The automation of routine calculations and graphing for alkaline filter elution analysis on a computer-controlled liquid scintillation analyzer

The data calculations and graphing functions for the widely used alkaline filter elution technique have been completely automated. This saves considerable time and increases both efficiency and accuracy by eliminating human error. The automation was accomplished utilizing Lotus 1-2-3 and Lotus Graphwriter II on a Packard Tri-Carb 1900CA liquid scintillation analyzer containing a built-in pico-XTE computer. A batch file is used to control the overall execution of the process. It copies the data stored by the 1900CA into the Lotus subdirectory and invokes Lotus 1-2-3. A Lotus macro automatically imports the data file, performs the calculations, and prints the results. Graphwriter II is then invoked by the batch file and the charts are composed and graphed. Finally, the instrument operating software for the 1900CA is reentered and sample analysis can be resumed for any unanalyzed samples.     

基于连分式逼近的精度测试方法

针对现有精度测试方法适应性低、收敛速度慢的问题,提出了一种基于连分式逼近的初等函数精度测试方法。通过对最后一位表示的单位(ULP)的误差的分析以及对几种计算函数真值方法的对比,给出了精度测试方法的主要算法实现,并从时间复杂度及收敛阶两个方面进行了理论分析及实验验证。结果表明,该方法在精度测试方面更有效,复杂度更低,收敛速度更快。     

Computing derivatives in interval type-2 fuzzy logic systems

This paper makes type-2 fuzzy logic systems much more accessible to fuzzy logic system designers, because it provides mathematical formulas and computational flowcharts for computing the derivatives that are needed to implement steepest-descent parameter tuning algorithms for such systems. It explains why computing such derivatives is much more challenging than it is for a type-1 fuzzy logic system. It provides derivative calculations that are applicable to any kind of type-2 membership functions, since the calculations are performed without prespecifying the nature of those membership functions. Some calculations are then illustrated for specific type-2 membership functions.     

Receptor-based QSAR studies of non-peptide human oxytocin receptor antagonists

In the present study, QSAR calculations were performed on the receptor-based alignment of 58 non-peptide human oxytocin receptor antagonists. With the aid of different scoring functions (AutoDock 3.05 built-in and X-Score 1.2) the evolved receptor-ligand complexes were characterized. By means of various datasets it was confirmed that the scoring functions were not capable to predict the biological activity correctly in compounds containing a rigid derivative in the variable region. To improve the pKi prediction 3D-QSAR calculation was performed. The regions related to the biological activity were determined by using cross-validated r2(q2)-guided region selection (q2-GRS) method. The predictive power of the CoMFA model [r(pred)2=0.89, q2(LMO, five groups)=0.695+/-0.034] allowed prediction of the biological activities of newly synthesized compounds and confirmed the receptor-based alignment.     

一种用于导航芯片设计的高精度运算处理器

设计了一种专用于卫星导航芯片设计的高精度运算处理器,可完成卫星导航定位计算涉及的所有运算。该处理器用5个字节(40 bit)定义自己的数据格式,并针对这种数据格式实现了加、减、乘、除和阶乘等基础运算。利用这些基础运算和适当的数据调度实现了导航定位计算所涉及的各种函数运算,精度达到了10-7。通过FPGA验证,该处理器具有运算速度快和计算准确的特点,同时具有很强的扩展能力。     

GTOBAS: fitting continuum functions with Gaussian-type orbitals

GTOBAS is a program for fitting Gaussian-type orbitals (GTOs) to Bessel and Coulomb functions over a finite range. The exponents of the GTOs are optimized using the method of Nestmann and Peyerimhoff [J. Phys. B 23 (1990) L773]. The appended module NUMCBAS provides the numerical Bessel and Coulomb functions required as input for the program. The use of GTO continuum basis sets is particularly important in electron-molecule scattering calculations when polyatomic targets are involved. Sample results for such calculations are also discussed.     

