利用Matlab语言对物理实验数据进行处理

本文讨论利用Matlab语言通过最小二乘法对物理实验数据进行处理的优点。     

Influence of UV pretreatment on the abies wood catalytic delignification in the medium “acetic acid–hydrogen peroxide–TiO2”

Some regularities of abies-wood oxidative delignification by acetic acid–hydrogen peroxide mixture under the action of suspended TiO₂ catalyst and UV pretreatment of wood pulp were studied. The combined action of TiO₂ catalyst and of UV-pretreatment of abies-wood allow to produce at optimal conditions of the delignification process the chemically pure cellulose containing no residual lignin. The major characteristics of cellulose product obtained from abies-wood correspond to the characteristics of microcrystalline cellulose.     

A redundant Klee–Minty construction with all the redundant constraints touching the feasible region

We have previously shown, by redundant Klee–Minty constructions, that the central path may arbitrarily closely visit every vertex of the Klee–Minty cube. In those constructions, the redundant constraints are far away from the feasible region. In this paper, we provide a construction in which all redundant constraints touch the feasible region.     

Polynomial function and derivative approximation of Sinc data

Sinc methods consist of a family of one dimensional approximation procedures for approximating nearly every operation of calculus. These approximation procedures are obtainable via operations on Sinc interpolation formulas. Nearly all of these approximations–except that of differentiation–yield exceptional accuracy. The exception: when differentiating a Sinc interpolation formula that gives an approximation over an interval with a finite end-point. In such cases, we obtain poor accuracy in the neighborhood of the finite end-point. In this paper we derive novel polynomial-like procedures for differentiating a function that is known at Sinc points, to obtain an approximation of the derivative of the function that is uniformly accurate on the whole interval, finite or infinite, in the case when the function itself has a derivative on the closed interval.     

Synthesis and Crystal Structure of Mercury(II) Metal Crown Ether with N‐Heterocyclic Carbene Linkage

The mercury(II) metal crown ether ( 2a ) was obtained in high yield by reaction of the carbene precursor 1,2‐bis[N‐(1‐naphthylmethylene)imidazoliumethoxy]benzene dihexafluorophosphate ( 1 ) and Hg(OAc)₂. Addition of NaI to the acetone solution of 2a resulted in precipitation of pale yellow solid 2b . The structures of 2a and 2b were determined by single‐crystal X‐ray diffractometry. Both molecules display a helical conformation with a torsional cycle. The mercury atom in complex 2a is tricoordinated by two intramolecular carbene carbon atoms and an acetate oxygen atom. The mercury atom in complex 2b is tetracoordinated by two intramolecular carbene carbon atoms and two cis‐iodine atoms.     

Positive solutions for Schrödinger–Poisson equations with a critical exponent

In this paper we establish the existence of a positive solution of the Schrödinger–Poisson equations with a critical Sobolev exponent. The methods used here are based on the concentration–compactness principle of P. L. Lions and methods of Brezis and Nirenberg.     

Spectral Analysis for HSS Preconditioners

In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.     

Increasing efficiency of inverse iteration

Inverse iteration is simple but not very efficient method for computing few eigenvalues with minimal absolute values and corresponding eigenvectors of a symmetric matrix. The idea is to increase its efficiency by technique similar to multigrid methods used for solving linear systems. This approach is not new, but until now multigrid was mostly used for solving linear system which appear in Rayleigh quotient iteration, inverse iteration and related iterative methods. Instead of choosing appropriate coordinates (grids), our algorithm performs inverse iteration on a sequence of subspaces with decreasing dimensions (multispace). Block Lanczos method is used for the selection of a smaller subspace. This will produce a banded matrix, which makes inverse iteration even faster in the smaller dimensions.      

On the interplay between interior point approximation and parametric sensitivities in optimal control

Infinite-dimensional parameter-dependent optimization problems of the form ‘minJ(u;p) subject to g(u)?0’ are studied, where u is sought in an L_∞ function space, J is a quadratic objective functional, and g represents pointwise linear constraints. This setting covers in particular control constrained optimal control problems. Sensitivities with respect to the parameter p of both, optimal solutions of the original problem, and of its approximation by the classical primal-dual interior point approach are considered. The convergence of the latter to the former is shown as the homotopy parameter μ goes to zero, and error bounds in various Lq norms are derived. Several numerical examples illustrate the results.