# Abbreviations mathematical

The second approximation in HF calculations is due to the fact that the wave function must be described by some mathematical function, which is known exactly for only a few one-electron systems. The functions used most often are linear combinations of Gaussian-type orbitals exp(—nr ), abbreviated GTO. The wave function is formed from linear combinations of atomic orbitals or, stated more correctly, from linear combinations of basis functions. Because of this approximation, most HF calculations give a computed energy greater than the Hartree-Fock limit. The exact set of basis functions used is often specified by an abbreviation, such as STO—3G or 6—311++g. Basis sets are discussed further in Chapters 10 and 28. [c.19]

Mathematical Symbols and Abbreviations 2.23 [c.75]

TABLE 2.3 Mathematical Symbols and Abbreviations [c.97]

TABLE 2.3 Mathematical Symbols and Abbreviations Continued) [c.98]

Section 2 combines the former separate section on Mathematics with the material involving General Information and Conversion Tables. The fundamental physical constants reflect values recommended in 1986. Physical and chemical symbols and definitions have undergone extensive revision and expansion. Presented in 14 categories, the entries follow recommendations published in 1988 by the lUPAC. The table of abbreviations and standard letter symbols provides, in a sense, an alphabetical index to the foregoing tables. The table of conversion factors has been modified in view of recent data and inclusion of SI units cross-entries for archaic or unusual entries have been curtailed. [c.1286]

Table 1-15 Mathematical Signs, Symbols, and Abbreviations.. 1-24 |

T vo main streams of computational techniques branch out fiom this point. These are referred to as ab initio and semiempirical calculations. In both ab initio and semiempirical treatments, mathematical formulations of the wave functions which describe hydrogen-like orbitals are used. Examples of wave functions that are commonly used are Slater-type orbitals (abbreviated STO) and Gaussian-type orbitals (GTO). There are additional variations which are designated by additions to the abbreviations. Both ab initio and semiempirical calculations treat the linear combination of orbitals by iterative computations that establish a self-consistent electrical field (SCF) and minimize the energy of the system. The minimum-energy combination is taken to describe the molecule. [c.25]

COMMON ABBREVIATIONS AND MATHEMATICAL SYMBOLS [c.1296]

COMMON ABBREVIATIONS AND MATHEMATICAL SYMBOLS [c.1297]

COMMON ABBREVIATIONS AND MATHEMATICAL SYMBOLS [c.1298]

COMMON ABBREVIATIONS AND MATHEMATICAL SYMBOLS [c.1299]

COMMON ABBREVIATIONS AND MATHEMATICAL SYMBOLS [c.1300]

COMMON ABBREVIATIONS AND MATHEMATICAL SYMBOLS [c.1301]

An attempt has been made to bring together most of the methods currently available for project evaluation and to present them in such a way as to make the methods amenable to modern computational techniques. To this end the practices of accountants and others have been reduced, where possible, to mathematical equations which are usually solvable with an electronic hand calculator equipped with scientific function keys. To make the equations smtable for use on high-speed computers an attempt has been made to devise a nomenclature vmich is suitable for machines using ALGOL, COBOL, or FORTRAN compilers. The number of letters and numbers used to define a variable has usually been limited to five. The letters are mnemonic in Enghsh wherever possible and are derived in two ways. First, when a standard accountancy phrase exists for a term, this has been abbreviated in capital letters and enclosed in parentheses, e.g., (ATR), for assets-to-turnover ratio (DCFRR), for discounted-cash-flow rate of return. Clearly, the parentheses are omitted when the letter group is used to define the variable name for the computer. Second, a general symbol is defined for a type of variable and is modified by a mnemonic subscript, e.g., an annual cash quantity Afc, annual total capital outlay, /year. Clearly, the symbols are written on one line when the letter group is used to define a variable name for the computer. In other cases, when well-known standard symbols exist, they have been [c.803]

Langes handbook of chemistry (1999) -- [ c.2 , c.23 ]