“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

General solutions of the Monge-Ampère equation in n-dimensional space

It is shown that the general solution of a homogeneous Monge-Ampère equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ξ_j/∂x₀ + Σ_k=1ⁿ⁻¹ ξ_k ∂ξ_j/∂x_k = 0 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Ga primary ion ToF-SIMS fragment pattern of inorganic compounds and metals

Regularity of Ga⁺ primary ion ToF-SIMS fragment pattern of inorganic compounds is discussed. For an inorganic compound as formulated M–A, where the valence of cation M is +n and that of anion A is −p, the chemical composition of appeared ToF-SIMS fragment are M_xA_y, which satisfy the rule nx≥py+1 for positive ion fragments and nx≤py+1 for negative ones. For example, for oxide fragment of chemical composition, M_xA_y (valence of M is +n), the fragment obeys the rule nx≥2y+1 for positive ions and nx≤2y+1 for negative ones, respectively. The regularity of ToF-SIMS fragment patterns of sulfides, nitrates, sulfates etc. is discussed.     

A new upper bound formula for the ground state energies of N-boson systems

The energy E_N of an N-body system of pairwise interacting bosons is shown to satisfy the inequality, E_N < [N(N − 1)/n(n − 1)] E_n, where N > n 2. This inequality generalizes the Bruch-Sawada result, E₃ < 3E₂, and is superior in its predictive ability to Lim et al.'s .     

The Arnol''d cat: Failure of the correspondence principle

The classical Hamiltonian H = p²/2m + ε(q²/2)Σδ[s-(t/T)] has an integrable mapping of the plane, [q_n+1, p_n+1]= [q_n+1+p_n, q_n+2p_n], as its equations of motion. But then by introducing periodic boundary conditions via (mod 1) applied to both q and p variables, the equations of motion become the Arnol'd cat map, [q_n+1, p_n+1] = [q_n + p_n, q_n + 2p_n], (mod 1), revealing it to be one of the simplest fully chaotic systems which can be derived from a Hamiltonian and analyzed. Consequently, we here quantize the Arnol'd cat and examine its quantum motion for signs of chaos using algorithmic complexity as the litmus. Our analysis reveals that the quantum cat is not chaotic in the deep quantum domain nor does it become chaotic in the classical limit as required by the correspondence principle. We therefore conclude that the correspondence principle, as defined herein, fails for the quantum Arnol'd cat.     

Density profile and flow of miscible fluid with dissimilar constituent masses

A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses (m_A=m_B/3) through an open matrix. The density profile is found to decay with the height ∝exp (−m_A(B)h), consistent with the barometric height law. The flux density shows a power-law increase ∝(p_c−p)^μ with μ2.3 at the porosity 1−p above the pore percolation threshold 1−p_c.     

Characterization of nonstoichiometric nickel manganite spinels NixMn3−x□3δ/4O4+δ by temperature programmed reduction

Cation deficient spinels Ni_xMn_3−x□_3δ/4O_4+δ (0≤x≤1) have been prepared by thermal decomposition of mixed oxalates Ni_x/3Mn_(3−x)/3(C₂O₄)·nH₂O in air at 623 K. They have been characterised by temperature programmed reduction (TPR) under H₂, the reaction being followed by gravimetric and powder X-ray diffraction measurements. It has been shown that TPR proceeds in several steps. The first steps correspond to the loss of nonstoichiometric oxygen leading to the formation of a stoichiometric oxide. During the following stages the manganese cations are reduced, causing the spinel structure to be destroyed, and the formation of solid solution of NiO in a cubic MnO. Subsequently, Ni²⁺ cations undergo a reduction to metallic nickel, and, finally, a mixture of nonstoichiometric MnO_1−δ and metallic nickel is formed. These oxides contain a high level of vacancies which vary with the nickel content with a maximum of δ≈1 near x=0.6. This nonstoichiometry is ascribed both to the presence of Ni³⁺ and excess of Mn⁴⁺.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

Effects of cation- or oxide ion-defect on conductivities of apatite-type La–Ge–O system ceramics

