Length of the Instability Intervals for Hill's Equation

The length of instability intervals is investigated for the Hill equation y′′+ω(ω− 2∈p(x)y = 0, where p(x) has an infinite Fourier series of coefficients c _n. For any small ∈ it is shown that these lengths are completely characterized by the c _n's.     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary

In this note, we propose to remove some small gaps in the theory of potential spaces H _p ^s (Ω) and Besov spaces B _p ^s (Ω), 1 < p < ∞, s ∈ ℝ, for a bounded Lipschitz domain Ω ⊂ ℝ ⁿ , n ⩾ 2. Namely, we discuss 1) the unified definitions of these spaces with s of any sign, the unified duality theorems and interpolation relations, 2) the possibility of constructing a function in these spaces with given array of traces of its derivatives on the boundary. To the memory of Leonid Romanovich Volevich The work was partially supported by the RFBR grant no. 07-01-00287.     

Study of N*(1440) from J/Ψ decays

For J/Ψ↦ pπ⁰ and pπ⁺π^-, the π⁰ p and pπ⁺π^- systems are limited to be pure isospin-(1/2) due to isospin conservation. This is a big advantage in studying N^* resonances from J/Ψ decays, compared with πN and γN experiments. The process J/Ψ↦ N ^* or p provides a new way to probe the internal structure of the N^* resonances. Here we report a quark model calculation for J/Ψ↦ p, N ^*(1440) and N ^*. The implication for the internal structure of N ^*(1440) is discussed. Received: 1 June 2001 / Accepted: 20 June 2001     

Helicity amplitudes and crossing relations for one-photon exchange antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time-like region. We present the helicity amplitudes for the unequal-mass single-photon reaction pˉ → l ⁺ l ^- in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for one-photon exchange annihilation reaction pˉ → Bˉ are also given, where B is any spin-one-half particle with structure. Crossing relations between the ep → ep scattering and the pˉ → l ⁺ l ^- annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space-like helicity amplitudes due to one-photon exchange.     

How to measure the pomeron phasein diffractive dipion photoproduction

The study of charge asymmetry of pions in the high-energy process ep → eπ⁺π^-p (γp → π⁺π^-p) at very small dipion momenta offers a method to measure the phase of the forward hadronic (quasi-) elastic amplitude γp → ρp. We estimate the potential of such measurements at HERA. Received: 19 February 2004, Revised: 1 August 2005, Published online: 3 November 2005     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

The challenge of polarizations in hadronic hyperon production

The large amount of data on hyperon polarizations in inclusive production by hadrons at high energies has recently been extended to Λ and Ξ ⁻ production by Σ ⁻ beams. The sign of the Ξ ⁻ polarization is negative and the same as in Λ and Ξ ⁻ production by protons. The sign of the Λ polarization, however, is positive, in contrast to the negative sign expected by analogy to the proton beam data for Λ and Ξ ⁻ polarization. Theoretical expectations, for instance from a recombination model, also favoured negative polarization of Λ produced by Σ ⁻. Moreover, while the Λ polarization increases with p _t at values below ≈1 GeV/c as observed for other hyperon polarizations, it vanishes above p _t ≈ 1.2 GeV/c. Such a breakdown at large pt has not been observed in any other beam/hyperon combination.     

Time-and-energy resolved measurement of the cascaded Auger decay in krypton

The cascaded Auger decay following ionization or excitation with 94 eV soft-X-ray pulses from the 3d subshell in krypton has been energy-and-time-resolved for the first time. The decay time of the 4s ⁻¹4p ⁻² nl → 4p ⁻³ + e and/or 4s ⁻¹4p ⁻¹ nl → 4p ⁻² + e transition is measured to be 74 ± 20 fs. Furthermore, our data shows that the electrons with a kinetic energy around 25 eV (generally assigned as 3d ⁻¹ np → 4s ⁻² n′p + e) emitted after core excitation are emitted in a second decay step suggesting an alternative assignment of the form 4s ⁻² np 4p ⁻² + e.     

Phenomenology of the Λ/Σproduction ratio in pp collisions

We show that the recently measured asymmetry in helicity-angle spectra of the Λ-hyperons, produced in the reaction pp → K ⁺Λp reaction, and the energy dependence of the total pp → K ⁺Λp cross-section can be explained consistently by the same Λp final-state interaction. Assuming that there is no final-state interaction in the Σ⁰ p channel, as suggested by the available data for the reaction pp → K ⁺Σ⁰ p, we can also reproduce the energy dependence of the Λ/Σ⁰ production ratio and, in particular, the rather large ratio observed near the reaction thresholds. The nominal ratio of the Λ and Σ⁰ production amplitudes squared, i.e. when disregarding the final-state interaction, turns out to be about 3, which is in line with hyperon production data from proton and nuclear targets available at high energies.     

K0πand K*0Σ+ photoproduction off the proton

The exclusive reactions γp → K ^*0Σ⁺(1189) and γp → K ⁰π⁰Σ⁺(1189) , leading to the p 4π⁰ final state, have been measured with a tagged photon beam for incident energies from threshold up to 2.5GeV. The experiment has been performed at the tagged photon facility of the ELSA accelerator (Bonn). The Crystal Barrel and TAPS detectors were combined to a photon detector system of almost 4π geometrical acceptance. Differential and total cross-sections are reported. At energies close to the threshold, a flat angular distribution has been observed for the reaction γp → K ⁰π⁰Σ⁺ suggesting dominant s -channel production. Σ^*(1385) and higher-lying hyperon states have been observed. An enhancement in the forward direction in the angular distributions of the reaction γp → K ^*0Σ⁺ indicates a t -channel exchange contribution to the reaction mechanism. The experimental data are in reasonable agreement with recent theoretical predictions.     

