Strongly consistent model selection for densities

Let f be an unknown multivariate density belonging to a set of densities \(\mathcal{F}_{k^{*}}\) of finite associated Vapnik–Chervonenkis dimension, where the complexity k ^* is unknown, and ? _k ?? _k+1 for all k. Given an i.i.d. sample of size n drawn from f, this article presents a density estimate \(\hat{f}_{K_{n}}\) yielding almost sure convergence of the estimated complexity K _n to the true but unknown k ^* and with the property \(\mathbf{E}\{\int|\hat{f}_{K_{n}}-f|\}=\mbox{O}(1/\sqrt{n}\,)\). The methodology is inspired by the combinatorial tools developed in Devroye and Lugosi (Combinatorial methods in density estimation. Springer, New York, 2001) and it includes a wide range of density models, such as mixture models and exponential families.     

Investigation of breakage behavior of different mineralogical and morphological characteristic pumices

The objective of this study is to analyze dry grinding behavior of four different pumices in terms of Bond grindability value, selection and breakage parameters values. For this purpose, firstly, Bond grindability test were made for four pumices. Then, eight different mono-size fractions for each of pumices were carried out between 1.7 and 0.106 mm formed by a \({\surd 2}\) sieve series, and ground batch wise in a laboratory ball mill for determination of breakage parameters. Finally, S _i and B _i,j equations were determined from the size distributions at different grinding times, and the model parameters (S _i , a _T , α, γ, β and \({\phi_{j}}\)) were compared for four different pumice samples.     

Influence of Nd doping on microwave dielectric properties of SrTiO<Subscript>3</Subscript> ceramics

Sr_1?x Nd _x TiO₃ (x?=?0.08–0.14) ceramics were prepared by conventional solid-state methods. The analysis of crystal structure suggested Sr_1?x Nd _x TiO₃ ceramics appeared to form tetragonal perovskite structure. The relationship between charge compensation mechanism, microstructure feature and microwave dielectric properties were investigated. Trivalent Nd³⁺ substituting Sr²⁺ could effectively decrease oxygen vacancies. This reduction and relative density were critical to improve Q?×?f values of Sr_1?x Nd _x TiO₃ ceramics. For ε _r values, incorporation of Nd could restrain the rattling of Ti⁴⁺ cations and led to the reduction of dielectric constant. The τ _f values were strongly influenced by tilting of oxygen octahedral. The τ _f values decreased from 883 to 650 ppm/°C with x increasing from 0.08 to 0.14. A better microwave dielectric property was achieved for composition Sr_0.92Nd_0.08TiO₃ at 1460 °C: ε _r ?=?160, Q?×?f?=?6602 GHz, τ _f ?=?883 ppm/°C.     

Numerical simulation of IR absorption,reflection, and scattering in dispersed water-oxygen media

The method of molecular dynamics along with the flexible model of molecules are used to study the spectral characteristics of systems of clusters of (H₂O) _n , (O₂) _m (H₂O) _n , and (O) _i (H₂O) _n , m ≤ 2, i ≤ 4, 10 ≤ n ≤ 50. It is demonstrated that the integral intensity of absorption of IR radiation decays after water clusters adsorb oxygen. In addition, the adsorption of oxygen causes a significant decrease in the reflection coefficient R of monochromatic IR radiation. In so doing, the R(ω) spectrum splits into bands and exhibits seven peaks in the frequency region of 0 ≤ ω ≤ 3500 cm^?1. The dissociation of oxygen molecules captured by clusters makes the peaks of R(ω) spectrum more resolved. The attachment of molecular oxygen by clusters leads to decay of the power of their IR radiation, while the capture of atomic oxygen, on the contrary, is accompanied by an increase in the rate of dissipation of energy accumulated by water aggregates.     

Microwave dielectric properties of Sr<Subscript>0.7</Subscript>Ce<Subscript>0.2</Subscript>TiO<Subscript>3</Subscript>–Sr(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> ceramics

