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.     

Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials

Any symmetric polynomial f∈R[X ₁, …, X _n] has a unique representation f = p(σ₁, …, σ_n) with p∈R[X ₁, …, X _n] in the elementary symmetric polynomials σ₁, …, σ_n. This paper investigates higher order symmetric polynomials; these are symmetric polynomials with a representation p, which is also symmetric. We present rewriting techniques for higher order symmetric polynomials and exact degree bounds for the generators of the corresponding invariant rings. Moreover, we point out how algorithms and degree bounds for these polynomials are related to Pascals triangle, Fibonacci numbers, Chebyshev polynomials, and cardinalities of finite distributive lattices of semi-ideals. Received: December 16, 1997     

n(p)-InP-n-In2O3-P2O5-Pd diode structures as potential sensors for near-infrared radiation, moisture, and hydrogen

Diode structures based on n(p)-InP with intermediate n-In₂O₃ and P₂O₅ layers were fabricated by electrochemical deposition of Pd. It is shown that when exposed to pulses of water vapor the photo-emf of the structures varies by 60–400% and in the presence of H₂ it can vary by 1.5–2 orders of magnitude. These n(p)-InP-n-In₂O₃-P₂O₅-Pd structures are potential sensors for near-infrared radiation, moisture, and hydrogen. Pis’ma Zh. Tekh. Fiz. 25, 72–78 (December 26, 1999)     

Limitation of a giant amplification surge by photoinduced space charge accompanying an increase in the concentration of recombination centers in intrinsic threshold photoresistors with extracting contacts

An analysis is made of the dependence of Ĝ on V under conditions of a giant surge of the photoelectric gain Ĝ as the concentration of recombination impurities N increases, where V is the applied voltage and Ĝ is the value of G at the maximum point of the function G(N). It is shown that as a result of the space charge induced by the optical radiation the function Ĝ(V) exhibits strongly nonmonotonic behavior. The optimum voltage V _opt applied to the sample is determined for which Ĝ(V) reaches the maximum Ĝ _max. This nonmonotonic dependence of Ĝ on V does not correlate with heating of carriers or the lattice or by injection of charge from the contacts. Pis’ma Zh. Tekh. Fiz. 25, 1–8 (March 12, 1999)     

Momentum distributions and the impulse approximation in helium

The momentum distributionn(p) of atoms in condensed matter may be determined from neutron inelastic scattering measurements. However, scattering at high momentum transfers Q (high enough that the impulse approximation holds) is required. A model of solid helium is used to assess the error introduced inn(p) by assuming the impulse approximation holds at severalQ values. AtQ=20 Å^–1 the error inn(p) is 5–10%. This error can be reduced by a factor of ten using a symmetrization procedure.     

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.     

Frequency effect on the electrical and dielectric properties of (TlGaS2) 1 ? x(TlInSe2)x (x = 0.005, 0.02) single crystals

The electrical properties (loss tangent (tanδ), real (ɛ) and imaginary (ɛ″) parts of complex dielectric permittivity, and ac conductivity across the layers (σ_ac)) of (TlGaS₂)_{1 − x} (TlInSe₂) _x (x = 0.005, 0.02) layered single crystals have been studied in the frequency range f = 5 × 10⁴ to 3.5 × 10⁷ Hz. The results demonstrate that the dielectric dispersion in the crystals has a relaxation nature. Almost throughout the frequency range studied, their ac conductivity follows the relation σ_ac ∼ f ^0.8, characteristic of hopping conduction through localized states near the Fermi level. The Fermi-level density of states (N _F ), the spread of their energies, the mean hop time τ and distance R, and the concentration of deep traps determining the ac conductivity of the crystals (N _t ) have been estimated. With increasing x in (TlGaS₂)_{1 − x} (TlInSe₂) _x , N _F and N _t increase, while τ and R decrease.     

On the Crosscorrelation of Sequences with the Decimation Factor

Let p be a prime with p≡3 (mod 4), let n be an odd natural number and let . Consider the crosscorrelation funtion C _d (t)=∑ _{i =1} ^pn−1 ζ ^{ai − adi−t} where ζ≠1 is a complex p-th root of unity and (a _i ) is a maximal linear shift register sequence. In 7 the bound has been computed for p = 3. In this note we generalize this to for p≥ 3. Furthermore we giv an upper bound for the probability of the crosscorrelation function achieving the maximum absolute value. Received: November 7, 1999; revised version: March 23, 2000     

Effect of temperature on W-shaped excess molar heat capacities and volumetric properties: Oxaalkane-nonane systems

Excess molar volumesV _m ^f of the mixtures diglyme (2,5,8-trioxanonane: TON), triglyme (2.5,8,11-tetraoxadodecane: TODD), or tetraglyme (2,5,8,11,14-pen-taoxapentadecane: POPD; E181)+n-nonane have been obtained from density measurements at 278.15, 288.15,298.15, and 308. 15 K. In addition, a micro DSC II differential scanning calorimeter was used to obtain excess molar heat capacitiesC _p ^E at constant pressure for the same mixtures except for TON+n-nonane and at the same temperatures except for 278.15 K. These results allowed us to calculate the following mixing quantities in the complete range of concentration: α(∂V _m ^υ /∂T) _p , and (∂H ^υ/∂p)nT at 298.15K. The excess molar volumes are positive with large maximum values located in the central concentration range with the exception of POPD +n-nonane at 278.15 K, which has a central miscibility gap. For these mixtures,C _p ^F has a W-shaped concentration dependence: two minima separated by a maximum.     

