FORTRAN Program Package Research Articles

AFMPB: An adaptive fast multipole Poisson–Boltzmann solver for calculating electrostatics in biomolecular systems

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson–Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of the fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. New version program summaryProgram title: AFMPBCatalogue identifier: AEGB_v1_1Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_1.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 2No. of lines in distributed program, including test data, etc.: 440784No. of bytes in distributed program, including test data, etc.: 8187139Distribution format: tar.gzProgramming language: FortranComputer: AnyOperating system: AnyRAM: Depends on the size of the discretized biomolecular systemClassification: 3External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS (http://www.scripps.edu/sanner/html/msmshome.html) for pre-processing, and VMD (http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad (http://www-users.cs.umn.edu/saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite (http://www.fastmultipole.org/).Catalogue identifier of previous version: AEGB_v1_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1150Does the new version supersede the previous version?: YesNature of problem: Numerical solution of the linearized Poisson–Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions.Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson–Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix–vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation.Reasons for new version: Some bugs are fixed in the new version.Summary of revisions:•The type definition of ippt1 in line 88 of FBEM/bempb.f and line 32 of FBEM/closecoef.f is changed from real *8 to integer*4, and a similar change is made for ippt in line 105 of FBEM/solvpb.f and in line 32 of FBEM/closecoef.f.•In FBEM/elmgeom.f, line 239 “ELSEIF (meshfmt.EQ.1.OR. meshfmt.EQ. 4.OR. meshfmt.EQ.5) THEN” is changed to “ELSEIF (meshfmt.EQ.1.OR. meshfmt.EQ. 4) THEN”, line 478 “KJ=IDFCL(K)+J-1” is changed to “i=IDFCL(K)+J-1”, line 479 “KJ=NE(KJ)” is changed to “KJ=NE(i)”, line 480 “KJ1=NE(KJ+1)” is changed to “KJ1=NE(i+1)”, and line 647 “ STOP” is changed to “c STOP”.•Five subroutines in FMM part (syukadap.f, syukdn.f, slapadap.f, slapdn.f, and treeadap.f) are substituted with the new ones in the new version.Restrictions: Only three or six significant digits options are provided in this version.Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines.Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/lubz/afmpb.html for updates and changes.Running time: The running time varies with the number of discretized elements (N) in the system and their distributions. In most cases, it scales linearly as a function of N.

SFOLD — A program package for calculating two-body sfermion decays at full one-loop level in the MSSM

SFOLD (Sfermion Full One-Loop Decays) is a Fortran program package for calculating all sfermion two-body decay widths and the corresponding branching ratios at full one-loop level within the MSSM. The package adopts the SUSY Parameter Analysis convention and supports the SUSY Les Houches Accord input and output format. With the SFOLD package we found non-negligible electroweak corrections in bosonic decays of b̃,t̃ and τ̃. Program summaryProgram title: SFOLDCatalogue identifier: AEMZ_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 263346No. of bytes in distributed program, including test data, etc.: 1481697Distribution format: tar.gzProgramming language: Fortran 77.Computer: Workstation, PC.Operating system: Linux.RAM: approx. 500 MbytesClassification: 11.1.External routines: LoopTools 2.6 (http://www.feynarts.de/looptools/), SLHALib 2.2 (http://www.feynarts.de/slha/)Nature of problem:If the MSSM is realized in nature, LHC will produce supersymmetric particles copiously. The best environment for a precise determination of the model parameters would be a high energy e+e− linear collider. Experimental accuracies are expected at the per-cent down to the per-mill level. These must be matched from the theoretical side. Therefore loop calculations are mandatory.Solution method:This program package calculates all sfermion two-body decay widths and the corresponding branching ratios at full one-loop level within the MSSM. The renormalization is done in the DR¯ scheme following the SUSY Parameter Analysis convention. The program supports the SUSY Les Houches Accord input and output format.Running time:The test provided just takes a few seconds to run.