xSr_0.7Ce_0.2TiO₃–(1???x)Sr(Mg_1/3Nb_2/3)O₃ ceramics, referred to xSCT–(1???x)SMN, were successfully produced by conventional solid-state sintered technology. The compounds, belonging to perovskites with a secondary phase of CeO₂, can be detected even with x down to 0.1 of SCT composition. The overall trend for grain growth illustrates the increase with increasing SCT doping level. The Raman peak at 825 cm^?1 splits into two peaks and causes red shift phenomenon. XPS spectra indicate that Ti and Nb ions exist respectively in tetravalence and pentavalence, and Ce ions exist in trivalence and tetravalence. Dielectrics constant (ε _r ) of SCT–SMN ceramics gradually increases with increasing theoretical dielectric polarizabilities. A wider width of the 825 cm^?1 for FWHM of A_1g mode Raman peaks suggests to a lower Q?×?f value. The increasing tolerance factor in agreement with temperature coefficient of resonant frequency (τ _f ), denotes that the rise of perovskite symmetry. The 0.1SCT–0.9SMN ceramic sintered at 1450?°C for 4 h illustrates excellent microwave dielectric properties with ε _r ?~?35.4, Q?×?f?~?11282 GHz and τ _f ?~?1.7 ppm/°C. Activation energies of 0.1SCT–0.9SMN ceramic at 100, 300 and 500 V, are ~0.436, 0.427 and 0.331 eV, respectively, indicative of a decreased trend with external electric field.     

Phase equilibria and crystal structures of solid solutions in the Sr-Fe-Ni-O system at 1100°C in air

The phase equilibria in the Sr-Fe-Ni-O system at 1100°C in air have been studied by x-ray diffraction, and the corresponding phase diagram at constant temperature and pressure has been constructed. The system has been shown to contain two solid-solution series at 1100°C in air: SrFe_{1 ? x} Ni _x O_{3 ? δ} (0 < x ≤ 0.075, sp. gr. Cmmm) and Sr₃(Fe_{1 ? y} Ni _y )₂O_{7 ? δ} (0 < y ≤ 0.15, sp. gr. I4/mmm). Neither Sr₄(Fe_{1 ? z} Ni _z )₆O₁₃ nor Sr(Fe_{1 ? z} Ni _z )₁₂O₁₉ solid solutions have been identified. The lattice constants and structural parameters of single-phase samples have been refined by the full profile Rietveld analysis method.     

Correlation between the Molecular Refractions of Crystals and the Ionic Radii of the Cations in the Rare-Earth Trifluoride Homologous Series

We have identified linear correlations between the molecular refractions R_mol (cm³/mol) of crystals and the ionic radii r_i (Å) of the cations in the RF₃ rare-earth trifluoride homologous series: R_mol = 8.33r_i + 0.102 for R = La–Nd and R_mol = 13.03r_i–4.42 for R = Sm–Lu. The fact that the RF₃ rare-earth trifluorides can be divided into two groups is related to the morphotropic transition from the LaF₃ (tysonite) structure to the β-YF₃ structure. The correlation found here for RF₃ crystals with the β-YF₃ structure because the electronic structure of Y (4d¹5s²) differs from that of Sm–Lu (4f^6–145d^0–16s²) in that it has no 4f electrons.     

Solid-state reactions in the system Li<Subscript>2</Subscript>CO<Subscript>3</Subscript>-Na<Subscript>2</Subscript>CO<Subscript>3</Subscript>-Nb<Subscript>2</Subscript>O<Subscript>5</Subscript>-Ta<Subscript>2</Subscript>O<Subscript>5</Subscript>

The formation mechanisms of Li _x Na_{1 ?x} Ta _y Nb_{1 ? y} O₃ perovskite solid solutions in the Li₂CO₃-Na₂CO₃-Nb₂O₅-Ta₂O₅ system have been studied by x-ray diffraction, differential thermal analysis, thermogravimetry, IR spectroscopy, and mass spectrometry at temperatures from 300 to 1100°C. The results indicate that the synthesis of Li _x Na_{1 ? x} Ta _y Nb_{1 ? y} O₃ solid solutions involves a complex sequence of consecutive and parallel solid-state reactions. An optimized synthesis procedure for Li _x Na_{1 ? x} Ta _y Nb_{1 ? y} O₃ solid solutions is proposed.     

Spectral sensitivity of (Si<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(CdS)<Subscript>x</Subscript> solid solutions

Epitaxial layers of n-type solid solutions of the (Si₂)_{1 ? x} (CdS)_x system (0 ≤ x ≤ 0.01) were grown by liquid phase epitaxy from a tin-based solution melt confined between two horizontal p-type single crystal silicon substrates. The photosensitivity spectra of p-Si/n-(Si₂)_{1 ? x} (CdS)_x structures have been measured. A photoresponse peak at E ≈ 2.35 eV (1.25 eV below the top of the valence band of silicon) has been observed, which is probably related to an impurity level due to CdS molecules.     

