Mathematical computing software

Logarithm The exponent that indicates the power to which a number is raised to produce a given number. Thus, as an example, 1000 to the base of 10 is 3. This type of mathematics is used extensively in computer software. 

Many other approaches for finding a correct structural model are possible. A short description of ab-initio, density functional, and semiempirical methods are included here. This information has been summarized from the paperback book Chemistry with Computation An Introduction to Spartan. The Spartan program is described in the Computer Software section below.65 Another description of computational chemistry including more mathematical treatments of quantum mechanical, molecular mechanical, and statistical mechanical methods is found in the Oxford Chemistry Primers volume Computational Chemistry,52... 

Other more mathematical techniques, which rely on appropriate computer software and are examples of chemometrics (p. 33), include the generation of one-, two- or three-dimensional window diagrams, computer-directed searches and the use of expert systems (p. 529). A discussion of these is beyond the scope of this text. 

Data reduction and interpretation are much aided by computer methods and the high speed of current microcomputers facilitates the real-time processing and display of data. The principle of extracting as much information as possible from analytical measurements through the application of statistical and other mathematical methods, usually with the aid of appropriate computer software, is known as chemometrics (p. 13). 

The signal processor is also measurement specific. A different mathematical treatment, such as a logarithmic conversion, is required for data from each kind of sensor, depending on what the operator desires as a readout. Some data treatment is often conducted with computer software. 

The software to do the SVD calculations is readily available (Computer Methods For Mathematical Computations, Forsythe, Malcolm, and Moler, Prentice-Hall, 1977). 

A fire model is a physical or mathematical representation of burning or other processes associated with fires. Mathematical models range from relatively simple formula that can be solved analytically to extensive hybrid sets of differential and algebraic equations that must be solved numerically on a computer. Software to accomplish this is referred to as a computer fire model. 

The library search is a mathematical comparison of the unknown compound s spectrum with that of all reference compounds in the database. The aim of the comparison is to find the spectrum that most resembles that of the unknown compound. At the end of the search, the computer software makes a list of all spectra that resemble the unknown spectrum. The software lists the spectra relative to the unknown, along with a reliability or correlation index, irrespective of the library used. Because the object of the library search is to help the analyst and not act as a substitute for him/her, the analyst must manually examine the results. The best approaches to identification are interactive approaches in which the analyst can define filters to reduce the field of investigation. Several different algorithms are used for comparison and can lead to different spectra listings. 

Whenever quantitative analysis is desired, care must be taken to use proper standards and account for interelement matrix effects since the inherent sensitivity of the method varies greatly between elements. Methods to account for matrix effects include standard addition, internal standard and matrix dilution techniques as well as numerous mathematical correction models. Computer software is also available to provide semi-quantitative analysis of materials for which well-matched standards are not available. 

In modern crystallography virtually all structure solutions are obtained by direct methods. These procedures are based on the fact that each set of hkl planes in a crystal extends over all atomic sites. The phases of all diffraction maxima must therefore be related in a unique, but not obvious, way. Limited success towards establishing this pattern has been achieved by the use of mathematical inequalities and statistical methods to identify groups of reflections in fixed phase relationship. On incorporating these into multisolution numerical trial-and-error procedures tree structures of sufficient size to solve the complete phase problem can be constructed computationally. Software to solve even macromolecular crystal structures are now available. 

Artificial neural networks are versatile tools for a number of applications, including bioinformatics. However, they are not thinking machines nor are they black boxes to blindly feed data into with expectations of miraculous results. Neural networks are typically computer software implementations of algorithms, which fortunately may be represented by highly visual, often simple diagrams. Neural networks represent a powerful set of mathematical tools, usually highly nonlinear in nature, that can be used to perform a number of traditional statistical chores such as classification, pattern recognition and feature extraction. 

An iterative approach is often taken to solve the equations. Iteration may be continued until the difference in the induced dipole for successive calculations is 0 to 0.1 D. Typically one uses a system of, say, 215 waters for one ion in a cubic cell with an 1860-pm side. The time step is 1 fs. Coulombic interactions may be cut off at as little as 800 pm. Each set of calculations involves computer software (the cost of which may be very high) and various mathematical procedures to solve the equations of motion. 

If we establish a relation between Fig. 1.2 and the computer software that assists the operation of the filtration plant, then we can say that this software can be the result of an assembly of mathematical models of different components or/ and an assembly of experimentally characterized components. 

In the past, the application of physiologically-based pharmacokinetics was limited by the complexity of the mathematics involved because of the large number of parameters in the models. In recent years, the advances in computer software have overcome this limitation. Thus, earlier this year, Clewell and Andersen (89) reported that by using the Advanced Continuous Simulation Language (ACSL), physiologically-based pharmacokinetic modelling may be carried out on personal computers with reasonably short turn-around times (i.e., execution time, 0.6-8 minutes) and in a user-friendly manner. 

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