Calculations of the equation of state by the Liberman mode

The algorithm of the calculation of self-consistent atomic potential accounting for resonant states of electrons is developed by the Liberman model. The resonant states are related to quasi-stationary states of electrons and appear at the squeezing of bound levels of energy into continuum accompanied by an increase in the density of a substance. Such states play an important role in calculations of thermodynamic functions of substance, since they facilitate the smooth dependences of pressure and internal energy on density. Appropriate software (RESEOS) was developed and calculations of the equations of state of aluminum and uranium were performed in a wide range of temperatures and densities. The resulted shock adiabats were compared with the experimental data.     

Symmetry-eigenfunctions for many-electron atoms and molecules: A unified and friendly approach for frontier research and student training

Atomic and molecular many-electron symmetry-eigenfunctions are obtained by means of a FORTRAN program based on projection operators and ordered Slater determinants. When degeneracies exist, Schmidt orthonormalization of a conveniently ordered manifold allows for the construction of a hierarchy of interacting spaces, unattainable through Racah algebra or group-theoretical methods, but necessary for compact many-electron theories and calculations beyond Hartree-Fock.Through a strict modular organization, this program offers a variety of concurrent evolution pathways covering all kinds of symmetry-eigenfunctions. Also, the results it generates can be fed into other modules for the general and efficient calculation of many-electron wave functions, or for symbolic evaluation of selected many-electron matrix elements of symmetry-operators such as the Hamiltonian.The program may be run interactively or in batch form to produce lists of configuration state functions for actual electronic structure calculations. In tutorial and interactive modes, help, status and overview commands can be invoked as an aid to gain working knowledge on many-electron symmetry-eigenfunctions. Standard FORTRAN 77 and full validation of array dimensions expressed in terms of parameters ensure widespread portability.     

EXCEL在矩阵相关计算中的应用

Excd不但具有强大的数据分析和处理功能，而且具有丰富的函数，在数学计算中发挥着不客忽视的作用。本文主要介绍Excel在进行计算行列式值、矩阵的转置、矩阵的逆、矩阵的秩、两矩阵的乘积、矩阵的特征向量和特征值以及矩阵在进行解线性方程组时的应用。     

Wavelength selection for synthetic image generation

The efficient synthesis of color in computer graphics is dependent on modelling the correct number and spacing of wavelengths across the visible spectrum. It has recently been shown that the opponent representation of the fundamental spectral sensitivity functions is optimal from the point of view of statistical communication theory. This result is used in this paper to guide the selection of wavelengths for synthetic image generation. Gaussian quadrature with the opponent fundamentals as weighting functions is used to choose the wavelengths. This approach is shown to be superior to using Gaussian quadrature with the fundamental spectral sensitivity functions or the CIE XYZ matching functions. The technique is evaluated by using color difference calculations and by comparisons between a real scene and a computer generated picture of that scene.     

Absolute and relative energies from polarized atomic orbital self-consistent field calculations and a second order correction. Convergence with size and composition of the secondary basis

Polarized atomic orbitals (PAO's) are molecule-adapted minimal basis functions that are variationally obtained as an atom-blocked transformation from a conventional extended basis set, as a Hartree-Fock calculation is performed in the PAO basis. This approximation yields a higher energy than a HF calculation performed in the extended basis, although the two results converge to the same limit as the extended basis approaches completeness on each atom. To test the rate of convergence, PAO-HF calculations were performed using cc-pVXZ and aug-cc-pVXZ basis sets for the water monomer and dimer, and six substituted ethylenes. The results show that the quality of PAO calculations converges smoothly with X. The use of augmented functions is recommended. To correct a PAO-HF calculation for residual deficiencies, a noniterative second order correction is introduced. This correction corresponds to an energy-weighted steepest descent step, and substantially improves the quality of PAO energies.     

