127 research outputs found
Catalytic oxidation of trace levels of methane in oxygen in a tubular reactor
An experimental investigation of catalytic oxidation of trace levels of methane in oxygen was conducted in a tubular reactor. Two noble metal solid catalysts were explored: a 1-percent platinum on gamma alumina and a 0.5-percent rhodium on gamma alumina. For each catalyst the activity was determined as a function of temperature, pressure, space velocity, and methane concentration. The rhodium catalyst was considerably more active than the platinum catalyst. For each catalyst mass transfer had a pronounced effect upon activity at low space velocity
Hopf Categories
We introduce Hopf categories enriched over braided monoidal categories. The
notion is linked to several recently developed notions in Hopf algebra theory,
such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We
generalize the fundamental theorem for Hopf modules and some of its
applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation
Theor
On the classification and properties of noncommutative duplicates
We give an explicit description of the set of all factorization structures,
or twisting maps, existing between the algebras k^2 and k^2, and classify the
resulting algebras up to isomorphism. In the process we relate several
different approaches formerly taken to deal with this problem, filling a gap
that appeared in a recent paper by Cibils. We also provide a counterexample to
a result concerning the Hochschild (co)homology appeared in a paper by J.A.
Guccione and J.J. Guccione.Comment: 11 pages, no figure
The Hopf modules category and the Hopf equation
We study the Hopf equation which is equivalent to the pentagonal equation,
from operator algebras. A FRT type theorem is given and new types of quantum
groups are constructed. The key role is played now by the classical Hopf
modules category. As an application, a five dimensional noncommutative
noncocommutative bialgebra is given.Comment: 30 pages, Letax2e, Comm. Algebra in pres
New types of bialgebras arising from the Hopf equation
New types of bialgebras arising from the Hopf equation (pentagonal equation)
are introduced and studied. They will play from the Hopf equation the same role
as the co-quasitriangular do from the quantum Yang Baxter equation.Comment: Latex2e, Comm Algebra, in pres
Structure of the Effective Potential in Nonrelativistic Chern-Simons Field Theory
We present the scalar field effective potential for nonrelativistic
self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons
gauge field. Fermions are non-minimally coupled to the gauge field via a Pauli
interaction. Gauss's law linearly relates the magnetic field to the matter
field densities; hence, we also include radiative effects from the background
gauge field. However, the scalar field effective potential is transparent to
the presence of the background gauge field to leading order in the perturbative
expansion. We compute the scalar field effective potential in two gauge
families. We perform the calculation in a gauge reminiscent of the
-gauge in the limit and in the Coulomb family gauges.
The scalar field effective potential is the same in both gauge-fixings and is
independent of the gauge-fixing parameter in the Coulomb family gauge. The
conformal symmetry is spontaneously broken except for two values of the
coupling constant, one of which is the self-dual value. To leading order in the
perturbative expansion, the structure of the classical potential is deeply
distorted by radiative corrections and shows a stable minimum around the
origin, which could be of interest when searching for vortex solutions. We
regularize the theory with operator regularization and a cutoff to demonstrate
that the results are independent of the regularization scheme.Comment: 24 pages, UdeM-LPN-TH-93-185, CRM-192
Bicrossed products for finite groups
We investigate one question regarding bicrossed products of finite groups
which we believe has the potential of being approachable for other classes of
algebraic objects (algebras, Hopf algebras). The problem is to classify the
groups that can be written as bicrossed products between groups of fixed
isomorphism types. The groups obtained as bicrossed products of two finite
cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor
The Ideal Intersection Property for Groupoid Graded Rings
We show that if a groupoid graded ring has a certain nonzero ideal property,
then the commutant of the center of the principal component of the ring has the
ideal intersection property, that is it intersects nontrivially every nonzero
ideal of the ring. Furthermore, we show that for skew groupoid algebras with
commutative principal component, the principal component is maximal commutative
if and only if it has the ideal intersection property
Scattering From a Two Dimensional Array of Flux Tubes: A Study of The Validity of Mean Field Theory
Mean Field Theory has been extensively used in the study of systems of anyons
in two spatial dimensions. In this paper we study the physical grounds for the
validity of this approximation by considering the Quantum Mechanical scattering
of a charged particle from a two dimensional array of magnetic flux tubes. The
flux tubes are arranged on a regular lattice which is infinitely long in the
``'' direction but which has a (small) finite number of columns in the
``'' direction. Their physical size is assumed to be infinitesimally small.
We develop a method for computing the scattering angle as well as the
reflection and transmission coefficients to lowest order in the Aharonov--Bohm
interaction. The results of our calculation are compared to the scattering of
the same particle from a region of constant magnetic field whose magnitude is
equal to the mean field of all the flux tubes. For an incident plane wave, the
Mean Field approximation is shown to be valid provided the flux in each tube is
much less than a single flux quantum. This is precisely the regime in which
Mean Field Theory for anyons is expected to be valid. When the flux per tube
becomes of order 1, Mean Field Theory is no longer valid.Comment: 23 pages, University of British Columbia Preprint UBCTP93-01
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