Necessary and Sufficient Conditions to be an Eigenvalue for Linearly Recurrent Dynamical Cantor Systems

Necessary and sufficient conditions are given for linearly recurrentCantor dynamical systems to have measurable and continuous eigenfunctions.Also an example of a linearly recurrent system with a nontrivialKronecker factor and a trivial maximal equicontinuous factoris constructed explicitly.     

Analysis of three-nucleon scattering using Faddeev equations up to third order

The Faddeev equations for three nucleons are iterated up to third order using separable interactions: the Tabakin potential for the first order and the Yamaguchi potential for the other orders. This method is applied to the quasi-free scattering ²H(p, 2p)n and ²H(s, np)p. Apparent convergence of the rescattering series is obtained for incident lab energies $\text{E}{}_{\mathrm{<mtext>lab</mtext>}}\text{? 40}\text{MeV}$ and the shape and magnitude of the experimental results are thus reproduced.     

Rayleigh scattering induced by static bends of layers in a smectic A liquid crystal

We observe the anisotropy and the polarization properties of the Rayleigh scattered light for a planar smectic A texture of butoxyl benziledene-p-n anilino-acetophenone (BBAA). This scattering is attributed to static bends of the smectic layers, with wave vectors parallel to the smectic planes. This effect gives a simple method to measure the ratio of the extraordinary to the ordinary indices: n_e/n₀ = 1.18 at 89°C.     

Reactivity and gelation. I. Intrinsic reactivity

The method of Case is used with the Flory-Stockmayer gelation criterion to derive a critical transition equation for polycondensation of multifunctional reactants bearing coreactive functional groups of two species A and B, where the B groups may be of unequal intrinsic reactivity. Systems of the types R(A)₂/R′(B)₄ and R(A)₂/R′(B)₄/R′′(B)₂ are considered with the B groups divided into two classes characterized by a reactivity ratio in the range 0.1 to 10. If the reactivities are sufficiently different the polymerization can be regarded as a multistage process. Intramolecular reactions are not considered.     

Angular distribution of 1.04 GeV protons scattered by 12C, 58Ni, 208Pb

Angular distribution measurements for elastic and inelastic scattering of 1.04 GeV proton by ¹²C, ⁵⁸Ni and ²⁰⁸Pb with an energy resolution of the order of 100 keV are presented.     

A model for the analysis of enthalpies and entropies of liquid binary alloys

The automatic treatment of calculations of chemical equilibrium in homogeneous phases requires analytical representation of the enthalpies and entropies of mixing of the components; therefore various approaches have been investigated, including in particular an attempt to find significant models. The ‘surrounded atom’ model provides a satisfactory method of representing all the thermodynamic characteristics of mixing in binary alloys, on the basis of four adjustable parameters.     

Limiting Absorption Principle for Stratified Operators with Thresholds: A General Method

Out problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto-acoustic operator H defined in ?² × I where I is a bounded interval of ? with coefficients depending only on z ∈ I. The “conjugate operator method” will be applied to an operator obtained by a spectral decomposition of the partial Fourier transform ? of H. Around each value of the spectrum (except the eigenvalues) including the thresholds, a conjugate operator is constructed which permits to get the ”good properties“ of regularity for H. A limiting absorption principle is then obtained for a large class of operators at every point of the spectrum (except eigenvalues).     

Multidimensional extension of the Morse–Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x$x$ over a finite alphabet is ultimately periodic if and only if, for some n$n$, the number of different factors of length n$n$ appearing in x$x$ is less than n+1$n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2$d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Z^d${\mathbb{Z}}^d$ definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉$〈\mathbb{Z};<,+〉$. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d$d$ and characterize sets of Z^d${\mathbb{Z}}^d$ definable in 〈Z;<,+〉$〈\mathbb{Z};<,+〉$ in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often.     

Observations of an ion-driven instability in non-neutral plasmas confined on magnetic surfaces

The first detailed experimental study of an instability driven by the presence of a finite ion fraction in an electron-rich non-neutral plasma confined on magnetic surfaces is presented. The instability has a poloidal mode number m=1, implying that the parallel force balance of the electron fluid is broken and that the instability involves rotation of the entire plasma, equivalent to ion-resonant instabilities in Penning traps and toroidal field traps. The mode appears when the ion density exceeds approximately 10% of the electron density. The measured frequency decreases with increasing magnetic field strength, and increases with increasing radial electric field, showing that the instability is linked to the E x B flow of the electron plasma. The frequency does not, however, scale exactly with E/B, and it depends on the ion species that is introduced, implying that the instability consists of interacting perturbations of ions and electrons.