MSTor: A program for calculating partition functions, free energies, enthalpies, entropies, and heat capacities of complex molecules including torsional anharmonicity

We present a Fortran program package, MSTor, which calculates partition functions and thermodynamic functions of complex molecules involving multiple torsional motions by the recently proposed MS-T method. This method interpolates between the local harmonic approximation in the low-temperature limit, and the limit of free internal rotation of all torsions at high temperature. The program can also carry out calculations in the multiple-structure local harmonic approximation. The program package also includes six utility codes that can be used as stand-alone programs to calculate reduced moment of inertia matrices by the method of Kilpatrick and Pitzer, to generate conformational structures, to calculate, either analytically or by Monte Carlo sampling, volumes for torsional subdomains defined by Voronoi tessellation of the conformational subspace, to generate template input files, and to calculate one-dimensional torsional partition functions using the torsional eigenvalue summation method. Program summaryProgram title: MSTorCatalogue identifier: AEMF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMF_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 77 434No. of bytes in distributed program, including test data, etc.: 3 264 737Distribution format: tar.gzProgramming language: Fortran 90, C, and PerlComputer: Itasca (HP Linux cluster, each node has two-socket, quad-core 2.8 GHz Intel Xeon X5560 “Nehalem EP” processors), Calhoun (SGI Altix XE 1300 cluster, each node containing two quad-core 2.66 GHz Intel Xeon “Clovertown”-class processors sharing 16 GB of main memory), Koronis (Altix UV 1000 server with 190 6-core Intel Xeon X7542 “Westmere” processors at 2.66 GHz), Elmo (Sun Fire X4600 Linux cluster with AMD Opteron cores), and Mac Pro (two 2.8 GHz Quad-core Intel Xeon processors)Operating system: Linux/Unix/Mac OSRAM: 2 MbytesClassification: 16.3, 16.12, 23Nature of problem: Calculation of the partition functions and thermodynamic functions (standard-state energy, enthalpy, entropy, and free energy as functions of temperatures) of complex molecules involving multiple torsional motions.Solution method: The multi-structural approximation with torsional anharmonicity (MS-T). The program also provides results for the multi-structural local harmonic approximation [1].Restrictions: There is no limit on the number of torsions that can be included in either the Voronoi calculation or the full MS-T calculation. In practice, the range of problems that can be addressed with the present method consists of all multi-torsional problems for which one can afford to calculate all the conformations and their frequencies.Unusual features: The method can be applied to transition states as well as stable molecules. The program package also includes the hull program for the calculation of Voronoi volumes and six utility codes that can be used as stand-alone programs to calculate reduced moment-of-inertia matrices by the method of Kilpatrick and Pitzer, to generate conformational structures, to calculate, either analytically or by Monte Carlo sampling, volumes for torsional subdomain defined by Voronoi tessellation of the conformational subspace, to generate template input files, and to calculate one-dimensional torsional partition functions using the torsional eigenvalue summation method.Additional comments: The program package includes a manual, installation script, and input and output files for a test suite.Running time: There are 24 test runs. The running time of the test runs on a single processor of the Itasca computer is less than 2 seconds.

HFOLD – A program package for calculating two-body MSSM Higgs decays at full one-loop level

HFOLD (Higgs Full One Loop Decays) is a Fortran program package for calculating all MSSM Higgs two-body decay widths and the corresponding branching ratios at full one-loop level. The package is done in the SUSY Parameter Analysis convention and supports the SUSY Les Houches Accord input and output format. Program summaryProgram title: HFOLDCatalogue identifier: AEJG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJG_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 340 621No. of bytes in distributed program, including test data, etc.: 1 760 051Distribution format: tar.gzProgramming language: Fortran 77Computer: Workstation, PCOperating system: LinuxRAM: 524 288 000 BytesClassification: 11.1External routines: LoopTools 2.2 (http://www.feynarts.de/looptools/), SLHALib 2.2 (http://www.feynarts.de/slha/). The LoopTools code is included in the distribution package.Nature of problem: A future high-energy e+e− linear collider will be the best environment for the precise measurements of masses, cross sections, branching ratios, etc. Experimental accuracies are expected at the per-cent down to the per-mile level. These must be matched from the theoretical side. Therefore higher order calculations are mandatory.Solution method: This program package calculates all MSSM Higgs two-body decay widths and the corresponding branching ratios at full one-loop level. The renormalization is done in the DR scheme following the SUSY Parameter Analysis convention. The program supports the SUSY Les Houches Accord input and output format.Running time: The example provided takes only a few seconds to run.

