Spurious resonances in a version of the algebraic Resonating-Group Method

It is shown that the conditions claimed to transform the algebraic version of the Resonating-Group Model, originally invented for scattering problems, into a complex eigenvalue problem corresponding to resonant states are necessary but not sufficient. This can be concluded from the fact that false resonances are produced along with true ones. They can be distinguished and discarded by introducing an arbitrary non-linear parameter. The true solutions are invariant against this parameter but the false ones can be swept out even into non-physical regions of the energy.Devoted to Prof. E.W.Schmid on the occasion of his 60th birthday     

On new measures of pseudorandomness of binary lattices

Hubert, Mauduit and Sárközy introduced the pseudorandom measure of order ? of binary lattices. This measure studies the pseudorandomness only on box lattices of very special type. In certain applications one may need measures covering a more general situation. In this paper the line measure and the convex measure are introduced.     

Pseudorandom sequences constructed by the power generator

Summary We study the pseudorandom properties of the power generator (which includes as special cases the RSA generator and the Blum--Blum--Shub generator). In order to estimate the pseudorandom measures character sums with exponential functions are used.     

New source of decoupling of E1 strength from the GDR: boundary condition mixing for s- and p-wave neutron states near threshold

Non-statistical effects in neutron capture reveal that E1 strength of neutron orbits of low l-value is partially decoupled from the GDR. Particle-hole diagonalisations with realistic forces do not show this effect. We show that it can arise from a new source, boundary condition mixing, which operates when fine-structure states are introduced. This may also explain the ‘pygmy dip’ in E1 strength reported for masses ～ 195.     

Syntheses and NMR,MS and X‐ray investigations of homoadamantane‐fused pyridopyrimidinones

The reactions of ethyl 5‐oxotricyclo[4.3.1.1^3,8]undecane‐4‐carboxylate (2) with methyl‐substituted 2‐aminopyridines in polyphosphoric acid (PPA) gave two products, linearly‐condensed pyridopyrimidinones 4a‐c and 2‐pyridylcarboxamides 5a‐c , whereas the reactions with amino, hydroxy and nitro derivatives of 2‐aminopyridine furnished only linearly‐condensed pyridopyrimidinones (4g‐j). Use of a mixture of PPA and phosphorus oxychloride as solvent afforded both linearly‐ (4a‐c,e,f) and angularly‐condensed (6a–c,e,f) pyridopyrimidinones. In toluene, with p‐toluenesulfonic acid as catalyst, 2‐pyridylcarboxamides 5a‐f were obtained. In a mixture of PPA and phosphorus oxychloride at 80–120 °C, 5a‐f yielded angularly‐condensed pyridopyrimidinones 6a‐f. All the products exhibited characteristic features, as determined by NMR and electron ionization mass spectrometry and X‐ray crystallography.     

Shifted products that are coprime pure powers

A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab+1 of two different elements a and b of A is always a pure power, and the occurring pure powers are all coprime. We prove that each coprime Diophantine powerset A⊂{1,…,N} has for sufficiently large N. The proof combines results from extremal graph theory with number theory. Assuming the famous abc-conjecture, we are able to both drop the coprimality condition and reduce the upper bound to for a fixed constant c.     

A note on calculating stripping to an unbound state

Acta physica Academiae Scientiarum Hungaricae - A comparison of the most often used methods for describing stripping to an unbound state has been performed in an exactly soluble...     

On sums which are powers

The cardinality of sets A is estimated under the conditions that every element of the sum set A+A is a power resp. powerful number (n is said to be powerful if p n implies p ² n). Subset sums with these properties are also studied. This revised version was published online in June 2006 with corrections to the Cover Date.