Phase equilibria and crystal structures of solid solutions in the system LaCoO<Subscript>3−δ</Subscript>-SrCoO<Subscript>2.5±δ</Subscript>-SrFeO<Subscript>3−δ</Subscript>-LaFeO<Subscript>3−δ</Subscript>

The composition region and structure of La_1?x Sr _x Co_1?y Fe _y O_3?δ solid solutions are determined by x-ray powder diffraction using the Rietveld profile analysis method. The solid solutions based on lanthanum cobaltite, LaCoO_3?δ, have a rhombohedrally distorted perovskite-like structure (sp. gr. R \(\bar 3\) c), and those based on lanthanum ferrite, LaFeO_3?δ, have an orthorhombically distorted structure (sp. gr. Pbnm). The rhombohedral distortion decreases with increasing strontium content, and the solid solutions with x ≥ 0.5 have an ideal cubic structure (sp. gr. Pm3m). The composition dependences of lattice parameters for the La_1?x Sr _x Co_1?y Fe _y O_3?δ solid solutions are presented, and the 1100°C isotherm of the LaCoO_3?δ-SrCoO_2.5±δ-SrFeO_3?δ-LaFeO_3?δ system in air is constructed.     

Investigation of the breakage parameters of gypsum as dependent on interstitial filling in a laboratory ball mill

Gypsum is an industrial material used in many applications such as building and chemical industry, fertilizer manufacture, medicine and dentistry. In these industries, there is need for finely ground gypsum. Energy consumption is very high in grinding processes. Therefore, the effects on breakage kinetics of powder filling and ball filling were investigated on gypsum samples taken from the Denizli-Honaz region (Turkey), for batch grinding conditions based on a kinetic model. For this purpose, firstly, eight different mono-size fractions between 1.7 and 0.106 mm formed by a \({\surd 2}\) sieve series were obtained. Then, S _i and B _i,j equations were determined from the size distributions at different grinding times, and the model parameters (S _i , a _T , α, γ and \({\phi_{j}}\)) were compared for four different proportions of powder filling (5, 7.5, 10 and 15%), and three different proportions of ball filling (25, 35 and 45%). Finally, model parameters are discussed for each test. From the result of tests, obtained of the effect of ball filling and powder filling on the grinding, it was found our results differed from those of other investigators.     

Effect of Ni<Superscript>2+</Superscript> substitution on crystal structure and microwave dielectric properties for MgZrNb<Subscript>2</Subscript>O<Subscript>8</Subscript> ceramics

Monoclinic structured Mg_1?xNi_xZrNb₂O₈ (0?≤?x?≤?0.12) ceramics were synthesized for the first time through traditional solid-state reaction process and pure phase were obtained in all range. Rietveld refinement was used to analyze the crystal structure. With the increase of Ni²⁺ substitution amount, ε _r decreased, Q?×?f rose first then fell, τ _f shifted for the positive direction. Bond ionicity, lattice energy and bond energy were separately calculated to investigate the correlations with microwave dielectric properties. Typically, ceramics samples with the composition of Mg_0.92Ni_0.08ZrNb₂O₈ sintered at 1280 °C for 4 h exhibited the optimum microwave dielectric properties: ε _r ?=?24.58, Q?×?f?=?74534.1 GHz, τ _f ?=???49.11 ppm/°C, which could be a promising material for application.     

Ab Initio Study of Structural,Electronic, and Magnetic Properties of $\mathrm {A}_{1-x}^{\text {III}}$MnxBVI: In1−xMnxS-Diluted Magnetic Semiconductor

First-principles density functional calculations on the new class of diluted magnetic semiconductor \(A_{1-x}^{III}{Mn}_{x}B^{VI}\) In_1?x Mn _x S for x =?0.25 and 0.5 are investigated to study the structural, electronic, and magnetic properties, employing the full-potential linearized augmented plane wave method. Electronic band structures and density of states revealed a half-metallic character of In_1?x Mn _x S and show the stability of anti-ferromagnetic states as compared with ferromagnetic states. The calculated exchange constants J _dd are in good agreement with experimental and theoretical results on magnetic properties of single crystalline \(\mathrm {A}_{1-x}^{\text {III}}{\text {Mn}}_{x}\mathrm {B}^{\text {VI}}\) in the anti-ferromagnetic case. Our predicated calculations on the s,p-d exchange constants N ₀ α and N ₀ β show that they are lower than in \(\mathrm {A}_{1-x}^{\text {II}}{\text {Mn}}_{x}\mathrm {B}^{\text {VI}}\) DMS. The local environment is found tetrahedral as in the II–VI DMS and other (III,Mn) VI compounds. The total magnetic moment for In_1?x Mn _x S for different concentrations is in accordance with the exact value 5 μ _B and comes mainly from impurity Mn. The local magnetic moments of Mn ions are reduced from their free space charges values due to the p-d hybridization which produces small magnetic moments on the nonmagnetic In and S sites. The Curie temperature of In_1?x Mn _x S is calculated within the mean field approximation and compared with other DMS systems.     

