Term coefficient

X The use of the term coefficient of variation ( variation coefficient ) is not recommended byIUPAC —> IUPAC Orange Book [1997, 2000]... 

Parameter Coefficient when using only linear term t-value when using only linear term Coefficient using square term t-value using square term... 

An important distinction between term coefficients A and is that, whereas the former are regarded as freely adjustable, the latter are formally inter-related for instance, although a relation... 

Two further comments about formula 8 and its parameters are noteworthy. The number of terms with coefficients l i in the double sum is formally doubly infinite so that formula 8 can represent spectral terms involving arbitrarily large values of V and 7 with data of finite extent the sums become truncated in a systematic and consistent manner conforming to parameters of a minimum number required according to that intermediate model. Instead of exact equalities in formulae 10 and 11, the approximations arise because each term coefficient constitutes a sum of contributions [5],... 

Dunham achieved inter-relations between term coefficients l i through use of an intermediate radial function V(J ) in an effective hamiltonian for motion of atomic nuclei of this form. 

Apart from the distance variable x that Dunham used in his function V(x) for potential energy, other variables are amenable to production of term coefficients in symbolic form as functions of the corresponding coefficients in a power series of exactly the same form as in formula 16. Through any method to derive algebraic expressions for Dunham coefficients l j, the hamiltonian might have x as its distance variable, but after those expressions are produced they are convertible to contain coefficients of other variables possessing more convenient properties. To replace x, two defined variables are y [38],... 

For molecules containing light atoms, we accordingly neglect this effect of finite nuclear volume or field shift, but other effects prevent exact application of isotopic ratios that one might expect on the basis of a proportionality with in formula 13 instead of total F. For this reason we supplement term coefficients in formula 8 for a particular isotopic species i with auxiliary coefficients [54],... 

In the present context of generation of consistent term coefficients Ym and Zki through coefficients in selected radial functions, the major points of interest in... 

Although authors [74,75] have claimed that a generator-coordinate theory yields an expression for spectral terms exactly of Dunham s form, as in formula 8, in which however term coefficients encompass intrinsically elfects of at... 

As expected. Equations 3 and 4 convey the same message as did Equations 1 and 2 and have improved t-ratios on term coefficients they are less confounded by the noise characteristic of the full datasets and are thereby more suitable for predictive work. 

Gelatinization Coefficient of Nitrocellulo es and Coefficient de plasticitd. In the paper entitled "Plasticites des psites de Poudre B , the term "coefficient de plasdeite is defined and a simple apparatus for its determination is described Ref Anon, MP 19, 146-53(1922)... 

The single electron spin—orbit coupling constant , / is fundamentally a positive quantity. The term coefficient XLS can be of either sign... 

The crossing of two curves bounding adjacent elements form nodes. The values of the field variables at the nodes form the desired solution. Common shapes of finite elements are triangular, rectangular, and quadrilateral in two-dimensional problems, and rectangular, prismatic, and tetrahedral in three-dimensional problems. Within each element, an interpolation function for the variable is assumed. These assumed functions, called trial functions or field variable models, are relatively simple functions such as truncated polynomials. The number of terms (coefficients) in the polynomial selected to represent the unknown function must at least equal the degrees of freedom associated with the element. For example, in a simple one-dimensional case [Fig. 15.6(a)], we have two degrees of freedom, Pt and Pj, for a field variable P(x) in element e. Additional conditions are needed for more terms (e.g., derivatives at nodes i and j or additional internal nodes). 

Ideally, a single A (or B) coefficient would be appropriate for each element type such as one AH for all hydrogens. It has been our experience, however, that atoms of the same element often require different coefficients in different functional groups. There would be, for example, different AH s for H in H-O, H-NR2, H-C(sp2), H-C(sp3), etc. Other complications may involve separate cross terms for each of the atom i - atom j interactions. For a simple molecule such as formaldehyde (H2CO), the Ay cross terms are handled in WMIN with three AH, Ac and Ao coefficients that are used to form the six possible cross terms. But other programs, (e.g. DMAREL) may require cross terms that encompass the Ahh, AHo> AHc, ACc, ACo and Aoo possibilities. This is undoubtedly more flexible and possibly more accurate but does have the disadvantage of requiring the evaluation of many cross term coefficients. Of course, in cases with separate cross terms, one can always use the WMIN simplification of AHo = (AH A0) /2, etc. 

The term coefficient describes the contribution of an individual atomic orbital to a molecular orbital. It is represented by the size of the lobes on each atom. 

Term Coefficients Standard error coefficient T-test value P-Value... 

The B term describes broadening due to axial molecular diffusion and is inversely proportional to the linear velocity. In other words, the faster an analyte zone migrates through the column, the less broadening due to diffusion it will experience. The B term coefficient is given by... 

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