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."

Time-related improvement of survival in resectable gastric cancer: the role of Japanese-style gastrectomy with D2 lymphadenectomy and adjuvant chemotherapy

Background: We investigated the change of prognosis in resected gastric cancer (RGC) patients and the role of radical surgery and adjuvant chemotherapy. Methods: We retrospectively analyze the outcome of 426 consecutive patients from 1975 to 2002, divided into 2 time-periods (TP) cohort: Before 1990 (TP1, n = 207) and 1990 or after (TP2; n= 219). Partial gastrectomy and D1-lymphadenetomy was predominant in TP1 and total gastrectomy with D2-lymphadenectomy it was in TP2. Adjuvant chemotherapy consisted of mitomycin C (MMC), 10¿20 mg/m2 iv 4 courses or MMC plus Tegafur 500 mg/m2 for 6 months. Results: Positive nodes were similar in TP2/TP1 patients with 56%/59% respectively. Total gastrectomy was done in 56%/45% of TP2/TP1 respectively. Two-drug adjuvant chemotherapy was administered in 65%/18% of TP2/TP1 respectively. Survival at 5 years was 66% for TP2 versus 42%for TP1 patients (p < 0.0001). Survival by stages II, IIIA y IIIB for TP2 versus TP1 patients was 70 vs. 51% (p = 0.0132); 57 vs. 22% (p = 0.0008) y 30 vs. 15% (p = 0.2315) respectively. Multivariate analysis showed that age, stage of disease and period of treatment were independent variables. Conclusion: The global prognosis and that of some stages have improved in recent years with case RGC patients treated with surgery and adjuvant chemotherapy.

To return or to discard? Randomised trial on gastric residual volume management

Background: The control of gastric residual volume (GRV) is a common nursing intervention in intensive care; however the literature shows a wide variation in clinical practice regarding the management of GRV, potentially affecting patients" clinical outcomes. The aim of this study is to determine the effect of returning or discarding GRV, on gastric emptying delays and feeding, electrolyte and comfort outcomes in critically ill patients. Method: A randomised, prospective, clinical trial design was used to study 125 critically ill patients, assigned to the return or the discard group. Main outcome measure was delayed gastric emptying. Feeding outcomes were determined measuring intolerance indicators, feeding delays and feeding potential complications. Fluid and electrolyte measures included serum potassium, glycaemia control and fluid balance. Discomfort was identified by significant changes in vital signs. Results: Patients in both groups presented similar mean GRV with no significant differences found (p=0.111), but participants in the intervention arm showed a lower incidence and severity of delayed gastric emptying episodes (p=0.001). No significant differences were found for the rest of outcome measurements, except for hyperglycaemia. Conclusions: The results of this study support the recommendation to reintroduce gastric content aspirated to improve GRV management without increasing the risk for potential complications.

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.

Eina per a la visualització de molècules

Aquest TFC consisteix a construir una eina que permet visualitzar molècules en aquest format de visualització. L'eina haurà de permetre navegar al voltant de la molècula i emprar tècniques de selecció que permetin identificar àtoms, calcular distàncies i angles de torsió. A més, s'haurà de poder definir un eix i sobre aquest eix generar una rotació i gravar-la en una pel·lícula (en el format que sigui més senzill).

Diseño de una herramienta para la visualización de moleculas

L'objectiu d'aquest TFC consisteix a desenvolupar i implementar l'eina de visualització molecular opengl: HVM. Aquesta aplicació, que permet la visualització i la inspecció de molècules, és de gran utilitat en àrees com la química, la farmàcia, la docència, etc., i admet definicions de molècules mitjançant un fitxer d'entrada (una variació simplificada del format XMOL XYZ), construint-ne el model, cosa que afavoreix que s'hi pugui navegar, com també la selecció i la identificació dels seus elements i el càlcul de distàncies i angles de torsió entre ells. A més, permet la definició d'un eix sobre el qual es pot generar una rotació del model i gravar una seqüència de sortida.

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2 H4+ X̃2B 3u←C2 H4X̃1 Ag band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B 3u←C2H4X̃1 Ag band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2 D4 results to be not as good as those for C2 H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested