Real Paley-Wiener Theorems

The aim of this paper is to exhibit a real Paley–Wienerspace sitting inside the Schwartz space, and to give a quickand simple proof of a Paley–Wiener-type theorem. A simpleand elementary proof of a theorem postulated by H. H. Bang isalso given. 2000 Mathematics Subject Classification 42A38.     

Multiscale convergence and reiterated homogenization of parabolic problems

Reiterated homogenization is studied for divergence structure parabolic problems of the form u /t–div (a(x,x/,x/²,t,t/ ^k)u )=f. It is shown that under standard assumptions on the function a(x, y ₁,y ₂,t,) the sequence {u } of solutions converges weakly in L ² (0,T; H ₀ ¹ ()) to the solution u of the homogenized problem u/t– div(b(x,t)u)=f.This revised version was published online in April 2005 with a corrected missing date string.     

RNA degradation in cell extracts: real-time monitoring by fluorescence resonance energy transfer

Short noncoding RNAs are increasingly recognized as key regulators of essential cellular processes such as RNA interference. A better understanding of the processes by which such RNAs are degraded is necessary to expand our knowledge of these processes and our ability to harness them. To this end we have developed a novel fluorescence resonance energy transfer (FRET) assay to monitor in real-time the degradation kinetics of short RNAs by a purified RNase and S100 cytosolic HeLa cell extract. An unstructured RNA is found to be degraded more rapidly than a stem-loop RNA under all conditions tested except for low concentrations of cell extract, showing that secondary structure confers protection against RNase activity. The assay also allows for the quantitative comparison of inhibitors such as Contrad70 and aurin tricarboxylic acid (ATA). Finally, gel electrophoretic FRET analysis confirms that HeLa cell extract is dominated by 5' to 3' exonucleolytic activity.     

Identification and Characterization of Monomeric,Volatile SiCl3NH2 as Product of the Reaction between SiCl4 and NH3: An Important Intermediate on the Way to Silicon Nitride?

We studied the reaction of SiCl(4) with NH(3) by mass spectrometry and IR spectroscopy. By means of mass spectrometry, SiCl(3)NH(2) was for the first time identified as an intermediate generated in significant amounts in the course of the reaction. In additional experiments, SiCl(3)NH(2) was formed as a stable gaseous product of the ammonolysis of SiCl(4), and the product was identified and characterized in detail by IR spectroscopic methods (gas phase and matrix isolation) in combination with quantum-chemical calculations. The calculations also gave access to important thermodynamical data.     

An operator splitting method for nonlinear convection-diffusion equations

Summary. We present a semi-discrete method for constructing approximate solutions to the initial value problem for the -dimensional convection-diffusion equation . The method is based on the use of operator splitting to isolate the convection part and the diffusion part of the equation. In the case , dimensional splitting is used to reduce the -dimensional convection problem to a series of one-dimensional problems. We show that the method produces a compact sequence of approximate solutions which converges to the exact solution. Finally, a fully discrete method is analyzed, and demonstrated in the case of one and two space dimensions. ReceivedFebruary 1, 1996 / Revised version received June 24, 1996     

Two simple models for gravitational-wave modes of compact stars

Two simple model problems relevant for the gravitational-wave modes of relativistic stars are discussed. It is shown that the entire mode-spectrum can be obtained if one considers the modes as arising because of the trapping of gravitational waves by the spacetime curvature. The stellar fluid need play no dynamic role. Furthermore, it is shown that two distinct families of gravitational-wave modes exist. The first corresponds to waves trapped inside the star, while the second is similar to acoustic waves scattered off a hard sphere. An infinite number of the first kind of modes exist, but the latter family will only have a few members.     

The spectrum of SiO in the vacuum ultraviolet region

The absorption spectrum of SiO has been photographed at high resolution in the region 1200–1500 Å. Several new electronic states have been observed, valence states as well as Rydberg states. Tables of the molecular constants of all the known states of SiO are given. Due to interactions between the electronic states, the constants of all states analyzed vary irregularly. From the Rydberg series a value of the ionization potential has been derived. It agrees with the value earlier reported, 11.6 ± 0.2 eV.