Convergencia del vector de probabilidad a posteriori bajo una distribucion predictiva

Resumen La convergencia casi segura de una sucesión de variables aleatorias, con respecto aP _{X, Q} (distribución predictiva), se estudia en relación con la convergencia casi segura, con respecto aP _{X, θ} (para todo θ∈Θ), donde{P _{X, θ}}_θ∈Θ es una familia de modelos de probabilidad sobre el espacio muestralX. Como consecuencia, se estudia la convergencia casi segura del vector de probabilidad a posteriori con respecto aP _{X, Q}.      

Testing the hypothesis of a general linear model using nonparametric regression estimation

Summary Given the modelY _i =m(χ _i )+ɛi,whereE(ɛ _i) =0,X _i ≠Ci=1, ...,n, andC is ap-dimensional compact set, we have designed a new method for testing the hypothesis that the regression function follows a general linear model,m(·) ∈ {m _θ(·) =A ^t (·)θ}_{θ∈Θ⊂ℛq} , withA a function fromℜ ^p toℜ ^q. The statistic, denoted ΔASE, used fortesting the given hypothesis is defined to be the difference between the average squared errors (ASE) associated with the non-parametric estimator ofm and the minimum distance parametric estimator ofm. The asymptotic normality of both ΔASE and the minimum distance estimators is proved under general conditions. Alternative bootstrap versions of ΔASE are also considered.     

Numerical Solution of Inverse Radiative–Conductive Transient Heat Transfer Problem in a Grey Participating Medium

The problem of simultaneous identification of the thermal conductivity Λ(T) and the asymmetry parameter g of the Henyey–Greenstein scattering phase function is under consideration. A one-dimensional configuration in a grey participating medium with respect to silica fibers for which the thermophysical and optical properties are known from the literature is accepted. To find the unknown parameters, it is assumed that the thermal conductivity Λ(T) may be represented in a base of functions {1, T, T ², . . .,T ^K } so the inverse problem can be applied to determine a set of coefficients {Λ₀, Λ₁, . . ., Λ _K ; g}. The solution of the inverse problem is based on minimization of the ordinary squared differences between the measured and model temperatures. The measured temperatures are considered known. Temperature responses measured or theoretically generated at several different distances from the heat source along an x axis of the specimen set are known as a result of the numerical solution of the transient coupled heat transfer in a grey participating medium. An implicit finite volume method (FVM) is used for handling the energy equation, while a finite difference method (FDM) is applied to find the sensitivity coefficients with respect to the unknown set of coefficients. There are free parameters in a model, so these parameters are changed during an iteration process used by the fitting procedure. The Levenberg– Marquardt fitting procedure is iteratively searching for best fit of these parameters. The source term in the governing conservation-of-energy equation taking into account absorption, emission, and scattering of radiation is calculated by means of a discrete ordinate method together with an FDM while the scattering phase function approximated by the Henyey–Greenstein function is expanded in a series of Legendre polynomials with coefficients {c _l } = (2l + 1)g ^l . The numerical procedure proposed here also allows consideration of some cases of coupled heat transfer in non-grey participating media. The inverse method may be treated, after performing a suitable validation, as an alternative method in relation to other classical measurement methods for investigation of thermophysical parameters of solid states.     

A Bayesian approach to the multivariate Behrens-Fisher problem under the assumption of proportional covariance matrices

Summary Two independent random samples of sizesN ₁ andN ₂ from multivariate normal populationsN _p (θ₁,∑₁) andN _p (θ₂,∑₂) are considered. Under the null hypothesisH ₀: θ₁=θ₂, a single θ is generated from aN _p(μ, Σ) prior distribution, while underH ₁: θ₁≠θ₂ two means are generated from the exchangeable priorN _p(μ,σ). In both cases Σ will be assumed to have a vague prior distribution. For a simple covariance structure, the Bayes factorB and minimum Bayes factor in favour of the null hypotheses is derived. The Bayes risk for each hypothesis is derived and a strategy is discussed for using the Bayes factor and Bayes risks to test the hypothesis.     

