Prepared Low Stress Cubic Boron Nitride Film by Physical Vapor Deposition

We present low stress cubic boron nitride (cBN) films with a transition layer deposited on the metal alloy substrates by tuned substrate radio-frequency magnetron sputtering. The films were characterized by Fourier transform infrared spectroscopy and transmission electron microscopy (TEM). The IR peak position of cubic boron nitride at 1006.3 cm⁻¹, which is close to the stressless state, indicates that the film has very low internal stress. The TEM image shows that pure CBN phase exists on the surface of the film. Several phases of boron nitride were found at the medium implantation dose. It is believed that the transition from the low ordered phases to cBN phase occurred during implantation.     

立方介孔相含钕氧化硅的合成与表征

以十六烷基三甲基溴化铵为结构导向剂，通过水热法合成了具有立方结构的含钕Nd-MCM-48介孔分子筛材料。XRD和TEM测试表明当n_Nd/n_Si<0.05时可以获得典型的长程有序介孔立方结构相，随n_Nd/n_Si比的增加，晶胞参数的增大和红外吸收光谱(FT-IR)的变化为Nd进入介孔分子筛骨架中提供了有力证据。N₂吸附-脱附实验给出了其BET表面积为1 195 m²·g^-1，BJH平均孔径为3.6 nm。紫外-可见漫反射光谱(UV-Vis)证明钕氧形成一种八面体结构。X射线光电子能谱(XPS)进一步证明钕主要以三价形式存在于立方介孔分子筛骨架中。     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Parameterized approximations for the two-sided assortment optimization

We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.     

导数振荡与应变能极小的平面分段三次参数Hermite插值

由于分段三次参数Hermite插值的切矢往往被作为变量,故可对其进行优化以使得构造的插值曲线满足特定的要求.为了构造兼具保形性与光顺性的平面分段三次参数Hermite插值曲线,给出了一种通过同时极小化导数振荡和应变能来确定切矢的方法.首先以导数振荡函数和应变能函数为双目标建立了切矢满足的方程系统;然后证明了方程系统存在唯一解,并给出了解的具体表达式;最后给出了误差分析,并通过数值算例表明方法的有效性.结果表明,相对于导数振荡极小化方法和应变能极小化方法,所提出的导数振荡和应变能极小化方法同时兼顾了平面分段三次参数Hermite插值曲线的保形性和光顺性.     

LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

An analysis of cubic approximation schemes for conic sections

In this paper a piece of a conic section is approximated by a cubic or piecewise cubic polynomial. The main tool is to define the two inner control points of the cubic as an affine combination, defined by [0, 1], of two control points of the conic. If is taken to depend on the weightw of the latter, a function (w) results which is used to distinguish between different algorithms and to analyze their properties. One of the approximations is a piecewise cubic havingG ⁴ continuity at the break points.     

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

A numerical basis for the accurate representation of the continuum spectrum of atomic Hamiltonians

We present a method for the accurate calculation of the complete spectrum of the Schrödinger equation in terms of B-splines polynomial basis. The method is capable to represent numerically the bound and continuum spectrum of complex atomic systems. The theoretical method is discussed, and an application to hydrogenic Hamiltonian is given.AMS subject classification: 65705, 34L40     

选相原位法合成立方氮化硼的关键影响因素

利用选相原位法在水溶液中成功制备出了立方氮化硼晶体，对反应条件进行了优化。结果表明，利用选相原位法合成立方氮化硼的最佳实验条件是：反应压力为10.0 MPa，在氯离子加入下利用混合氮源进行反应。在该条件下得到了纯相的立方氮化硼晶体。