修正PRP共轭梯度方法求解无约束最优化问题

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。     

A law of the iterated logarithm for processes with independent increments

ＡＬＡＷＯＦＴＨＥＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＦＯＲＰＲＯＣＥＳＳＥＳＷＩＴＨＩＮＤＥＰＥＮＤＥＮＴＩＮＣＲＥＭＥＮＴＳＷＡＮＧＪＩＡＧＡＮＧ（汪嘉冈）（ＥａｓｔＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅ＆Ｔｅｃｈｎｏｌｏｇｙ,Ｓｈａｎｇ...     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.     

The Employ of Multiple Voltammetric Pulses for the Study of the Adsorption of Bipyridilium Pesticides in River Sediment

The multiple square‐wave voltammetry (MSWV) allied to gold microelectrode (Au‐ME) was used to establish an electroanalytical procedure for the determination of the paraquat and diquat pesticides in river sediment samples. For both pesticides, two reduction peaks, at around ?0.70 V (peak 1) and around ?1.00 V vs. Ag/AgCl 3.00 mol L^?1 (peak 2), with profile of the totally reversible redox process, were observed. The experimental and voltammetric conditions showed that the best conditions to reduce paraquat and diquat were a pH of 6.0, a frequency of 250 s^?1, a scan increment 2 mV, a square‐wave amplitude of 50 mV and pulse number of 8 pulses of potential in each step of staircase of potential. Under such conditions, the detection limit of 0.044 μg L^?1 (0.044 ppb) and 0.360 μg L^?1 (0.360 ppb ) for peak 1 and peak 2 of paraquat and 0.159 μg L^?1 (0.159 ppb) and 0.533 μg L^?1 (0.533 ppb) for peak 1 and peak 2 of diquat, respectively, were obtained. These results are an order of magnitude of about two less than those obtained and published in the literature. Also, the electroanalytical procedure proposed was applied for the determination of adsorption isotherms of pesticides on river sediments samples collected from Mogi‐Guaçu River in Sao Paulo State, Brazil. The experimental data were fitted using the Langmuir and Freundlich isotherms models; and the results indicated low intensities of adsorption process of the pesticides in the samples employed with distribution coefficients (K_d) lower 5.0, and paraquat showed slightly higher affinity than diquat in the sediments. The increase in organic matter and organic carbon leads to an increase in the K_d values, and consequently an increase in the organic matter constant (K_OM) organic carbon constant (K_OC) values. All results demonstrated that isotherms “L” type in the Giles classification were obtained, indicating that sediments have a medium affinity for the pesticides, and no strong competition from the solvent used (in this case Na₂SO₄) for adsorption sites occurs.     

Isolated square planar metal complexes of carbon

Based on the group theory analysis and quantum chemical calculations within the framework of SW X _α method (in relativistic approximation for core electrons and non-relativistic for valence ones), the existence possibility of square planar complexes [M₄C] and [M₄C]^2? (M = Al, Ga, In, Tl, Sc, and Y) in gas phase has been shown. The extraction of Kt₂[M₄C] square planar complexes of carbon in the crystal state is possible too. A high stability of these complexes, in comparison with usual tetrahedral, is achieved due to the formation of five-and four-center bonds (bonds M-M and M-C).     

导数阴极溶出方波伏安法测定卡那霉素注射液含量

研究了汞 卡那霉素络合物的电化学行为 ,并建立了导数阴极溶出方波伏安法测定卡那霉素注射液含量的方法。在 pH 4 .7的HOAc NaOAc缓冲溶液中 ,在约 0 .12 6V (vs.SCE)处出现一个汞 卡那霉素络合物的还原峰 ,卡那霉素的浓度在 0 .0 2～ 1.5mg·ml- 1之间与导数方波伏安图的峰高存在良好的线性关系 ,回归方程ip(10 - 4A) =3.6C(mg·ml- 1) + 0 .4 6 ,相关系数为 0 .992 0。方法简便、灵敏、准确 ,可用于卡那霉素注射液含量测定     

傅里叶变换近红外光谱法测定大麦中蛋白质、淀粉和赖氨酸含量

采用傅里叶变换近红外光谱法测定大麦中蛋白质、淀粉、赖氨酸的含量，并用光谱影响值法(leverage)对异常值进行判断和处理。蛋白质、淀粉和赖氨酸含量近红外光谱分析模型的测定系数R。分别为0．985、0．973和0．978；检验集的化学值与模型预测值的相关系数r分别为0．9853、0．9644和0．9172，分析模型的预测相对标准偏差RSD分别为4．0％、2．4％和5．4％，该结果可替代经典分析方法，满足农产品快速分析的需要。     

High-performance liquid chromatography with continuous gradient elution in screening for unknown metabolites of butoprozine directly in dog bile

This paper describes the screening for metabolites of butoprozine, a new anti-anginal drug, in dog bile by means of reverse-phase HPLC. Although it does involve a simple clean-up step to remove a substantial amount of endogenous bile compounds, this screening method nevertheless avoids extraction of metabolites and thus allows all metabolites to be introduced into the chromatographic system. A single run of 100 minutes from 100% water to 100% methanol in a linear gradient effects adequate separation of the great majority of metabolites without interference from remaining endogenous compounds. Two methods of differentiating between metabolite peaks and endogenous peaks have been worked out. The first one makes use of ¹⁴C-labeled butoprozine by measuring the amount of radioactivity in the column effluent while simultaneously recording the UV absorbance. The second method compares continuous gradient chromatograms of bile recorded before and after butoprozine administration under very similar conditions. The latter method can be applied to both radioactive and non-radioactive materials.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.