Structural analysis of sodium silicate glasses containing TiO2 by pulsed neutron scattering

By the use of the time-of-flight pulsed neutron total-scattering spectrometer HIT at the Japanese National Laboratory for High Energy Physics, measurement of structure factorsS(Q) for glasses of type 10Na₂O·(90–x)SiO₂·xTiO₂ (x=0, 5 and 20 mol%) was made over a wide range of scattering vectors up toQ (=4 sin/) ~ 500 nm^–1. High-resolution real-space information was obtained from the Fourier transform ofS(Q). The influence of TiO₂ on the nearest-neighbour Si-O bond length of the silicate anions existing in the glass samples studied is different from that of alkali oxides such as Na₂O. It is concluded that most of the Ti⁴⁺ ions predominantly substitute for Si⁴⁺ ions in their tetrahedrally coordinated sites, leading to the formation of TiO₆ octahedra.     

Thermal conductivity, heat capacity, and compressibility of atactic poly(propylene) under high pressure

The thermal conductivity λ and the heat capacity per unit volume of atactic poly(propylene) have been measured in the temperature range 90–420 K at pressures up to 1.5 GPa using the transient hot-wire method. The bulk modulus has been measured in the range 200–295 K and up to 0.7 GPa. These data were used to calculate the volume dependence of λ,g=−[∂λ/λ)/(∂V/V)] _T , which yielded the following values for the glassy state (T<256 K at atmospheric pressure): 3.80±0.19 at 200 K, 3.74±0.19 at 225 K, 3.90±0.20 at 250 K, 3.77±0.19 at 271 K, and 3.73±0.19 at 297 K. The resultant value forg of the liquid state was 3.61±0.15 at 297 K. Values forg which are calculated at 295 K, using theoretical models of λ(T), agree to within 12% with the experimental value for the glassy state.     

On the Lattice Structure of Pseudorandom Numbers Generated over Arbitrary Finite Fields

Marsaglia's lattice test for congruential pseudorandom number generators modulo a prime is extended to a test for generators over arbitrary finite fields. A congruential generator η₀,η₁,…, generated by η _n =g(n), n = 0, 1,…, passes Marsaglia's s-dimensional lattice test if and only if s≤ deg(g). It is investigated how far this conditin holds true for polynomials over arbitrary finite fields F _q , particularly for polynomials of the form g _d (x)=α(x+β) ^d +γ, α, β, γ∈F _q , α≠ 0, 1 ≤d≤q− 1. Received: December 13, 1999; revised version: November 17, 2000     

A Note on Strong Dickson Pseudoprimes

In 1994 the infinitude of Fermat pseudoprimes to any bases (i.e. Carmichael numbers) has been established (cf. [2, 42]), the smallest being 561 = 3 ċ 11 ċ 17. If, instead of the power function the Dickson polynomial, respectively Lucas sequence, V _n (P, Q) ≡P (mod n), is being used as the primality testing function for P, Q∈ℤ, then the smallest pseudoprime to this test with respect to all parameters P and Q is 443372888629441 = 17 ċ 31 ċ 41 ċ 43 ċ 89 ċ 97 ċ 167 ċ 331. Not more than about 50 of such strong Dickson pseudoprimes are known at present, each of them having a more complex structure than the (Fermat-) Carmichael numbers. Those particular properties will be the focus of our attention in this note. After summarizing some results on strong Dickson pseudoprimes their connections to other types of pseudoprimes are described and characterizations of superstrong Dickson pseudoprimes are presented. Furthermore, an algorithm for an effective generation of those kinds of numbers is introduced. Received: April 25, 1997; revised version: July 20, 1998     

Critical importance of the single-level approximation to account for the highly nonmonotonic dependences of carrier lifetimes on recombination impurity concentration

This paper is a continuation of an analysis regarding an increase in the lifetimes of nonequilibrium electrons π_n and holes πp by several orders of magnitude, observed with increasing concentration of recombination centers. It is shown that a substantial increase in πn and πp may also occur for three charge states of the recombination impurities N, and the curves πn=f(N) and π n=f(N) may each have two minima and maxima. Pis’ma Zh. Tekh. Fiz. 23, 39–45 (April 12, 1997)     

