An application of the effective Sato-Tate conjecture

Based on the Lagarias-Odlyzko effectivization of the Chebotarev density theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for an elliptic curve conditional on analytic continuation and Riemann hypothesis for the symmetric power $L$-functions. We use Murty's analysis to give a similar conditional effectivization of the generalized Sato-Tate conjecture for an arbitrary motive. As an application, we give a conditional upper bound of the form $O((\log N)^2 (\log \log 2N)^2)$ for the smallest prime at which two given rational elliptic curves with conductor at most $N$ have Frobenius traces of opposite sign.Comment: 12 pages; v2: refereed versio

The probability that a complete intersection is smooth

Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case of a single hypersurface, due to Poonen. We use this result to give a probabilistic model for the number of rational points of such a complete intersection. A somewhat surprising corollary is that the number of rational points on a random smooth intersection of two surfaces in projective 3-space is strictly less than the number of points on the projective line.Comment: 14 pages; v3: final journal versio

Effective Sato-Tate conjecture for abelian varieties and applications

From the generalized Riemann hypothesis for motivic L-functions, we derive an effective version of the Sato-Tate conjecture for an abelian variety A defined over a number field k with connected Sato-Tate group. By effective we mean that we give an upper bound on the error term in the count predicted by the Sato-Tate measure that only depends on certain invariants of A. We discuss three applications of this conditional result. First, for an abelian variety defined over k, we consider a variant of Linnik's problem for abelian varieties that asks for an upper bound on the least norm of a prime whose normalized Frobenius trace lies in a given interval. Second, for an elliptic curve defined over k with complex multiplication, we determine (up to multiplication by a nonzero constant) the asymptotic number of primes whose Frobenius trace attain the integral part of the Hasse-Weil bound. Third, for a pair of abelian varieties defined over k with no common factors up to k-isogeny, we find an upper bound on the least norm of a prime at which the respective Frobenius traces have opposite sign.Comment: 28 page

SENSOR ARRAY ABLE TO DETECT AND RECOGNISE CHEMICAL WARFARE AGENTS

In this paper we studied a device based on array of six different sensors with surface acoustic wave for detections and recognition of three chemical warfare agents (chloropicrin, soman and lewisite). The sensors are “delay line” type with a center frequency of 69.4 MHz. It presents an original algorithm to identify the nature and concentration of gas from a finite range of possible gases. Numerical program developed to implement this algorithm, provides to operators all the particulars of gas and an indicator of credibility of the results provided as a measure of the degree of disturbance of the signals received from sensors.SAW, chemical warfare agent, array of sensors, algorithm

All functions are (locally) ss-harmonic (up to a small error) - and applications

The classical and the fractional Laplacians exhibit a number of similarities, but also some rather striking, and sometimes surprising, structural differences. A quite important example of these differences is that any function (regardless of its shape) can be locally approximated by functions with locally vanishing fractional Laplacian, as it was recently proved by Serena Dipierro, Ovidiu Savin and myself. This informal note is an exposition of this result and of some of its consequences

ASPECTS REGARDING THE ENERGETICALLY EFFICIENCY OF IRRIGATION OF SOME CROPS IN NORTH-EAST ROMANIA

On the basis of some registered information in three areas from Moldova, it was calculated the energy balance and the energetically efficiency of the applied irrigation on eight species of plants. The information's obtained proved that the irrigation process is efficient from the energetically point of view for all the field crops which have been seen in south droughty zone and this process is less efficient in central and moderate warm and moist zone. In the cool moist zone from northern, the irrigation process is efficient only in a few cultures. On the slope lands, where the cultures need more water, the energetically efficiency of the irrigation process is greater than on a plat field. The greatest values of the balance and energetically efficiency were obtained in sugar beet, followed by alfalfa, maize for grain or silage, potato, wheat and sunflower, on the last places coming soybean and bean. There reacted favourable to irrigation the sugar beet, followed by maize for grain or silage, sunflower, potato and wheat, in bean and soybean being registered an energy balance very reduced

