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, •):

     

Conductometric Study of Some Metal Halides in Glycerol + Water Mixtures

Electrolytic conductivities of potassium halides, KX (X = Cl⁻, Br⁻, I⁻) have been investigated in 10, 20, and 30 mass% glycerol + H₂O mixtures at 298.0, 308.0, and 318.0 K. The conductance data have been analyzed by the Fuoss-conductance–concentration equation in terms of the limiting molar conductance (Λ⁰), the association constant (K _A ), and the distance of closest approach of ion (R). The association constant (K _A ) tends to increase in the order: 10 mass% < 20 mass% < 30 mass% glycerol + water mixtures, while it decreases with temperature. Thermodynamic parameters ΔH ⁰, ΔG ⁰, and ΔS ⁰ are obtained and discussed. Also, Walden products (Λ⁰η) are reported. The results have been interpreted in terms of ion–solvent interactions and structural changes in the mixed solvents.     

How Grain-Boundaries Influence the Intergranular Critical Current Density of Cu1−x Tl x Ba2Ca3Cu4O12−δ Superconductor Thin Films?

The insulating and metallic behavior of the grain-boundary weak links has been studied in thallium rich and the samples with small amount of thallium in the charge reservoir layer of Cu_1−x Tl _x Ba₂Ca₃Cu₄O_12−δ superconductor thin films. The influence of the nature of grain boundaries on the inter-granular critical current density (J _c) has also been investigated. From the power law dependence of H _ac∼(1−T _p/T _c) ⁿ , it was observed that n=1 gives a best fit for the J _c of thallium rich samples and n=2 provides a best fit for the J _c of the samples with small amount of thallium. The polycrystalline thin film samples showing the power law dependence of J _c as n=1 make superconductor-insulator-superconductor (SIS) type while the samples with n=2 follow superconductor-normal metal-superconductor (SNS) types of Josephson junctions. The insulating grain boundaries decrease the inter-granular Josephson coupling and hence the transport properties are suppressed.      

Optical absorption and fluorescence properties of Er3+ in sodium borate glass

Spectroscopic properties of Er³⁺ ions in sodium borate glass have been studied. The indirect and direct optical band gaps (E_opt) and energy level parameters (RacahE ¹, E² and E³), spin-orbit (ξ_4f) and configurational interaction (α)) are evaluated. Spectral intensities for various absorption bands of Er₃₊ doped sodium borate glass are calculated. Using Judd-Ofelt intensity parametersΩ ₂, Ω₄, Ω₆, radiative transition probabilities (A), branching ratios (β) and integrated absorption cross sections (Σ) are reported for certain transitions. The radiative lifetimes (τ_R) for different excited states are estimated. From the fluorescence spectra, the emission cross section (σ_P) for the transition,⁴I_13/2 → ⁴I_15/2 is reported.     

Acoustic investigations on PbO-Al2O3-B2O3 glasses doped with certain rare earth ions

Elastic moduli (Y, η), Poisson’s ratio (σ), microhardness (H) and some thermodynamical parameters such as Debye temperature (θ_D), diffusion constant (D _i),latent heat of melting (ΔH _m) etc of PbO-Al₂O₃-B₂O₃ glasses doped with rare earth ions viz. Pr³⁺, Nd³⁺, Sm³⁺, Eu³⁺, Tb³⁺, Dy³⁺, Ho³⁺, Er³⁺ and Yb³⁺, are studied as functions of temperatures (in the temperature range 30–200°C) by ultrasonic techniques. All these parameters are found to increase with increasing atomic numberZ of the rare earth ions and found to decrease with increasing temperature of measurement. From these results (together with IR spectra of these glasses), an attempt is made to throw some light on the mechanical strength of these glasses.     

Theory of Plane Copper and Oxygen Nuclear Spin–Lattice Relaxation Rates in Lightly Doped La2− x Sr x CuO4

Using a Mori-Zwanzig projection operator procedure the relaxation function theory of doped two-dimensional Heisenberg antiferromagnetic (AF) system in the paramagnetic state is presented taking into account the hole subsystem as well as both the electron and AF correlations. At low temperatures the main contribution to the nuclear spin–lattice relaxation rate, ⁶³(1/T ₁), of plane ⁶³Cu, arises from the AF fluctuations, and ¹⁷(1/T ₁), of plane ¹⁷O, has the contributions from the wave vectors in the vicinity of (π,π) and small q ∼ 0. The effects of thermal spin-wave damping Γ _q on ¹⁷(1/T ₁) in lightly doped regime are investigated, suggesting either a polynomial of up to third order (not simply (T/J)³) or exponential temperature dependence of Γ _q at low temperatures. It is shown that the theory is able to explain the main features of experimental data on temperature and doping dependence of ^17,63(1/T ₁) in the paramagnetic state of La_{2− x} Sr _x CuO₄ compounds.     

