Surface characterization by nitrogen adsorption of silica aerogels synthesized from various Si(OR)4 and R″Si(OR′)3 precursors

We report the surface characterization by nitrogen adsorption-desorption technique of organically surface-modified silica aerogels. These solids were prepared through a sol-gel process from various combinations of silicon precursors and co-precursors with the aim of obtaining identically modified materials. The silicon precursors are based on four identical hydrolysable alkoxy groups (methoxy or ethoxy) whereas one of the alkoxy groups in the co-precursors is substituted by a non-hydrolysable alkyl group (methyl, ethyl, n-propyl, iso-butyl, n-octyl, vinyl or phenyl). Obtained alcogels were dried under carbon dioxide supercritical conditions and their specific surface area, pore volume, mesoporosity and pore size distribution were investigated. Mesoporous materials exhibiting high specific surface areas and total pore volumes were obtained, revealing a decreasing porosity along with the use of co-precursors having larger side chains.     

基于辛格式的深度哈密尔顿神经网络

HNN是一类基于物理先验学习哈密尔顿系统的神经网络.本文通过误差分析解释使用不同积分器作为超参数对HNN的影响.如果我们把网络目标定义为在任意训练集上损失为零的映射,那么传统的积分器无法保证HNN存在网络目标.我们引进反修正方程,并严格证明基于辛格式的HNN具有网络目标,且它与原哈密尔顿量之差依赖于数值格式的精度.数值实验表明,由辛HNN得到的哈密尔顿系统的相流不能精确保持原哈密尔顿量,但保持网络目标;网络目标在训练集、测试集上的损失远小于原哈密尔顿量的损失;在预测问题上辛HNN较非辛HNN具备更强大的泛化能力和更高的精度.因此,辛格式对于HNN是至关重要的.     

Intuitionistic nonstandard bounded modified realisability and functional interpretation

We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles.The functional interpretation is the intuitionistic counterpart of Ferreira and Gaspar's functional interpretation and has similarities with Van den Berg, Briseid and Safarik's functional interpretation but replacing finiteness by majorisability.We give a threefold contribution: constructive content and proof-theoretical properties of nonstandard arithmetic; filling a gap in the literature; being in line with nonstandard methods to analyse compactness arguments.     

A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half‐line

In this work, we discuss the coupled modified nonlinear Schrödinger (CMNLS) equation, which describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. By use of the Fokas approach, the initial‐boundary value problem for the CMNLS equation related to a 3×3 matrix Lax pair on the half‐line is to be analyzed. Assuming that the solution {u(x,t),v(x,t)} of CMNLS equation exists, we will prove that it can be expressed in terms of the unique solution of a 3×3 matrix Riemann‐Hilbert problem formulated in the plane of the complex spectral parameter λ. Moreover, we also get that some spectral functions s(λ) and S(λ) are not independent of each other but meet a global relationship.     

An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization

In this paper, we first present an adaptive nonmonotone term to improve the efficiency of nonmonotone line search, and then an active set identification technique is suggested to get more efficient descent direction such that it improves the local convergence behavior of algorithm and decreases the computation cost. By means of the adaptive nonmonotone line search and the active set identification technique, we put forward a global convergent gradient-based method to solve the nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which we introduce a modified Barzilai-Borwein (BB) step size. The new modified BB step size and the larger step size strategy are exploited to accelerate convergence. Finally, the results of extensive numerical experiments using both synthetic and image datasets show that our proposed method is efficient in terms of computational speed.     

The homotopy analysis method to solve the modified equal width wave equation

In this article, to solve the modified equal width wave (MEW) equation, the homotopy analysis method (HAM) is proposed. The initial approximation can be freely chosen with possible unknown constant, which can be determined by using the boundary and initial conditions. The HAM contains the auxiliary parameter ?, which provides us to adjust and control the convergence region of solution series with a simple way. Three conservative quantities are reported. Numerical results show that this method is a promising and powerful tool to solve the MEW equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Banach空间中Mann迭代和Ishikawa迭代的等价性问题

用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{βn}仅需lim sup n→∞βn〈k/L（L＋1）,这推广和改进了目前需假设lim n→∞ βn=0和两迭代程序初始点的取值需相同条件下的已有结果.     

上半空间中修改的Poisson积分和Green位势的例外集

本文刻画了修改的Poisson积分和的Green位势在上半空间中的例外集.所得结论推广了关于解析函数、调和函数和超调和函数增长性质的已有结果.     

Crystallization Behavior of Modified Polyester with Varied Macromolecular Architecture

Several modified polyesters with varied macromolecular architecture, such as branched poly(ethylene terephthalate) (PET) based on glycerol (GL) from 0.004 to 0.05 mol ratio as a branching agent, blocked and branched poly(butylene terephthalate)‐polyether containing poly(tetramethylene oxide) (PTMO) as soft segment and GL as a branching unit, as well as segmented poly(ethylene terephthalate)‐polyether,were prepared. Their crystallization behavior was studied by differential scanning calorimetry (DSC), wide‐angle X‐ray diffraction (WAXD), and polarized optical microscopy (POM). It was found that a small extent of branching may enhance the crystallization of poly(ethylene terephthalate), while high degrees of branching (0.035–0.05) could block the development of crystallization. On the other hand, for even a small extent of incorporation of GL in the more flexible poly(butylene terephthalate)‐polyether chains, no enhanced crystallization was observed; blocking of crystallization from a branching defect may play the main role. The introduction of PTMO in poly(ethylene terephthalate) chains to a small degree facilitated the nucleation and speeded crystallization, but decreased the melting points of the polymers. A small number of nuclei and the greater induction time were found for branched PETs. The spherulities developed in branched PETs were larger and more perfect than those in PET due to less truncation of spherulites resulting from fewer nuclei, whereas the size of spherulities in poly(ethylene terephthalate)‐polyether became smaller with the increase of PTMO.     

Synthesis and Characterization of Magnetic Polymer Microspheres

In this study, amino group–modified magnetic polymer microspheres were synthesized in a well‐shaped spherical form with a size range of 0.6 μm to 0.8 μm by mini‐emulsion polymerization. The morphology, composition, and thermal properties of the magnetic polymer microspheres were characterized by infrared (IR) spectra, transmission electron microscopy (TEM) photographs, particle size analysis, and thermogravimetric analysis (TGA) spectra. The results demonstrate that acrylic acid used for stabilizing the reaction system greatly affects the particle size, magnetite contents, and thermal stability of magnetic polymer microspheres.