THE STEP-TRANSITION OPERATORS FOR MULTI-STEP METHODS OF ODE'S

1.'IntroductionThedisad~ageofsymplecticmethodsinusingtheinformationfrompasttimestepsleadstotheirneedingmorefunctionevaluationthannonsymplecticmethods.Thisdisadvantagecanbeovercomeifonecouldconstructsymplecticmulti-stepmethods.But'theaestProblemshouldbesolvedistogiveoutthedefinitionofsymplecticmultistepmethod.Ulltilnow,apopularideaisthatanm-stepmethodonMmaybewrittenasaone-stepmethodonMa.Inpaper12,71,theauthorshaveinvestigatedthecircumstanceunderWhichadifferenceschemecanpreservetheproductsympl…     

Phenomenological πN→ππN amplitude and the modelling of the Olsson–Turner and Chew–Low approaches

The phenomenological amplitude for the reaction πN→ππN fixed by fittings to the experimental data in the energy region 0.300 ≤P _Lab≤ 500 MeV/c is used for modelling the Chew–Low extrapolation and Olsson–Turner threshold approach. It is shown that the uncritical application of the former results in enermous theoretical errors, the extracted values being in fact random numbers. The results of the Olsson–Turner method are characterized by significant systematic errors coming from unknown details of the isobar physics. Received: 10 December 1997     

Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins. Received: 19 March 1998 / Revised and Accepted: 25 May 1998     

A high spin isomer in 153Eu

A search for new isomers of nanosecond lifetimes were carried out in ¹⁵³Eu via the ¹⁵⁰Nd(⁷Li,xnγ) reaction. The single particle angular momentum alignment and dynamical moment of inertia estimated from the experimental data indicate a configuration change at rotational energy ħω∼ 0.30 MeV. A decrease of B(E2) values is also observed at the same frequency. An isomeric level is identified at an excitation energy of 3100 keV (J^π=35/2⁻) which corresponds to this frequency. The lifetime of the level is found to be 8.6 ± 1.3 nanosecond. Received: 22 April 1997 / Revised version: 26 September 1997     

Anomalies of attenuation and phase velocity of surface acoustic waves in YBa2Cu3O7‒δ thin films in the vicinity of Tc

We present measurements of the attenuation and phase velocity of surface acoustic waves in thin YBa₂Cu₃O films as a function of temperature, in magnetic fields up to 3.6 T applied parallel to the c-axis of the films. We have observed anomalies in both, the attenuation and the phase velocity in the vicinity of the superconducting critical temperature which do not depend on the magnetic field. Possible origins of these anomalies, observed, to our knowledge, for the first time in YBa₂Cu₃O thin films, are discussed and compared to bulk acoustic wave experiments. We present a kind of feedback technique for surface acoustic waves which improves the sensitivity of this type of measurement. The actual sensitivity limits are mentioned. Received: 7 August 1997 / Revised: 7 November 1997 / Accepted: 17 November 1997     

Towards an universal classification of scale invariant processes

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed. Received: 7 November 1997 / Received in final form: 26 March 1998 / Accepted: 30 March 1998     

Mn-site doping induced CMR properties in calcium rich manganites Pr1‒xCaxMnO3(0.6 ≤ x ≤ 0.7)

Doping of Mn-site by chromium, cobalt and nickel has been investigated in the calcium rich manganites and . Whatever the nature of the doping element, a rapid disappearance of the charge ordered (CO) state is observed, decreasing as the doping rate increases. But the most important result concerns the Cr-doped compounds for which a re-entrant insulator to metal transition at 90-120 K is observed for x =0.10-0.12, in a zero magnetic field. The possibility to induce colossal magnetoresistance (CMR) properties for high (IV) contents ((IV)/) for x =0.07-0.12 is shown for the first time, the resistance ratios reaching at 30 K. This study also shows differently that the small size of the A-site cation (Pr, Ca) is not a redhibitory obstacle to the appearance of CMR properties in manganites, in contrast with previously established phase diagrams. Received: 18 June 1997 / Revised: 4 August 1997 / Accepted: 10 November 1997     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997