scholarly journals CoxIter – Computing invariants of hyperbolic Coxeter groups

2015 ◽  
Vol 18 (1) ◽  
pp. 754-773 ◽  
Author(s):  
R. Guglielmetti
Keyword(s):  
Computer Program ◽  
Euler Characteristic ◽  
Coxeter Groups ◽  
Source Code ◽  
Theoretical Background ◽  
Combinatorial Structure ◽  
Fundamental Polyhedron ◽  
Supplementary Material

CoxIter is a computer program designed to compute invariants of hyperbolic Coxeter groups. Given such a group, the program determines whether it is cocompact or of finite covolume, whether it is arithmetic in the non-cocompact case, and whether it provides the Euler characteristic and the combinatorial structure of the associated fundamental polyhedron. The aim of this paper is to present the theoretical background for the program. The source code is available online as supplementary material with the published article and on the author’s website (http://coxiter.rgug.ch).Supplementary materials are available with this article.

A New Method for Quantitative X-Ray Fluorescence Analysis of Mixtures of Oxides or Other Compounds by Empirical Parameter Methods

1982 ◽  
Vol 26 ◽  
pp. 351-354 ◽  
Author(s):  
Michael Mantler
Keyword(s):  
Computer Program ◽  
Chemical Elements ◽  
Fluorescence Analysis ◽  
Theoretical Background ◽  
New Method ◽  
Fundamental Parameter ◽  
Mathematical Methods ◽  
Empirical Parameter ◽  
X Ray ◽  
New Type

Two principal mathematical methods are used for quantitative XRFA: fundamental parameter calculations and the evaluation of empirical parameter equations. A comprehensive computer program based upon fundamental parameter equations was introduced in 1976 by D. Laguitton and M. Mantler (LAMA-I) and improved by T. C. Huang in 1979 (LAMA-II). The present paper describes the features of the theoretical background of a computer program using a new type of empirical (alpha*-) parameter equations. It is essentially designed for convenient analysis of compounds including those containing chemical elements, that cannot be directly measured by conventional X-ray spectrometers, such as oxides, nitrides, and others. The program also communicates automatically with LAMA in order to establish theoretical tables of alpha*-coefficients as well as conventional alpha-coefficients.

Software Development for Shear Stress Distribution in Multicell Beams of Isotropic Materials

2010 ◽  
Vol 442 ◽  
pp. 453-461 ◽  
Author(s):  
Muhammad Mushtaq Tariq ◽  
Malik Nazir Ahmed
Keyword(s):  
Shear Stress ◽  
Isotropic Material ◽  
Source Code ◽  
Visual Basic ◽  
Theoretical Background ◽  
Shear Stresses ◽  
Torsional Loading ◽  
Isotropic Materials ◽  
Mathematical Formulas ◽  
User Friendly

Main purpose of this work is to present the constrained torsional loading of multicell beam of isotropic materials in a user friendly format, using the computer programming. This computer program has been written in Microsoft Visual Basic, and its source code consists of 593 lines. Distribution of Saint Venant shear stresses in multicell beam of isotropic material has been calculated. Importance of shear stress in processing of materials has been discussed. The design and development of this software has also been enlightened by providing Algorithm and flow chart in paper. Although this software is restricted to multicell beam of three cells, yet future versions can have ability to address more complicated shapes and cases of multicell beams. Software also describes nomenclature and mathematical formulas applied to help user understand the theoretical background. The geometry of multicell beam is defined for three cells. Four main sections of software are; input data, intermediate calculations, numerical results and graphical output. The results of this software have been verified using MATLAB. Different contour displays indicating magnitude and direction of stress and displacement are plotted in MATLAB for multicell beam of isotropic material. MSC Patran has also been utilized to get the results for multicell beam of isotropic materials for comparison and validation. Development and use of this software provides inspiration to highlight new areas of consideration and research.

Paper 10: A Computer Program for Calculating the Performance of an Internal Combustion Engine Exhaust System

1967 ◽  
Vol 182 (12) ◽  
pp. 91-108 ◽  
Author(s):  
R. S. Benson
Keyword(s):  
Computer Program ◽  
Internal Combustion Engine ◽  
Method Of Characteristics ◽  
Combustion Engine ◽  
Exhaust System ◽  
Theoretical Background ◽  
Experimental Measurements ◽  
Design Calculation ◽  
Exhaust Pipe ◽  
Engine Exhaust

The paper describes the method of presenting data for a computet program, based on the method of characteristics, which calculates the pressure and temperature in the exhaust system and cylinders in two- or four-stroke engines with valves or ports. The program is arranged so that the performance of an exhaust pipe can be assessed for a number of pipe configurations. A brief description of the theoretical background and program format is given, followed by a suggested design calculation procedure. Examples are then given of the application of the program to both two- and four-stroke supercharged engines. The results of the calculation are compared with experimental measurements. A description of the subroutines and the organization of a calculation on the computer, together with the data order are given in two of the appendices.

scholarly journals Automatic Differentiation in ROOT

2020 ◽  
Vol 245 ◽  
pp. 02015
Author(s):  
Vassil Vassilev ◽  
Aleksandr Efremov ◽  
Oksana Shadura
Keyword(s):  
Computer Program ◽  
Automatic Differentiation ◽  
Source Code ◽  
Constant Factor ◽  
Control Flow ◽  
Chain Rule ◽  
Elementary Functions ◽  
Arithmetic Operations ◽  
Small Constant ◽  
Derivatives Of

In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.), elementary functions (exp, log, sin, cos, etc.) and control flow statements. AD takes source code of a function as input and produces source code of the derived function. By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program. This paper presents AD techniques available in ROOT, supported by Cling, to produce derivatives of arbitrary C/C++ functions through implementing source code transformation and employing the chain rule of differential calculus in both forward mode and reverse mode. We explain its current integration for gradient computation in TFormula. We demonstrate the correctness and performance improvements in ROOT’s fitting algorithms.

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