Scaling Results for Superfluid 3He in 98% Open Aerogel

We present experimental observations of the suppressed superfluid transition temperature, T _ca , superfluid fraction, ρ _s /ρ and Leggett frequency of ³He-B in aerogel, Ω _Ba . We determine T _ca from mass decoupling and the vanishing of the frequency shift away from the Larmor frequency in our different samples and different laboratories. We find that the suppressed transition temperature for ³He in aerogel occurs at a sample dependent, but approximately pressure independent, length, , where T _c and ξ ₀(P), are the transition temperature and the pressure dependent zero temperature coherence length for bulk ³He. T _ca also occurs at a pressure independent value of the Leggett frequency of bulk ³He-B. Further, we find that when the superfluid fraction and square of the Leggett frequency are plotted against T _ca −T (and not (T _ca −T)/T _ca ), the results of each measurement nearly collapse on to a pressure independent but sample dependent plot, with no further scaling. When plotted on a log–log scale, both measurements exhibit power laws in the range 1.33–1.45.      

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Towards All Electrical Spin Injection and Detection in GaAs in a Lateral Geometry

Herein we discuss our approach to realizing all electrical spin injection and detection in GaAs. We propose a lateral geometry, with two ferromagnetic electrodes crossing an n-doped GaAs channel. AlO _x tunnel barriers are to be used in order to overcome the impedance mismatch and different widths of the two electrodes ensure different coercive fields. We present a detailed theoretical analysis of the expected magnetoresistance. Differences in behavior between lateral and vertical devices, the influence of the applied bias (electric field), and opportunities offered by different measurement geometries were explored. The MBE grown wafer consisted of 100 nm Al_0.3Ga_0.7As, acting as confinement layer, 100 nm n-doped (4 × l0¹⁷ cm⁻³) GaAs, 3 nm n⁺⁺ GaAs (10²¹ cm⁻³), to suppress Schottky barrier formation, and 1.5 nm Al. The Al was oxidized naturally in order to obtain tunnel barriers. By making use of in-situ shadow masks, a 0.1 mm wide channel is defined by covering the rest of the sample by insulating SiO₂, followed by deposition of Ta bonding pads. Finally, 500 and 1000 nm wide CoFe electrodes crossing the GaAs channel are obtained by e-beam lithography and sputtering. We show that the I–V characteristics of the CoFe/AlO _x /GaAs interface are consistent with tunneling as the main injection mechanism. However, the resistance-area (5 × 10⁹ Ω μm²) of our barriers is too high compared to the GaAs conductance (50 Ω square resistance) leading to a strong suppression of magnetoresistance. Further experiments are in progress toward optimizing barrier and channel impedance matching.     

Tricritical Dynamics at the Demixing-λ-Transition in 3He-4He Mixtures

We calculate in two loop order the dynamical critical behavior at the tricritical point occuring in ³He-⁴He mixtures. Model F^′ introduced by Siggia and Nelson (Phys. Rev. B 15:1427, [1977])—already problematic in one loop order—is shown in two loop order to lead to a divergence of the mass diffusion D in contradiction to experiments. Within the complex symmetric version of this model (model E ^⋆′) the dynamical critical exponents of the kinetic coefficients can be calculated exactly leading to a mass diffusion going to zero at the tricritical point as D(t _X )∼t _X ^1/2 (t _X is the relative temperature distance at constant concentration) and the thermal diffusion ratio k _T ∼t _X ⁻¹ diverges proportional to the concentration susceptibility in the experimental region. We also discuss effective dynamical critical exponents and compare them with recent simulations of the vector Blume-Emery-Griffths model.      

Electrical properties of Schottky diodes based on Carbazole

Sandwich structures of Carbazole thin films have been prepared by using vacuum deposition technique. The plot of current density versus voltage (J–V characteristics) shows two distinct regions. In the lower voltage region ohmic conduction and in the higher voltage region space charge limited conduction (SCLC) is observed. Number of states in the valence band (Nv) is calculated from the temperature dependence of J in the ohmic region. From the temperature dependence of J in the SCLC region trap density (Nt) and activation energy are determined. The values of Nv and Nt are in the order 10²³ m⁻³ and 10²⁷ m⁻³ respectively. The value of activation energy is nearly equal to 0.1 eV and that of the effective mobility is 4.5 × 10⁻⁷ cm² V⁻¹ S⁻¹. Schottky diodes are fabricated using Aluminium (Al) as Schottky contact. It is observed that gold (Au) is more suitable for ohmic contact compared to silver (Ag). From a semi logarithmic plot of J versus V, the barrier height (ϕb), diode ideality factor (n) and saturation current density (J₀) are determined. The value of n increases and ϕb decreases on annealing.     