A series of apatite-type La–Ge–O ceramics were prepared and their cation-defect at the 4f+6h sites and oxide ion-defect at 2a site were investigated. In La_xGe₆O_12+1.5x ceramics of x=6–12, the higher conductivities were obtained in the region of apatite composition, La_x(GeO₄)₆O_1.5x−12 (x=8–9.33), and the highest conductivity was achieved for La₉(GeO₄)₆O_1.5 (x=9), where the number of cation (La³⁺) occupying the 4f+6h sites is 9 and the number of oxide ion occupying the 2a site is 1.5. The ceramics with cation- and oxide ion-defects were La_9−0.66xSr_x(GeO₄)₆O_1.5 (x=0–1), La_9−1.33xZr_x(GeO₄)₆O_1.5 (x=0–1), La_9−xSr_x(GeO₄)₆O_1.5−0.5x (x=0–3), La_9−xZr_x(GeO₄)₆O_1.5+0.5x (x=0–1), La_x(GeO₄)_3x−21(AsO₄)_27−3xO_1.5 (x=0–3), La_x(GeO₄)_33−3x(AlO₄)_3x−27O_1.5 (x=0–3), La₉(GeO₄)_6−x (AlO₄)_xO_1.5−0.5x (x=0–3), La₉(GeO₄)_6−x(AsO₄)_xO_1.5+0.5x (x=0–1), La_9.33−xSr_x(GeO₄)₆O_2−0.5x (x=0–1.2) and La_x(GeO₄)_4.5(AlO₄)_1.5O_1.5x−12.75 (x=8.8–9.83), which were prepared by the partial substitution of La³⁺and GeO₄⁴⁻of the basic apatite La₉(GeO₄)₆O_1.5 with Sr²⁺ or Zr⁴⁺ and AlO₄⁵⁻ or AsO₄³⁻. Such substitutions lowered the conductivity of La₉(GeO₄)₆O_1.5. These results were discussed by the electrostatic interaction between Sr²⁺, Zr⁴⁺, AlO₄⁵⁻ or AsO₄³⁻ and oxide ion as a conductive species.     

Mixed electronic and ionic conductivity of LaCo(M)O3 (M=Ga, Cr, Fe or Ni).: V. Oxygen permeability of Mg-doped La(Ga, Co)O3−δ perovskites

The LaGa_1−x−yCo_xMg_yO_3−δ solid solutions with rhombohedrally-distorted perovskite structure were ascertained to form in the concentration range of 0≤y≤0.10 at x=0.60 and 0≤y≤0.20 at x=0.35–0.40. Increasing cobalt content results in increasing electrical conductivity and thermal expansion of the perovskites. Thermal expansion coefficients of the LaGa_1−x−yCo_xMg_yO_3−δ ceramics were calculated from the dilatometric data to vary in the range of 12.4–19.8×10⁻⁶ K⁻¹ at 300–1100 K. Doping La(Ga,Co)O_3−δ solid solutions with magnesium leads to increasing oxygen nonstoichiometry, electronic and oxygen ionic conductivity. Oxygen permeation fluxes through LaGa_1−x−yCo_xMg_yO_3−δ membranes were found to be limited by the bulk ionic conduction and to increase with magnesium concentration, being essentially independent of cobalt content.     

Positive linear magnetoresistance in Fex–C1−x composites

A large positive magnetoresistance (MR) has been found in micro-sized Fe_x–C_1−x composites. At a magnetic field of 5 T, the Fe_0.2–C_0.8 composite has the largest MR, 53.8% and 190% at room temperature and at 5 K, respectively. The magnetic field dependence of the MR can be described approximately as MR∝Bⁿ, and the value of exponent n is determined by the Fe weight concentration and temperature, ranging from 1/4 to 6/4. It appears that Fe_x–C_1−x has a linear field dependence of the positive MR at different temperatures. The possible mechanism for the positive MR is discussed.     

1/f-type fluctuation of electron transmission in one-dimensional disordered systems

A universal feature of 1/f-type fluctuation is numerically observed in the system-size n dependence of the transmission amplitude t_n in various one-dimensional disordered systems. The power spectrum P(f) of the transmission coefficient T(n)=|t_n|² exhibits the power law of 1/f², irrespective to the type of disorder of the system whether it is of short-range or of long-range correlation. That of the phase θ_t(n) of t_n also does the universal power law of 1/f^1.4.     

Measurement of recoil proton polarizations in the electrodisintegration of deuterium by polarized electrons

In order to test modern theories of two-nucleon bound and scattering states, we have measured the spin polarization of ejectile protons in the electrodisintegration reaction . Compared with spin-averaged observations, these observables offer the potential of enhanced sensitivity to details of the reaction process. The experiment was carried out in quasielastic kinematics (q_μq^μ=−2m_pω=−0.38 GeV²/c²). Protons were detected at two angles corresponding to neutron recoil momenta p_r of 0 and 100 MeV/c. Full nonrelativistic calculations of the polarization transfer components s_l and s_t, including leading order relativistic contributions, describe our measurements well, but calculations of the induced polarization s_n at p_r=100 MeV/c underpredict the experimental result.     

