Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

Efectividad de la terapia cognitivo-conductual en la pérdida de peso tras dos años de cirugía bariátrica en pacientes con obesidad mórbida.

To evaluate the effectiveness of Cognitive Behavioral Therapy (CBT) in the success of postoperative weight loss after 2 years of CB. METHODS: A prospective observational study was conducted in consecutive patients with morbid obesity aged between 18 and 59 yrs and enrolled in the bariatric surgery program of the Obesity Surgery Unit of our hospital from June 2007 through June 2010, with two years postoperative follow-up. Participants were divided into two groups according to their participation in Cognitive Behavioral Therapy or not. Over a 3-month period, CBT was applied in 12 2-h sessions. The main dependent variables studied were body weight and height, from which we calculated BMI and percentage of excess weight lost (weight lost x 100)/(initial weight-ideal weight), classifying patients as successful (E ) those with EPP > 50%, and unsuccessful (NE) those with EPP <50%. Participants were also, assessed for general (stress, anxiety, depression and self-esteem) and specific (binge eating and food craving) psychopathology. RESULTS: Of the 35 patients with bariatric surgery, 30 responded postoperative evaluations, 16 underwent CBT before CB and 14 underwent surgery without receiving psycho-nutritional therapy, (76% female) with a mean age of 41 ± 9.5 years. The mean baseline BMI was 42 ± 10 and 45% of patients were classified as super obese (BMI: 56 ± 6). Mean excess weight loss (EPP) was 77%. According to the EPP were classified as "successful" (S) (59%) and "unsuccessful" (U) (41%). Of the patients assigned to S, 94% received CBT (15 individuals of 17 total), compared with only 12% who did not receive (2 individuals of the 17 total) with statistically significant differences (p < 0.05). Also, the S patients appeared to be significantly less anxious and stressed and have higher self-esteem (P < 0.05). Regarding specific psychopathology, the food craving guided by hunger, loss of control over food intake and guilt was lower in patients who achieved > 50% of EPP (p < 0.04, p < 0.001, p < 0.001, respectively). It was also noted that these patients were plans to eat less and ate less for positive reinforcement (p < 0.03 and p < 0.000, respectively) than the patient group NE

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

El rol de la marca en la comunicación del espacio turístico

El turismo es a menudo el aspecto promocional más visible en el proceso de creación y proyección de una determinada imagen territorial. Esto es debido a que la actividad turística acumula un amplio bagaje en aspectos vinculados a la comercialización de espacios geográficos, y esta circunstancia incide, por ejemplo, en la presencia de numerosa literatura relacionada con la promoción, el marketing y el branding de espacios turísticos. A nivel metodológico, se ha optado por un análisis de fuentes documentales, que ha servido para fijar los cimientos de la evolución de la comunicación de los espacios turísticos mediante el uso de marcas. Se concluye que el registro de la comunicación turística ha experimentado una clara mutación en base a una doble dualidad: de la información a la persuasión y de la promoción a la emoción. Asi mismo, el trabajo en cuestión muestra de qué forma la estrategia comunicativa transcurre nuevamente entorno a las necesidades emociona les del potencial turista y/o visitante en detrimento de las necesidades de información subyacentes al propio destino turístico.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Taller de ciudadanos : la educaci??n integral en la Instituci??n Libre de Ense??anza

Resumen basado en el de la publicaci??n

Contribution to The World Goes Pop exhibition catalogue

Biographies for artists Barel, Joav (p.174), Brudascu, Cornel (p.177), Bucan, Boris (p.178), Chicago, Judy (p.182), Ivekovic, Sanja (p.197), Komar and Melamid (p.200), Lach-Lachowicz, Natalia (p.203), Otasevic, Dusan (p.212), Overstreet, Joe (p.214), Pininska - Beres, Maria (p.215), Rosler, Martha (p.222), Schifano, Mario (p.223), Self, Colin (p.224), Tajiri, Thinkichi (p.228), Tanaami, Keiichi (p.229), Tilson, Joe (p.231), Vardea, Chryssa (p.233), Yokoo, Tadanori (p.234), Zelibska, Jana (p.235) and Zielinski, Jerzy (p.236).

