On a necessary condition for B-spline Gabor frames

In a previous note Gröchenig et al. prove that if g is a continuous function with compact support such that the translates of g form a partition of unity, then g cannot generate a Gabor frame for integer values of the frequency shift parameter b greater than 1 (Gröchenig et al. in IEEE Trans Inform Theory 49:3318–3320, 2003). We give a simpler proof of this result which applies also to windows g which are neither continuous nor with compact support. Our proof is based on a necessary condition for Gabor frames due to Heil and Walnut.     

Frames and oversampling formulas for band limited functions

In this article, we obtain families of frames for the space B _ω of functions with band in [?ω, ω] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of Ron and Shen and a variant, due to Bownik, of their characterization of families of functions whose shifts form frames or Riesz bases. We give necessary and sufficient conditions for the translates of a finite number of functions (generators) to be a frame or a Riesz basis for B _ω . We also give explicit formulas for the dual generators, and we apply them to Hilbert transform sampling and derivative sampling. Finally we provide numerical experiments that support the theory.     

Cracking of Homogeneous Self-Gravitating Compact Objects Induced by Fluctuations of Local Anisotropy

We discuss the effect that small fluctuations of local anisotropy (principal stresses unequal) may have on the occurrence of cracking in spherical compact objects. Two families of homogeneous fluid distributions are considered. For both it is shown that departures from equilibrium may lead to the appearance of cracking, only if fluctuations of local anisotropy are allowed. The case of fluctuations in an initially locally isotropic (perfect fluid) configuration deserves particular attention.     

New measurements of proton-proton total cross section at the CERN intersecting storage rings

Measurements of the proton-proton total cross section have been made with increased precision (±0.6%) over the ISR energy range $\text{s}\text{=23.5?62.7}\text{GeV}$. Two different experimental methods gave consistent results, showing that the total cross section increases 10% over the ISR range and in addition that the absolute value of the ISR luminosity can be measured to ±0.9%.     

Observation of double-Pomeron exchange in alpha-alpha collisions at the CERN intersecting storage rings

We observed the process αα→ααX in which the α′s were emitted uncorrelated in the forward direction and the charged component of the clusterX was confined to a limited portion (|η|?2) of the central region. We identified such reactions as being due to double-Pomeron exchange, for which we found a cross-section of (720±140)μb. The raw mean charged multiplicity of the clusterX was found to be 6.76±0.07 with a dispersionD=4.8. The measurements were performed at the CERN ISR at a centre-of-mass energy of \(\sqrt s = 126\) GeV. Similarities are drawn between double-Pomeron exchange in αα and inpp collisions.     

Study of superdeformed bands in nuclei withA ∼ 150 by heavy-ion-γ coincidences

Superdeformed (SD) bands in¹⁵²Dy,¹⁵¹Dy and¹⁵¹Tb have been populated via the 5n, 6n and 5np evaporation channels, respectively, with the³³S+¹²⁴Sn reaction at 160 and 170 MeV bombarding energies. Population intensities are in good agreement with existing data for SD bands in^{151, 152}Dy and SD yrast band in¹⁵¹Tb. The excited twin SD band in¹⁵¹Tb with the same-transitions as the band in¹⁵²Dy is populated about 5 times more strongly than by the 6n evaporation channel. This might be explained in terms of competition between proton and emission out of an intermediate, excited superdeformed configuration of¹⁵²Dy.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

On Lower Bounds for the Redundancy of Optimal Codes

The problem of providing bounds on the redundancy of an optimal code for a discrete memoryless source in terms of the probability distribution of the source, has been extensively studied in the literature. The attention has mainly focused on binary codes for the case when the most or the least likely source letter probabilities are known. In this paper we analyze the relationships among tight lower bounds on the redundancy r. Let r _D,i(x) be the tight lower bound on r for D-ary codes in terms of the value x of the i-th most likely source letter probability. We prove that _D,i-1(x) _D,i(x) for all possible x and i. As a consequence, we can bound the redundancy when only the value of a probability (but not its rank) is known. Another consequence is a shorter and simpler proof of a known bound. We also provide some other properties of tight lower bounds. Finally, we determine an achievable lower bound on r in terms of the least likely source letter probability for D 3, generalizing the known bound for the case D = 2.     

Fast Runge–Kutta methods for nonlinear convolution systems of Volterra integral equations

In this paper fast implicit and explicit Runge–Kutta methods for systems of Volterra integral equations of Hammerstein type are constructed. The coefficients of the methods are expressed in terms of the values of the Laplace transform of the kernel. These methods have been suitably constructed in order to be implemented in an efficient way, thus leading to a very low computational cost both in time and in space. The order of convergence of the constructed methods is studied. The numerical experiments confirm the expected accuracy and computational cost. AMS subject classification (2000)  65R20, 45D05, 44A35, 44A10