New Insights on the Intrinsic Anisotropy of YBCO Films

Careful investigation of the angular dependence of resistivity ρ(θ) (θ is the angle between the magnetic field and the ab-planes) and the temperature dependence of resistivity ρ(T) within the superconducting transition in an applied magnetic field B up to 1 T for a series of YBa₂Cu₃O_7−δ (YBCO) thin films revealed a large variation of intrinsic anisotropy factor γ. The series of films studied included both optimally doped and underdoped samples of different T _c , critical current density J _c , film thickness, and preparation techniques. The variation in the shape and depth of the minimum measured for ρ(θ) near θ=0° could be directly correlated to the intrinsic anisotropy of the YBCO films. The results of fitting of ρ(θ) using Bardeen–Stephen theory allowed a quantitative determination of the value of γ which varies between 7 and 230, and is independent of T _c , film thickness, or J _c . The sharper the minimum in ρ(θ) around θ=0° the larger is the anisotropy. For highly anisotropic film, ρ(θ) showed an identical behavior for B ∥ J and B ⊥ J (i.e., ρ(θ) is independent of the angle θ between B and J for this film). The large variation in γ could be attributed to the “buckling” of the CuO₂ planes.     

Determination of optical constants of CdS x Se y electrodeposits

The optical constantsn(λ) and α(λ) have been determined for CdS_xSe _y films electrodeposited on to glass doped with SnO₂. From a (αhv)² versus photon energy plot, a value for the direct band gap of the electrodeposited polycrystalline semiconductor ofE _g=1.83 eV was obtained, which indicates a low proportion of S²⁻ in the thin films formed.     

Luminescence and EPR studies of Y2O3:Gd3+ phosphors prepared via solution combustion method

Gadolinium-activated Y₂O₃ phosphor has been prepared by combustion process in a short time of 5 min. The phosphors are well characterized by X-ray diffraction, scanning electron microscopy, and energy-dispersive analysis of X-ray. The as-prepared Y₂O₃:Gd powder shows that all the peaks are due to the Y₂O₃ cubic phase. Upon UV light excitation (276 nm), the phosphor exhibits a strong and sharp UV emission at 314 nm and is ascribed to ⁶ \textP _{7/ 2}  ?  ⁸ \textS _{7/ 2} ^{ 6} {\text{P}}_{ 7/ 2} \, {\to}\, ^{ 8} {\text{S}}_{ 7/ 2} transition of Gd³⁺ ions. The EPR spectrum of Y₂O₃:Gd phosphor exhibits resonance signals with effective g values at g = 1.96, g = 2.88, and g = 6.08 and are attributed to Gd³⁺ ions located at sites with weak, intermediate, and strong cubic symmetry fields, respectively. It is observed that the population of spin levels (N) and linewidth depends on temperature. The paramagnetic susceptibility (χ) is also evaluated as a function of temperature and discussed.     

Theory of the Self-Organized Critical State in Nonequilibrium 4He

A near-critical sample of superfluid ⁴He subjected to a combination of a heat current Q and a gravitational field g has recently been confirmed experimentally to exhibit a self-organized critical (SOC) state, in which the local temperature profile T(z) parallels the local superfluid transition temperature, T (z), so that T(z)–T (z) is independent of the vertical coordinate z. We show that there is a particular heat current Q ₀(g)g such that the SOC state lies in the normal phase only when Q<Q ₀(g). The SOC state is shown to be dynamically stable and, surprisingly, to possess a propagating mode in which perturbations travel upstream at a particular speed c _SOC(Q). For Q>Q ₀(g) the SOC state is pushed below the superfluid transition. We present a model based on the Model F equations that shows that the resulting superfluid state is intrinsically dynamical and supports an average temperature gradient by way of an approximately uniform density of recurring phase slips. The role of a certain local dynamical instability temperature, T _c(Q, z), in the nucleation of the phase slips is emphasized.     

Experiments on the Self-Organized Critical State of 4He

When a heat flux Q is applied downward through a sample of ⁴He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity-induced gradient in T _λ . All the helium in the sample is then at the same reduced temperature and the helium is said to be in the Self-Organized Critical (SOC) state. We have made the first measurements of the ⁴He SOC state specific heat, C _{∇ T} (T(Q)). There is no measurable difference between C _{∇ T} and the static zero-gravity ⁴He specific heat for temperatures between 650 and 250 nK below T _λ . Closer to T _λ , the specific heat is depressed and reaches a maximum value at 50 nK below T _λ . This depression is similar to that predicted theoretically as reported by R. Haussmann (Phys. Rev. B 60, 12349, 1999). Contrary to the expectations of theory, however, we see another depression far below T _λ . In addition, over the heat flux range of 30 nW/cm² to 13 μW/cm², we have made improved measurements of the speed of a recently discovered propagating thermal mode, which travels only upstream against the nominal heat flux of the SOC state. We are able to accurately predict the speed of this wave by treating the helium of SOC state as a traditional fluid with a temperature dependent thermal conductivity.     

