18,184 research outputs found
Topological finiteness properties of monoids. Part 1: Foundations
We initiate the study of higher dimensional topological finiteness properties
of monoids. This is done by developing the theory of monoids acting on CW
complexes. For this we establish the foundations of -equivariant homotopy
theory where is a discrete monoid. For projective -CW complexes we prove
several fundamental results such as the homotopy extension and lifting
property, which we use to prove the -equivariant Whitehead theorems. We
define a left equivariant classifying space as a contractible projective -CW
complex. We prove that such a space is unique up to -homotopy equivalence
and give a canonical model for such a space via the nerve of the right Cayley
graph category of the monoid. The topological finiteness conditions
left- and left geometric dimension are then defined for monoids
in terms of existence of a left equivariant classifying space satisfying
appropriate finiteness properties. We also introduce the bilateral notion of
-equivariant classifying space, proving uniqueness and giving a canonical
model via the nerve of the two-sided Cayley graph category, and we define the
associated finiteness properties bi- and geometric dimension. We
explore the connections between all of the these topological finiteness
properties and several well-studied homological finiteness properties of
monoids which are important in the theory of string rewriting systems,
including , cohomological dimension, and Hochschild
cohomological dimension. We also develop the corresponding theory of
-equivariant collapsing schemes (that is, -equivariant discrete Morse
theory), and among other things apply it to give topological proofs of results
of Anick, Squier and Kobayashi that monoids which admit presentations by
complete rewriting systems are left-, right- and bi-.Comment: 59 pages, 1 figur
Method of measuring the thickness of radioactive thin films
Thickness monitor consists of proportional X-ray counter coupled to pulse counting system, copper filter over face of counter, rotatable collimator containing radioactive source, and rotatable shutter. Monitor can be used as integral part of neutron generator. It has been used to measure titanium tritide film thicknesses from 0.1 to 30 micrometers
A superior process for forming titanium hydrogen isotopic films
Process forms stoichiometric, continuous, strongly bonded titanium hydrogen isotopic films. Films have thermal and electrical conductivities approximately the same as bulk pure titanium, ten times greater than those of usual thin films
An X-ray monitor for measurement of a titanium tritide target thickness
An X-ray device capable of measuring titanium tritide film thickness from 0.1 to 30 micrometers has been built and tested. The monitor was designed for use in a rotating target system which used thick targets and incorporated a sputtering electrode to remove depleted layers from the target surface. The thickness measurement can be done in the presence of an intense background of bremsstrahlung and characteristic titanium X-radiation. A measurement can be accomplished in situ in two hours with reasonable accuracy
A proposed method for regeneration of neutron producing targets, within an accelerator, by ion sputtering techniques
Sputtering electrode system design for regeneration of targets within accelerato
Access to uncombined titanium through an inhibiting film in sublimation pumping of deuterium
It was demonstrated, through a series of experiments, that it is possible (by the addition of a thin layer of titanium to an apparently occluded surface) to gain access to previously deposited sublayers of uncombined titanium in spite of the presence of an inhibiting film (such as an oxide) on the surface
A high yield neutron target
Target, in cylinder form, rotates rapidly in front of beam. Titanium tritide film is much thicker than range of accelerated deutron. Sputtering electrode permits full use of thick film. Stream of high-velocity coolant provides efficient transfer of heat from target
Passage of a Bessel beam through a classically forbidden region
The motion of an electromagnetic wave, through a classically-forbidden
region, has recently attracted renewed interest because of its implication with
regard to the theoretical and experimental problems of superluminality. From an
experimental point of view, many papers provide an evidence of superluminality
in different physical systems. Theoretically, the problem of a passage through
a forbidden gap has been treated by considering plane waves at oblique
incidence into a plane parallel layer of a medium with a refractive index
smaller than the index of the surrounding medium, and also confined (Gaussian)
beams, still at oblique incidence. In the present paper the case of a Bessel
beam is examined, at normal incidence into the layer (Secs. II and III), in the
scalar approximation (Sec. IV) and by developing also a vectorial treatment
(Sec. V). Conclusions are reported in Sic. VI
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