A brief review on micro-implants and their use in orthodontics and dentofacial orthopaedics

The aim of this study was to review the literature and evaluate the failure rates and factors that affect the stability and success of temporary anchorage devices (TADs) used as orthodontic anchorage. Data was collected from electronic databases: MEDLINE database and Google Scholar. Four combinations of term were used as keywords: \u201cmicro-implant\u201d, \u201cmini-implant\u201d, \u201cmini-screw\u201d, and \u201corthodontics\u201d. The following selection criteria were used to select appropriate articles: articles on implants and screws used as orthodontic anchorage, published in English, with both prospective and retrospective clinical and experimental investigations. The search provided 209 abstracts about TADs used as anchorage. After reading and applying the selection criteria, 66 articles were included in the study. The data obtained were divided into two topics: which factors affected TAD success rate and to what degree and in how many articles they were quoted. Clinical factors were divided into three main groups: patient-related, implant related, and management-related factors. Although all articles included in this meta-analysis reported success rates of greater than 80 percent, the factors determining success rates were inconsistent between the studies analyzed and this made conclusions difficult

Estrategia pedag?gica para disminuir la deserci?n escolar

68 p. Recurso Electr?nicoEste proyecto de investigaci?n hace parte del proceso de formaci?n de la Especializaci?n en Gerencia de Instituciones Educativas del IDEAD, Universidad del Tolima, cuyo prop?sito fundamental es contribuir a la disminuci?n de los ?ndices de deserci?n escolar de la Instituci?n Educativa T?cnica Musical Amina Melendro de Pulecio, Sede San Jorge, de la ciudad de Ibagu?; mediante la formulaci?n de una estrategia pedag?gica. Luego de avanzar en el proceso de investigaci?n diagn?stica sobre la problem?tica observada por docentes y funcionarios especialmente en el Grado Quinto de la secci?n primaria de la instituci?n educativa y la aplicaci?n de algunas herramientas como entrevistas semi-estructuradas y estructuradas, encuestas, observaci?n y revisi?n directa de documentos institucionales y de emprender una revisi?n bibliogr?fica en busca de la fundamentaci?n y comprensi?n de la problem?tica observada, se pudo determinar que la principal causa de deserci?n escolar en esta Instituci?n es la p?rdida paulatina del inter?s musical por parte de los estudiantes. Mediante el desarrollo de un ejercicio de an?lisis reflexivo de los resultados obtenidos y el planteamiento de diferentes opciones, finalmente se opt? por el dise?o y formulaci?n del proyecto de aula trasversal ?Aprendiendo al son de la m?sica? como estrategia pedag?gica, que involucra a los docentes de las ?reas b?sicas y que pretende incentivar continuamente el gusto por la m?sica en los estudiantes, para que as? permanezcan y contin?en su proceso de formaci?n acad?mica y musical. Palabras Claves: Deserci?n escolar, estrategia pedag?gica.This research project makes part of the process of formation of the specialization in management of educational institutions of the IDEAD, Tolima University, whose fundamental purpose is to contribute to decrease the index of school desertion of the Educational Technical Musical Institution Amina Melendro in Puelcio, San Jorge headquarters, in the city of Ibagu?; Through the formulation of a pedagogical strategy. After advancing in the diagnostic research process about the problem observed by the teachers and functionaries, especially in grade 5th of the elementary section in the educational institution and the application of some tools, such as semi-structured interviews, surveys, observation and direct revision of institutional documents and of undertaking a bibliographic review searching for the foundation and comprehension of the problem observed, it could be determined that the main cause of school desertion in this institution is the gradual loss of the musical interest on behalf of the students. Though the development of an exercise of reflexive analysis of the results obtained and the careful study of different options, it was finally decided the design and formulation of the cross classroom project named ?learning to the sound of music? as a pedagogical strategy that involves teachers from the basic areas and that pretends to encourage continuously the students? taste for music, so in this way they may remain in the school and continue their academic and musical formation. Keywords: School desertion, pedagogical strategy, cross classroom project