A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Comment on the existence of a long range correlation in the geomagnetic disturbance storm time (Dst) index

Very recently (Banerjee et al. in Astrophys. Space, doi:1007/s10509-011-0836-1, 2011) the statistics of geomagnetic Disturbance storm (Dst) index have been addressed, and the conclusion from this analysis suggests that the underlying dynamical process can be modeled as a fractional Brownian motion with persistent long-range correlations. In this comment we expose several misconceptions and flaws in the statistical analysis of that work. On the basis of these arguments, the former conclusion should be revisited.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Evidence for the existence of a sulfonylurea-receptor-like protein in plants: Modulation of stomatal movements and guard cell potassium channels by sulfonylureas and potassium channel openers

Limitation of water loss and control of gas exchange is accomplished in plant leaves via stomatal guard cells. Stomata open in response to light when an increase in guard cell turgor is triggered by ions and water influx across the plasma membrane. Recent evidence demonstrating the existence of ATP-binding cassette proteins in plants led us to analyze the effect of compounds known for their ability to modulate ATP-sensitive potassium channels (K-ATP) in animal cells. By using epidermal strip bioassays and whole-cell patch-clamp experiments with Vicia faba guard cell protoplasts, we describe a pharmacological profile that is specific for the outward K+ channel and very similar to the one described for ATP-sensitive potassium channels in mammalian cells. Tolbutamide and glibenclamide induced stomatal opening in bioassays and in patch-clamp experiments, a specific inhibition of the outward K+ channel by these compounds was observed. Conversely, application of potassium channel openers such as cromakalim or RP49356 triggered stomatal closure. An apparent competition between sulfonylureas and potassium channel openers occurred in bioassays, and outward potassium currents, previously inhibited by glibenclamide, were partially recovered after application of cromakalim. By using an expressed sequence tag clone from an Arabidopsis thaliana homologue of the sulfonylurea receptor, a 7-kb transcript was detected by Northern blot analysis in guard cells and other tissues. Beside the molecular evidence recently obtained for the expression of ATP-binding cassette protein transcripts in plants, these results give pharmacological support to the presence of a sulfonylurea-receptor-like protein in the guard-cell plasma membrane tightly involved in the outward potassium channel regulation during stomatal movements.

On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

A note on the non-existence of multivalue A-stable methods of order greater than two /

Bibliography: leaf 3.

An error analysis of solutions to sparse linear programming problems,

"Supported in part by the Advanced Research Projects Agency ... contract no. US AF 30(602) 4144."

On the existence of non-static plane symmetric space-times /

"July 30, 1958"

The existence of evil spirits proved; and their agency, particularly in relation to the human race, explained and illustrated.

Mode of access: Internet.

On the uniqueness of solutions for passage of shock waves through ducts of variable cross section.

"Sponsored by Project SQUID which is supported by the Office of Naval Research under Contract Nonr-1858(25), NR-098-038."

Experimental program to determine the thermodynamic properties of solutions of liquefied light gases /

"October 1964."

Report of the International commission of inquiry into the existence of slavery and forced labor in the republic of Liberia. Monrovia, Liberia, September 8, 1930.

Cuthbert Christy, chairman.

Death and its mystery : before death, proofs of the existence of the soul /

Mode of access: Internet.