相关论文: Clocks are $e$-positive
We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
In this work we show that the null result of the Michelson-Morley experiment in vacuum is deeply connected with the notion of time. It can be deduced without any mathematics only from the assumption that all good clocks can be used to…
We study the $^1$S$_0 - ^3$D$_2$ and $^1$S$_0 - ^3$D$_3$ transitions in Cu II and the $^1$S$_0 - ^3$P$^{\rm o}_2$ transition in Yb III as possible candidates for the optical clock transitions. A recently developed version of the…
This article explores the relationship between Garding cones, demonstrating that the shift cone $\overline{\Gamma}^{+}_{2}(\alpha)$ is contained in $\overline{\mathcal{P}}_{m}$. By combining these results with the study of positivity…
David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are "simply wrong" because they rely on an incorrect account of how the time…
A digraph $G$ is weightable if its edges can be weighted with real numbers such that the total weight in each directed cycle equals 1. There are several equivalent conditions: that $G$ admits a 0/1-weighting with the same property, or that…
For a periodically shaken optical lattice, effective time-reversal is investigated numerically. For interacting ultra-cold atoms, the scheme of [J. Phys. B 45, 021002 (2012)] involves a quasi-instantaneous change of both the…
Gessel and Sagan investigated the Tutte polynomial, $T(x,y)$ using depth first search, and applied their techniques to show that the number of acyclic partial orientations of a graph is $2^gT(3,1/2)$. We provide a short deletion-contraction…
It is proved that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
Qualitativ arguments are presented which show the incompatibility of the positive results obtaned in experiments on the gravitational redshift of photones and in experiments investigating the behavior of clocks in the gravitational field.
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we…
Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
We examine when the composition of two entire functions f and g is even, and extend some of our results to cyclic compositions in general. We prove some theorems for the cases when f or g is a polynomial. Two of the key theorems we use are…
Lov\'asz has completely characterised the structure of graphs with no two vertex-disjoint cycles, while Slilaty has given a structural characterisation of graphs with no two vertex-disjoint odd cycles; his result is in fact more general,…
Questioning the presumably most basic assumptions about the structure of space and time has revolutionized our understanding of Nature. State-of-the-art atomic clocks make it possible to precisely test fundamental symmetry properties of…
We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass.…