Author : J. W. S. Cassels
Publisher : Courier Dover Publications
Page : 429 pages
File Size : 21,92 MB
Release : 2008-08-08
Category : Mathematics
ISBN : 0486466701
Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
Author : Roelof W. Bruggeman
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 28,58 MB
Release : 2009-01-21
Category : Mathematics
ISBN : 0821842021
The authors prove a general form of the sum formula $\mathrm{SL}_2$ over a totally real number field. This formula relates sums of Kloosterman sums to products of Fourier coefficients of automorphic representations. The authors give two versions: the spectral sum formula (in short: sum formula) and the Kloosterman sum formula. They have the independent test function in the spectral term, in the sum of Kloosterman sums, respectively.
Author : Dirk Kussin
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 35,5 MB
Release : 2009-08-07
Category : Mathematics
ISBN : 0821844008
In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.
Author : Ping-Shun Chan
Publisher : American Mathematical Soc.
Page : 185 pages
File Size : 17,49 MB
Release : 2010
Category : Mathematics
ISBN : 0821848224
"Volume 204, number 957 (first of 5 numbers)."
Author : Volkmar Liebscher
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 17,61 MB
Release : 2009-04-10
Category : Mathematics
ISBN : 0821843184
In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
Author : Drew Armstrong
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 42,94 MB
Release : 2009-10-08
Category : Mathematics
ISBN : 0821844903
This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.
Author : Skip Garibaldi
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 43,39 MB
Release : 2009-06-05
Category : Mathematics
ISBN : 0821844040
This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.
Author : Eugene Shargorodsky
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 28,85 MB
Release : 2008
Category : Mathematics
ISBN : 0821841890
Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.
Author : Sergiu Aizicovici
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 25,57 MB
Release : 2008
Category : Mathematics
ISBN : 0821841920
In this paper the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one.
Author : Joel Friedman
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 39,51 MB
Release : 2008
Category : Mathematics
ISBN : 0821842803
A $d$-regular graph has largest or first (adjacency matrix) eigenvalue $\lambda_1=d$. Consider for an even $d\ge 4$, a random $d$-regular graph model formed from $d/2$ uniform, independent permutations on $\{1,\ldots,n\}$. The author shows that for any $\epsilon>0$ all eigenvalues aside from $\lambda_1=d$ are bounded by $2\sqrt{d-1}\;+\epsilon$ with probability $1-O(n^{-\tau})$, where $\tau=\lceil \bigl(\sqrt{d-1}\;+1\bigr)/2 \rceil-1$. He also shows that this probability is at most $1-c/n^{\tau'}$, for a constant $c$ and a $\tau'$ that is either $\tau$ or $\tau+1$ (``more often'' $\tau$ than $\tau+1$). He proves related theorems for other models of random graphs, including models with $d$ odd.
