Exponential convergence for high-order recurrent neural networks with a class of general activation functions

In this paper, we consider high-order recurrent neural networks with a class of general activation functions. By using some mathematical analysis techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point.     

单位多圆盘加权Bergman空间上Toeplitz算子的本质谱

本文研究了单位多圆盘加权Bergman空间AΦp(Dn)上的Toeplitz算子.利用多圆盘函数论,获得了L∞(Dn)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱.     

Study on radiative heat transfer property of fiber assemblies using FTIR

Radiative heat transfer could be a significant contribution to the total heat transfer within the highly porous materials. This article reports on the use of a conventional instrument, viz. Fourier transform infrared (FTIR) spectroscopy, for the characterization of radiative heat properties of fiber assemblies with low bulk densities. Experimental measurements on spectral transmission with FTIR were performed on five types of fiber assemblies commonly used for insulating materials. From the measurements, radiative heat conductivity was determined by calculating extinction coefficient using Beer’s Law and applying the diffusion approximation approach. Bulk density, fiber arrangement, and temperature influences to radiative heat transfer were discussed. Results show that radiative heat conductivity decreases with bulk density and that of the random arranged fiber assemblies shows lower radiative heat conductivity than the random ball and parallel arranged fiber assemblies. Radiative heat conductivity is proportional to the cubic temperature. The existing theoretical model was modified by comparing theoretical and experimental radiative heat conductivity results.     

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

In the past decades, there was considerable controversy over the Lucas–Washburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the [`(L)] _s(t) ~ t^1/2D_T{\overline L _{\rm {s}}(t)\sim t^{1/{2D_{\rm {T}}}}} law is obtained (here D _T is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D _T = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.     

Multiplication operators on the Bergman space via analytic continuation

In this paper, using the group-like property of local inverses of a finite Blaschke product ?, we will show that the largest C^?-algebra in the commutant of the multiplication operator M? by ? on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of ?−1°? over the unit disk. If the order of the Blaschke product ? is less than or equal to eight, then every C^?-algebra contained in the commutant of M? is abelian and hence the number of minimal reducing subspaces of M? equals the number of connected components of the Riemann surface of ?−1°? over the unit disk.     

Commutators of weighted lipschitz functions and multilinear singular integrals with non-smooth kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.     

Morita contexts and Galois theory for weak Hopf comodulelike algebras

We investigate the Morita context and graded cases for weak group corings and derive some equivalent conditions for μ to be surjective. Furthermore, we develop Galois theory for weak group corings. As an application, we give Galois theory for comodulelike algebras over a weak Hopf group coalgebra.     

Beurling Type Theorem on the Hilbert Space Generated by a Positive Sequence

Let H²(γ) be the Hilbert space over the bidisk D² generated by a positive sequence γ={γ_nm}_n,m ≥ 0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H²(γ) with γ={γ_nm}_n,m ≥ 0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D².     

Immunocytochemical and structural comparative study of committed versus multipotent stem cells cultured with different biomaterials

The aim of this work was the comparison of the behavior of committed (human osteoblast cells – hOB – from bone biopsies) versus multipotent (human dental pulp stem cells – hDPSC – from extracted teeth) cells, cultured on shot-peened titanium surfaces, since the kind of cell model considered has been shown to be relevant in techniques widely used in studies on composition/morphology of biomaterial surfaces. The titanium surface morphology, with different roughness, and the behavior of cells were analyzed by confocal microscope (CM), scanning electron microscope (SEM) and X-ray microanalysis. The best results, in terms of hOB adhesion/distribution, were highlighted by both CM and SEM in cultured plates having 20-μm-depth cavities. On the contrary, CM and SEM results highlighted the hDPSC growth regardless the different surface morphology, arranged in overlapped layers due to their high proliferation rate, showing their unfitness in biomaterial surface test. Nevertheless, hDPSC cultured inside 3D-matrices reproduced an osteocyte-like three-dimensional network, potentially useful in the repair of critical size bone defects. The behavior of the two cell models suggests a different use in biomaterial cell cultures: committed osteoblast cells could be appropriate in selecting the best surfaces to improve osseointegration, while multipotent cells could be suitable to obtain in vitro osteocyte-like network for regenerative medicine. The originality of the present work consists in studying for the first time two different cell models (committed versus multipotent) compared in parallel different biomaterial cultures, thus suggesting distinct targets for each cellular model.