Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

Twisted Reidemeister torsion for twist knots

The aim of this paper is to give an explicit formula for the SL2(C)-twisted Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables given approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.

On uniform conjugators in torsion-free hyperbolic groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Incidencia de hipertensión ocular y glaucoma agudo por bloqueo pupilar tras implante de lente intraocular fáquica tipo ICL. Resultados anatómicos y funcionales a corto y medio plazo. Resultados preliminares

L'implant d’una lent intraocular fàquica tipus ICL (Implantable Collamer Lens) pot produir glaucoma agut per tancament angular degut a un bloqueig pupil•lar amb el consegüent augment de la pressió intraocular, el mecanisme i epidemiologia del qual no són ben coneguts. Aquest estudi preliminar pretén avaluar la incidència d'hipertensió ocular i glaucoma agut per tancament angular degut a bloqueig pupil·lar després de l'implant d'una lent posterior fàquica tipus ICL i plantejar hipòtesis sobre el seu mecanisme fisiopatològic.

Characteristics of the cornea and ocular surface in patients with congenital aniridia

We performed complete eye exams on 50 eyes in 25 patients with congenital aniridia. Factors such as age, history of ocular surgery, dry eye score and aesthesiometry results correlated with the degree of aniridia-related keratopathy. Schirmer’s test I in 86.8%, Schirmer’s test II in 94.4% and TFBUT in 83.3% of cases were all normal. Corneal staining was altered in 54.2%, and conjunctival staining was altered in 45.7%. The tear ferning pattern was abnormal in 80%. Conjunctival metaplasia was present in 76.9%.Corneal endothelial cell density was normal. Ultrasonic pachymetry was higher than average in all eyes examined.

Purinergic receptors in ocular inflammation

Inflammation is a complex process that implies the interaction between cells and molecular mediators, which, when not properly 'tuned,' can lead to disease. When inflammation affects the eye, it can produce severe disorders affecting the superficial and internal parts of the visual organ. The nucleoside adenosine and nucleotides including adenine mononucleotides like ADP and ATP and dinucleotides such as P(1),P(4)-diadenosine tetraphosphate (Ap4A), and P(1),P(5)-diadenosine pentaphosphate (Ap5A) are present in different ocular locations and therefore they may contribute/modulate inflammatory processes. Adenosine receptors, in particular A2A adenosine receptors, present anti-inflammatory action in acute and chronic retinal inflammation. Regarding the A3 receptor, selective agonists like N(6)-(3-iodobenzyl)-5'-N-methylcarboxamidoadenosine (CF101) have been used for the treatment of inflammatory ophthalmic diseases such as dry eye and uveoretinitis. Sideways, diverse stimuli (sensory stimulation, large intraocular pressure increases) can produce a release of ATP from ocular sensory innervation or after injury to ocular tissues. Then, ATP will activate purinergic P2 receptors present in sensory nerve endings, the iris, the ciliary body, or other tissues surrounding the anterior chamber of the eye to produce uveitis/endophthalmitis. In summary, adenosine and nucleotides can activate receptors in ocular structures susceptible to suffer from inflammatory processes. This involvement suggests the possible use of purinergic agonists and antagonists as therapeutic targets for ocular inflammation.

Control and femtosecond time-resolved imaging of torsion in a chiral molecule

We study how the combination of long and short laser pulses can be used to induce torsion in an axially chiral biphenyl derivative (3,5-difluoro-3 ,5 -dibromo-4 -cyanobiphenyl). A long, with respect to the molecular rotational periods, elliptically polarized laser pulse produces 3D alignment of the molecules, and a linearly polarized short pulse initiates torsion about the stereogenic axis. The torsional motion is monitored in real-time by measuring the dihedral angle using femtosecond time-resolved Coulomb explosion imaging. Within the first 4 picoseconds (ps), torsion occurs with a period of 1.25 ps and an amplitude of 3◦ in excellent agreement with theoretical calculations. At larger times, the quantum states of the molecules describing the torsional motion dephase and an almost isotropic distribution of the dihedral angle is measured.We demonstrate an original application of covariance analysis of two-dimensional ion images to reveal strong correlations between specific ejected ionic fragments from Coulomb explosion. This technique strengthens our interpretation of the experimental data

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Galois extension of CP-Graded ring extensions

In this paper, we investigate galois theory of CP-graded ring extensions. In particular, we generalize some galois results given in [1, 2] and, without restriction to nor graded fields nor torsion free of the grade groups, we show that some results of graded field extensions given in [3] hold.

Petits points et conjecture de Bogomolov

This paper is devoted to the statement known as the Bogomolov conjecture on small points. We present the outline of Zhang’s proof of the generalized version of the conjecture. An explicit bound for the height of a non-torsion variety of an abelian variety is obtained in the frame of Arakelov theory. Some further developments are mentioned.

On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

Correlación entre los hallazgos anatomopatológicos y los hallazgos clínicos y de laboratorio en pacientes con arteritis de células gigantes

L’arteritis de cèl•lules gegantes (ACG) és una emergència mèdica i una causa comú de ceguesa en la nostra població major, la qual cosa converteix al oftalmòleg en el responsable del diagnòstic precoç i tractament oportú. Realitzem un estudi retrospectiu de 82 pacients amb sospita clínica de ACG, i es va observar la relació entre les troballes de la biòpsia d'artèria temporal (BAT) amb les troballes clíniques i de laboratori. Trobem que la BAT és poc sensible (50%) i altament específica (100%). 20 (40%) pacients van presentar compromís ocular. El símptoma clínic i el paràmetre de laboratori que es va relacionar amb BAT positiva van ser la claudicació mandibular (P=0,003) i la VSG (P= 0,006) respectivament.

Sedación profunda con propofol en anestesia peribulbar: ¿una opción segura?

L'anestèsia peribulbar és una tècnica anestèsica vàlida per a la cirurgia de cataractes. Consisteix en dues puncions que produeixen bloqueig motor i sensitiu del globus ocular. Per disminuir el dolor i l'ansietat de la punció es pot sedar els pacients. L'objectiu d'aquest treball és avaluar la seguretat de la sedació profunda amb propofol (un fàrmac hipnòtic), en termes de variabilitat hemodinàmica, depressió respiratòria i presència de moviments involuntaris que dificultin la punció.