Phase equilibria and crystal structures of phases in the La-Fe-Ni-O system at 1370 K in air

The phase equilibria in the La-Fe-Ni-O system have been studied at 1370 K in air, and the La-Fe-Ni-O phase diagram at constant temperature and pressure has been constructed. Based on x-ray diffraction results for samples prepared by standard solid-state reactions and via citrate and nitrate routes, the following solid solutions have been shown to exist at 1370 K in air: LaFe_{1 ? x} Ni _x O_{3 ? δ} (0 < x ≤ 0.4, sp. gr. Pbnm; 0.6 ≤ x ≤ 0.8, sp. gr. R-3 c), La₄(Ni_{1 ? y} Fe _y )₃O_{10 ? δ} (0 < y ≤ 0.3), La₃(Ni_{1 ? z} Fe _z )₂O_{7 ? δ} (0 < z ≤ 0.05), La₂Ni_{1 ? v} Fe _v O_{4 + δ} (0 < v ≤ 0.05), Ni_kFe_{3 ? k} O₄ (0.81 ≤ k ≤ 1.05), Ni_{1 ? m} Fe _m O (0 < m ≤ 0.05), and Fe_{2 ? p} Ni _p O₃ (0 < p ≤ 0.04). The lattice constants and structural parameters of single-phase samples have been refined by the Rietveld profile analysis method.     

Simultaneous Action of Intra- and Interband Pair Channels in Multiband Superconductivity

Interband superconductivity channels with pairs formed from the same (a) and different bands (b) are compared in common action. A simple mean-field multiband model is inspected. There are three order parameters Δ _a , Δ _{a d} and \({\Delta }_{b} \left ({\Delta }_{b1}^{2}={\Delta }_{b2}^{2} \right )\). Complicated quasiparticle energies induced by interactions of strengths W _a and W _b follow. The calculated operator averages lead to a coupled nonlinear system for the gap-type parameters. Illustrative calculations of them vs temperature have been made. Overlapping dispersive bands intersected by the chemical potential have been used. A novel result is that at a fixed parameter set the system of basic equations has two independent solutions. The free energy is of a complicated structure under the action of both channels. There are stable and metastable states. The W _a and W _b channels compete in simultaneous functioning. The phenomenon of the effective logout of one of the channels can be traced. Starting by the temperature where Δ _i reached zero, the solutions induced by W _j behaving as W _i were zero and define T _{c i} . The pairs Δ _a and Δ _{a d} have the same vanishing temperature. The general results are very sensible to |W _b | inclusive to critial behaviour. Reduced |W _b | stimulates the formation of closed “bubbles” built up by Δ _a , Δ _b and Δ _{a d} belonging to parallel solutions. The corresponding metastable state vanishes when the bubble closes.     

Production of double-layer epitaxial structures based on the solid solution of the Cd-Hg-Te system using a combination of LPE and MOCVD techniques

The technique of growing CdTe and Cd _x Hg_{1 ? x} Te layers utilizing chemical metalloorganic compound vapor deposition (MOCVD) onto a CdZnTe(111) substrate with a preliminarily deposited Cd _y Hg_{1 ? y} Te layer using liquid phase epitaxy (LPE) has been developed. No noticeable changes in the electrophysical parameters and composition of the Cd _y Hg_{1 ? y} Te layer take place under such conditions during MOCVD deposition.     

