Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

Electric Field Control of Spin Transport

Spintronics is an approach to electronics in which the spin of the electrons is exploited to control the electric resistance R of devices. One basic building block is the spin-valve, which is formed if two ferromagnetic electrodes are separated by a thin tunneling barrier. In such devices, R depends on the orientation of the magnetisation of the electrodes. It is usually larger in the antiparallel than in the parallel configuration. The relative difference of R, the so-called magneto-resistance (MR), is then positive. Common devices, such as the giant magneto-resistance sensor used in reading heads of hard disks, are based on this phenomenon. The MR may become anomalous (negative), if the transmission probability of electrons through the device is spin or energy dependent. This offers a route to the realisation of gate-tunable MR devices, because transmission probabilities can readily be tuned in many devices with an electrical gate signal. Such devices have, however, been elusive so far. We report here on a pronounced gate-field controlled MR in devices made from carbon nanotubes with ferromagnetic contacts. Both the amplitude and the sign of the MR are tunable with the gate voltage in a predictable manner. We emphasise that this spin-field effect is not restricted to carbon nanotubes but constitutes a generic effect which can in principle be exploited in all resonant tunneling devices.Comment: 22 pages, 5 figure

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

On beta-function of tube of light cone

We construct $B$-function of the Hermitian symmetric space \OO(n,2)/\OO(n)\times \OO(2) or equivalently of the tube $(Re z_0)^2> (Re z_1)^2+...+ (Re z_n)^2$ in $C^{n+1}Comment: 7 page

Selection before backcross during exotic germplasm introgression

Introgression of genes from exotic germplasm into breeding populations can broaden the genetic base of crop improvement. Only a very small percentage of genetic variability has been used in crop breeding programs. Traditionally, F1 plants are used to backcross to the adapted lines or populations. An alternative approach is to backcross the F2 individuals selected for agronomic acceptability. Our objective was to determine whether selection before backcross would lead to more progenies with both high yield and acceptable levels of agronomic performance than direct backcross without selection. To test the feasibility of the proposed approach, we conducted parallel experiments in which two exotic sorghum accessions were crossed to two adapted sorghum parents and further backcrossing was conducted with either F1 or selected F2 plants. Fifty random S1 families were evaluated in three test environments. Although selection before backcross resulted in a higher frequency of families with maturity equal to or earlier than those of the adapted parents, no consistent changes in grain yield and plant height were observed between populations with and without selection. Similar results were found with either an inbred or a population as the recurrent parents. Given these findings and the extra generation required, we do not recommend selection before backcross in the process of introgression of exotic germplasm

Phylogeny of the Infraorder Pentatomomorpha Based on Fossil and Extant Morphology, with Description of a New Fossil Family from China

<div><h3>Background</h3><p>An extinct new family of Pentatomomorpha, Venicoridae Yao, Ren & Cai <b>fam. nov.</b>, with 2 new genera and 2 new species (<em>Venicoris solaris</em> Yao, Ren & Rider <b>gen. & sp. nov.</b> and <em>Clavaticoris zhengi</em> Yao, Ren & Cai <b>gen. & sp. nov.</b>) are described from the Early Cretaceous Yixian Formation in Northeast China.</p> <h3>Methodology/Principal Findings</h3><p>A cladistic analysis based on a combination of fossil and extant morphological characters clarified the phylogenetic status of the new family and has allowed the reconstruction of intersuperfamily and interfamily relationships within the Infraorder Pentatomomorpha. The fossil record and diversity of Pentatomomorpha during the Mesozoic is discussed.</p> <h3>Conclusions/Significance</h3><p>Pentatomomorpha is a monophyletic group; Aradoidea and the Trichophora are sister groups; these fossils belong to new family, treated as the sister group of remainder of Trichophora; Pentatomoidea is a monophyletic group; Piesmatidae should be separated as a superfamily, Piesmatoidea. Origin time of Pentatomomorpha should be tracked back to the Middle or Early Triassic.</p> </div

Coherent Structures at the Ocean Surface in Convectively Unstable Conditions

The turbulent boundary layer at the ocean surface has some dynamical similarities to the atmospheric boundary layer. The atmospheric turbulent boundary layer may exhibit not only random fluctuations but also spatially coherent, organized motion. Thorpe conjectured that such organized motion should also be found in the upper ocean boundary layer in convectively unstable conditions. Here I report on observations made in the tropical Atlantic Ocean which confirm this view. Horizontal temperature profiles obtained at a depth of 2m at night revealed ramp-like structures. Vertical velocity profiles in the upper few metres of the ocean was determined using a free-rising profiler, and exhibited abrupt changes corresponding to sudden changes in temperature. These features are known to be characteristic of spatially coherent, organized motions in turbulent boundary layers

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Mapping transmembrane residues of proteinase activated recpetor 2 (PAR2) that influence ligand-modulated calcium signaling

Proteinase-activated receptor 2 (PAR(2)) is a G protein -coupled receptor involved in metabolism, inflammation, and cancers. It is activated by proteolysis, which exposes a nascent N -terminal sequence that becomes a tethered agonist. Short synthetic peptides corresponding to this sequence also activate PAR(2), while small organic molecules show promising PAR(2) antagonism. Developing PAR(2) ligands into pharmaceuticals is hindered by a lack of knowledge of how synthetic ligands interact with and differentially modulate PAR(2). Guided by PAR(2) homology modeling and ligand docking based on bovine rhodopsin, followed by cross-checking with newer PAR(2) models based on ORL-1 and PART, site-directed mutagenesis of PAR(2) was used to investigate the pharmacology of three agonists (two synthetic agonists and trypsin-exposed tethered ligand) and one antagonist for modulation of PAR(2) signaling. Effects of 28 PAR2 mutations were examined for PAR(2)-mediated calcium mobilization and key mutants were selected for measuring ligand binding. Nineteen of twenty-eight PAR(2) mutations reduced the potency of at least one ligand by>10-fold. Key residues mapped predominantly to a cluster in the transmembrane (TM) domains of PAR(2), differentially influence intracellular Ca2+ induced by synthetic agonists versus a native agonist, and highlight subtly different TM residues involved in receptor activation. This is the first evidence highlighting the importance of the PAR(2) TM regions for receptor activation by synthetic PAR(2) agonists and antagonists. The trypsin-cleaved N-terminus that activates PAR(2) was unaffected by residues that affected synthetic peptides, challenging the widespread practice of substituting peptides for proteases to characterize PAR(2) physiology. (C) 2017 Elsevier Ltd. All rights reserved