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.     

Esperanza condicionada para probabilidades finitamente aditivas

Let (Ω, θ,J) be a finitely additive probabilistic space formed by any set Ω, an algebra of subsets θ and a finitely additive probabilityJ. In these conditions ifF belongs toV ¹ (Ω, θ,J) there existsf, element of the completion ofL ¹ (Ω, θ,J), such thatF(E)=∫ _E fdJ for allE of θ and conversely. This integral representation gives sense to the following result, which is the objetive of this paper, in terms of the, point function: If β is a subalgebra of θ, for everyF ofV ¹ (Ω, θ,J) there exists a unique element ofV ¹ (Ω, β,J) which we note down byE(F/gb), conditional expetation ofF given β. E(F/β) is characterized by (E(F/β),G)=(F, G) for every ofV ^∞(Ω,β, J). Aside from this, the mappingE(./β):V ¹ (Ω, θ,J)→V ¹ (Ω, β,J) is linear, positive, contractive, idempotent andE(J/β)=J. IfF is ofV ^p (Ω, θ,J),p>1,E(F/β) is ofV ^p (Ω, β,J).

     

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.     

The theory of search from a statistical viewpoint

Summary The statistical approach to search is a subject which interfaces with many other fields. This work continues a series of papers which studies these relationship with special emphasis on geometric problems in non-sequential search. A targetT is sought using a series of testsX ₁,X ₂.... From each test there is an observationY _i=f(X _i , θ), where θ is an unknown parameter andT=T(θ). Spacing theories and the theories of Voronoi regions can be used to represent the solutions to Bayes and entropy-based formulations to the search problem by partitioning the search field intoconsistent regions where the target is known to lie, given the observations. Other examples are from integration where the target is a function. Covering theory is studied and the last section gives a brief comparison with a sequential approach. Read before the Spanish Statistical Society at a meeting organized by the Universidad de Almería on Friday, April 29, 1994     

Thermodynamic properties of NaZr2(PO4)3

The heat capacity of crystalline NaZr₂(PO₄)₃ was measured between 7 and 340 K by adiabatic calorimetry. The results were used to calculate the thermodynamic functionsC _p ⁰ ,H ⁰(T) -H ⁰(0),S ⁰(T), andG ⁰(T) -H ⁰(0) in the range 0-340 K. The absolute entropy was found to be S⁰NaZr₂(PO₄)₃, cr, 298.15 K) = 327.1 ±1.0 J/(mol K), and the standard entropy of formation Δ_fS⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -1101±1 J/(mol K). Solution calorimetry was used to determine the standard enthalpy of formation, Δ_f H ⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -5236 ±5 kJ/mol. By combining the data obtained by the two techniques, the standard Gibbs energy of formation was determined to be Δ_fG⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -4908 ±5 kJ/mol.     

Density and deposition rates of amorphous CVD-Si3N4 including carbon

Amorphous Si₃N₄ containing uniformly distributed carbon was prepared by chemical vapour deposition [Am. CVD-(Si₃N₄-C)] using SiCl₄ vapour and NH₃, H₂ and C₃ H₈ gases at deposition temperatures (T _dep) of 1100 to 1300° C and at total gas pressures (P _tot) of 30 to 70 torr. The density of Am.CVD-(Si₃N₄-C) is between 2.80 and 3.00 g cm⁻³, depending upon the deposition conditions. Rate of growth in thickness increases with increasingT _dep andP _tot, and has the largest value of 0.6 mm h⁻¹ atT _dep=1300° C,P _tot=70 torr and propane gas flow rates [FR(C₃H₈)] of 0 to 20 cm³ min⁻. The activation energy of the formation decreases from 38 to 20 kcal mol⁻¹ with increasingP _tot andFR(C₃H₈).     

Thermodynamic properties of NaZr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The heat capacity C _p ⁰ of crystalline NaZr₂(AsO₄)₃ has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: C _p ⁰, enthalpy H ⁰(T) − H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) − H ⁰(0) from T → 0 to 650 K. The standard entropy of its formation from elements is Δ_f S ⁰(NaZr₂(AsO₄)₃, cr, 298.15 K) = −1087 ± 1 J/(mol K).     

Flux trapping and its effect on AC susceptibility of granular superconductors

Experimental data on the real (x′) and imaginary (x″) parts of AC magnetic susceptibility as a function of DC bias field (H) shows the effect of trapped flux in granular highT _c superconductors. The aim was to substantiate our recent theoretical findings on the basis of a two-component critical state model suitable for granular highT _c superconductors. Stress has been given to understanding the origin of hysteresis inx′(H) andx″(H). It was seen in the experimental data that above a certain value of DC field range irreversibility appears inx′(H) andx″(H) creating hysteresis like loops. Comparison of data with calculated loops shows good agreement.x′(H) andx″(H) curves show considerable asymmetry in presence of trapped flux.     

