Completeness condition

Restrictions for a curve of source movement reffer to as a completeness condition. This condition determines whether the information that is contained within some geometry of cone vertices is enough to perform an artifact-free reconstruction. 

Bilinear combinations composed of creation and annihilation operators can be expressed in terms of triple tensors W KkK (see (15.59) and (15.61)). In this case, these tensors are generators of the Rsi+4 group, and relationship (15.64) determines the completeness condition for the generator set of this group in relation to the commutation operation. Out of this set we shall single out two subsets of operators - and Each of... 

The reaction completeness condition means that on the surface of the catalyst the concentration of one of the components (for equality of the diffusion coefficients of the ith—of which there is not enough in the mixture) is equal to zero. Let this be the Ith component. From this we find the flux of this component... 

Let us assume that a complete set of the orthonormalized functions y n(r) of the spatial coordinates r is known. They form a basis in the space L = L2(R3) of the square integrable functions of r, known in this context as orbitals. The completeness condition means that the following holds ... 

The main limitation of this approach is that any departure from livingness because of premature termination reaction results in the partial end-functionalization of the chains. Moreover, for the derivatization reaction to be complete, conditions of ultrahigh purity are required. The chains prepared by this technique are thus (W-functional. 

Complete conditions for the preparative separation and corresponding chromatogram are given in Tab. 5.7 and Fig. 5.36. 

It is very probable that the constant of integration, like the other coefficients of the differential equation, is a definite function of certain physical properties of the reacting substances. Determination of the nature of the function would lead to a full knowledge of the laws of equilibrium. It would determine, a priori and independently of new experimental data, the complete conditions of equilibrium corresponding with a given chemical reaction. It has hitherto been impossible to determine the exact nature of this constant. ... 

The theory developed here has its most important application in the study oi reversible galvanic cells. Galvanic cells may be separated into two classes those with and those without liquid junction. In Sec. 13-2, we consider a galvanic cell without liquid junction using the necessary criterion for equilibrium [Eq. (13-23)]. In Sec. 13-3, we discuss a cell with liquid junction in terms of the complete conditions for heterogeneous equilibrium. 

The limifafion on fhe angle 0 resulfs from the quantization condition (49) and from the fact that at the boundary the normal modes have to vanish, i.e., Xm(9o) = 0. This ansatz modifies fhe formula for the decay rate because the completeness condition is changed according to... 

First cycle strain is invariably uncharacteristic, enforcing mechanical conditioning until behaviour is reproducible. There are suggestions that in some materials complete conditioning is unattainable. 

The spots become visible after a time lag on account of the induction time (i.e., time required for the induction reaction to complete) conditioned by induction properties of the particular compound. The induction time should not be too long because it may cause disappearance of the background owing to iodine sublimation. 

In calculations on small molecules the basis sets have in recent years approached the completeness condition and under these circumstances gauge invariance will be achieved automatically without introducing expheit transformations of the localized orbitals. Such procedures impose very heavy demands on computation time. 

The ANSI/ISEA Z308.1-2009 standard states that first aid kits should be reguiariy inspected to ensure completeness, condition of supplies, and expiration dates to maintain compliance. Expired supplies should be removed and additional quantities should be added as needed. 

In the quantum formalism, with a finite number of reactant states, Eq. (28) can be solved by Cramer s rule, thereby leading to a determinantal formula for 1. Such a formula was given by Kim, though Z did not appear in it because the completeness condition of Eq. (9) was not used. 

The complete condition for mechanical equilibrium of a two-phase system with a curved phase boundary in a gravitational field is now available. It shows that the pressure difference between two curved phases depends on the properties of the D-face interfacial tension, curvature, and adsorptions... 

These chain-length probabilities must sum to 1 (i.e., the complete condition, meaning that something must happen) ... 

There are only two independent terminal conditional probabilities, that is, there is the completeness condition indicating that only an A or a B be added to an A ... 

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