Natural, definition

Our hyper-Kahler metric on (C ) " depends on the choice of the hermitian metric on V and W. This hermitian metric should be defined naturally under the identification V = Fd iOz)- Recall that the hyper-Kahler metric on the moduli space of instantons on a hyper-Kahler manifold is induced from the natural L -metric . Do we have a similar natural definition for the hermitian metric on 1/ ... 

We start our discussion with a definition of the tip-sample distance. Because the STM deals with atoms, the basic definition should be microscopic. If at least part of the sample surface is atomically flat, a natural definition of the tip-sample distance is the distance from the plane of the topmost nuclei of the sample to the nucleus of the apex atom of the tip. Throughout the book, this microscopic distance is denoted by a lower-case letter, d, zo, or... 

Fig. 11.5. Hymenolepis diminuta comparative development in the rat (the natural definitive host) and the mouse (a non-permissive host). In most mice, growth ceases abruptly on day 10+1 and destrobilisation commences, leaving only a scolex and a neck 0.5-2 mm in length. (Modified from Hopkins et at., 1972.)...

In the simple bond charge model for the diatomic AB, the natural definition of the electronegativity of atom A, in the final molecule after charge transfer, has the form... 

If the term with the metallic energies, 2(V + K ), becomes larger than the other terms, the gap disappears altogether, so that the ratio becomes a natural definition of the metallicity, a , then... 

Having established that creation and annihilation operators are rank 1 covariant and contravariant tensors, respectively, with respect to the operator ( )L,S, we can define an rath-rank boson operator as consisting of a like number of fermion creation and annihilation operators. Then the normal product of an rath-rank boson operator is a natural definition for the irreducible tensor. 

On the other hand, G. Wyruboff as late as 1896 considered the periodic system as " a very interesting and highly ingenious table of the analogies and dissimilarities of the, . . elements " and proposed to reject the whole generalization because of its defects, reasoning that since the laws of nature admit of no exception, the periodic law must be considered as a law of nature definitely established which must be accepted or rejected as a whole. In spite of the bitter attacks made upon the system by those who claim that it has done more harm than good, the fact remains that it is a convenient basis for the classification of an endless array of facts. In addition it has been a vast benefit to the science of chemistry by reason of its-stimulation bo research,... 

There is a natural definition of the effective number Ne of final states when the spectrum is uniform. Then pf = l/Ne for all the lines that carry any... 

For simplicity, only nondegenerate nonrelativistic ground states will be considered. The reference-state density function is p = , niPi = X/ lli4>i4>i-where the occupation numbers nt are one or zero and , ni — N. Because p has this orbital decomposition, any density functional F p] is also an orbital functional F[ j, ip. This implies a natural definition of an energy functional E = E0 + Ec,... 

This, coupled with the natural requirement that we want our Wick-like theorem to be defined in terms of the new normal ordered products with contractions (i.e. numbers ), indicates that the most natural definition of the new normal ordered products is the following ... 

The integrals provide a natural definition of the term "mode" that is appropriate in the context of reaction, and they are a consequence of the (local) integrability in a neighborhood of the equilibrium point of saddle-center-----center stability type. Moreover, the expression of the normal form Hamiltonian in terms of the integrals provides us a way to partition the "energy" between the different modes. We will provide examples of how this can be done in the following. 

The purpose of this work is to start from the basic equations of density functional theory to describe the changes in the energy associated with the transition from one ground-state to another, in terms of different sets of variables. In this process one will find the natural definitions of the hardness and softness kernels, the local hardness, the local softness, the global hardness and the global softness [23]. Then, we will proceed to establish their relation with ionization potentials and electron affinities, in order to confirm their behavior as a measure of chemical hardness or softness [14, 24]. Finally, this theoretical framework will be used to analyze the maximum hardness and the HSAB principles. 

Although heuristic search has proved useful on some problems, natural definitions of neighborhoods often lead to poor local optima, that is, final feasible solutions that cannot be improved in the neighborhood. Of course, a richer family of allowed moves would make it possible to reach stronger local optima, but the cost of examining the neighborhood at each iteration rapidly becomes prohibitive. 

Rubber Rubber dust Rubber, natural Definition Coagulated and dried exudate of the rubber tree, Hevea brasiliensis natural rubber contains 89-92% elastomeric hydrocarbon (cis-1,4-polyisoprene)... 

See also Polyisoprene Natural rubber latex Synonyms Rubber latex, natural Definition Vise. liq. contg. > 60% rubber classified by method of concentration and type of preservative (e.g., low-ammonia centrifuged grade, creamed latex, evaporated latex)... 

Here /S.Ex2 is the vertical adiabatic energy gap introduced in Equation (11) for the special case of resonant D and A sites). The natural definition of the effective D/A separation, /-da, now becomes, ... 

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