On R-duals and the duality principle in Gabor analysis

The concept of R-duals of a frame was introduced by Casazza, Kutyniok and Lammers in 2004, with the motivation to obtain a general version of the duality principle in Gabor analysis. For tight Gabor frames and Gabor Riesz bases the three authors were actually able to show that the duality principle is a special case of general results for R-duals. In this paper we introduce various alternative R-duals, with focus on what we call R-duals of type II and III. We show how they are related and provide characterizations of the R-duals of type II and III. In particular, we prove that for tight frames these classes coincide with the R-duals by Casazza et el., which is desirable in the sense that the motivating case of tight Gabor frames already is well covered by these R-duals. On the other hand, all the introduced types of R-duals generalize the duality principle for larger classes of Gabor frames than just the tight frames and the Riesz bases; in particular, the R-duals of type III cover the duality principle for all Gabor frames

Lattice vibrations and structural instability in Cesium near the cubic to tetragonal transition

Under pressure cesium undergoes a transition from a high-pressure fcc phase (Cs-II) to a collapsed fcc phase (Cs-III) near 4.2GPa. At 4.4GPa there follows a transition to the tetragonal Cs-IV phase. In order to investigate the lattice vibrations in the fcc phase and seek a possible dynamical instability of the lattice, the phonon spectra of fcc-Cs at volumes near the III-IV transition are calculated using Savrasov's density functional linear-response LMTO method. Compared with quasiharmonic model calculations including non-central interatomic forces up to second neighbours, at the volume $V/V_0= 0.44$ ($V_0$ is the experimental volume of bcc-Cs with $a_0$=6.048{\AA}), the linear-response calculations show soft intermediate wavelength $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons. Similar softening is also observed for short wavelength $L[\xi\xi\xi]$ and $L[00\xi]$ phonons and intermediate wavelength $L[\xi\xi\xi]$ phonons. The Born-von K\'{a}rm\'{a}n analysis of dispersion curves indicates that the interplanar force constants exhibit oscillating behaviours against plane spacing $n$ and the large softening of intermediate wavelength $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons results from a negative (110)-interplanar force-constant $\Phi_{n=2}$. The frequencies of the $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons with $\xi$ around 1/3 become imaginary and the fcc structure becomes dynamically unstable for volumes below $0.41V_0$. It is suggested that superstructures corresponding to the $\mathbf{q}{\neq}0$ soft mode should be present as a precursor of tetragonal Cs-IV structure.Comment: 12 pages, 5 figure

Cyclicity in families of circle maps

In this paper we will study families of circle maps of the form x↦x+2πr+af(x)(mod2π) and investigate how many periodic trajectories maps from this family can have for a ‘typical’ function f provided the parameter a is small

PROGRAMMED EFFECTS OF SURFACE WATER PRICE LEVELS ON U.S. AGRICULTURAL WATER USE AND PRODUCTION PATTERNS

Resource /Energy Economics and Policy,

Seismic signatures of stellar cores of solar-like pulsators: dependence on mass and age

Useful information from the inner layers of stellar pulsators may be derived from the study of their oscillations. In this paper we analyse three diagnostic tools suggested in the literature built from the oscillation frequencies computed for a set of main sequence models with masses between $1.0\, {\rm M}_{\odot}$ and $1.6\, {\rm M}_{\odot}$, to check what information they may hold about stellar cores. For the models with convective cores ($M \geq 1.2\,{\rm M}_{\odot}$) we find a relation between the frequency slopes of the diagnostic tools and the size of the jump in the sound speed at the edge of the core. We show that this relation is independent of the mass of the models. In practice, since the size of the jump in the sound speed is related to the age of the star, using these seismic tools we may, in principle, infer the star's evolutionary state. We also show that when combining two of the three diagnostic tools studied, we are able to distinguish models with convective cores from models without a convective core but with strong sound-speed gradients in the inner layers

On the positive eigenvalues and eigenvectors of a non-negative matrix

The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.Comment: Version 2 allows the matrix to have zero row(s) and rows with infinitely many non-zero entries. In addition the introduction has been rewritte

Sources of nitrogen for winter wheat in organic cropping systems

In organic cropping systems, legumes, cover crops, residue incorporation, and manure application are used to maintain soil fertility, but the contributions of these management practices to soil nitrogen (N) supply remain obscure. We examined potential sources of N for winter wheat (Triticum aestivum L.) in four experimental cropping systems established in 1997 on three soil types. Three of the four systems were under organic management. Topsoil N, depth of the A horizon, and cumulated inputs of N since 1997 were determined at plot level. Labile soil N pools (mineral N, potentially mineralizable N [PMN], microbial biomass N [MBN]) were monitored during two growth periods; at one site, biomass C/N ratios were also determined. Soil for labile N analysis was shielded from N inputs during spring application to isolate cumulated system effects. PMN and MBN were correlated across all sites and rotations (r2=0.72). The MBN corresponded to 46-85, 85-145 and 74-172 kg N ha-1 at the three sites and differed significantly between cropping systems, but MBN could not explain differences in wheat grain N yields. Instead, a multiple linear regression model explained 76 and 82% of the variation in grain N yields in organic cropping systems in 2007 and 2008, showing significant effects of, respectively, topsoil N, depth of A horizon, cumulated inputs of N, and N applied to winter wheat in manure. Thus, soil properties, and past and current management all contributed to winter wheat N supply