Space definition

A sieve is an open container, usually cylindrical, having definitely spaced and uniform openings in the base. The openings are square when wire or filter mesh is used and may be circular or slit shaped when the openings are formed by... 

The problem treated in this paper is complicated by the fact that the linear operator T is supposed to be linearly defined on a linear space A = F of all complex functions F = F(X) of a real composite variable X = jcl5 x2, , xN, of which the L2 Hilbert space is only a small subspace. We will refer to this space A = F as the definition space of the operator T. Since it contains all complex functions, it is stable under complex conjugation, and, according to Eq. (1.50) one has T F = (TF ), which means that also the complex conjugate operator T is defined on this space. 

So far, we have included in the definition space A = F only complex functions F = F(X) of the real compositive variable X = xt, x2,..., xN. We will now extend this space by also including complex functions F = F(Z) of a composite complex variable Z = zx, z2,..., zN, and we will introduce such functions essentially through complex similarity transformations. 

At this point it should be observed that even if it is natural to assume that all the functions F = F(Z) in the definition space A = F are analytic functions of the composite complex variable Z = zt, z2,..., zN, one has still to be very careful in the definition of the complex transformation U. Some of the complications which may occur are well illustrated by the simple example of complex scaling as defined in Eq. (2.26). 

One of the most important tools in applications of fuzzy set theory is the concept of linguistic variables (LV). These are groups of fuzzy sets with (partially) overlapping membership functions over a common (crisp) basic variable x. To represent several classes within an LV, the membership functions should cover all the relevant definition space of the basic variable x. The overlaps of these functions define the fuzziness. A linguistic variable L, classified by n fuzzy sets Aj, can be defined as... 

Oxidation of polymer is accompanied by the change of their structure - physical properties - crystallinity, molecular mobility, strength and so on. Orientation of crystalline regions is disturbed in stressed samples the number of crystals with definite space orientation of crystal lattice axes decreases, the form of the curve of crystal distribution axes in respect to orientation axis changes. Change for the worse of crystals orientation is explained by stress relief, occurring in polymer at the expense of oxidative destruction of macromolecules in amorphous intercrystalline region [301]. 

The turbid liquids which were thus obtained were found to possess not only the usual properties of liquids (such as the property of flowing and of assuming a perfectly spherical shape when suspended in a liquid of the same density), but also those properties which had hitherto been observed only in the case of solid crystalline substances, viz. the property of double refraction and of giving interference colours when examined by polarised light the turbid liquids are anisotropic. To such liquids, the optical properties of which were discovered by 0. Lehmann, the name liquid crystals, or crystalline liquids, was given." Since the term crystal implies the existence of a definite space lattice, which is not found in the case of liquid crystals, it is perhaps better to use the term anisotropic liquids, ... 

Grizzly, stationary Inclined or level parallel rails, bars, or rods with definite spacing Scalping of coarse rock... 

We can also assume that these configurations are subject to a constraint. For instance, the constraint may be that a set of points 0 belonging to the molecules have definite space positions and then 0 represents the set of these positions. We thus define the restricted partition function Q (0, 0) by... 

Let us now see how correlations can be calculated. In a general way, we consider a function (P(12) of the configuration of the system. In practice, this function imposes that certain points belonging to the polymer chain are fixed at definite space points which we call anchoring points. For instance, the function 0(L) could be the density of area at the point of position vector r, namely... 

Furthermore this geometrization implies the assumption of a definite space structure of the world. This structure consists in fact of nothing but the existence of ten position functions... 

The following conclusions may be drawn from a review of the above mentioned results of x-ray examination of inorganic, solid substances to a first approximation, every lattice component in the lattices of salts, metals and intermetallic compounds is characterized by a definite space requirement, corresponding to a definite particle radius. This particle radius is,... 

There has been discussion as to the size and distribution of the Smekal blocks in a mosaic crystal. Zwicky(i8) suggested that a lattice is subdivided into a periodic block structure with definite spacings, basing his theory in part upon the appearance... 

The molecular structure is introduced into the unit cell and the potential packing motifs are examined for the definite space group symmetry. 

The Langmuir s and BET s two-parameter equations are the extreme cases at n = 1 and n = oo, respectively. If adsorption happens on definite space, such as pores with limited sizes, rather than free space, the layers of adsorption would be limited. In this case, three-parameter BET equation should be used ... 

Multiple-layer insulation has a definite place when maximum insulating effectiveness must be obtained and when definite space and weight limitations are imposed. Theoretically, radiation shielding has no lower limit in thermal conductivity and therefore presents the ideal insulation. Ways are open to improve its practical performance with the development of the better materials and techniques suitable to the outlined purposes. No doubt such improvements will be accomplished to permit construction of cryogenic transporting and storage vessels which are essential to our successful space exploration efforts and to meet our defense needs. 

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