The present book collects most of the courses and seminars delivered at the
meeting entitled “ Frontiers in Number Theory, Physics and Geometry”, which
took place at the Centre de Physique des Houches in the French Alps, March 9-
21, 2003. It is divided into two volumes. Volume I contains the contributions on
three broad topics: Random matrices, Zeta functions and Dynamical systems.
The present volume contains sixteen contributions on three themes: Conformal
field theories for strings and branes, Discrete groups and automorphic forms
and finally, Hopf algebras and renormalization....
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number ﬁelds. Suppose K/k is a quadratic extension of number ﬁelds, E is an elliptic curve deﬁned over k, and p is an odd prime. Let K− denote the maximal abelian p-extension of K that is unramiﬁed at all primes where E has bad reduction and that is Galois over k with dihedral Galois group (i.e., the generator c of Gal(K/k) acts on Gal(K− /K) by inversion). We prove (under mild hypotheses on p) that if the Zp -rank of the pro-p Selmer group Sp...
Mathematical theories and methods and effective computational algorithms are crucial
in coping with the challenges arising in the sciences and in many areas of their
application. New concepts and approaches are necessary in order to overcome the
complexity barriers particularly created by nonlinearity, high-dimensionality, multiple
scales and uncertainty. Combining advanced mathematical and computational
methods and computer technology is an essential key to achieving progress, often
even in purely theoretical research.
Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: The inverse problem associated to the Davenport constant for C2 ⊕ C2 ⊕ C2n, and applications to the arithmetical characterization of class groups...
This is a report on the recent proof of the fundamental lemma. The fundamental lemma and the related transfer conjecture were formulated by R. Langlands in the context of endoscopy theory in . Important arithmetic applications follow from endoscopy theory, including the transfer of automorphic representations from classical groups to linear groups and the construction of Galois representations attached to automorphic forms via Shimura varieties.
C H A P T E R
General directions – summarizing data
This chapter will help you to:
■ ■ ■ ■ ■ ■
understand and use summary measures of location; the mode, median and arithmetic mean understand and use summary measures of spread; the range, quartiles, semi inter-quartile range, standard deviation, variance present order statistics using boxplots find summary measures from grouped data use the technology: summarize data in EXCEL,
Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.
Data of unknown quality are useless! All laboratory measurements contain experimental error.
It is necessary to determine the magnitude of the accuracy and reliability in your measurements. Then you can make a judgment about their usefulness.
Replicates - two or more determinations on the same sample Example 3-1: One student measures Fe (III) concentrations six times. The results are listed below: 19.4, 19.5, 19. 6, 19.8, 20.1, 20.3 ppm (parts per million) 6 replicates = 6 measurements The "middle" or "central" value for a group of results: Mean: average or arithmetic mean