Acoustical parameters of polyethylene glycol/water mixtures

Ultrasonic velocity (v) and density (d) have been measured for polyethylene glycol/water mixtures at 30°C. The adiabatic compressibility (β _ad), molar compressibility (β), specific acoustic impendance (Z), Rao number (R) and van der Waals constant (b) have been computed. The variations ofv, d, β _ad,β, Z, R andb with mole ratio of water/ether group oxygen have been studied. The association between the components and the formation of tetrahydrate have been reported.     

Ni1−x Pt x (x=0–0.08) films as the photocathode of dye-sensitized solar cells with high efficiency

Films of Ni_1−x Pt _x (x=0, 0.02, 0.04, 0.06, and 0.08) have been prepared on fluorine-doped tin oxide-coated (FTO) glass substrates by a chemical plating method and used as the photocathode for dye-sensitized solar cells (DSCs). The Ni_0.94Pt_0.06 film consisted of nanoparticles with a size of 4–6 nm and a Pt loading of 5.13 μg/cm². The Ni_0.94Pt_0.06 photocathode exhibited high catalytic performance toward triiodide reduction, high light reflectance, and low charge-transfer resistance. The DSC assembled with the Ni_0.94Pt_0.06 photocathode gave a short-circuit photocurrent density (J _sc) of 16.79 mA/cm², an open-circuit photovoltage (V _oc) of 736 mV, and a fill factor (FF) of 66.4%, corresponding to an overall conversion efficiency of 8.21% under standard AM 1.5 irradiation (100 mW/cm²), which is higher than that for the DSC with a pure Pt photocathode obtained by conventional thermal decomposition. Furthermore, the DSC based on the Ni_0.94Pt_0.06 photocathode showed good stability. The results indicate that Ni_0.94Pt_0.06 films are promising lowcost and high-performance photocathodes for use in DSCs. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users.     

Extraction of Critical Current Density and Flux Creep Exponent in the Magnetic Superconductor Ru-1212 Using the ac Magnetic Susceptibility Measurements

The ac susceptibility data was employed to extract the temperature dependence of the critical current density, J _c(T), as well as the variation of flux-creep exponent n(T,H _ac) with temperature and ac field amplitude in bulk samples of polycrystalline magnetic superconductor RuSr₂GdCu₂O₈ (Ru-1212). The critical state models and the collective flux-creep approximation model were successfully accounted to describe such behavior below the transition temperature. The calculated values of n(T,H) are well fitted to a power law of the following form: n(T,H)=n ₀(H)T ^−s(H), where s is field dependent exponent whose values varied from −2.4, −1.01 for field amplitudes ranging from 0.5 G and 3.8 G. The power law describing the frequency dependence of χ′ is found to be consistent with the results of the current-dependent effective activation energy of the form U(J)=U ₀ln (J _c/J). Additionally, the dependence of the current density is found to scale according as: J _c(T)=J _c0(1−T/T _c) ⁿ , where the exponent n values varied from 1.05 to 1.25. Such dependence is an indication of intergrain coupling that could be ascribed in terms of superconductor–insulator–superconductor junctions. The derived temperature dependence of J _c(T) is in good agreement with the data obtained from the measurements using the traditional “loss-maximum” approach. Furthermore, the flux-creep effect increased with increasing both ac fields and temperatures except at about 15–25 K below the onset of T _c, where a slowing down of the flux creep was observed.     

Spectroscopic investigations of Nd3+ ion in lead acetate glass

Using the optical absorption spectra and the Judd-Ofelt theory, intensity parameters (Ω_λ) are calculated. Radiative lifetimes (T _R), branching ratios (β) and integrated absorption cross sections (Σ) are reported for certain excited levels of Nd³⁺ ion in lead acetate glass.     