AFMPB: An adaptive fast multipole Poisson–Boltzmann solver for calculating electrostatics in biomolecular systems

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson–Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node–patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summary Program title: AFMPB: Adaptive fast multipole Poisson–Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson–Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node–patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson–Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix–vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

A Fortran program package is introduced for the rapid evaluation of the screened Coulomb interactions of N particles in three dimensions. The method utilizes an adaptive oct-tree structure, and is based on the new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related packages are also available at http://www.fastmultipole.org/. This paper is a brief review of the program and its performance. Program summaryProgram title: FMM-YukawaCatalogue identifier: AEEQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPL 2.0No. of lines in distributed program, including test data, etc.: 12 385No. of bytes in distributed program, including test data, etc.: 79 222Distribution format: tar.gzProgramming language: Fortran77 and Fortran90Computer: AnyOperating system: AnyRAM: Depends on the number of particles, their distribution, and the adaptive tree structureClassification: 4.8, 4.12Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation.Solution method: An adaptive oct-tree is generated, and a new version of fast multipole method is applied in which the “multipole-to-local” translation operator is diagonalized.Restrictions: Only three and six significant digits accuracy options are provided in this version.Unusual features: Most of the codes are written in Fortran77. Functions for memory allocation from Fortran90 and above are used in one subroutine.Additional comments: For supplementary information see http://www.fastmultipole.org/Running time: The running time varies depending on the number of particles (denoted by N) in the system and their distribution. The running time scales linearly as a function of N for nearly uniform particle distributions. For three digits accuracy, the solver breaks even with direct summation method at about N=750.

FDCSUSYDecay: An MSSM decay package

FDCSUSYDecay is a FORTRAN program package generated by FDC (Feynman Diagram Calculation) system fully automatically. It is dedicated to calculate at tree-level all the possible 2-body decays of SUSY and Higgs particles in the Minimal Supersymmetric extension of the Standard Model (MSSM). The format of its output files complies with SUSY Les Houches Accord and can be easily imported by other packages. Program summary Manuscript title:FDCSUSYDecay: An MSSM decay package Authors:Wei Qi, Jian-xiong Wang Program title:FDCSUSYDecay (Version 1.00) Catalogue identifier:ADYV_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYV_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:22 008 No. of bytes in distributed program, including test data, etc.:622 751 Distribution format:tar.gz Programming language:FORTRAN 77 Operating system:Linux Keywords:SUSY decay, MSSM, FDC PACS:02.70.-c, 12.60.Jv Classification:11.1, 11.6 External routines:CERNLIB 2003 (or up) Nature of problem: This package can calculate all the possible SUSY particle and Higgs 2-body decay width and branch ratio at tree-level in the MSSM model. Solution method: By running FDC, the Feynman rules for the MSSM model are generated, all the decay widths are calculated analytically and corresponding FORTRAN codes are generated for this package. Running time: Less than 1 second for both high-scale and low-scale modes on a Pentium IV 2.4 GHz machine (512 MB memory).

High-precision, variational, bound-state calculations in coulomb three-body systems

The present study contains high-precision variational results for a number of bound states in various Coulomb three-body systems. In particular, we discuss the bound-state properties for the 2(3)S state of the infinityHe atom, the bound S(L=0) and P(L=1) states in symmetric muonic molecular ions, and ground states in the 3He2+&mgr;(-)e(-) and 4He2+&mgr;(-)e(-) atoms. The accuracy achieved for the total energies in these systems is significantly higher than known from the previous works. These results have been obtained by using a package of FORTRAN programs and a pretranslator written by D. H. Bailey from NASA [D.H. Bailey, ACM Trans. Math. Softw. 21, 379 (1995)]. This multiprecision FORTRAN package can completely eliminate all problems related to numerical instabilities at large dimensions, which are crucial for high-precision, bound-state calculations in few-body systems. In fact, the multiprecision FORTRAN programs open another avenue in the study of bound states in few-body systems.

Parsimonious Estimation of Sex-Specific Map Distances by Stepwise Maximum Likelihood Regression

In human genetic maps, differences between female (xf) and male (xm) map distances may be characterized by the ratio,R = xf/xm, or the relative difference,Q= (xf−xm)/(xf+xm) = (R− 1)/(R+ 1). For a map of genetic markers spread along a chromosome,Q(d) may be viewed as a graph ofQversus the midpoints,d, of the map intervals. To estimate male and female map distances for each interval, a novel method is proposed to evaluate the most parsimonious trend ofQ(d) along the chromosome, whereQ(d) is expressed as a polynomial ind. Stepwise maximum likelihood polynomial regression ofQis described. The procedure has been implemented in a FORTRAN program package, TREND, and is applied to data on chromosome 18.

