Compact space

Can be easily integrated into the structural member Compact, space-saving form Takes over other functions like bearing, spring cushioning, fixing... 

Figure 6.24 Photographic representation of a range of filter types and their stainless steel housing. Most filters used on an industrial scale are of a pleated cartridge design, which facilitates housing of maximum filter area within a compact space (a). These are generally housed in stainless steel housing units (b). Some process operations, however, still make use of flat (disc) filters, which are housed in a tripod-based stainless steel housing (c). All photographs courtesy of Pall Life Sciences, Ireland...

Whiston, G. S. (1974) Hyperspace (the cobordism theory of spacetime). International Journal of Theoretical Physics. 11(5) 285—88 (A compact space- and time-orientable spacetime is cobordant in the unoriented sense—that is, it bounds a compact five-manifold. The bounding property is a direct consequence of the triviality of the Euler number.)... 

Nevertheless the radial-turbo-compressors demonstrate significant advantages with respect to compactness, space requirements, quieter operation, and lower level of vibrations, as well as giving a smooth non-pulsating flow. Their application for high-pressures in the range of above 5000 N/m3 intake volume, is well established up to pressures of 400 bar and more. 

Molski showed [91] that (5) and (6) can be viewed as a five-dimensional version of Corben s tachyonic theory. In particular I (x ) may be interpreted as a B-wave associated with a bradyon of mass m0 moving in four-space M4 wheras (.x4) is a purely space-like D-wave associated with a transcendent tachyon of mass p0 and infinite speed moving in compact space S1 about the bradyonic constituent and satisfying a wave equation... 

If you begin with a handwritten draft, do eventually work on a typed copy. Frankly, the more compact spacing of typed prose allows you to see better the relationship of the parts in your essay, making it easier for you to organize and develop your ideas. It is also far more likely that you will catch spelling and other mechanical errors if they are printed. 

Vol. 527 M. Denker, Ch. Grilfenberger, and K. Sigmund, Ergodic Theory on Compact Spaces. IV, 360 pages. 1976. 

An affine variety can be embedded in a projective variety, by a birational inclusion. Can a projective variety be embedded birationally in anything even bigger The answer is no there is a type of variety, called complete, which in our algebraic theory plays the same role as compact spaces do in the theory of topological spaces. These are maximal and projective varieties turn out to be complete. 

The analogous property in the category of topological spaces characterizes compact spaces X, at least as long as X is a reasonable space - say completely regular or with a countable basis of open sets. This definition is very nice from a category-theoretic point of view. It gives the elementary properties of completeness very easily ... 

In determining the density of states of protein models by MC methods, a number of other approaches are also useful. For systems for which it is feasible, exhaustive enumeration of all the conformations of the system by computer provides a viable and exact solution to the problem [61-66]. A number of powerful techniques have been developed, some for exhaustive enumeration of all conformations of relatively short lattice chains [61,63] others, for enumeration of protein conformations that are confined to a compact space [62,64-66]. However, in general protein models, the number of conformations is beyond the power of computer enumeration for these systems, MC methods are the main effective techniques. 

As for (4.1), the classical abstract method was introduced by Verdier in his treatment of duality for locally compact spaces, then adapted to schemes by Deligne [De ] to show that with j D(.A ) —> Dqc(X) the natural functor, R/ oj has a right adjoint. This suffices only when / is separated, see (3.9.6). The proof given below (for historical reasons, because of the compactness of Deligne s original presentation) is just an elaboration of Deligne s arguments. 

Minkowski space, M, is assumed embedded in a more general universal closed (compact) space M, the so-called conformal space. This is the projective space proposed as a model of the universe by Oswald Veblen (1933), translated in the Appendix. Roughly speaking, M is obtained from M by adding a light cone at infinity. More precisely, it is the double cover of the space so generated. Segal (1976) refers to M as unispace and to the natural time r in this space as unitime. 

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