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

Automedicação e guarda de medicamentos por universitários das áreas de saúde e tecnologia

This study aimed to compare self-medication and domestic drug storage among undergraduate students in the areas of health and technology. This is a descriptive study of cross-sectional type and quantitative approach, conducted in a Public University of Natal, Rio Grande do Norte, Brazil. The sample consisted of 300 students of the third year of undergraduate courses at the Center for Health Sciences and Technology Center, selected through a simple random sample. The project was authorized by the Ethics Committee of Federal University of Rio Grande do Norte (CAAE 0137.0.051.000-10). Data collection lasted twelve months and was conducted during the period of study participants, in the university environment. The instrument for data collection was a structured questionnaire consisting of open and closed questions. For data analysis, we used descriptive statistics and applied Fisher s exact test and Chi-square test with adopted level of significance α=5% and 10%. For the variables that correlated with self-medication (p<0.05), we subsequently calculated the odds ratios and confidence intervals. The prevalence of undergraduate students who performed self-medication in the 15 days prior to the collection accounted for 33.7% and, by analyzing each knowledge area, we verified was a higher prevalence of self-medication among students in the technological area (37.3%). The analysis of the socio-demographic characteristics of the participants in this practice revealed a significant difference between the knowledge areas in the income and self-medication variables (p=0.005). General analgesics and antipyretics (N02) represent the therapy group most used in self-medication (57.4%), especially acetaminophen (28.7%), and the main health situations that motivated this practice related to pain, especially headaches (48.5%). Regarding the indication of the drugs used, the majority of students self-medicated themselves on their own (71.3%). As regards to the in-home drug storage, most of the participants had a home pharmacy (88%). By analyzing the socioeconomic characteristics, the variables medical service and home medicine presented a significant difference (p=0.002). General 10 analgesics and antipyretics constituted the medicinal products most found in the home pharmacies, especially acetaminophen. The main room used for the drug storage was the kitchen (36.4%), most students kept these products in boxes of different materials (38.6%) and the medicines stored at home of most of the participants were not easily accessible to children (75%). The results reinforce the need to develop strategies, from the reality found, aiming to encourage and implement educational and preventive activities with undergraduate students on the importance of proper self-medication and in-home drug storage. Despite the sample in our study is relatively small, not representative for the whole country, we believe that, at national level, the panorama of the subject does not present major differences

Über die Linearität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen

Über die Liniarität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. In meiner Arbeit beschäftige ich mich mit Darstellungen der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. Mein Ansatz hierbei ist, die Teichmüllersche Modulgruppe in eine p-adische Liegruppe einzubetten. Sei nun F die von zwei Elementen erzeugte freie Gruppe und Aut(F) die Automorphismengruppe von F. Inhalt des ersten Kapitels ist es nun zu zeigen, daß folgende Aussagen äquivalent sind: - Die Teichmüllersche Modulgruppe des Torus mit zwei Punktierungen ist linear, - Aut(F)ist linear, - F besitzt eine p-Kongruenzstruktur, deren Folgen- glieder von Aut(F) festgehalten werden, also charak- teristisch sind. Im zweiten Kapitel wird unter anderem gezeigt, daß es eine Einbettung einer Untergruppe endlichen Indexes der Aut(F) in die Automorphismengruppe einer einfachen p-adischen Liegruppe gibt. Bisher ist unbekannt, ob die Buraudarstellung treu ist.In dieser Arbeit wird ein unendliches, lineares Gleichungssystem, dessen Lösungen gerade die Koeffizienten der Wörter des Kernes der Buraudarstellung sind, vorgestellt.Im dritten Kapitel wird mit den Methoden des 1.Kapitels gezeigt, daß der Torus mit zwei Punktierungen genau dann linear ist, wenn die Teichmüllersche Modulgruppe der Sphäre mit 5 Punktierungen es auch ist. Bekanntlich ist die 4. Braidgruppe linear. Nun ist aber die 4. Braidgruppe letztlich die Teichmüllersche Modulgruppe der abgeschlossenen Kreisscheibe mit 5 Punktierungen. Wenn man nun deren Randpunkte miteinander identifiziert und anschließend wegläßt, erhält man die 5-fach punktiereSphäre.Mit der eben beschriebenen Abbildung kann man zeigen, daß die Teichmüllersche Modulgruppe der fünffach punktierten Sphäre linear ist.