如何利用Excel97进行规划求解

Ｅｘｃｅｌ９７通过窗口操作,提供了超强的数学运算、统计分析等程序。本文通过例子介绍了其中的线性规则程序的运用。用Ｅｘｃｅｌ工具栏的下拉菜单中的“规划求解”即可求解线性规划问题,并进行灵敏度分析。     

Individually selecting multi-reference CI and its application to biradicalic cyclizations

In the present review a new algorithm to perform individually selecting MR-CI calculations is discussed. The new algorithm exploits the advantages arising from the subdivision of the molecular orbitals (MOs) into an internal and an external part and avoids the recalculation of representation matrices by the use of a specially designed cache. With the new algorithms we are able to perform calculations including more than 10 million selected configurations state functions (CSFs) as a matter of routine. As an example for the possibilities of the new approach the regioselectivity of thermal biradical cyclizations (C2-C7 vs. C2-C6 cyclization) is investigated in the second part of the present work. After studying the accuracy of various quantum chemical methods (MR-CI, density functional theory, and coupled cluster approaches) using (Z)-1,2,4 Heptatriene-6-yne as a model system the influence of substituents (R = H, Ph, t-Bu, NH2) on the regioselectivity is investigated. Our results rationalize the switch between the two biradical cyclizations on the basis of mainly steric (t-Bu) or electronic (Ph) substituent effects. Moreover, the results for R = NH2 predict that the activation energy of the C2-C6 cyclization can be lowered even more. However, a change in the reaction mechanism is found.     

Phase equilibria in ternary Cd-Sb-Zn system

Both the author's and literature data on phase equilibria in ternary Cd-Sb-Zn alloys were carefully analyzed and, selected and thermodynamic functions of ternary phases were optimised by TER-GSS. Phase equilibria calculations were performed by ThermoCalc resulting in invariant reaction's parameters, liquidus surface and a number of vertical and isothermal sections of the system under investigation. Metastable tendency was explained by using of Cd-Sb system as an example.     

MathPartner computer algebra

In this paper, we describe general characteristics of the MathPartner computer algebra system (CAS) and Mathpar programming language thereof. MathPartner can be used for scientific and engineering calculations, as well as in high schools and universities. It allows one to carry out both simple calculations (acting as a scientific calculator) and complex calculations with large-scale mathematical objects. Mathpar is a procedural language; it supports a large number of elementary and special functions, as well as matrix and polynomial operators. This service allows one to build function images and animate them. MathPartner also makes it possible to solve some symbolic computation problems on supercomputers with distributed memory. We highlight main differences of MathPartner from other CASs and describe the Mathpar language along with the user service provided.     

Conversion of ab-initio force fields and structures to molecular mechanics energy functions

The rapid development of computers in recent years has brought increasingly complex compounds into the range of high level ab-initio calculations. Such calculations produce valuable results which in many cases would be difficult or even impossible to obtain, with comparable accuracy, in any other way (Fogarasi & Pulay, Annu. Rev. Phys. Chem. 35, 191, 1984). Thus, it is highly desirable to be able to utilize these results in the construction of potential energy functions used in molecular mechanics (MM), molecular dynamics and Monte-Carlo calculations. For instance, the significance of quadratic cross terms in MM energy functions is still insufficiently explored (Lii & Allinger, J. Am. Chem. Soc. 111, 8566, 1989). In order to make possible the complete utilization of ab-initio results in MM calculations, we have developed a method by which scaled ab-initio (or empirical) force fields and structures can be directly converted to MM potential energy parameters, without sacrificing any of the original accuracy with regard to vibrational frequencies or structure. Here we briefly outline the conversion procedure, a more complete analysis being published separately.     

CIJET: A program for computation of jet cross sections induced by quark contact interactions at hadron colliders

We describe CIJET1.0, a Fortran program aimed at calculating single-inclusive jet or dijet production cross sections induced by quark contact interactions from new physics at hadron colliders, up to next-to-leading order in QCD. It covers various contact interactions with different chiral and color structures. The code is designed in a way that could be used for fast calculations with arbitrary parton distribution functions based on interpolations of the QCD coupling constant and parton distribution functions.