Partial Minimization for Vector Variational Problems

The basic idea of performing a partial minimization with respect to some components in a vector variational problem, while keeping the other fixed, is explored and implemented in various examples. In one-dimensional problems, it leads sometimes to nonstandard variational problems. We also include a situation for a genuine vector variational problem coming from the reformulation of some optimal design problems in conductivity.     

合肥光源横向束流反馈系统中矢量运算单元和光纤陷波滤波器的研制

 合肥光源横向束流反馈系统已经建成,着重介绍了系统中矢量运算单元和光纤陷波滤波器的研制。矢量运算单元中使用混频器控制信号的衰减,调节控制电压的大小以控制反馈信号的相位;光纤陷波滤波器创新性地提出用光纤延时制作陷波滤波器,很好地滤除了信号中的回旋频率分量,节省了反馈功率。     

基于矢量波像差理论的计算机辅助装调技术研究

在三阶矢量波像差理论的基础上,建立了系统内失调量与系统波像差Zernike系数的关系式,并以共轴三反射光学系统为数学模型进行了仿真分析.结果表明,基于矢量波像差理论的装调技术可行,并可用于大型光学系统的装调.利用该理论对一共轴非球面三反系统进行装调,最终使系统波像差RMS<0.080λ.     

Optimization of heterogeneous Catalyst-assisted fatty acid methyl esters biodiesel production from Soybean oil with different Machine learning methods

There is a growing attention to the bio and renewable energies due to fast depletion of fossil fuels as well as the global warming problem. Here, we developed a modeling and simulation method by means of artificial intelligence (AI) for prediction of the bioenergy production from vegetable bean oil. AI methods are well known for prediction of complex and nonlinear process. Three distinct Adaptive Boosted models including Huber regression, LASSO, and Support Vector Regression (SVR) as well as artificial neural network (ANN) were applied in this study to predict actual yield of Fatty acid methyl esters (FAME) production. All boosted utilizing the Adaptive boosting algorithm. The important influencing parameters on the biodiesel production such as the catalyst loading (CAO/Ag, wt%) and methanol to oil (Soybean oil) molar ratio were selected as the input variables of models while the yield of FAME production was selected as output. Model hyper-parameters were tuned to maintain generality while improving prediction accuracy. The models were evaluated using three distinct metrics Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R². Error rates of 8.16780E-01, 4.43895E-01, 2.06692E + 00, and 3.92713 E-01 were obtained with the MAE metric for boosted Huber, SVR, LASSO and ANN models. On the other hand, the RMSE error of these models were about 1.092E-02, 1.015E-02, 2.669E-02, and 1.01174E-02, respectively. Finally, the R-square score were calculated for boosted Huber, boosted SVR, and boosted LASSO as 0.976, 0.990, 0.872, and 0.99702, respectively. Therefore, it can be concluded that although the boosted SVR and ANN models were better models for prediction of process efficiency in terms of error, but all algorithms had high accuracy. The optimum yield of 83.77% and 81.60% for biodiesel production were observed at optimum operating values from boosted SVR and ANN models, respectively.     

Holomorphic rank of hypersurfaces with an isolated singularity

LetV be a germ at 0 C ²,n3, of hypersurface with an isolated singularity at 0. In this paper we prove that the maximal number of germs of vector fields inV ^*=V–0, which are linearly independent in all points ofV ^* is two. In the casesn=3,4 and of quasi homogeneous hypersurfaces (n3), we prove that this number is one.Dedicated to the memory of R. MañéThis research was partially supported by Pronex.     

A Banach lattice approach to convergent integrably bounded set-valued martingales and their positive parts

Denote by cf(X) the set of all nonempty convex closed subsets of a separable Banach space X. Let (Ω,Σ,μ) be a complete probability space and denote by (L¹[Σ,cf(X)],Δ) the complete metric space of (equivalence classes of a.e. equal) integrably bounded cf(X)-valued functions. For any preassigned filtration (Σi), we describe the space of Δ-convergent integrably bounded cf(X)-valued martingales in terms of the Δ-closure of in L¹[Σ,cf(X)]. In particular, we provide a formula to calculate the join of two such martingales and the positive part of such a martingale. Our object is achieved by considering the more general setting of a near vector lattice (S,d), endowed with a Riesz metric d. By means of Rådström's embedding theorem for such spaces, a link is established between the space of convergent martingales in S and the space of convergent martingales in the Rådström completion R(S) of S. This link provides information about the former space of martingales, via known properties of measure-free martingales in Riesz normed vector lattices, applicable to R(S). We also apply our general results to the spaces of Δ-convergent ck(X)-valued martingales, where ck(X) denotes the set of all nonempty convex compact subsets of X.     

振动激发对O+DCl→OD+Cl反应动力学性质的影响

采用准经典轨线方法讨论了反应物分子的振动激发对O+DCl→OD+Cl反应动力学性质的影响.计算结果表明,反应物分子的振动激发对(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt)和(2π/σ)(dσ22+/dωt)3个极化微分反应截面和产物分子转动角动量取向程度的影响比较显著.变化规律反映出反应物分子的高振动激发使产物分子倾向于在平行于散射面的平面内转动.