L is nondegenerate. In particular, we quantize any manifold admitting a positive line bundle. The quantum spaces are the spectral spaces corresponding to [0,k^?N], where N>1 is fixed, of the Kodaira Laplace operator acting on forms with values in tensor powers L^k. We establish the asymptotic expansion of associated Toeplitz operators and their composition in the semiclassical limit k→∞ and we define the corresponding star-product. If the Kodaira Laplace operator has a certain spectral gap this method yields quantization by means of harmonic forms. As applications, we obtain the Berezin–Toeplitz quantization for semi-positive and big line bundles.     

关于分数幂算子(-△)~(α/2)的一个非线性估计

利用广义Young不等式给出了分数幂算子(一△)~(α/2)(α1)的一个加权非线性估计,为非线性分数幂耗散方程在加权了空间中讨论解的存在性提供帮助.     

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This paper investigates the investment-dividend optimization problem for a corporation with transaction costs and investment constraints. The main feature is that we assume general constraints on investments including the special case of short-sale and borrowing constraints. This results in a regular-impulse stochastic control problem. The nontrivial case is that the investment can't meet the loss of wealth due to discounting. In this case, delicate analysis is carried out on QVI w.r.t. three possible situations, leading to an explicit construction of the value functions together with the optimal policies. We also give explicit conclusion of the trivial case at last.     

Functional inequalities for the Wright functions

In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function.     

带权散度型椭圆算子的低阶特征值估计

本文首先给出紧致带边(边界可以为空集)光滑度量测度空间上带权散度型算子的低阶特征值的一个一般不等式,通过使用这个一般不等式,可以得到光滑度量测度空间中有界连通区域上带权散度型算子的低阶特征值的一些万有不等式.     

Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces

Multivalued equilibrium problems in general metric spaces are considered. Uniqueness and Hölder continuity of the solution are established under Hölder continuity and relaxed Hölder-related monotonicity assumptions. The assumptions appear to be weaker and the inclusion to be properly stronger than that of the recent results in the literature. Furthermore, our theorems include completely some known results for variational inequalities in Hilbert spaces, which were demonstrated via geometrical techniques based on the orthogonal projection in Hilbert spaces and the linearity of the canonical pair\(\langle .,.\rangle\).     

Dual extrapolation and its applications to solving variational inequalities and related problems

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators ( $O({1 \over \epsilon})In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators ( iterations), and for the operators with bounded variations ( iterations). Our technique can be applied for solving non-smooth convex minimization problems with known structure. In this case the worst-case complexity bound is iterations. The research results presented in this paper have been supported by a grant “Action de recherche concertè ARC 04/09-315” from the “Direction de la recherche scientifique, Communautè fran?aise de Belgique”. The scientific responsibility rests with its author(s).