Elastic properties of ZnF2-PbO-TeO2 glasses doped with certain rare earth ions

The elastic moduli (Y, η, σ andH) and some thermodynamical parameters, such as Debye temperatureθ _D, diffusion constantD _i and latent heat of melting ΔH _m, of ZnF₂-PbO-TeO₂ glasses doped with some rare earth (Pr³⁺, Nd³⁺, Eu³⁺ and Tb³⁺) ions are determined as functions of temperature using piezo electric composite oscillator technique. All the parameters are found to decrease with increase in the atomic number Z of the rare earth ions and with increase in the temperature of measurement. The results are explained on the basis of the density of localized bonding defect states within the band gap of the material.     

Thermodynamics of the Superconducting State in Calcium at 200 GPa

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa were calculated. The Coulomb pseudopotential values (μ ^⋆) from 0.1 to 0.3 were taken into consideration. It has been shown that the specific heat’s jump at the critical temperature and the thermodynamic critical field near zero Kelvin strongly decrease with μ ^⋆. The dimensionless ratios r ₁≡ΔC(T _C)/C ^N (T _C) and r₂ o T_CC^N(T_C)/H²_C(0)r_{2}\equiv T_{\mathrm{C}}C^{N}(T_{\mathrm{C}})/H^{2}_{\mathrm{C}}(0) significantly differ from the predictions based on the BCS model. In particular, r ₁ decreases from 2.64 to 1.97 with the Coulomb pseudopotential; whereas r ₂ increases from 0.140 to 0.157. The numerical results have been supplemented by the analytical approach.     

The Activation Energy <Emphasis Type="Italic">U</Emphasis>(<Emphasis Type="Italic">T</Emphasis>,<Emphasis Type="Italic">H</Emphasis>) in Y-based Superconductors

Based on the Arrhenius equation, a method to calculate the activation energy from the resistance transition is proposed for high temperature superconductors. This method is applied to the Y-based superconductors. The activation energy is found to be U(T,H)∼(1−T/T _c )^4.8(H/H ₀)^−3.8 of YBCO crystal, and U(T,H)∼(1−T/T _c )^3.3(H/H ₀)^−2.2 of Er doped MTG YBCO crystal, respectively. With the obtained activation energy U(T,H), the lower part of the experimental curve ρ(T,H) and its derivative can be reproduced.      

Superconducting gap function and upper critical field in the presence of inhomogeneous magnetic order

Rare earth ternary superconductors are known to exhibit oscillatory magnetic orders below their superconducting transition temperatures. The study of behaviour of superconducting electrons in an inhomogeneous magnetic field is therefore important for such systems. We report here the results of our theoretical study of superconducting gap function Δ(T) and upper critical fieldH _c2 (T). The results are applied to analyse and explain the variation of Δ(T) andH _c2 (T) in case of NdRh₄B₄.     

Upper Critical Field Hc2 on c Axis of Ag/Bi-2223 Polycrystal Tape

The upper critical field H _c2, based on Ginzburg–Landau theory at medial magnetic fields, can be calculated from the relationship of the magnetization intensity M(H) versus magnetic field H if M is linear with ln₀ H. For Ag/Bi-2223 tapes, the measured M(H) was found to be linear with ln₀ H. In this case, the values of H _c2(T) may in principle be determined. To do this, we will meet another problem in that the obliquity of crystal planes is not equal for different grains in tapes, and values of grain-oblique angle will appear in the calculated H _c2. Obviously, for Ag/Bi-2223 tapes is an uncertain parameter and hard to determine. To avoid the effects of , we only study the H _c2 in the c axis direction and the projections of H onto the c axis is taken as the actual applied fields. Thus, the effects of grain-oblique angle may be counteracted when measuring critical current density J, if the external magnetic fields are applied to the tape along both the parallel to and perpendicular to the c axes directions (on the narrow surfaces of the tape). On medial fields (H = 0 – 3 T), the upper critical fields H _c2(T) on c axis for the Ag/Bi-2223 tape are obtained and fitted as ₀ H _c2(T) = 830 e ^–0.07T . The average slope d[₀ H _c2(T)]/dT – 8T/K is found to be as large as that of Bi-2212. On extrapolating the relation to T = 0 K, the value of ₀ H _c2(0) 800T. The coherence length _ab is determined from H _c2(c), and _ab (0) = 0.63 nm at T = 0 K.     

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)     

An analytical equation of state for mercury

This paper presents a procedure for predicting the equation of state of mercury, by including mercury in the scope of a new statistical mechanical equation of state that is known for normal fluids. The scaling constants are the latent heat of vaporization and the density at the melting temperature, which are related to the cohesive energy density. Since experimental data for the second virial coefficient of mercury are scarce, a corresponding-states correlation of normal fluids is used to calculate theB(T) of mercury. The free parameter of the ISM equation, λ, compensates for the uncertainties inB(T). Also, we can predict the values of two temperature-dependent parameters, α(T) andb(T), with satisfactory accuracy from a knowledge of ΔH _vap andp _m, without knowing any details of the intermolecular potentials. While the values ofB(T) are scarce for mercury and the vapor pressure of this metal at low temperatures is very small, an equation of state for mercury from two scaling parameters (ΔH _vap,p _m) predicts the density of Hg from the melting point up to 100° above the boiling temperature to within 5%.     

