Hole, definition

A quantum system of N particles may also be interpreted as a system of (r — N) holes, where r is the rank of the one-particle basis set. The complementary nature of these two perspectives is known as the particle-hole duality [13, 44, 45]. Even though we treated only the iV-representability for the particles in the formal solution, any p-hole RDM must also be derivable from an (r — A)-hole density matrix. While the development of the formal solution in the literature only considers the particle reduced Hamiltonian, both the particle and the hole representations for the reduced Hamiltonian are critical in the practical solution of N-representability problem for the 1-RDM [6, 7]. The hole definitions for the sets and are analogous to the definitions for particles except that the number (r — N) of holes is substituted for the number of particles. In defining the hole RDMs, we assume that the rank r of the one-particle basis set is finite, which is reasonable for practical calculations, but the case of infinite r may be considered through the limiting process as r —> oo. 

If all these holes were filled, the hydrogen-metal ratio would be a definite and fixed number in practice, this rarely happens, and... 

Because the metal structure is locked by these atoms, the resulting compound is often much harder than the original metal, and some of the compounds are therefore of industrial importance (see under iron). Since there is a definite ratio of holes to atoms, filling of all the holes yields compounds with definite small atom-metal atom ratios in practice, all the holes are not always filled, and compounds of less definite composition non-stoichiometric compounds) are formed. 

We may begin by describing any porous medium as a solid matter containing many holes or pores, which collectively constitute an array of tortuous passages. Refer to Figure 1 for an example. The number of holes or pores is sufficiently great that a volume average is needed to estimate pertinent properties. Pores that occupy a definite fraction of the bulk volume constitute a complex network of voids. The maimer in which holes or pores are embedded, the extent of their interconnection, and their location, size and shape characterize the porous medium. 

This number is in the range of acceptable performance for bottom section and should be punched. If performance indicates fewer holes are preferable, blanking strips can be added (or even added before the trays are installed). The top trays definitely require blanking of holes. 

Increase in pit level. This is a definite signal of formation fluid invasion into the hole. The well must be closed as soon as ptossible. 

For definiteness, the oxidation of copper to copper(l) oxide may be considered. Our picture of the process is that cation vacancies and positive holes formed at the Cu O/Oj interface by equation, 1.166 are transported to the Cu/CujO interface where they are destroyed by copper dissolving in the non-stoichiometric oxide. We require an expression for the rate of oxidation. 

A definite correlation of the results of the measurements can be achieved by using the adiabatic compressor power per unit volume of reactor according to Eq. (10) which is shown in Fig. 15 [27]. The experimentally determined loss factor is required in Eq. (10). The measured data for spargers with holes dL= 0.2 - 2 mm can be correlated with Eq. (24). 

As seen from Fig. 5, upon absoption of photons with the energy hv > Eg, an electron and hole centres are formed. They migrate to different sites on the PC surface, thus becoming spatially separated. Note, that what solid state physisists call surface electron and hole centers, in fact are some definite chemical species with strong reducing and oxidizing... 

I wish to stress that the meaning of the word Hole here is different and far more general than in Many Body Perturbation Theory. Indeed, no specific reference state is required in this definition and the difference between the RO s and the HRO"s follows exclusively from the different order of the creator operators with respect to the annihilator operators in E and in E respectively. 

As a result of strong electronic interactions between the two metalloporphyrin units, there is a substantial uncertainty in assigning oxidation states in mixed-valence group 2 complexes of redox-active metals, such as Co. Thus, although reduced neutral C02 derivatives can be reasonably well described as those of Co the location (metal versus porphyrin) of the electron hole(s) in the singly and doubly oxidized derivatives is not known definitively, and may be very sensitive to the medium [LeMest et al., 1996, 1997]. For example, in benzonitrile, the UV-vis spectmm of [(FTF4)Co2]" ... 

Sump holes are usually a collection point for the drainage system. Almost by definition, this is a terrifically good radon collection system. It must have access to large areas of soil beneath the... 

Not all scientific statements are testable hypotheses, laws or theories. For example, scientific paradigms, by one definition (Masterman, 1970 Horgan, 1996), are organizing principles which encompass much of the work of ordinary science, in the language of Thomas Kuhn (1970) but are not necessarily testable. Ordinary science is not the source of revolutionary science (except, possibly when it breaks down) and is not hypothesis driven so much as driven by the requirement to fill in the holes opened in a field by the scientific paradigm. 

According to the electronic theory, a particle chemisorbed on the surface of a semiconductor has a definite affinity for a free electron or, depending on its nature, for a free hole in the lattice. In the first case the chemisorbed particle is presented in the energy spectrum of the lattice as an acceptor and in the second as a donor surface local level situated in the forbidden zone between the valency band and the conduction band. In the general case, one and the same particle may possess an affinity both for an electron and a hole. In this case two alternative local levels, an acceptor and a donor, will correspond to it. 

We shall assume that the electron and hole gases on the surface of semiconductor are not degenerate. Then, by definition, ... 

How then, can one recover some quantity that scales with the local charge on the metal atoms if their valence electrons are inherently delocalized Beyond the asymmetric lineshape of the metal 2p3/2 peak, there is also a distinct satellite structure seen in the spectra for CoP and elemental Co. From reflection electron energy loss spectroscopy (REELS), we have determined that this satellite structure originates from plasmon loss events (instead of a two-core-hole final state effect as previously thought [67,68]) in which exiting photoelectrons lose some of their energy to valence electrons of atoms near the surface of the solid [58]. The intensity of these satellite peaks (relative to the main peak) is weaker in CoP than in elemental Co. This implies that the Co atoms have fewer valence electrons in CoP than in elemental Co, that is, they are definitely cationic, notwithstanding the lack of a BE shift. For the other compounds in the MP (M = Cr, Mn, Fe) series, the satellite structure is probably too weak to be observed, but solid solutions Coi -xMxl> and CoAs i yPv do show this feature (vide infra) [60,61]. 

Acute closed-angle glaucoma with high IOP requires rapid reduction of IOP. Iridectomy is the definitive treatment, which produces a hole in the... 

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