The universal modality, the center of a Heyting algebra, and the Blok–Esakia theorem

We introduce the bimodal logic , which is the extension of Bennett’s bimodal logic by Grzegorczyk’s axiom □(□(p→□p)→p)→p and show that the lattice of normal extensions of the intuitionistic modal logic WS5 is isomorphic to the lattice of normal extensions of , thus generalizing the Blok–Esakia theorem. We also introduce the intuitionistic modal logic WS5.C, which is the extension of WS5 by the axiom (p¬p)→(p→p), and the bimodal logic , which is the extension of Shehtman’s bimodal logic by Grzegorczyk’s axiom, and show that the lattice of normal extensions of WS5.C is isomorphic to the lattice of normal extensions of .     

基于投影算子的正则化最小二乘回归

通过引入经验覆盖数（empirical covering number）和投影算子（projection-operator）,从理论上研究正则化最小二乘回归学习算法.与已有的方法相比,一方面简化了回归分析的过程;另一方面,提高了最小二则回归学习算法的误差收敛阶.即,通过引入投影算子,得到了O（m-1）型的收敛阶,这是统计学习理论中关于泛化误差的最佳逼近阶.     

镁基复合材料的放氢性能

将混合粉末Ni和Ti覆盖于纯Mg锭表面制备Mg基复合材料.此方法有利于吸/放氢相Mg2Ni和催化相NiTi规则地生成与分布.纯Mg锭位于中心位置,而粉末Ni和Ti包覆于纯Mg锭表面.首先确定生成Mg2Ni和NiTi的温度范围为600℃左右;根据此温度范围,计算在650℃和850℃ Mg2Ni和NiTi的晶粒尺寸,从而确定最优化的烧结温度;建立晶体结构模型,确定Mg2Ni合金相主要分布在烧结体表面;最终实现了5 min放氢量为4wt;,实现了短时间内大放氢量的目的.     

药品近红外光谱通用性定量模型评价参数的选择

为寻找药品近红外通用性定量模型在建立过程中用于确立最优模型的关键评价参数组合,收集整理了目前各种商品化化学计量学软件及文献中的13个常用于评价近红外定量模型的统计学参数,结合人用药品注册技术要求国际协调会对于药品定量分析方法验证基本要求,对92个药品近红外通用性定量分析模型的这些参数进行了计算和分析。通过对各个参数之间相互关系的研究,确定了适合于药品近红外通用性定量分析模型评价的参数组合,并统计出了这些参数的数值范围：用于模型准确性评价的关键参数为交叉验证均方根误差/预测均方根误差、平均相对偏差和相对分析误差;大部分交叉验证均方根误差/预测均方根误差结果在3%以内,其中交叉验证均方根误差在数值上与平均绝对偏差相当,大部分相对分析误差值大于2,而平均相对偏差的数值与所建模型的类型(剂型、样品的包装形式)和待测成分含量的分布有关。模型线性评价关键参数为决定系数;大部分模型的决定系数在80%～100%之间。模型耐用性关键评价参数为预测均方根误差与交叉验证均方根误差的比值,大部分模型该参数在1.5以内。精密度评价关键参数为重复测定结果的标准差;该参数对于规范近红外的操作,以及考核模型能否在不同仪器间传递具有重要的意义,但目前药品近红外通用性定量模型对于分析精密度的关注较少,无法估计出具体数值范围。该研究不仅为药品近红外通用性模型的建立者和使用者提供了评价模型优劣的依据,也为完善药品近红外光谱通用性定量分析模型的参数评价体系提供了基础数据。     

The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

Some sharp estimates for coefficients, distortion and the growth order are obtained for harmonic mappings $f \in TL^{\alpha}_H,$ which are locally univalent harmonic mappings in the unit disk $\mathbb{D}:=\{z:|z|<1\}.$ Moreover, denoting the subclass $TS^{\alpha}_H$ of the normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f \in TS^α_H,$ and their covering theorems.     

On the use of universal relations in the modeling of transversely isotropic materials

A material is of coaxial type   if the Cauchy stress tensor T$\mathit{T}$ and the strain tensor B$\mathit{B}$ are coaxial for all deformations. Clearly a hyperelastic material is of coaxial type if and only if it is isotropic. Here we present a weaker definition of materials of coaxial type. Anisotropic materials may be of a coaxial type in a weak sense if for a given specific  B$\mathit{B}$ we have that TB=BT$\mathit{TB}=\mathit{BT}$. We denote these materials B$\mathit{B}$-coaxial. We show that for transverse isotropic materials weak coaxial constitutive equations may be characterized using universal relations. We discuss the impact of B$\mathit{B}$-coaxial materials in the modeling of soft tissues. We conclude that B$\mathit{B}$-coaxial materials are a strong evidence that in real world materials two anisotropic invariants are always necessary to model in a meaningful and correct way single fiber reinforced materials.     

GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架,采用转动惯量描述气体分子自旋运动,确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分,得到计及转动非平衡效应气体分子速度分布函数方程组,使用离散速度坐标法对分布函数方程所依赖速度空间离散降维;应用拓展计算流体力学有限差分方法,构造直接求解分子速度分布函数的气体动理论数值格式;基于物面质量流量通量守恒与能量平衡关系,发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法,提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1：5～25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数（9×10^-4～10）Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究,将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析,验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度.     

Magnetocaloric effect and transition order of Mn5Ge3 ribbons

Single phase Mn₅Ge₃ ribbons were successfully synthesized by single roller melt-spinning method followed by an annealing procedure at 800 °C for 1 h. The magnetocaloric effect and transition order were investigated by dc magnetization measurement. A maximum entropy change of 4.92 J/kg K and a refrigerant capacity of 201.3 J/kg were observed at an external field change of 30 kOe. The Banerjee criterion was adopted to discriminate the order of the transition, indicating a second order transition. The calculated entropy changes were also obtained by Landau theory, which are in agreement with the experimental values at the temperature region above the Curie temperature. This phenomena implies a potential transition of the magnetic interaction in the vicinity of the Curie temperature. Universal behavior was also indicated in that all of the experimental entropy change curves collapse into one universal curve, which is consistent with the Banerjee criterion.     

Estimates of learning rates of regularized regression via polyline functions

Based on the simplicity and calculability of polyline function, we consider, in this paper, the regularized regression learning algorithm associated with the least square loss and the set of polyline function . The target is the error analysis for the regression problem. The approach presented in the paper yields satisfactory learning rates. The rates depend on the approximation property of and on the capacity of measured by covering numbers. Under some certain conditions, the rates achieve m^?4/5 log m. Copyright © 2012 John Wiley & Sons, Ltd.