Widths of weighted Sobolev classes on the ball

We study the Kolmogorov n-widths and the linear n-widths of weighted Sobolev classes on the unit ball B^d in L_q,μ, where L_q,μ, 1≤q≤∞, denotes the weighted L_q space of functions on B^d with respect to weight . Optimal asymptotic orders of and as n→∞ are obtained for all 1≤p,q≤∞ and μ≥0.     

造纸污泥中提取的木质素改性研究

为提高以造纸污泥为原料制备的木质素减水剂的减水性,用H2O2 和Na2SO3分别对木质素进行氧化、磺化.氧化工艺条件为:对10g木质素,过氧化氢用量为1.5g,反应温度80℃,pH=9,反应时间2 h.所得到的产品比一般磺化产品的减水性能优越,经检测各项主要指标达到普通减水剂的国家标准(GB8076-1997).     

Existence and Uniqueness Theorems for a Three-step Newton-type Method under $L$-Average Conditions

In this paper, we study the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weaker hypothesis. More precisely, we derive the existence and uniqueness theorems, when the first-order derivative of nonlinear operator satisfies the $L$-average conditions instead of the usual Lipschitz condition, which have been discussed in the earlier study.     

Evaluation of the suitability of low hazard surfactants for the separation of phenols and carotenoids from red‐flesh orange juice and olive mill wastewater using cloud point extraction

Natural antioxidants derived from plant sources attract considerable scientific interest. While classic extraction methods consume high volumes of toxic organic solvents, cloud point extraction requires surfactant not exceeding 15% of the waste volume. In preliminary tests, the suitability of various low hazard surfactants (Span 20, PEG 400, Tween 80 and 20) was explored for separation of phenols and carotenoids from olive mill wastewater and red‐flesh orange juice. Tween 80 showed the highest recovery and further applied to the next experiments. The most appropriate surfactant concentrations were 5% (for olive mill wastewater) and 7% (for orange juice) as indicated by recovery % and the rest cloud point extraction parameters (analyte concentration, concentration factor, and phase volume ratio). A double step CPE with 5% + 5% of Tween 80 recovered up to 94.4% of the total phenols from olive mill wastewater, while a 7% + 7% of Tween 80 recovered up to 72.4% of the total carotenoids from orange juice. Evaluation of the final effects and extraction efficiency of single and double step cloud point extraction shows that double step scheme seems to be preferable in both cases. Finally, phenols and carotenoids recovered by Tween 80 maintained high antiradical activity (DPPH test).     

Sharp bounds for the first non-zero Stekloff eigenvalues

Let (M,,) be an n(2)-dimensional compact Riemannian manifold with boundary and non-negative Ricci curvature. Consider the following two Stekloff eigenvalue problems

where Δ is the Laplacian operator on M and ν denotes the outward unit normal on ∂M. The first non-zero eigenvalues of the above problems will be denoted by p₁ and q₁, respectively. In the present paper, we prove that if the principle curvatures of the second fundamental form of ∂M are bounded below by a positive constant c, then with equality holding if and only if Ω is isometric to an n-dimensional Euclidean ball of radius , here λ₁ denotes the first non-zero eigenvalue of the Laplacian of ∂M. We also show that if the mean curvature of ∂M is bounded below by a positive constant c then q₁nc with equality holding if and only if M is isometric to an n-dimensional Euclidean ball of radius . Finally, we show that q₁A/V and that if the equality holds and if there is a point x₀∂M such that the mean curvature of ∂M at x₀ is no less than A/{nV}, then M is isometric to an n-dimensional Euclidean ball, being A and V the area of ∂M and the volume of M, respectively.     

Exact L 2-Small Ball Asymptotics of Gaussian Processes and the Spectrum of Boundary-Value Problems

We sharpen a classical result on the spectral asymptotics of boundary-value problems for self-adjoint ordinary differential operator. Using this result, we obtain the exact L ₂-small ball asymptotics for a new class of zero-mean Gaussian processes. This class includes, in particular, the integrated generalized Slepian process, integrated centered Wiener process, and integrated centered Brownian bridge. Partially supported by RFFR grant No.07-01-00159 and by grant NSh-227.2008.1.     

A Theorem of Nehari Type on the Bergman Space

In this paper we concern with the characterization of bounded linear operators S acting on the weighted Bergman spaces on the unit ball. It is shown that, if S satisfies the commutation relation STzi = Tzi（i =1,..,n）, where Tzi = zif and Tzi= P（zif） where P is the weighted Bergman projection, then S must be a Hankel operator.     

Toeplitz and Hankel Products on Bergman Spaces of the Unit Ball

The authors give some new necessary conditions for the boundedness of Toeplitz products Tf^aTg^a on the weighted Bergman space Aa^2 of the unit ball, where f and g are analytic on the unit ball. Hankel products HfH9^＋ on the weighted Bergman space of the unit ball are studied, and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.     

Norms of some operators on the Bergman and the Hardy space in the unit polydisk and the unit ball

Let H(X) be the class of all holomorphic functions on the set and uH(X). We calculate operator norms of the multiplication operators M_u(f)=uf, on the weighted Bergman space , as well as on the Hardy space H^p(X), where X is the unit polydisk or the unit ball in . We also calculate the norm of the weighted composition operator from the weighted Bergman space , and the Hardy space , to a weighted-type space on the unit polydisk.