161 research outputs found
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
The K-theory of free quantum groups
In this paper we study the K -theory of free quantum groups in the sense of Wang and Van Daele, more precisely, of free products of free unitary and free orthogonal quantum groups. We show that these quantum groups are K -amenable and establish an analogue of the Pimsner–Voiculescu exact sequence. As a consequence, we obtain in particular an explicit computation of the K -theory of free quantum groups. Our approach relies on a generalization of methods from the Baum–Connes conjecture to the framework of discrete quantum groups. This is based on the categorical reformulation of the Baum–Connes conjecture developed by Meyer and Nest. As a main result we show that free quantum groups have a γ -element and that γ=1 . As an important ingredient in the proof we adapt the Dirac-dual Dirac method for groups acting on trees to the quantum case. We use this to extend some permanence properties of the Baum–Connes conjecture to our setting
MAT-756: INVESTIGATION OF THE IMPACT OF RAP GRADATION ON THE EFFECTIVE BINDER CONTENT IN HOT MIX ASPHALT
Nowadays, it is common to add a little amount of Reclaimed Asphalt Pavement (RAP) in asphalt mixes without changing too much properties such as modulus and low temperature cracking resistance. Not only will those mixes be able to make roads last longer, but they will be a greener alternative to usual mixes. In order to make a flexible pavement design, the mixture behavior is usually characterized with the complex modulus. To have a high modulus mix, you need to control the gradation precisely even when RAP is added. When performing a mix design to incorporate RAP, it is desirable to know the RAP binder characteristics and content and its gradation. In the literature, there is no clear vision of the RAP gradation impacts on the mixture properties and field performance. The objective of this study, performed at the Pavements and Bituminous Materials Laboratory (LCMB), is to evaluate the impact of RAP gradation on Hot Mix Asphalt. This is needed to understand how much binder can be transferred during mix from RAP to virgin aggregate. In this study, a single source of RAP was separated into different sizes and mixed with a specific group of virgin aggregates. Then, according to their size, the mixes were separated again into the RAP group and virgin aggregate. While these were mixed, active RAP binder transferred to virgin aggregate. Then ignition test (ASTM D6307) was adapted to separate RAP binder from virgin aggregate. With this procedure, it was possible to see that, for a given temperature and mixing time, activated binder amount of coarse RAP particles and fine RAP particles. The Ignition test result showed that coarse RAP particles have more active binder in mix but ITS test indicated that fine RAP particles have higher strength
On globally non-trivial almost-commutative manifolds
Within the framework of Connes' noncommutative geometry, we define and study
globally non-trivial (or topologically non-trivial) almost-commutative
manifolds. In particular, we focus on those almost-commutative manifolds that
lead to a description of a (classical) gauge theory on the underlying base
manifold. Such an almost-commutative manifold is described in terms of a
'principal module', which we build from a principal fibre bundle and a finite
spectral triple. We also define the purely algebraic notion of 'gauge modules',
and show that this yields a proper subclass of the principal modules. We
describe how a principal module leads to the description of a gauge theory, and
we provide two basic yet illustrative examples.Comment: 34 pages, minor revision
Bicrossproduct approach to the Connes-Moscovici Hopf algebra
We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf
algebra H_CM is isomorphic to a bicrossproduct Hopf algebra linked to a group
factorisation of the group of positively-oriented diffeomorphisms of the real
line. We construct a second bicrossproduct U_CM equipped with a nondegenerate
dual pairing with H_CM. We give a natural quotient Hopf algebra of H_CM and
Hopf subalgebra of U_CM which again are in duality. All these Hopf algebras
arise as deformations of commutative or cocommutative Hopf algebras that we
describe in each case. Finally we develop the noncommutative differential
geometry of the quotient of H_CM by studying covariant first order differential
calculi of small dimension over this algebra.Comment: 21 page
Noncommutative elliptic theory. Examples
We study differential operators, whose coefficients define noncommutative
algebras. As algebra of coefficients, we consider crossed products,
corresponding to action of a discrete group on a smooth manifold. We give index
formulas for Euler, signature and Dirac operators twisted by projections over
the crossed product. Index of Connes operators on the noncommutative torus is
computed.Comment: 23 pages, 1 figur
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
Quantum Field Theory on the Noncommutative Plane with Symmetry
We study properties of a scalar quantum field theory on the two-dimensional
noncommutative plane with quantum symmetry. We start from the
consideration of a firstly quantized quantum particle on the noncommutative
plane. Then we define quantum fields depending on noncommutative coordinates
and construct a field theoretical action using the -invariant measure
on the noncommutative plane. With the help of the partial wave decomposition we
show that this quantum field theory can be considered as a second quantization
of the particle theory on the noncommutative plane and that this field theory
has (contrary to the common belief) even more severe ultraviolet divergences
than its counterpart on the usual commutative plane. Finally, we introduce the
symmetry transformations of physical states on noncommutative spaces and
discuss them in detail for the case of the quantum group.Comment: LaTeX, 26 page
Equivariant comparison of quantum homogeneous spaces
We prove the deformation invariance of the quantum homogeneous spaces of the
q-deformation of simply connected simple compact Lie groups over the
Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the
translation action by maximal tori. This extends a result of Neshveyev-Tuset to
the equivariant setting. As applications, we prove the ring isomorphism of the
K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the
Borsuk-Ulam theorem for quantum spheres.Comment: 21 page
Overview of the Role of 308 Monochromatic Excimer Phototherapy for the Treatment of Alopecia Areata
Treatment of alopecia areata (AA) remains challenging despite the advancement in all these years. Excimer phototherapy has been claimed to offer a practical alternative therapeutic option without significant risks. It is considered a “super-narrowband” UVB light source that emits energy at 308 nm. Excimer laser treatment achieves a remarkable effect in T cell-mediated disorders; thus, it has been used successfully in patients with AA. Compared with narrowband UVB, the excimer laser can induce apoptosis in vitro, paralleled by improved clinical efficacy. Both excimer laser and lamp have a similar effect, but they differ in technology. In this chapter, an evaluation of the effectiveness of 308 nm monochromatic excimer phototherapy in AA treatment is clinically warranted. The evidence-based studies that adopted this option using both laser and light are discussed. In addition, the formulation of therapeutic protocol to study the outcome of excimer treatment on moderate-to-severe AA in adults and children is described
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