The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Inelastic electron scattering from the three-nucleon bound states with polarization

Spin-dependent inelastic electron scattering from polarized 3He is studied. The theoretical description uses the plane-wave impulse approximation. A spin-dependent spectral function, which summarizes all of the nuclear structure information on the process, is introduced. The formalism is developed for inclusive processes in all kinematic regimes of inelastic electron scattering. A comparison between theoretical predictions and experimental data is carried out in the region of quasifree scattering. The use of a polarized 3He target as a neutron spin target is discussed

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Polarization effects in pion electroproduction from 3He

Inelastic electron scattering from 3He is studied in the kinematic region of pion production. Inclusive processes with polarization of the electron probe and of the 3He target are described in the plane wave impulse approximation. The question to what extent polarized 3He can serve in this kinematic regime as a substitute for unavailable neutron spin targets is discussed

PhosPhAt goes kinases--searchable protein kinase target information in the plant phosphorylation site database PhosPhAt

Reversible phosphorylation is a key mechanism for regulating protein function. Thus it is of high interest to know which kinase can phosphorylate which proteins. Comprehensive information about phosphorylation sites in Arabidopsis proteins is hosted within the PhosPhAt database (http://phosphat.mpimp-golm.mpg.de). However, our knowledge of the kinases that phosphorylate those sites is dispersed throughout the literature and very difficult to access, particularly for investigators seeking to interpret large scale and high-throughput experiments. Therefore, we aimed to compile information on kinase-substrate interactions and kinase-specific regulatory information and make this available via a new functionality embedded in PhosPhAt. Our approach involved systematic surveying of the literature for regulatory information on the members of the major kinase families in Arabidopsis thaliana, such as CDPKs, MPK(KK)s, AGC kinases and SnRKs, as well as individual kinases from other families. To date, we have researched more than 4450 kinase-related publications, which collectively contain information on about 289 kinases. Users can now query the PhosPhAt database not only for experimental and predicted phosphorylation sites of individual proteins, but also for known substrates for a given kinase or kinase family. Further developments include addition of new phosphorylation sites and visualization of clustered phosphorylation events, known as phosphorylation hotspots

Polarized deep-inelastic lepton scattering from the polarized two- and three-nucleon bound states

A relativistic description of polarized deep-inelastic lepton scattering from polarized nuclei is presented. It is based on front form dynamics. Convolution formulas for the nuclear spin structure functions gA1 and gA2 are derived. They require the front form spin distributions of nuclei and the nucleonic spin structure functions. The description is applied to the deuteron and the trinucleon bound states. The numerical calculations show that relativistic effects arising from the consistent quantum mechanical treatment of spin are small. Simple approximations to the convolution formulas for gA1 and gA2 are justified. The approximative convolution formulas allow the subtraction of nuclear effects from measured spin structure functions and therefore the experimental determination of the neutron spin structure functions. Polarized 3He turns out to be a rather reliable effective neutron spin target for deep-inelastic scattering of polarized leptons. The differences between descriptions based on front form and on instant form dynamics are also discussed

Altitude Performance and Operational Characteristics of an XT38-A-2 Turboprop Engine

The overall engine performance and the starting and windmilling characteristics of an XT38-A-2 turboprop engine have been investigated in the NACA Lewis altitude wind tunnel. The simulated flight conditions ranged from altitudes of 5000 to 45,000 feet at a flight Mach number of 0.30 and from Mach numbers of 0.301 to 0.557 at an altitude of 35,000 feet. The engine, equipped with a standard-area exhaust nozzle, was operated with independent control of fuel flow and propeller pitch; operation was thereby allowed over a wide range of engine conditions. Windmilling characteristics were obtained at altitudes of 15,000 feet and 35,000 feet. Analysis of the performance maps obtained at each flight condition revealed that both altitude and flight Mach number had a major effect on corrected engine variables. The large reductions in corrected shaft horsepower occurring when the altitude was increased were the result of decreases in compressor and turbine efficiencies. Windmilling engine starts were made at altitudes as high as 35,000 feet at an engine speed of 2000 rpm