Inference based on censored samples from exponentiated populations

Maximum likelihood and Bayes estimators of the parameters, survival and hazard rate functions of an exponentiated population whose cumulative distribution function takes the form H(x)=[G(x)] ^α , where α is an unknown positive parameter and G(x) is a cumulative distribution function, are obtained in two cases: when the parameters of G(x) are all known so that α is the only unknown parameter of H and when the k-dimensional vector of parameters β of G(x) are all unknown so that the (k+1)-dimensional vector of parameters (α,β) of H is unknown. In both cases, estimation is based on a Type II censored sample. In such cases, the predictive density and predictive survival functions of future observables are obtained when based on the two-sample scheme. This enables us to obtain Bayes prediction bounds of future observables. Subjective priors are used which reflect the prior belief of the experimenter. Numerical results are obtained under three exponentiated models and compared with the results obtained by using the MCMC algorithm.     

Preparation and properties of Pb0.99Nb0.02(Zr0.52Ti0.48)0.98O3 by a new sol–gel technique

A new sol–gel processing technique has been developed for preparing Nb-doped lead zirconate titanate (PZT) with the composition Pb_0.99Nb_0.02(Zr_0.52Ti_0.48)_0.98O₃. The sol was prepared from Pb(NO₃)₂, NbCl₅, Ti(OC₃H₇)₄ and Zr(C₄H₉O)₄, dissolved in N, N-dimethyl-formamide with stirring at ambient atmosphere. The gel was calcined at 500 °C for 30 min and pressed pellets were sintered in air at 1000 °C for 2–20 h. The average grain size in the pellets sintered for 4 h was about 1.4 μm, which was smaller than that in undoped PZT pellets. Nb doping decreased angle α in the rhombohedral crystal structure, thereby enhancing electromechanical coupling. This revised version was published online in November 2006 with corrections to the Cover Date.     

Crystal Structure of (H3O)6[(UO2)5(SeO4)8(H2O)5](H2O)5

Crystals of (H₃O)₆[(UO₂)₅(SeO₄)₈(H₂O)₅](H₂O)₅ were prepared from aqueous solutions by evaporation. The crystal structure [monoclinic system, space group P2₁/m, a = 13.835(2), b = 13.4374(16), c = 14.310(3) Å, β = 108.004(14)°, V = 2530.1(7) Å ³] was solved by the direct method and refined to R ₁ = 0.090 for 4409 reflections with |F _hkl ≥ 4σ|F _hkl |. The structure is based on [(UO₂)₅(SeO₄)₈(H₂O)₅]⁶⁻ layers arranged parallel to the (101) plane; these layers have a unique topological structure. The U(1)O₆(H₂O) and U(3)O₆(H₂O) linked through selenate groups form chains running along [ [`1]\bar 1 01] direction. The chains are combined in layers by U(2)O₆(H₂O) bipyramids. The layers are linked with each other by hydrogen bonds through the H₂O and H₃O⁺ groups located between the layers.     

Interaction of intermetallic compounds of rare-earth metals, nickel, and aluminum with hydrogen

AtT=293 K andp _H2≤10 MPa. we synthesized hydridesR _3Ni8Al-H_7.2–15.2 (R=Nd. Sm. Gd. Tb. Dy, Ho, Er, Tm, and Lu). The X-ray analysis revealed an isotropic deformation of the original crystal lattice due to hydrogen penetration. For the hydrides obtained, the lattice constanta exceeds that of the original intermetallide by 3.9–6.0% and the constantc and the cell volumeV are increased by 6.0–12.6% and 15.6–26.4%, respectively. The volume expansion per absorbed hydrogen atom is (2.4–3.6)·10⁻³ nm⁻³. By construction of the isotherms of hydrogen desorption for the systemsR _3Ni>8Al-H, we established the existence of the α-solid hydrogen solution and the region of its coexistence with β-hydride, the region of coexistence of β- and γ-hydrides, and the β- and γ-hydride phases. Heats of the phase transitions were determined as follows: ΔH=31.4±0.8 kJ/(mole H₂) in the system Gd₃Ni₈Al-H for the transition γ→β, ΔH=39.8±1.1 kJ/(mole H₂) in the system Tb₃Ni₈Al−H for the transition β→α. and ΔH=37.1±5.1 kJ/(mole H₂) in the system Tm₃Ni₈Al−H for the transition γ→β. Among the products of hydrogenation, intermetallic compounds Lu₃Ni8Al and Tm₃Ni₈Al. we revealed the β′- and γ-phases. We also found that, atp _H2≤10 MPa andT=400–430 K, the phases of Sm₃Ni₈Al and Gd₃Ni₈Al decay into two hydridesRH_2–3 andR(Ni.Al)₅H _x . Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 1, pp. 76–82, January–February, 2000.