Optogalvanic detection of NaNe molecule

Summary The formation of NaNe molecule has been detected in a hollow cathode lamp containing traces of sodium and neon using the optogalvanic technique. Two broad continuum peaks have been observed in the structure. They have been analysed to result due to transitions {Na(3s) + Ne(2p ⁶)}²Σ¹→ →{Na*(3p) + Ne(2p ⁶)}²Π,²Σ and {Na*(3p) + Ne(2p ⁶)}²Π,²Σ→{Na*(5s) + Ne(2p ⁶)}²Σ¹. A third peak in between these is probably due to a two-photon transition from 3s→5s of Na in NaNe. The authors of this paper have agreed to not receive the proofs for correction.     

Total scattering cross-section and extraction of low energy parameters of Σ±p scattering

The lowest momentum at which the total scattering cross-section data are available for Σ⁺ p and Σ⁻ p scattering is 145 MeV/c and 142.5 MeV/c respectively. Thus extracting low energy parameters amounts to extrapolating the data to still lower energies. Using the analytic structure of foward scattering amplitude to advantage a parameterization of theσ _T is presented which is hoped to be more reliable and stable for deriving results through extrapolation. The scattering lengths and effective ranges for the Σ⁺ p and Σ⁻ p are also estimated.     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar     

The search for and study of the strange multibaryon states in systems with Λ-hyperon and Ks0 -meson in pA collision at momentum of 10 GeV/c

Exotic strange multibaryon states have been observed in the effective mass spectra of: Λπ^±, Λπ⁺π⁻, Λp, Λpp, Λπp, ΛΛ and ΛK _s ⁰, K _s ⁰ p, K _s ⁰π^± subsystems. The measured Λ/π⁺ ratio for average multiplicities from the pC reaction is equal to (5.3 ± 0.8) × 10⁻², and it is approximately two times larger than the Λ/π⁺ ratio simulated by the FRITIOF model and than that of experimental pp reactions at the same energy. The observed wellknown resonances Σ*⁺ (1385) and K*^± (892) from PDG are good tests of this method. The mean value of the mass for the Σ*⁻(1385) resonance is shifted to 1370 MeV/c ² and the width is two times larger than the same value from PDG. Such kind of behavior for the width and invariant mass of Σ*⁻ (1385) resonance is interpreted as an extensive contribution from stopped Ξ⁻ → Λπ⁻ and medium effect. There is enhancement of the production contribution for all observed hyperons. A few events were registered by hypothesis of light H ⁰ and heavy H ^{0, +} dihyperons. Dihyperons were observed by weak decay channels: (Σ⁻ p), (Λpπ⁻), (Λpπ⁰), and (K ⁻ pp). The text was submitted by the author in English.     

ω(→ π+π?π0) meson photoproduction on proton

The cross-section for the π ⁺ π ⁻ π ⁰ invariant mass distribution in the γp reaction in the GeV region is calculated. This reaction is assumed to proceed through the formation of the ω-meson in the intermediate state, because the production cross-section for this meson in the γp reaction in the GeV region is significant and it has a large branching ratio (88.8%) in the π ⁺ π ⁻ π ⁰ channel. The cross-sections for this reaction are calculated using the energy-dependent reaction amplitude, f _γp→ωp(0), extracted from the latest ω-meson photoproduction data. We use established procedure to calculate other factors, like width and propagator of the ω-meson, so that our calculation can provide reliable cross-section. The calculated results reproduce the measured π ⁺ π ⁻ π ⁰ invariant mass distribution spectra in the γp reaction.     

Anomalously low elastic stability of NaCl-H<Subscript>2</Subscript>O ice at low temperatures

Water-NaCl solid solutions with the salt weight fraction p = 0.0001–0.1000 subjected to high uniaxial compression exhibit elastic instability (similar to the Bridgman explosive effect) in the temperature range 100–260 K. At temperatures from 225 to 260 K, stability threshold P _c (or a critical pressure at which the explosive instability occurs) of these solutions is equal to, or higher than, P _c for pure water ice. However, in the temperature interval 100–225 K, thresholds P _c for the NaCl-water solid solutions with p ≥ 0.001 are anomalously low. The largest drop of P _c (by 15 to 30 times relative to P _c for pure water ice) is observed for low p, 0.001 ≤ p ≤ 0.010. The possible structure of the solid ice solutions in all the temperature ranges mentioned above is analyzed in terms of the percolation theory as applied to elastic networks.     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

Isospin symmetry violation, meson production and η-nucleus interaction studies

We have studied isospin symmetry violation in nuclear reactions by measuring simultaneously the cross-section of the following two reactionsp +d →³H π⁺ andp +d →³He π⁰. The experiment was perfomed at the cooler synchrotron accelerator COSY, Jülich at several beam energies close to the correspondingη production threshold. We also have ongoing programmes onη-nucleus final-state interaction studies viap+⁶ Li →⁷ Be +η reactions, high resolution search for dibaryonic resonances and lambda-proton final state interaction studies. The experimental details and results obtained so far are presented here