On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

On the global optimization properties of finite-difference local descent algorithms

The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special -convex structure. It is assumed that the objective function can be closely approximated by some smooth convex function. Stability properties of the perturbed gradient descent and coordinate descent methods are investigated. Basing on this results some global optimization properties of finite-difference local descent algorithms, in particular, coordinate descent method, are discovered. These properties are not inherent in methods using exact gradients.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

SYNTHESIS OF SODALITE BY DRY POWDER METHOD

用新颖的干粉方法合成系列沸石的研究已从五元环沸石延伸到具有四元环和六元环的方钠石。本研究运用干粉方法在Ｎａ２Ｏ－ＳｉＯ２－Ａｌ２Ｏ３混合物中分别以乙醇胺和乙二胺－氟化物为模板，合成出了方钠石。有机模板剂以吸附态模板方式进入体系。用ＸＲＤ数据、扫描电镜图及红外光谱测试结果对实验产品做了表征。结果表明，干粉体系制备的方钠石的晶胞参数小于水热体系和非水体系合成的方钠石的相应值。而以乙醇胺为模板制备的方钠石与以乙二胺－氟化物为模板的样品比较，后者具有较快的晶化速度、较小的晶胞体积和晶粒     

Thermodynamics of electrolyte solutions. The system HCl + CaCl2 + H2O at 298.15°K

Activity coefficients of hydrochloric acid have been determined from electromotive-force measurements of cells containing mixtures of hydrochloric acid and calcium chloride at constant total ionic strengthsI=0.1, 0.5, 1.0, 2.0, and 3.0 mole-kg^–1 at 298.15°K. Interpretations based on Scatchard's and Pitzer's equations indicate that Pitzer's equations probably provide a more convenient guide to the thermodynamic properties of the mixed-electrolyte solutions. Activity coefficients for calcium chloride were derived from these equations.     

Determination of Y,Sm, Eu,Gd, Dy,Ho, Er in high purity terbium oxide by ICP-AES

Inductively coupled plasma atomic emission spectrometry (ICP-AES) was employed to determine Y, Sm, Eu, Gd, Dy, Ho and Er in high purity terbium oxide. Terbium oxide was dissolved in 0.5 mol/l HNO₃ and nebulized into the plasma generated by a 56 MHz RF generator at 1.5 kW output power. Using a Jobin-Yvon 1-m Czenry-Turner high resolution, high dispersion scanning monochromator, lines mutually interference-free as well as free of interference from the matrix Tb were chosen for the seven analytes. A set of standards containing the analytes in the concentration range 0.01–1.0 gmg/ml with 1 mg/ml Tb was used for calibration. It was necessary to apply background correction to the gross analyte line intensities in order to obtain linear calibration plots for the analytes.     

Determination of trace elements in human serum by inductively coupled plasma atomic emission spectrometry with flow injection

An analytical method for the simultaneous determination of some trace elements (Au, Fe, Mg, Li, Sr, Zn) in human serum by inductively coupled plasma atomic emission spectrometry (ICP-AES) with flow injection is described. Physical interference caused by the change of sample viscosity is discussed. When 100 μl of serum was injected, the relevant recoveries of > 99% for Li, > 98% for Cu and Mg, > 95% for Fe were obtained for an NIST SRM with R.S.D. > 1.3% using optimized flow injection parameters. The prepared lyophilized control serum for routine analysis in clinical laboratories was analyzed and verified for the validity of the technique employed in this experiment using NIST SRM 909 as a primary reference material.     

Evolution of the structural stability of large Cu,Ni, Pd,and Ag clusters with size: An analysis within the embedded atom method

A study of the structural stability of clusters made up of a single component has been carried out within the Embedded Atom Method. Perfect icosahedral and cuboctahedral Cu, Ni, Pd, and Ag clusters with up to 5083 atoms have been compared. The icosahedron is found to be the stable structure for small clusters, and a change of structure from icosahedral to cuboctahedral is found as the cluster size increases. A contraction of the interatomic distances results when the cluster size decreases.     

碱金属和重金属叠氮化物的感度和导电性研究

分别用EHCO和DV－X_α方法，计算研究了α－NaN_3、β-NaN_3和AgN_3的能带结构和原子簇电子结构. AgN_3与NaN_3相比：带隙(△Eg)较小、带宽(BW)较大，因而电导率较大. 比较前沿晶体轨道(CO)和前沿分子轨道(MO)的能级、组成及电子在其间的跃迁；预示AgN_3比NaN_3更敏感、更易分解和起爆．还从电子微观层次揭示了金属叠氮化物的导电性和爆炸性之间的联系．