In the absence of the axiom of choice there are several possible nonequivalent ways of translating the intuitive idea of “infinity” into a mathematical definition. In [10], Tarski investigated some natural infinity notions notions, and his research was continued by Levy [8], Truss [12], Spǐsiak and Vojtas [9], Howard and Yorke [4] and others. The most prominent definitions of finiteness are the...

We show how the nearly bi-maximal mixing scenario comes out naturally from gauged SO(3) F flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle, i.e., ∆m 2 µe /∆m 2 τ µ ≃ 2|U e3 | 2 is obtained. The smallness of the ratio (or |U e3 |) can also naturally be understood from an approximate permutation symmetry....

Let K be a non-archimedean field with residue field k, and suppose that k is not an algebraic extension of a finite field. We prove two results concerning wandering domains of rational functions φ ∈ K(z) and Rivera-Letelier’s notion of nontrivial reduction. First, if φ has nontrivial reduction, then assuming some simple hypotheses, we show that the Fatou set of φ has wandering components by any...

A unit x in a commutative ring R with identity is called exceptional if 1−x is also a unit in R. For any integer n ≥ 2, define φe(n) to be the number of exceptional units in the ring of integers modulo n. Following work of Shapiro, Mills, Catlin and Noe on iterations of Euler’s φ-function, we develop analogous results on iterations of the function φe, when restricted to a particular subset of t...

The title compound, C(11)H(16)O(3), was obtained by reaction of dimedone, 5,5-dimethylcyclohexane-1,3-dione, and α-chloro-acetone. The cyclo-hexenone ring exhibits an envelope conformation with puckering amplitudes Q = 0.433 (2) and Φ = -109.0 (3)°. The 2-oxopropyl fragment is almost perpendicular to the cyclo-hexa-none ring [dihedral angle = 77.72 (8)°]. In the crystal, the mol-ecules are link...

In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite étale extension of R[p−1] is “almost” finite étale over R. Here, we use almost purity to lift the finite étale extension of R[p−1] to a finite étale extension of rin...

S (in alphabetic order by speaker surname) Speaker: Abdelmejid Bayad (Université d’Evry Val d’Essonne) Title: Some facets of multiple Dedekind-Rademacher sums Abstract: We introduce two kind of multiple Dedekind-Rademacher sums, in terms of Bernoulli and Jacobi modular forms. We prove their reciprocity Laws, we establish the Hecke action on these sums and we obtain new Knopp–Petersson identies....

Let φ : X → Y be a generically finite morphism. The purpose of this paper is to show how the OY -algebra structure on φ∗OX controls algebro-geometric aspects of X like the ring generation of graded rings associated to X and the very ampleness of line bundles on X . As the main application of this we prove some new results for certain regular surfaces X of general type. Precisely, we find the de...

We classify a quasiperiodic flow as either algebraic or transcendental. For an algebraic quasiperiodic flow φ on the n-torus, Tn, we prove that an absolute invariant of the smooth conjugacy class of φ, known as the multiplier group, is a subgroup of the group of units of the ring of integers in a real algebraic number field F of degree n over Q. We also prove that for any real algebraic number ...

We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski’s theory of complete ideals and of representation theory. Let R be a commutative ring. The determinantal ideals attached to matrices with entries in R play ubiquitous roles in the study of the syzygies of R–modules. In this note, we describe so...