A reduced hamiltonian model for U(∞) gauge theories

A reduced version of the Kogut-Susskind gauge theory is presented for U(∞) gauge theories. The reduced hamiltonian , where V_ij=trU_iD_iD_jD_j(U_iD_j) ⁺ (U_iD_j)⁺, is obtained by representing the group of space translations in the diagonal part of U(∞) U(∞). The space of states is invariant to the reduced gauge transformation U_i→ωU_iD_iω⁺D_i⁺ and the scalar product carries a gauge invariant constraint on U_i The hamiltonian is also expr essed in terms of the string variables of Bars. We present the linear potential between static quarks at strong coupling and sketch the weak coupling expansion.     

Contribution of asymmetric strange–antistrange sea to the Paschos–Wolfenstein relation

The NuTeV Collaboration reported a value of sin²θ_w measured in neutrino–nucleon deep inelastic scattering, and found that the value is three standard deviations from the standard model prediction. This result is obtained under the assumption that the strange quark–antiquark sea of nucleons are symmetric, and that the up and down quark distributions are symmetric with the simultaneous interchange of u↔d and p↔n. We discuss the contribution of asymmetric strange–antistrange sea to the Paschos–Wolfenstein relation in the extraction of weak mixing angle sin²θ_w. We also point out that the contribution of asymmetric strange–antistrange sea should remove roughly 30–80% of the discrepancy between the NuTeV result and other determinations of sin²θ_w when using the light-cone meson–baryon model to calculate the contribution of the strange–antistrange sea.     

On nonanalytic solitary waves formed by a nonlinear dispersion

We study the prototypical, genuinely nonlinear, K(m, n) equation, u_t ± a(u^m)_x + (uⁿ)_xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m, n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.     

Material design of new lithium ionic conductor, thio-LISICON, in the Li2S–P2S5 system

A new lithium ionic conductor of the thio-LISICON (LIthium SuperIonic CONductor) family was found in the binary Li₂S–P₂S₅ system; the new solid solution with the composition range 0.0≤x≤0.27 in Li_3+5xP_1−xS₄ was synthesized at 700 °C and characterized by X-ray diffraction measurements. Its electrical and electrochemical properties were studied by ac impedance and cyclic voltammetry measurements, respectively. The solid solution member at x=0.065 in Li_3+5xP_1−xS₄ showed the highest conductivity value of 1.5×10⁻⁴ S cm⁻¹ at 27 °C with negligible electronic conductivity and the activation energy of 22 kJ mol⁻¹ which is characteristic of high ionic conduction state. The extra lithium ions in Li₃PS₄ created by partial substitution of P⁵⁺ for Li⁺ led to the large increase in ionic conductivity. In the solid solution range examined, the minimum conductivity was obtained for the compositions, Li₃PS₄ (x=0.0 in Li_3+5xP_1−xS₄) and Li₄P_0.8S₄ (x=0.2 in Li_3+5xP_1−xS₄); this conductivity behavior is similar to other thio-LISICON family with the general formula, Li_xM_1−yM_y′S₄ (M=Si, Ge, and M′=P, Al, Zn, Ga, Sb). Conduction mechanism and the material design concepts are discussed based on the conduction behavior and the structure considerations.     

Tuning the multiferroic properties of Pb(Fe1/2Nb1/2)O3 by cationic substitution

A series of substituted lead iron niobate compounds with the general formula Pb²⁺_(1−x)A^Z_x(Fe_{{(1−(2−Z)x)/2}}Nb_{{(1+(2−Z)x)/2}})O₃ (0<x<0.6 and A=La³⁺, K⁺ or Sr²⁺) were prepared by a modified solid-state synthesis. The relative concentrations of Fe³⁺ and Nb⁵⁺ were adjusted to compensate the charge imbalance due to the aliovalent substitution. The dielectric constant and magnetic susceptibilities were studied as a function of temperature. The temperature of the dielectric maximum, T_M, of the substituted compounds decreased linearly with increasing concentration of the substituent ions. The magnetic measurements showed an antiferromagnetic transition at temperatures T_N1 due to the superexchange interactions mediated by Fe–O–Fe and an additional antiferromagnetic-type transition at T_N2. T_N1 linearly increased with the increasing concentration of Fe³⁺ ion at the B-site of ABO₃-type substituted compounds. T_M is shown to be directly dependent on the concentration of the ferroactive Nb⁵⁺ ions at the B-site and Pb²⁺ ions at the A-site.