On the Role of Fermi Energy in Determining Properties of Superconductors: a Detailed Comparative Study of Two Elemental Superconductors (Sn and Pb), a Non-cuprate (MgB<Subscript><Emphasis Type="Bold">2</Emphasis></Subscript>) and Three Cuprates (YBCO,Bi-2212 and Tl-2212)

Fermi energies (E _Fs) of high- T _c superconductors (SCs) have of late been evincing considerable interest because they are believed to be the cause of their high T _cs and gap structures. Since Bardeen-Cooper-Schrieffer (BCS) equations for elemental and generalized-BCS equations for non-elemental SCs are derived under the blanket of the assumption E _F/ k θ > > 1 (k = Boltzmann constant, θ = Debye temperature), they cannot shed light on the E _Fs of these SCs. This fact leads us to address the gaps (Δ₀s) and T _cs of both types of SCs via recently derived equations which incorporate E _F as a variable. For the specification of the E _F of any SC, we now need another of its properties. Choosing j ₀, the critical current density of the SC at T = 0, and following an idea due to Pines, we present for both types of SCs new equations for j ₀ that depend solely on the following properties of the SC: E _F, θ, gram-atomic volume, electronic specific heat constant and a dimensionless construct \(y=k\theta \sqrt {2m\ast } \text {/}P_{\text {0}} \sqrt {E_{\mathrm {F}} } \text {,}\) where m* is the effective mass of superconducting electrons and P ₀ their critical momentum. Appeal to the experimental values of Δ₀, T _c and j ₀ of any SC then not only leads to values of E _F, m* and P ₀ but also provides plausible clues about how its j ₀—and therefore T _c—may be increased.     

The Effect of Charge Transport Mechanisms on the Efficiency of Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>As/GaAs Photodiodes

Photovoltaic characteristics of heterostructure Al_xGa_{1 – x}As/GaAs p–i–n photodiodes fabricated by molecular-beam epitaxy have been studied. Efficiencies of 50% were reached in conversion of monochromatic light in the photovoltaic mode at power density of up to 200 W/cm² at a wavelength λ = 830 nm. A relationship was demonstrated between the “saturation currents” for the diffusion-related charge-transport mechanism (Shockley) in p–i–n photodiodes, calculated from dark current–voltage characteristics, and the experimental values of efficiency. As the “saturation current” of the diffusion-related charge-transport mechanism increases by an order of magnitude, a relative decrease in the efficiency from the maximum value by more than 10% is observed under excitation by constant or pulsed monochromatic light.     

Enhancement of Pinning Role by Nonstoichiometry in YBa2Cu3O7−y Superconductors

Considerably improved flux pinning and critical current density Jc values have been achieved in Y-deficient Y-123 superconductors by directional solidification in air. In comparison with the regular Y-123 composition, Y-deficient one also has an orthorhombic structure and Y-123 main crystal phase remains in it. Whereas with the shortage of Y, Y_1?xBa₂Cu₃O_7?y can be regarded as (YBa₂Cu₃)_1?xO_7?t(Ba₂Cu₃) _x O_t?y or (YBa₂Cu₃O_7?z)(□ _x ^YO_z?y), so there may develop several kinds of microstructure defects as pinning sites in the system, such as highly dense, fine-scale, and faultlike defects, as well as localized superstructure, which are able to induce the increasing in flux pinning and Jc values in higher external magnetic fields. This kind of simple nonstoichiometric route could lead to a commercial technique for flux-pinning enhancement in Y-123 bulk materials.     

Effect of Zr Addition on Bi<Subscript>1.8</Subscript>Pb<Subscript>0.4</Subscript>Sr<Subscript>2.0</Subscript>Ca<Subscript>1.1</Subscript>Cu<Subscript>2.1</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> Superconductor

The polycrystalline Bi_1.8Pb_0.4Sr_2.0Ca_1.1Cu_2.1 M_xO _y , with M = Zr (x = 0.0, 0.02, 0.04), were synthesized by solid-state reaction method and studied by X-ray diffraction analysis (XRD), scanning electron microscopy equipped with energy dispersive of X-ray analysis (SEM/EDX) and resistivity versus temperature measurements. The influence of the Zr addition on the Tc and microstructure properties of the superconducting compounds has been studied. SEM observations show whiskers grains randomly distributed and microstructural change due to the addition of Zr. The ZrO₂ was incorporated into the crystalline structure of BSCCO system in all samples. The crystallographic structure remains in a tetragonal form where a= b≠c. Generally, all samples exhibit semiconductor behaviour above \(T_{\mathrm {c}}^{\text {onset}}\). The onset critical temperature \(T_{\mathrm {c}}^{\text {onset}}\) increases up to 86 with x = 0.02. There is an enhancement in the critical temperature for doped samples as compared with pure Bi_1.8Pb_0.4Sr_2.0Ca_1.1Cu_2.1O _y .Changes in superconducting properties of ZrO₂ nanoparticle added Bi-2212 system were discussed.