196,969 research outputs found
Polarised ATR-FTIR characterisation of cellulosic fibres in relation to historic artefacts
No full textThe utility of polarised attenuated-total-reflectance (ATR) FTIR spectroscopy was investigated for the identification of cellulosic fibres and characterisation of their state of degradation.Turning the polariser so that the electric vector is parallel (Epll) or perpendicular (Eprp) provides a means of assessing the orientational crystallinity of cellulose from the polarised spectra of aligned plant fibres. Analysis of the spectra can reveal both the angle of microfibrillar wind and its directionality. Here, the best fits to the data suggest: flax 7?/S-spiral; sisal 25?/Z-spiral; coir 70?/S-spiral, where the predominant twist is given for the outer cell-wall regions sampled. Polarised-ATR-FTIR also allows degradation of the amorphous component of cellulose to be highlighted, by recording spectra with the optimum alignment of fibre and polariser. Changes observed on thermal ageing of flax in air at 190 ?C are consistent with oxidation of amorphous cellulose and formation of carbonyl and carboxylate moieties; the non-dichroic nature of the carbonyl band confirms that the ordered crystalline regions were not primarily involved
Ordering Garside groups
No full textWe introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I 2 (m), m ≥ 4, have Dehornoy structures. We show that the left orders on the Artin groups of type A obtained from their Dehornoy structures are the Dehornoy orders. In the case of the Artin groups of type I 2 (m), m ≥ 4, we show that the left orders derived from their Dehornoy structures coincide with the orders obtained from embeddings of the groups into braid groups. 20F3
Ordres sur les groupes de Garside
No full textWe introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I2(m), m ≥ 4, have Dehornoy structures. We show that the left orders on the Artin groups of type A obtained from their Dehornoy structures are the Dehornoy orders. In the case of the Artin groups of type I2(m), m ≥ 4, we show that the left orders derived from their Dehornoy structures coincide with the orders obtained from embeddings of the groups into braid groups.Nous pre´sentons une condition sur les groupes de Garside que nous appelons la structure de Dehornoy. Une ite´ration d’une telle structure conduit a` une ordre a` gauche sur le groupe. Nous montrons des conditions pour qu’un groupe de Garside admet une structure de Dehornoy, et nous appliquons ce crite`re pour prouver que les groupes d’Artin de type A et I2(m), m ≥ 4, ont des structures de Dehornoy. Nous montrons que les ordres a` gauche sur les groupes d’Artin de type A obtenus a` partir de leurs structures de Dehornoy sont les ordres de Dehornoy. Dans le cas des groupes d’Artin du type I2(m), m ≥ 4, nous montrons que les ordres a` gauche de´rive´es de leurs structures de Dehornoy co¨ıncident avec les ordres obtenus a` partir des plongements de ces groupes dans les groupes de tresses
A new Garside structure on torus knot groups and some complex braid groups
No full text24 pages, 1 figure. Comments welcome !Several distinct Garside monoids having torus knot groups as groups of fractions are known. For two coprime integers, we introduce a new Garside monoid having as Garside group the -torus knot group, thereby generalizing to all torus knot groups a construction that we previously gave for the -torus knot group. As a byproduct, we obtain new Garside structures for the braid groups of a few exceptional complex reflection groups of rank two. Analogous Garside structures are also constructed for a few additional braid groups of exceptional complex reflection groups of rank two which are not isomorphic to torus knot groups, namely for and for dihedral Artin groups of even type
A new Garside structure on torus knot groups and some complex braid groups
No full text24 pages, 1 figure. Comments welcome !Several distinct Garside monoids having torus knot groups as groups of fractions are known. For two coprime integers, we introduce a new Garside monoid having as Garside group the -torus knot group, thereby generalizing to all torus knot groups a construction that we previously gave for the -torus knot group. As a byproduct, we obtain new Garside structures for the braid groups of a few exceptional complex reflection groups of rank two. Analogous Garside structures are also constructed for a few additional braid groups of exceptional complex reflection groups of rank two which are not isomorphic to torus knot groups, namely for and for dihedral Artin groups of even type
GARSIDE AND QUADRATIC NORMALISATION: A SURVEY
No full textAbstract. Starting from the seminal example of the greedy normal norm in braid monoids, we analyze the mechanism of the normal form in a Garside monoid and explain how it extends to the more general framework of Garside families. Extending the viewpoint even more, we then consider general quadratic normalisation procedures and characterise Garside normalisation among them. This text is an essentially self-contained survey of a general approach of nor-malisation in monoids developed in recent years in collaboration with several co-authors and building on the seminal example of the greedy normal form of braids independently introduced by S.Adjan [1] and by M.El-Rifai and H.Morton [22]. The main references are the book [17], written with F.Digne, E.Godelle, D.Kram-mer, and J.Michel, the recent preprint [19], written with Y.Guiraud, and, for algorithmic aspects, the article [16], written with V.Gebhardt. If M is a monoid (or a semigroup), and S is a generating subfamily of M, then, by definition, every element of M is the evaluation of some S-word.
A note on Garside monoids and Braces
No full textA left brace is a triple , where is an abelian group, is a group, and there is a left-distributivity-like axiom that relates between the two operations in . In analogy with a left brace, we define a left -brace to be a triple , where is a commutative monoid, is a monoid, and the axiom of left distributivity holds. A lcm-monoid is a left-cancellative monoid such that is the unique invertible element in , and every pair of elements in admit a lcm with respect to left-divisibility. The class of lcm-monoids contains the Gaussian, quasi-Garside and Garside monoids. We show that every lcm-monoid induces a left -brace. Furthermore, we show that every Gaussian group induces a partial left brace.12 pages, 5 figures- updated version with added assumption in Theorem 2 and changes in its proof. arXiv admin note: text overlap with arXiv:2105.1244
A novel method to allow noninvasive, longitudinal imaging of the murine immune system in vivo
No full textIn vivo imaging has revolutionized understanding of the spatiotemporal complexity that subserves the generation of successful effector and regulatory immune responses. Until now, invasive surgery has been required for microscopic access to lymph nodes (LNs), making repeated imaging of the same animal impractical and potentially affecting lymphocyte behavior. To allow longitudinal in vivo imaging, we conceived the novel approach of transplanting LNs into
the mouse ear pinna. Transplanted LNs maintain the structural and cellular organization of conventional secondary lymphoid organs. They participate in lymphocyte
recirculation and exhibit the capacity to receive and respond to local antigenic challenge. The same LN could be repeatedly imaged through time without the requirement for surgical exposure, and the dynamic behavior of the cells within the transplanted LN could be characterized. Crucially, the use of blood vessels as fiducial markers also allowed precise re-registration of the same regions for
longitudinal imaging. Thus, we provide the first demonstration of a method for repeated, noninvasive, in vivo imaging of lymphocyte behavior
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