A Restriction Theorem on the Reduced Product Heisenberg Group

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔΩｂｅａｒｅｇｕｌａｒｃｏｎｅｉｎＲｎ,Φ：Ｃｍ×Ｃｍ→Ｃｎ＝Ｒｎ＋ｉＲｎａｎΩ－ｐｏｓｉｔｉｖｅＨｅｒｍｉｔｉａｎｍａｐ．ＴｈｅＳｉｅｇｅｌｄｏｍａｉｎＤΩ,ΦｏｆｔｙｐｅｔｗｏｉｎＣｎ×ＣｍｉｓｄｅｆｉｎｅｄｂｙＤΩ,Φ＝｛（ｚ,ｗ）∈：Ｃｎ×Ｃｍ：Ｉｍｚ－Φ（ｗ,ｗ）∈Ω｝（１）（ｓｅｅ［６］）．Ｓｐｅｃｉａｌｌｙ,ｗｅａｓｓｕｍｅｔｈａｔｎ＝ｍ,Ω＝｛ｔ＝（ｔ１,ｔ２,…,ｔｎ）∈Ｒｎ：ｔｉ＞０,ｉ＝１,２,…,ｎ｝,Φ（ｕ,ｖ）＝ｕ·ｖ＝（ｕ１ｕ…     

Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace formula and eliminates the parameter of our previous approach.     

关于含有Stirling公式的双边不等式(英)

本文证明了有关n！的一个便于应用的双边不等式,它对一切自然数都成立,且当n变大时,上界不等式能给出误差界为O（n^－3）的Stirling渐近公式,从一定意义上说,文中的上界不等式具有最优形式,因为其中的常数0．5已作了最佳选择．文末还给出了关于Catalan数的一个双边不等式．     

求非线性系统对称群的新方法

(1)从Lax可积系统的Lax对出发, 寻找非线性系统的对称及精确解, 利用这种方法可以解决不少(2＋1)维的可积系统, 它的优点在于比较简洁方便, 这从KP方程的求解对比就可以看出. (2)从CK直接法入手, 将这种方法进行修正, 利用这种修正的CK直接法求非线性系统的对称和精确解; 这种方法的最大优点在于不但可以用于可积系统, 而且也适用于不可积系统, 还可以求出离散群. 另外, 这种方法也适用于高维的不可积模型.     

DYNAMICAL EXPLANATION ON TOROFLUX'S PHENOMENA

本文分析了流动环特殊现象的力学原理。流动环是由细长钢带缠绕形成的环状螺旋玩具,具有瞬间几何形态突变和绕圆柱物体运动时迅速旋转两种独特现象。文中利用封闭曲杆的拓扑学规律确定其曲率和扭率,用于计算和比较流动环两种平衡状态的弹性变形势能。证实流动环的形态突变源于最小弹性势能原理。以组成流动环的单个圆环为分析对象,且考虑邻近圆环的牵拉效应。分析了流动环下落时相对圆柱体的滚动过程,以解释旋转现象的产生原因。导出了流动环下落旋转的角加速度公式。理论计算结果与实验数据较好吻合。     

A GENERALIZED QUASI-NEWTON EQUATION AND COMPUTATIONAL EXPERIENCE

The quasi-Newton equation has played a central role in the quasi-Newton methods forsolving systems of nonlinear equations and/or unconstrained optimization problems.In-stead,Pan suggested a new equation,and showed that it is of the second order while thetraditional of the first order,in certain approximation sense[12].In this paper,we makea generalization of the two equations to include them as special cases.The generalizedequation is analyzed,and new updates are derived from it.A DFP-like new update out-performed the traditional DFP update in computational experiments on a set of standardtest problems.     

基于波段注意力卷积网络的近红外奶粉皮革水解蛋白掺假检测

近年来,深度学习技术在近红外光谱、拉曼光谱、荧光光谱等的光谱学数据建模上取得一系列突破。由于深度学习方法对于样本数量的需求高,而在分析化学领域获得大量有标签样本较为困难,因此过拟合问题一直是深度神经网络在化学计量学中应用时研究者高度关注的问题。该工作提出基于波段注意力卷积网络(WA-CNN)的近红外数据建模方法,并应用于婴儿配方奶粉皮革水解蛋白(HLP)掺假定量分析。WA-CNN在传统卷积网络的基础上加入波段注意力模块,该模块采用卷积操作自训练波段注意力权值,并以乘法加权形式对有效波段进行激活,从而有效缓解深度神经网络在近红外数据建模中的波段信息冗余问题,达到抑制过拟合,提升预测精度的目的。研究中共测试100个皮革水解蛋白掺假婴儿配方奶粉样本的近红外光谱数据,其中皮革水解蛋白的掺假比例范围是0%～20%。采用60%的样本训练,剩余40%样本测试,随机采样10次,通过测试集均方根误差(RMSEP)、决定系数(R²)以及相对分析误差(RPD)的均值来进行模型评价。并建立偏最小二乘回归(PLS)、支持向量机回归(SVR)和常规的一维卷积神经网络(CNN)三种传统模型用于...     

基于液相色谱-四极杆/飞行时间质谱和化学计量学的婴幼儿配方乳粉化学指纹图研究

在反相色谱条件下,采用液相色谱-飞行时间串联质谱技术检测了18种婴幼儿配方乳粉,并应用主成分分析技术对大量的实验数据进行统计分析处理,研究了不同数据提取参数对分析结果的影响,通过T值检验筛选出3种罐标显示添加水解蛋白的婴幼儿配方乳粉的特征组分,提出了其中G号样品的16个特征组分的化学信息,并构建了相关的化学指纹图。     

Melamine detection by mid- and near-infrared (MIR/NIR) spectroscopy: a quick and sensitive method for dairy products analysis including liquid milk, infant formula, and milk powder

Melamine (2,4,6-triamino-1,3,5-triazine) is a nitrogen-rich chemical implicated in the pet and human food recalls and in the global food safety scares involving milk products. Due to the serious health concerns associated with melamine consumption and the extensive scope of affected products, rapid and sensitive methods to detect melamine's presence are essential. We propose the use of spectroscopy data-produced by near-infrared (near-IR/NIR) and mid-infrared (mid-IR/MIR) spectroscopies, in particular—for melamine detection in complex dairy matrixes. None of the up-to-date reported IR-based methods for melamine detection has unambiguously shown its wide applicability to different dairy products as well as limit of detection (LOD) below 1 ppm on independent sample set. It was found that infrared spectroscopy is an effective tool to detect melamine in dairy products, such as infant formula, milk powder, or liquid milk. ALOD below 1 ppm (0.76 ± 0.11 ppm) can be reached if a correct spectrum preprocessing (pretreatment) technique and a correct multivariate (MDA) algorithm—partial least squares regression (PLS), polynomial PLS (Poly-PLS), artificial neural network (ANN), support vector regression (SVR), or least squares support vector machine (LS-SVM)—are used for spectrum analysis. The relationship between MIR/NIR spectrum of milk products and melamine content is nonlinear. Thus, nonlinear regression methods are needed to correctly predict the triazine-derivative content of milk products. It can be concluded that mid- and near-infrared spectroscopy can be regarded as a quick, sensitive, robust, and low-cost method for liquid milk, infant formula, and milk powder analysis.     

Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition

We consider the numerical solution for the Helmholtz equation in R~2 with mixed boundary conditions.The solvability of this mixed boundary value problem is estab- lished by the boundary integral equation method.Based on the Green formula,we express the solution in terms of the boundary data.The key to the numerical real- ization of this method is the computation of weakly singular integrals.Numerical performances show the validity and feasibility of our method.The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.