Growth of correlation in the Hopfield model

Introducing a finite correlation ₀ between any two learned patterns (others remaining uncorrelated), we observe in a numerical simulation that the Hopfield model stores these two patterns with correlation _f such that _f0 for any loading capacity. The patterns are memorized perfectly (with _f= ₀) up to -0.05 for finite correlations ₀ not exceeding a value _c(), where _c() decreases continuously to zero at -0.05.     

Self-diffusion in simple models: Systems with long-range jumps

We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self-diffusion coefficientD _N() in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set ofN neighboring sites. We obtain positive upper and lower bounds onF _N()=N{(1–)–[D_N()/D_N(0)]}/[(1–)]x for [0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest thatF _N becomes effectively independent ofN forN20.     

Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

On spherically symmetric perfect fluid distributions and class one property

It is shown that for a spherically symmetric perfect fluid solution to be of class one, either (i) =0, or (ii) +R=0, andR being respectively the eigenvalue of the Weyl tensor in Petrov's classification and spur of the Ricci tensor. Hence, it is deduced that whereas every conformally flat perfect fluid solution is of class one, the converse is not true in general. However, the converse does hold for all solutions with=3p.     

Metastable states in the van der Waals-Maxwell theory

A slight modification of the recent Penrose and Lebowitz treatment of thermodynamic metastable states is presented. For the case of periodic boundary conditions, this modification allows the condition of metastability to be extended to all the metastable states in the van der Waals-Maxwell theory of the liquid-vapor phase transition, that is, for all states satisfyingf ₀()+1/2 ²>f(, 0+) andf₀()+x>0 wheref(, 0+) is the (stable) Helmholtz free energy density of the generalized van der Waals-Maxwell theory andf ₀() is the Helmholtz free energy density of a reference system with no long-range interaction, is a mean field-type term arising from a long-range Kac interaction, is the overall mean particle density, andx is any positive number. For the case of rigid-wall boundary conditions, a more restrictive condition is placed onx.     

A comparison of two models of theρ-meson

A renormalization of the-propagator is presented. It is shown that if the-wave, isovector - amplitude is assumed to be dominated by this renormalized, many scattering parameters are predicted that agree well with experimental data. The model is compared with one presented by Tschang and Parkinson. It is shown that the predictions of the two models are the same, but that the renormalization model does not contain some of the theoretical problems of the Tschang and Parkinson scheme.Research partially supported by NSF Institutional Grant No. GU3220 and a grant from the Research Corporation.     

Relative change of the electron density at the Cu nucleus in Cu-Ag alloys

The decay constant of⁶⁴Cu in Cu–Ag solid solutions has been measured at various Cu concentrations. Deduced values of the relative changes of electron densities (0)/(0) at the Cu nucleus are given. The observed concentration dependence of (0)/(0) is discussed in terms of a volume effect and charge transfer from Cu to Ag.     

Spinor Factorizations of the Bel-Robinson Tensor

Recently Bonilla and Senovilla studied factorizations of the symmetric and tracefree rank four Bel-Robinson tensor T_abcd into two symmetric tracefree rank two tensors. While the Bel-Robinson tensor has the dimension of energy density squared, each of these factors has the dimension of energy density. When the two factors can be chosen to be equal they are called the square root of T_abcd. The approach used was purely tensorial. In this paper we use spinors and show that the factors can be found in a very simple way using the principal null directions of the Weyl tensor. We obtain a factorization of the Weyl spinor into two symmetric rank two spinors, which when multiplied by their complex conjugates give the tracefree and symmetric factors of T_abcd. The factorization is immediately seen to be non-unique in most cases and the number of essentially non-equivalent factorizations becomes clear. It also becomes obvious that the square root only can exist in spacetimes of Petrov types N, D and O, in which cases one can equally well speak about the square root of the Weyl spinor. Explicit formulas for the factors of the Weyl spinor are given for all Petrov types.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

Hall effect in heterogeneous Fe-Ni vacuum condensates

The temperature dependence of the electric conductivity and the Hall and Nernst-Ettinghausen effects of amorphous and microcrystalline Fe-Ni films obtained by ion-plasma sputtering, with a content of technological impurities of about 3 at. %, was studied for the first time. The relationship R_a(T) a²(T), was found between the anomalous Hall constant R_a and . R_a was found to be more sensitive to peculiarities of the complex transformation amorphous, microheterogeneous-crystalline state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–33, September, 1990.     