A simulation study comparing GT vs. job shop manufacturing systems

Two discrete simulation models were developed, one representing a typical job shop (JS) manufacturing system (process layout) and the other representing group technology (GT) manufacturing system (cellular layout). Hypothetical data generated by FORTRAN program and MICRO-CRAFT layout package were used to validate the two models. Simulations were performed using SLAM II. The two layouts were compared with one another under controlled experimental conditions using various combinations of four operating variables: batch size, demand rate, ratio of setup time to process time, and transporter speed. Six indicators of systems performance were used in the study. These were: average time in system, products completed, jobs in process, average machine utilization, average queue length, and average waiting time. The study found that for environment as set for the models, GT system outperformed JS system as expected. However, using large batch size (more than 75) in Experiment 1 (changing batch size) allowed JS system to perform as well as GT system. Certain specific changes in batch size also allowed to establish optimum results in both systems. No individual change of demand rate (Experiment 2), ratio of setup time to process time (Experiment 3), or transporter speed (Experiment 4) allowed JS system to outperform GT system.

Analysis of the lineament pattern in the Rhodope massif (after computer processing of satellite remote sensing data)

A statistical processing of lineament network obtained by independent analysis of space images of the Bulgarian and Greek parts of the Rhodope Mountains, has been performed by means of a package of FORTRAN programs. Computer algorithms include a sequence of preparatory, subsidiary, and properly processing procedures. The end product represents schemes for the azimuthal and areal distribution of the lineaments. The predominant lineament trends are marked by maxima on the rose diagrams. They are grouped into five sets (5-10°, 60°; 95°; 115°; 165°) which correspond fairly well to the principal fault sets in the eastern part of the Balkan Peninsula. The analysis of these trends confirms the relative independence of the five blocks previously outlined on the basis of more general geological considerations. Maps of the total and partial densities outline areas of different degree of lineamentation, and reveal areal interrelations of zones rich in lineaments of the sets existing in the region. The results of the study are related to problems of the seismicity and the mineral deposits.

Computation of correlation characteristics of nuclear reactions induced by semi-heavy ions

The present paper suggests a consistent approach to the calculation of different characteristics of nuclear reactions with the production of high-lying quasistationary states of nuclei induced by light and semi-heavy ions with an incident energy up to 10 MeV/nucleon. To investigate this subject it is expedient to analyze the angular correlations of nuclear reaction products. The approach is based on some basic theoretical statements, namely, the general theory of angular correlations in terms of the density matrix and its spin-tensors, two supplementary nuclear reaction models — direct and statistical reaction models — on some methods of computation of quasistationary state characteristics such as the cluster wave functions, width, spectroscopic factors, and, the experimentally observable quantities — differential cross-sections, spin-tensors of the density matrix of the final nuclear state, particle-particle and particle-γ-quantum angular correlation functions and populations of magnetic sublevels of the final nucleus. The approach has been implemented as a package of FORTRAN programs, applied to the analysis of concrete nuclear reactions.

Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions

ABDPACK is a package of FORTRAN programs for the solution of systems of linear equations with the almost block diagonal structure arising in spline collocation at Gaussian points with monomial spline basis functions, when applied to two-point boundary value problems with separated boundary conditions. The package ABBPACK is designed to handle a subclass of such linear systems which have what may be called an almost block bidiagonal structure. Such systems result, for example, when condensation is applied to the full spline collocation linear system. This package may also be used to solve the almost block bidiagonal systems arising in multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems. The algorithms implemented in the package are based on an alternate column and row pivoting scheme which avoids most of the fill-in introduced by more commonly used techniques.

GNOM – a program package for small-angle scattering data processing

The Fortran program package GNOM carries out SAS data treatment and interpretation for the disperse non-interacting dilute systems of different types. A general operator method based on Tikhonov's regularization technique is used. Here a finite real-space distribution function [the correlation function p(r) for monodisperse systems and size distribution function D(R) for polydisperse ones] is searched for to fit the experimental data in accordance with the experimental conditions and the error bounds. It is possible to require non-negativity of the solution. The package GNOM is applicable for arbitrary experimental conditions (arbitrary weighting functions and form factors) and provides solutions stable to statistical noise and termination effects. The program makes it possible to treat together experimental curves from the same object measured under different experimental conditions and to choose the best model from the given set. Interactive and batch versions are available. The program is adapted to NORD, VAX and IBM-PC computers. It possesses convenient graphics possibilities.

