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A Consistency Proof for Some Restrictions of Tait's Reflection Principles
Consistency Proof Restrictions Tait's Reflection Principles
2010/12/9
In [4] Tait identifies a set of reflection principles which he calls (2)n -reflection
principles which Peter Koellner has shown to be consistent relative to an Erd¨os cardinal
(!) in [1].
Recently groups giving rise to irrational l2-Betti numbers have been found.All the examples known so far share a common property: they have one of the lamplighter groups Z/p o Z as a subgroup. In this...
The maximal linear extension theorem in second order arithmetic
maximal linear extension theorem second order arithmetic
2010/12/1
We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA...
Muntz-type theorems on the half-line with weights
Muntz-type theorems half-line with weights
2010/12/14
We consider the linear span S of the functions tak (with some ak > 0)in weighted L2 spaces, with rather general weights. We give one necessary and one sufficient condition for S to be dense. Some comp...
We show that the Cauchy problem for the defocusing generalized Boussinesq equation utt − uxx + uxxxx − (|u|2ku)xx = 0, k 1, on the real line is globally well-posed in Hs(R) for s > 1W...
On the Banach space valued Azuma inequality and small set isoperimetry of Alon-Roichman graphs
Banach space valued Azuma inequality small set isoperimetry of Alon-Roichman graphs
2010/12/14
We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrix. In conjunction with a variant of the Azuma inequality for uniformly smooth no...
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry),which is also a generalization of Conn’s linearization t...
On a possible definition of the moving preferred basis
Decoherence preferred basis relaxation tine decoherence time
2010/12/15
There are many formalisms to describe quantum decoherence. However, many of them give a
non general and ad hoc definition of “pointer basis” or “moving preferred basis”, and this fact is a problem fo...
An asymptotic equivalence between two frame perturbation theorems
asymptotic equivalence two frame perturbation theorems
2010/12/3
In this paper, two stability results regarding exponential frames are compared.The theorems, (one proven herein, and the other in [3]), each give a constant such that if supn∈Z kenk¥ < C, and (eih...
Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples
Trace formula dielectric cavities Regular pseudo-integrable chaotic examples
2010/12/16
Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE 78, 056202 (2008), Ref. [3]] the trace formula f...
Decomposition Theorem for Perverse sheaves on Artin stacks
Decomposition Theorem Perverse sheaves Artin stacks
2010/12/10
We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine automorphism groups over finite fields and over the complex numbers. During the proof, we also give the generic...
Grothendieck $\infty$-groupoids, and still another definition of $\infty$-categories
1-groupoid 1-category homotopy type weak factorization system
2010/12/6
The aim of this paper is to present a simplified version of the notion of 1-groupoid developed by Grothendieck in “Pursuing Stacks” and to introduce a definition of 1-categories inspired by Grothendie...
The most widely known result of Chevalley–Warning type states that if one has a polynomial over a finite field of characteristic p, and the number of variables exceeds the degree, then the number of z...
The Witt construction in characteristic one and Quantization
Witt construction Quantization Entropy
2010/12/2
We develop the analogue of the Witt construction in characteristic one. We construct a functor from pairs (R, ) of a perfect semi-ring R of characteristic one and an element > 1 of R to real Banach...
A Simple Proof of Thue's Theorem on Circle Packing
Simple Proof Thue's Theorem Circle Packing
2010/12/10
Thue's theorem states that the regular hexagonal packing is the densest circle packing in the plane. The density of this circle con guration is p12 0:906 90: