Symbolic expression

The meaning of the symbolic expression indicating a nuclear reaction ... 

In the CVM, the free energy of a given alloy is approximated in terms of probabihties for a selected set of finite clusters. The largest cluster explicitly considered in the free energy functional specifies the level of the approximation. The common practice for an fcc-based system is the tetrahedron approximation [26] in which nearest neighbor tetrahedron cluster is taken as the largest cluster. Hence, within the tetrahedron approximation, the free energy expression, F,is symbolically expressed as... 

Physical qnantity SI nnit Name Symbol Expression in terms of base or derived SI nnits... 

Finally, 3 " (j)[f (x )] is a short symbol expressing the m-th order partial derivative operators, acting first over the function f (x) and then, the resultant function, evaluated at the point x . The differential operators can be defined in the same manner as the terms present in equation (9), but using as second argument the nabla vector ... 

Physical quantity SI unit Symbol Expression in SI Pimpnql 1 i ... 

Physical Quantity Name Symbol (Expression in Terms of Other SI Units)... 

Evaluate parentheses left to right. In the first grouping symbol, do multiplication first 10 + 14 = 24. The second grouping symbol expression is 2 + 4 = 6. Finally, evaluate division 24 6 = 4. 

Derived quantity Name (symbol) Expression in terms of other SI units Expression in terms of SI base units... 

Physical Quantity SI Name SI Symbol Expression in SI Base Units... 

The above example is only a simple illustration of a weight balance. Similarly, the reaction between elements and compounds may be symbolically expressed to portray the principle of conseivation of matter. For example, if hydrogen is completely burned to water, the reaction between it and oxygen can be represented as follows ... 

Quantity Name of SI derived unit Symbol Expressed in terms of SI base oi derived units... 

The scheme for achieving the core-valence separation which we wish to discuss in this Report is embodied in the idea of a pseudopotential . The hamiltonian for the electronic part of the wavefunction can be symbolically expressed within the Bom-Oppenheimer ( clamped nucleus ) approximation as... 

Open-shell Pseudohamiltonians.—The majority of atoms do not have valence structures which can be represented by the fully closed-shell wavefunction of equation (14), and consequently ab initio pseudopotentials cannot be derived directly from the theory outlined above. Acceptable wavefunctions for such atoms require either more than one determinant or the use of the symmetry-equivalenced or generalized Hartree-Fock method, and usually include partially filled shells. The total all-electron wavefunction may be symbolically expressed in terms of four subspaces,... 

If the valence-electron wavefunction is also symbolically expressed,... 

Figure 8.6 In tree-based genetic programming, individuals are represented as trees. A sample individual is shown on the left. This individual represents a symbolic expression that evaluates to 2x — 1. 

Property Unit Symbol Expression in Terms of Si Base Units... 

An example using symbols (expressed slightly differently) is... 

Formula, n. A group of symbols expressing the composition of a compound. 

Name Quantity Symbol Expression in other units... 

Figure 5.13. The approximate regions of uniaxial (100) and (111) growth obtained using an ASTeX 5-kW MPCVD reactor. The symbols express the data points of and c for given P and [67].

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