Fourier analysis of EXAFS and XANES data - a self-contained FORTRAN program-package - the third version

A third version of Fourier analysis of XANES and EXAFS data, a self-contained FORTRAN program-package, is described. By the direct dialog between the user and the indirect command processor, based on XANES and EXAFS spectra, there is the possibility to obtain the electronic and structural parameters. An improved smoothed procedure is used to extract more informations from XANES spectra by second derivative analysis. The true energy position of maxima and the full width at half maximum (FWHM) can be determined. The XANES spectrum and the first and second derivative are determined by cubic spline functions, the phase-shift function and numerical values of structural parameters for the Ni foil spectrum are given.

Generation and analysis of high order strong coupling series for SU(2) lattice gauge theory

We present a package of VAX FORTRAN programs that analyze the information coming from two sets of FORTRAN routines. The first set of routines perform strong coupling series expansions in pure SU(2) lattice gauge theory mixed actions. The most general mixed action we are able to analyze is a mixing of the spin 1 2 , 1, 3 2 and 2 representations. This set is a symbiosis between the use of algebraic outputs from REDUCE and its execution using the VAX FORTRAN language. The second set of FORTRAN routines perform the Padé approximants analysis of the series. Making a systematic study of the Padé table will give the mean value of the significant real (and complex) poles put together with its standard deviation. The programs perform the series analysis and graphical representation of the results for all the cases.

Fourier analysis of EXAFS data — A self-contained FORTRAN program-package — A second version

A new version of Fourier analysis of EXAFS data, a self-contained FORTRAN program-package, is described. The EXAFS spectra analyses has been processed by hybrid Fourier transform and curve-fitting procedure. The purpose of the program package is, based on EXAFS measurements, to obtain the structural parameters: R j - distance from the central absorbing atom to atoms in the jth coordination shell, N j - number of atoms in the jth shell, σ j - root mean square deviation of t he interatomic distance about R j , λ j - mean free path for inelastic scattering, A j - amplitude envelope function and δ j ( k) - phase shift. The main numerically methods used are: 1. (i) smoothing and interpolation by 3rd order piecewise polynomial functions, Newton's interpolation formula for unequally spaced value of the argument and by cubic spline in the least squares sense. 2. (ii) Fourier transformation by Filon's quadrature formulae. 3. (iii) iterative least squares linear Taylor differential-correction technique. The quantitative and graphical results for Ni spectrum are given.

ON THE COUPLING METHODS FOR COUPLED PROBLEMS

The coupled problem means fluid-structure interaction widely encountered in aviation, offshore and nuclear engineerings[1–7] The coupling method here means the combination of finite and boundary elements (FE/BE) to improve the computational efficiency considerably. In this paper, a general math. Model for simulation of the wetted structure dynamic response to inter/external fluid flow is presented. In particular, the various boundary conditions for fluid region are treated sophsticatedly. In this way, only the displacement and pressure remain to be the independent variables so that both computer cost and accuracy could be improved. The FORTRAN program package of this model has been compiled on #Univac-1110 in Madison (MACC), USA, and on #M340S computer in Wuhan University, China. As a first approximation, in this paper a 2-D example for the ship-wave interaction analysis is illustrated.

DATALIN—An interactive data entry program for use with NONLIN

A package of FORTRAN programs for data entry into NONLIN (version II) is described which may be used in the analysis of plasma-concentration time curves after single or multiple doses for fourteen pharmacokinetic models described in terms of the model's microconstants (volume of compartments, rate constants). In all cases, infusion rates must be zero-order and absorption rates first-order. The program contains an edit subroutine allowing for changes in initial parameter estimates and their lower and upper limits, weighting factors, number of iterations in the NONLIN analysis, and plot option. Individual X and Y values may be changed and listed and X-Y data pairs may be inserted or deleted. Factors pertaining to each of the data entries in relation to NONLIN are discussed.

A minicomputer program for rapid graphical and statistical analysis of laboratory data

The utility of a FORTRAN program package, which enables the scientific investigator to make a rapid assessment of laboratory data is described. Data are submitted from the keyboard or specified disk files in the form of coordinate pairs. The program includes routines for plotting values as a series of X-Y pairs on the computer video monitor or for comparing the X and Y arrays via paired differences and Student's t-test. A least squares linear regression of plotted data may also be called. Data modification, curve fitting, and I/O are easily handled in either single pair or column format. Examples of both statistical and graphical data analysis are presented.