Determination of the electron density at the Cu nucleus in Cu-Au alloys

The half-life of⁶⁴Cu in Cu–Au solid solutions has been measured as a function of the Cu concentration. Relative changes of electron densities (0)/(0) at the Cu nucleus are deduced. The observed nonlinear concentration dependence of (0)/(0) is discussed in terms of volume and charge transfer effects.     

Contribution of the new vector mesons to the total cross section of hadron photoabsorption

The new vector mesons with mass 1.1 < M < 2 GeV as well as the ⁰,, ,, and mesons are included in the sum rules that relate the total cross section of hadron photoabsorption on the proton to the total cross sections for interaction of vector mesons with the proton. Satisfactory agreement with experiment is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 108–111, September, 1977.     

Product Cocycles and the Approximate Transitivity

Some criteria of the approximate transitivity in the terms of Mackey actions and product cocycles are proved. The Mackey action constructed by an amenable type II or III transformation group G and a 1-cocycle × , where is the Radon–Nikodym cocycle while is an arbitrary 1-cocycle with values in a locally compact separable group A, is approximately transitive (AT) if and only if the pair (G,(, )) is weakly equivalent to a product odometer supplied with a product cocycle. Besides, in the case when the given AT action from the very beginning was a range of a type II action and a nontransient cocycle, then this cocycle turns out to be cohomologous to a -product cocycle. An example is constructed that shows that it is necessary to consider the double Mackey actions since they can not be reduced to the single ones.     

Radius,perimeter, and density profile for percolation clusters and lattice animals

Monte Carlo simulation and series expansion shows the radius of gyration of large clusters withs sites each to vary ass with0.56 in two and0.47 in three dimensions at the percolation threshold, and with(d=2)0.65 and(d=3)0.53 for random lattice animals (zero concentration). Clusters up tos=100 were used. The perimeter of random animals approaches 2.8s for larges on the simple cubic lattice. Monte Carlo simulation of the Eden process (growing animals) up tos=5,000 indicates a systematic variation of about ±0.05 for the effective exponent=(s) and thus suggests that the true asymptotic exponents may be compatible with the predictions of hyper-scaling.     

Scaling Cosmology

We show that with the help of a suitable coupling between dark energy and cold dark matter it is possible to reproduce any scaling solution _{X M} a , where _X and _M are the densities of dark energy and dark matter, respectively. We demonstrate how the case = 1 alleviates the coincidence problem. Future observations of supernovae at high redshift as well as quasar pairs which are planned to discriminate between different cosmological models will also provide direct constraints on the coupling between dark matter and dark energy.     

A comment on an exact solution with a stiff equation of state

Recently, an analytical stellar model with a stiff equation of state and density distribution= _c (1-r ²/r _o ² ) was presented. We show that such a solution cannot exist.     

Superselection rules in quantum theory: Part I. A new proposal for state restriction violation

It is argued that preparation of a quantum state characterized by density operator not commuting with a superselection operatorQ does not by itself constitute an instance of superselection rule violation. It would, however, be an instance of state restriction violation. It is held that superselection rule violation is only possible with simultaneous observable and state restriction violations. It is shown that it is a priori conceivable to subdivide an ensemble whose satisfies[, Q] = 0 into subensembles whose density operators violate the state restrictions. The dynamics of the subdivision process is not considered.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Electrogravitational induction and rotation

The Faradayan hypothesis of inductive coupling of the electromagnetic and gravitational fields is briefly discussed. An experiment designed to test the hypothesis wherein samples are spun to see if any electrogravitational charge is induced is described. Results of the experiment are reported. They imply the induction of a charge density * for spinning samples that behaves as *=_ma, where _m is the mass density of an element of matter experiencing an acceleration a, and is the coupling coefficient for the hypothetical electrogravitational induction effect. In this experiment, is found to have the value(9.6±3.3)×10 ^–13 statcoulombs/dyne. Tests that seem to rule out explanations of the observed charges in terms of conventional charging mechanisms are considered.