A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods

The essential features of the Meshless Local Petrov-Galerkin (MLPG) method, and of the Local Boundary Integral Equation (LBIE) method, are critically examined from the points of view of a non-element interpolation of the field variables, and of the meshless numerical integration of the weak form to generate the stiffness matrix. As truly meshless methods, the MLPG and the LBIE methods hold a great promise in computational mechanics, because these methods do not require a mesh, either to construct the shape functions, or to integrate the Petrov-Galerkin weak form. The characteristics of various meshless interpolations, such as the moving least square, Shepard function, and partition of unity, as candidates for trial and test functions are investigated, and the advantages and disadvantages are pointed out. Emphasis is placed on the characteristics of the global forms of the nodal trial and test functions, which are non-zero only over local sub-domains Ω_tr ^J and Ω_te ^I , respectively. These nodal trial and test functions are centered at the nodes J and I (which are the centers of the domains Ω_tr ^J and Ω_te ^I ), respectively, and, in general, vanish at the boundaries ∂Ω_tr ^J and ∂Ω_te ^I of Ω_tr ^J and Ω_te ^I , respectively. The local domains Ω_tr ^J and Ω_te ^I can be of arbitrary shapes, such as spheres, rectangular parallelopipeds, and ellipsoids, in 3-Dimensional geometries. The sizes of Ω_tr ^J and Ω_te ^I can be arbitrary, different from each other, and different for each J, and I, in general. It is shown that the LBIE is but a special form of the MLPG, if the nodal test functions are specifically chosen so as to be the modified fundamental solutions to the differential equations in Ω_te ^I , and to vanish at the boundary ∂Ω_te ^I . The difficulty in the numerical integration of the weak form, to generate the stiffness matrix, is discussed, and a new integration method is proposed. In this new method, the Ith row in the stiffness matrix is generated by integrating over the fixed sub-domain Ω_te ^I (which is the support for the test function centered at node I); or, alternatively the entry K _{I J} in the global stiffness matrix is generated by integrating over the intersections of the sub-domain Ω_tr ^J (which is the sub-domain, with node J as its center, and over which the trial function is non-zero), with Ω_te ^I (which is the sub-domain centered at node I over which the test function is non-zero). The generality of the MLPG method is emphasized, and it is pointed that the MLPG can also be the basis of a Galerkin method that leads to a symmetric stiffness matrix. This paper also points out a new but elementary method, to satisfy the essential boundary conditions exactly, in the MLPG method, while using meshless interpolations of the MLS type. This paper presents a critical appraisal of the basic frameworks of the truly meshless MLPG/LBIE methods, and the numerical examples show that the MLPG approach gives good results. It now apears that the MLPG method may replace the well-known Galerkin finite element method (GFEM) as a general tool for numerical modeling, in the not too distant a future. Received 15 January 1999     

Luminescence of europium-doped BaO-Bi<Subscript>2</Subscript>O<Subscript>3</Subscript>-B<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

We have prepared europium-doped BaO-Bi2O₃-B2O₃ glasses and investigated the doping effect on the main physicochemical properties and local structure of the glasses. Using Judd-Ofelt analysis, we calculated intensity parameters (Ω₂, Ω₄, and Ω₆), spontaneous emission probabilities, the radiative lifetime, luminescence branching factors, the quantum yield of luminescence, and the stimulated emission cross sections for ⁵ D ₀ → ⁷ F _J transitions.     

Volumetric measurements under pressure for 2,2,4-trimethylpentane at temperatures up to 353.15 K and for benzene and three of their mixtures at temperatures up to 348.15 K

(p, V, T) data have been obtained in the form of volume ratios relative to 0.1 MPa for benzene (298.15 to 348.15 K), 2,2,4-trimethylpentane (TMP) (313.15 to 353.15 K), and their mixtures near 0.25, 0.5, and 0.75 mole fraction of benzene (313.15 to 348.15 K) for pressures up to near the freezing pressures for benzene and the mixtures, and up to 400 MPa for TMP. Isothermal compressibilitiesκ _T, isobaric expansivitie α, changes in heat capacity at constant pressureΔC _p, and excess molar volumesV ^E have been determined from the data. Literature data at atmospheric pressure have been used to convert theΔC _p toC _p at several temperatures. The isobars for α over the temperature range 278.15 to 353.15 K for TMP intersect near 47 MPa and reverse their order in temperature when plotted against pressure; normalization of the α's by dividing the values at each temperature by the α at 0.1 MPa prevents both the intersection and the reversal of the order. TheV ^E are positive and have an unusual dependence on pressure: they increase with temperature and pressure so that the order of the curves for 0.1, 50, and 100 MPa changes in going from 313.15 to 348.15 K.     

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.     

Synthesis and photoluminescence properties of Yb doped Ba5(PO4)3Cl phosphor for white light-emitting diodes

Yb²⁺ ion doped Ba₅(PO₄)₃Cl phosphor was synthesized by solid state reaction. Four distinct absorption bands were observed in the Ultraviolet (UV) light region due to the electronic transitions of Yb²⁺ ion from ¹S₀ ground state to ²F_5/2(t_2g), ²F_5/2(e_g), ²F_7/2(t_2g), and ²F_7/2(e_g) excited states. The main emission wavelength of the phosphor was around 630 nm. The optimized Yb²⁺ ion concentration was 0.2 mol% (λ_exc. = 400 nm). The calculated critical distance was about 8.729 Å and the concentration quenching was observed above 0.2 mol% due to the electric dipole–dipole interaction.