Liouville numbers, Liouville sets and Liouville fields

Following earlier work by E.Maillet 100 years ago, we introduce the definition of a Liouville set, which extends the definition of a Liouville number. We also define a Liouville field, which is a field generated by a Liouville set. Any Liouville number belongs to a Liouville set S having the power of continuum and such that the union of S with the rational number field is a Liouville field.Comment: Proceedings of the American Mathematical Society, to appea

Liouville Numbers and Schanuel's Conjecture

In this paper, using an argument of P. Erdos, K. Alniacik and E. Saias, we extend earlier results on Liouville numbers, due to P. Erdos, G.J. Rieger, W. Schwarz, K. Alniacik, E. Saias, E.B. Burger. We also produce new results of algebraic independence related with Liouville numbers and Schanuel's Conjecture, in the framework of G delta-subsets.Comment: Archiv der Math., to appea

Waldschmidt constants for Stanley-Reisner ideals of a class of graphs

In the present note we study Waldschmidt constants of Stanley-Reisner ideals of a hypergraph and a graph with vertices forming a bipyramid over a planar n-gon. The case of the hypergraph has been studied by Bocci and Franci. We reprove their main result. The case of the graph is new. Interestingly, both cases provide series of ideals with Waldschmidt constants descending to 1. It would be interesting to known if there are bounded ascending sequences of Waldschmidt constants.Comment: 7 pages, 2 figure

Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT

Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian $H$ has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and $\tau$) whose coefficients are, in general, formal power series in $q^{1/2}=e^{i\pi\tau}$ involving spherical functions of the "space-like" fields' arguments. As a corollary, if the resulting expansions converge to meromorphic functions, then the finite temperature correlation functions are elliptic. Thermal 2-point functions of free fields are computed and shown to display these features. We also study modular transformation properties of Gibbs energy mean values with respect to the (complex) inverse temperature $\tau$ ($Im(\tau)=\beta/(2\pi)>0$). The results are used to obtain the thermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a historical perspective (new Sect. 1.1 in the Introduction), references added; minor corrections in the rest of the pape

Laparoscopic Sacropexy: A Retrospective Analysis of the Subjective Outcome in 310 Cases

Background and Objective. The aim of this study was to assess the subjective outcome following laparoscopic sacropexy. Methods. We performed a retrospective cohort study among women treated for descensus with laparoscopic sacropexy between January 2000 and December 2007. 310 patients received questionnaires during followup assessing major pre- and postoperative symptoms and overall satisfaction. Results. 214 (69%) patients responded to the questionnaire. Mean followup was 24.5 months. The number of patients with back or lower abdominal pain, foreign body sensation in the vagina and prolapse-related symptoms, urinary symptoms, vaginal and bladder infections, and the need for pessary usage decreased significantly postsurgically. Bowel symptoms increased slightly but not significantly. Two years after surgery, nearly 2 thirds of the women were satisfied or very satisfied with the outcome. Conclusion. Laparoscopic sacropexy is an effective treatment of descensus, with favorable or satisfactory subjective outcomes

Genetics of Euglossini bees (Hymenoptera) in fragments of the Atlantic Forest in the region of Viçosa, MG

With uncontrolled deforestation, forest fragments remain, which in most cases are in different stages of regeneration and present isolated populations. In the present study we analyzed the genetic patterns of Eulaema nigrita populations in seven Atlantic Forest fragments of different sizes and successional stages in the region of Viçosa, MG. This was done by RAPD molecular markers. We observed that the area of the fragments had no effect on the genetic variability of E. nigrita in the direction predicted by meta-population models. Medium-sized well-preserved woods presented the lowest variability, whereas large and small woods were statistically identical. The evidence supports the notion that rural areas present greater dispersal among fragments, implying greater similarity between the populations of fragments located in rural areas when compared to fragments in urban areas.Com o desmatamento descontrolado das florestas há a formação de fragmentos de mata que, na maioria das vezes, se encontram em distintos estágios de regeneração, mantendo populações isoladas. Neste trabalho foi feita a análise dos padrões genéticos de populações de Eulaema nigrita de fragmentos de mata Atlântica de diferentes tamanhos e estágios sucessionais por meio de marcadores moleculares RAPD da região de Viçosa, MG. Pode-se verificar que a área dos fragmentos não apresentou efeito sobre a variabilidade genética em E. nigrita na direção predita pelos modelos de metapopulação. Uma mata de tamanho médio e bem preservada apresentou a menor variabilidade, enquanto matas grandes e pequenas foram estatisticamente iguais. As evidências sustentam que áreas rurais apresentam maior dispersão entre fragmentos, implicando maior similaridade entre as populações de fragmentos localizados em áreas rurais se comparados com fragmentos nas áreas urbanizadas

Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

A Novel Target-Height Estimation Approach Using Radar-Wave Multipath Propagation for Automotive Applications

This paper introduces a novel target height estimation approach using a Frequency Modulation Continuous Wave (FMCW) automotive radar. The presented algorithm takes advantage of radar wave multipath propagation to measure the height of objects in the vehicle surroundings. A multipath propagation model is presented first, then a target height is formulated using geometry, based on the presented propagation model. It is then shown from Sensor-Target geometry that height estimation of targets is highly dependent on the radar range resolution, target range and target height. The high resolution algorithm RELAX is discussed and applied to collected raw data to enhance the radar range resolution capability. This enables a more accurate height estimation especially for low targets. Finally, the results of a measurement campaign using corner reflectors at different heights are discussed to show that target heights can be very accurately resolved by the proposed algorithm and that for low targets an average mean height estimation error of 0.03 m has been achieved by the proposed height finding algorithm

Variation and genetic structure of Melipona quadrifasciata Lepeletier (Hymenoptera, Apidae) populations based on ISSR pattern

For a study of diversity and genetic structuring in Melipona quadrifasciata, 61 colonies were collected in eight locations in the state of Minas Gerais, Brazil. By means of PCR analysis, 119 ISSR bands were obtained, 80 (68%) being polymorphic. He and H B were 0.20 and 0.16, respectively. Two large groups were obtained by the UPGMA method, one formed by individuals from Januária, Urucuia, Rio Vermelho and Caeté and the other by individuals from São João Del Rei, Barbacena, Ressaquinha and Cristiano Otoni. The Φst and θB values were 0.65 and 0.58, respectively, thereby indicating high population structuring. UPGMA grouping did not reveal genetic structuring of M. quadrifasciata in function of the tergite stripe pattern. The significant correlation between dissimilarity values and geographic distances (r = 0.3998; p < 0.05) implies possible geographic isolation. The genetic differentiation in population grouping was probably the result of an interruption in gene flow, brought about by geographic barriers between mutually close geographical locations. Our results also demonstrate the potential of ISSR markers in the study of Melipona quadrifasciata population structuring, possibly applicable to the studies of other bee species