Frobenius polynomials for Calabi-Yau equations

Sei $\pi:X\rightarrow S$ eine \&quot;uber $\Z$ definierte Familie von Calabi-Yau Varietaten der Dimension drei. Es existiere ein unter dem Gauss-Manin Zusammenhang invarianter Untermodul $M\subset H^3_{DR}(X/S)$ von Rang vier, sodass der Picard-Fuchs Operator $P$ auf $M$ ein sogenannter {\em Calabi-Yau } Operator von Ordnung vier ist. Sei $k$ ein endlicher K\&quot;orper der Charaktetristik $p$, und sei $\pi_0:X_0\rightarrow S_0$ die Reduktion von $\pi$ \uber $k$. F\ur die gew\ohnlichen (ordinary) Fasern $X_{t_0}$ der Familie leiten wir eine explizite Formel zur Berechnung des charakteristischen Polynoms des Frobeniusendomorphismus, des {\em Frobeniuspolynoms}, auf dem korrespondierenden Untermodul $M_{cris}\subset H^3_{cris}(X_{t_0})$ her. Sei nun $f_0(z)$ die Potenzreihenl\osung der Differentialgleichung $Pf=0$ in einer Umgebung der Null. Da eine reziproke Nullstelle des Frobeniuspolynoms in einem Teichm\uller-Punkt $t$ durch $f_0(z)/f_0(z^p)|_{z=t}$ gegeben ist, ist ein entscheidender Schritt in der Berechnung des Frobeniuspolynoms die Konstruktion einer $p-$adischen analytischen Fortsetzung des Quotienten $f_0(z)/f_0(z^p)$ auf den Rand des $p-$adischen Einheitskreises. Kann man die Koeffizienten von $f_0$ mithilfe der konstanten Terme in den Potenzen eines Laurent-Polynoms, dessen Newton-Polyeder den Ursprung als einzigen inneren Gitterpunkt enth\alt, ausdr\ucken,so beweisen wir gewisse Kongruenz-Eigenschaften unter den Koeffizienten von $f_0$. Diese sind entscheidend bei der Konstruktion der analytischen Fortsetzung. Enth\alt die Faser $X_{t_0}$ einen gew\ohnlichen Doppelpunkt, so erwarten wir im Grenz\ubergang, dass das Frobeniuspolynom in zwei Faktoren von Grad eins und einen Faktor von Grad zwei zerf\allt. Der Faktor von Grad zwei ist dabei durch einen Koeffizienten $a_p$ eindeutig bestimmt. Durchl\auft nun $p$ die Menge aller Primzahlen, so erwarten wir aufgrund des Modularit\atssatzes, dass es eine Modulform von Gewicht vier gibt, deren Koeffizienten durch die Koeffizienten $a_p$ gegeben sind. Diese Erwartung hat sich durch unsere umfangreichen Rechnungen best\atigt. Dar\uberhinaus leiten wir weitere Formeln zur Bestimmung des Frobeniuspolynoms her, in welchen auch die nicht-holomorphen L\osungen der Gleichung $Pf=0$ in einer Umgebung der Null eine Rolle spielen.

Periodic Higgs-de Rham flows and representations of algebraic fundamental groups

Let k := bar{F}_p for p > 2, W_n(k) := W(k)/p^n and X_n be a projective smooth W_n(k)-scheme which is W_{n+1}(k)-liftable. For all n > 1, we construct explicitly a functor, which we call the inverse Cartier functor, from a subcategory of Higgs bundles over X_n to a subcategory of flat Bundles over X_n. Then we introduce the notion of periodic Higgs-de Rham flows and show that a periodic Higgs-de Rham flow is equivalent to a Fontaine-Faltings module. Together with a p-adic analogue of Riemann-Hilbert correspondence established by Faltings, we obtain a coarse p-adic Simpson correspondence.

The Hasse-Minkowski Theorem

The Hasse-Minkowski theorem concerns the classification of quadratic forms over global fields (i.e., finite extensions of Q and rational function fields with a finite constant field). Hasse proved the theorem over the rational numbers in his Ph.D. thesis in 1921. He extended the research of his thesis to quadratic forms over all number fields in 1924. Historically, the Hasse-Minkowski theorem was the first notable application of p-adic fields that caught the attention of a wide mathematical audience. The goal of this thesis is to discuss the Hasse-Minkowski theorem over the rational numbers and over the rational function fields with a finite constant field of odd characteristic. Our treatments of quadratic forms and local fields, though, are more general than what is strictly necessary for our proofs of the Hasse-Minkowski theorem over Q and its analogue over rational function fields (of odd characteristic). Our discussion concludes with some applications of the Hasse-Minkowski theorem.