Some multiple comparisons using sample quasi ranges on censored data

We considerk(k)≥2 independent populations (treatments or systems) and an solutely continuous member of location-scale family of distributions, index by the location parameter μ _i (-∞ < μ _i < ∞) and scale parameter θ _i (θ _i > 0), is used to model the observations from the ith population,i=1,...k. The problem of simultaneous selection of two subsets, one containing population associated with the smallest ϕ-value and other containing population with the largest ϕ-value with probability at least a pre-specified value is considered when the data are censored. We also construct 100P ^*% simultaneous upper and two-sided confidence intervals for where θ_[1] ≤ ... ≤ θ_[k] denotes the ordered values of ϕs. The proposed procedures, based on sample quasi ranges, are useful when the experimenter has smaller samples or censored samples or there is suspicion of outliers in the samples. The results are applied to exponential populations model and, for thes casi: (i) the constants have been computed to apply the proposed multiple comparisons; (ii) two members of the proposed class have been compared with the existing procedure. A numerical example is also given.     

Semi-recorrido condicionado (Expresion asintotica de la r-esperanza condicionada)

Summary In a probability space (Ω, σ,P), for α⊂σ a sub-σ-field, in general the best approximation inL ^∞ by elements ofL ^∞(α) has not an unique solution. For the election between these, we prove the convergenceP-almost surely of the conditionalr-means, whenr→∞, to one solution, which we call conditional mid-range. This is characterized for each ω∈Ω by the mid-range, of one regular conditional distributionQ (ω, •):

     

Characterization of ZrO<Subscript>2</Subscript> thin films deposited by MOCVD as ceramic coatings

Transparent cubic-, tetragonal-zirconia thin films were successfully deposited on glass and quartz substrates by using the metalorganic chemical deposition technique. The thin films were achieved by adjusting deposition parameters such as substrate temperature, oxygen partial pressure, and zirconium acetylacetonate (Zr(acac)₄) used as precursor. Structural and morphological characterizations of the as-deposited thin films were studied by XRD, Raman spectroscopy, SEM, and AFM techniques, while some optical properties such as transmittance and refractive index were determined by means of the UV–vis technique. The ZrO₂ films, grown at 700 °C and different P_{\textO 2} :P_{\textZr(acac)4} P_{{{\text{O}}_{ 2} }}{:}P_{{\text{Zr(acac)}_{4} }} ratios, displayed very variable particle sizes ranging from ~0.2 to 1.0 μm, and crystallite sizes within 10–30 nm forming a uniform film. Low mean roughness was obtained in the samples, which varied from 0.674 to 1.33 nm. These films grew with a columnar structure and apparently with low carbon content (<0.2%). All the synthesized thin films showed an adequate optical transmission, but the most transparent (>80%) was obtained with a P_{\textO 2} :P_{\textZr(acac)4} P_{{{\text{O}}_{ 2} }} {:}P_{{\text{Zr(acac)}_{4} }} ratio of (Pa) 107:0.2. The oxygen partial pressure influences the crystallinity of the as-deposited films, while the refractive index remains constant.     

Mixed convection flow near an axisymmetric stagnation point on a vertical cylinder

The mixed convection flow near an axisymmetric stagnation point on a vertical cylinder is considered. The equations for the fluid flow and temperature fields reduce to similarity form that involves a Reynolds number R and a mixed convection parameter λ, as well as the Prandtl number σ. Numerical solutions are obtained for representative values of these parameters, which show the existence of a critical value λ _c  = λ _c (R, σ) for the existence of solutions in the opposing (λ < 0) case. The variation of λ _c with R is considered. In the aiding (λ > 0) case solutions are possible for all λ and the asymptotic limit λ → ∞ is obtained. The limits of large and small R are also treated and the nature of the solution in the asymptotic limit of large Prandtl number is briefly discussed.