Some supports of Fourier transforms of singular measures are not Rajchman

The notion of Riesz sets tells us that a support of Fourier transform of a measure with non-trivial singular part has to be large. The notion of Rajchman sets tells us that if the Fourier transform tends to zero at infinity outside a small set, then it tends to zero even on the small set. Here we present a new angle of an old question: Whether every Rajchman set should be Riesz

An example of a minimal action of the free semi-group \F^{+}_{2} on the Hilbert space

The Invariant Subset Problem on the Hilbert space is to know whether there exists a bounded linear operator $T$ on a separable infinite-dimensional Hilbert space $H$ such that the orbit $\{T^{n}x;\ n\ge 0\}$ of every non-zero vector $x\in H$ under the action of $T$ is dense in $H$. We show that there exists a bounded linear operator $T$ on a complex separable infinite-dimensional Hilbert space $H$ and a unitary operator $V$ on $H$, such that the following property holds true: for every non-zero vector $x\in H$, either $x$ or $Vx$ has a dense orbit under the action of $T$. As a consequence, we obtain in particular that there exists a minimal action of the free semi-group with two generators \F^{+}_{2} on a complex separable infinite-dimensional Hilbert space $H$.Comment: 10

Conjugacy of real diffeomorphisms. A survey

Given a group G, the conjugacy problem in G is the problem of giving an effective procedure for determining whether or not two given elements f, g of G are conjugate, i.e. whether there exists h belonging to G with fh = hg. This paper is about the conjugacy problem in the group Diffeo(I) of all diffeomorphisms of an interval I in R. There is much classical work on the subject, solving the conjugacy problem for special classes of maps. Unfortunately, it is also true that many results and arguments known to the experts are difficult to find in the literature, or simply absent. We try to repair these lacunae, by giving a systematic review, and we also include new results about the conjugacy classification in the general case.Comment: 53 page

A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces

We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of operators without non-trivial invariant subspaces on the spaces $\ell_{1}$, $c_{0}$ or $\oplus_{\ell_{2}}J$, and without non-trivial invariant subsets on $\ell_{1}$. We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasireflexive dual Banach space which has no non-trivial $w^{*}$-closed invariant subspace.Comment: Minor modification

Flowability of plane homeomorphisms

We describe necessary and sufficient conditions for an orientation preserving fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.Comment: 20 pages, 3 figure

The spectral radius formula for Fourier-Stieltjes algebras

In this short note we first extend the validity of the spectral radius formula obtained in \cite{ag} to Fourier--Stieltjes algebras. The second part is devoted to showing that for the measure algebra on any locally compact non-discrete Abelian group there are no non-trivial constraints between three quantities: the norm, the spectral radius and the supremum of the Fourier--Stieltjes transform even if we restrict our attention to measures with all convolution powers singular with respect to Haar measure

Analysis of Novel Intermediate of Guanine-Guanine Crosslink Produced in Reactions of One-Electron Oxidation of Guanine Derivatives by Using 8-Substituted 2´-Deoxyguanosines as Analog Compounds

Oxidative damage to DNA has been implicated in a plethora of pathologies, such as cancer, neurodegenerative diseases, cardiovascular diseases, and aging. One-electron transfer (OET) plays a significant role in oxidative DNA damage in vivo. Guanine as the most oxidizable part of DNA is the major focus of studies on oxidation damage to DNA initiated by OET. Until recently, the pathway of guanine one-electron oxidation via its neutral guanine radical, G·, has been poorly studied. Our recent research has discovered a novel type of products of G· dimerization, D1 and D2, formed as a result of oxidation reaction of guanine derivatives, initiated by OET. A proposed reaction mechanism contains an early intermediate (Int1) generated by recombination of the two G· radicals. We were not able to isolate Int1, so that its role in the proposed reaction mechanism is only hypothetical. Literature data have reported that 8-arylamino-substituted 2´-deoxyguanosine (dGuo) compounds can be oxidized to create structural analogs of D1 and D2. As a result, the original 8-substituted dGuo compounds can serve as analogs of Int1. The goal of this work is therefore to confirm that Int1 is a precursor to D1 and D2 using the analogy approach. Two 8-aryl- and three 8-alkyl-substituted dGuo compounds were synthesized, purified by semipreparative HPLC, and their structures were confirmed by 1H-NMR. 8-subsituted oxidation products analogous to D1 and D2 were obtained from 8-substituted dGuo analogs upon illumination the reaction mixture in the presence of S2O82- as a oxidant and Ru(II)bpy32+ as a photosensitizer at 470 nm. The products were purified by semipreparative HPLC, and their structures were confirmed by 1H-NMR. The purified analogs of D1 were successfully tested for conversion into the D2 analog. Finally, the analogs of D2 were successfully tested for the reaction with primary amines to form analogs of 2-aminoimidozalone (AIz), in agreement with the mechanism characteristic of D2

Infrared and THz studies of polar phonons and improper magnetodielectric effect in multiferroic BFO3 ceramics

BFO3 ceramics were investigated by means of infrared reflectivity and time domain THz transmission spectroscopy at temperatures 20 - 950 K, and the magnetodielectric effect was studied at 10 - 300 K, with the magnetic field up to 9 T. Below 175 K, the sum of polar phonon contributions into the permittivity corresponds to the value of measured permittivity below 1 MHz. At higher temperatures, a giant low-frequency permittivity was observed, obviously due to the enhanced conductivity and possible Maxwell-Wagner contribution. Above 200 K the observed magnetodielectric effect is caused essentially through the combination of magnetoresistance and the Maxwell-Wagner effect, as recently predicted by Catalan (Appl. Phys. Lett. 88, 102902 (2006)). Since the magnetodielectric effect does not occur due to a coupling of polarization and magnetization as expected in magnetoferroelectrics, we call it improper magnetodielectric effect. Below 175 K the magnetodielectric effect is by several orders of magnitude lower due to the decreased conductivity. Several phonons exhibit gradual softening with increasing temperature, which explains the previously observed high-frequency permittivity increase on heating. The observed non-complete phonon softening seems to be the consequence of the first-order nature of the ferroelectric transition.Comment: subm. to PRB. revised version according to referees' report