The real part of AC conductance in amorphous nanocomposites ferromagnetic alloy–dielectric

Results of AC conductivity of the granular nanocomposites consisting of amorphous ferromagnetic alloy nanoparticles (Fe_0.45Co_0.45Zr_0.10) embedded into amorphous dielectric matrix (Al₂O₃) are presented and analyzed here. Conductivity measurements were made for the samples of different metal-to-dielectric ratio x (25 < x < 65 at.%) in the frequency range of 0.1–1000 kHz at temperature of 80–340 K. Real part of AC conductance at low frequencies (f ≤ 5 kHz) have shown temperature dependencies σ_real(T) corresponding to Mott hopping regime at x below the percolation threshold and metallic one beyond the percolation threshold. It was shown that σ_real(T) dependencies satisfactorily follow the known relations of 3D percolate models with critical indexes t ≈ 1.6, q ≈ 0.9, and s = 0.62. The numerical estimations of the density of localized states N(E _F) displayed a tendency to be decreased with x increase and the electron wave-function localization length a was about 11 nm.     

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 characterization of (Si2)1? x ? y (Ge2) x (GaAs) y continuous solid solutions

Epitaxial layers of p-type continuous solid solutions of the (Si₂)_1−x−y (Ge₂) _x (GaAs) _y system (0 ≤ x ≤ 0.9, 0 ≤ y ≤ 0.92) have been grown by liquid phase epitaxy from a lead-based solution melt confined between two horizontal n-type single crystal silicon substrates. Depth-composition profiles of the solid solution layers have been obtained. The photosensitivity spectra of nSi-p(Si₂)_1−x−y (Ge₂) _x (GaAs) _y structures have been measured. Original Russian Text ? A.S. Saidov, Sh.N. Usmonov, K.T. Kholikov, D. Saparov, 2007, published in Pis’ma v Zhurnal Tekhnicheskoĭ Fiziki, 2007, Vol. 33, No. 16, pp. 59–64.     

Nature of the Pseudogap in High-Tc Cuprates: Analysis?of?the?Bulk Magnetic Susceptibility of?La2?xSrxCu1?yZnyO4

The nature of the pseudogap in the quasiparticle spectral density in high-T _c cuprates is a matter of intense debate. In this study we have investigated the effects of Zn substitution on the uniform (q=0\boldsymbol{q}=0, where q\boldsymbol{q} is the wave vector) magnetic susceptibility, χ(T), of La_2−x Sr _x Cu_1−y Zn _y O₄ sintered samples with different hole concentrations, p(≡x), over a wide range of Zn contents (y). Non-magnetic Zn suppressed T _c most effectively and enhanced χ(T) systematically at low temperatures. We have extracted the characteristic pseudogap energy scale, ε _g, from the analysis of χ(T) data. Unlike T _c,ε _g was found to be fairly insensitive to the level of Zn substitution, even when T _c was completely suppressed by Zn. The Zn-induced Curie-like enhancement of the χ(T) was also found to be closely related to the PG energy scale. We discuss the possible implications of these findings in this paper.     

Structure and microwave dielectric properties of Ba3Ti4−x (Fe1/2Nb1/2) x Nb4O21 solid solutions

Ba₃Ti_4−x (Fe_1/2Nb_1/2) _x Nb₄O₂₁ (0 ≤ x ≤ 4) ceramics with the substitution of (Fe_1/2Nb_1/2) for Ti were investigated. The modified Ba₃Ti₄Nb₄O₂₁ dielectric ceramics prepared via the solid state reaction route exhibited single hexagonal structure. The dielectric constant and the quality factor of Ba₃Ti_4−x (Fe_1/2Nb_1/2) _x Nb₄O₂₁ (0 ≤ x ≤ 4) ceramics decreased with an increase of x. Improved temperature coefficient of the resonant frequency of samples was obtained by the substitution of (Fe_1/2Nb_1/2) for Ti. Optimal microwave dielectric properties of ε _r = 50, Q × f = 5200 GHz, and τ _f = 10 ppm/°C in Ba₃Ti₂(Fe_1/2Nb_1/2)₂Nb₄O₂₁ were obtained, which indicated its potential for microwave application.     

Eliminating nuisance parameters: two characterizations

Given a statistical modelP = {P_θ : θ ∈ x} and a surjective functiong: ϑ→Λ the problem of transformingP into a new modelQ= {_λ : λ ∈ Λ} indexed by Λ is investigated. Two characterizations are given for those modelsQ of the form Q_λ = ∫ P_θ π_λ(dθ), where π_λ is some probability such that π_λ(g=λ)=1. The first is related to a geometric property ofQ, while the second rests on the inferential implications of adoptingQ. Also, in the first π_λ is allowed to be finitely additive, while in the second π_λ is σ-additive. Finally, integrated likelihoods are revisited in light of the second characterization.     

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).     

The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity

The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. By investigating the lower bound of the nonlinearity of the derivative of the function f, this paper tightens the lower bound of the second-order nonlinearity of a class of Boolean functions over F2n{F_{2^n}} with high nonlinearity in the form f(x) = tr(λ x d ), where l ? F2r*, d=22r+2r+1{\lambda\in F_{2^r}^*, d=2^{2r}+2^{r}+1} and n = 4r.     

On Intrinsic Bounds in the Nullstellensatz

 Let k be a field and  f ₁, . . . ,  f _s be non constant polynomials in k[X ₁, . . . , X _n ] which generate the trivial ideal. In this paper we define an invariant associated to the sequence  f ₁, . . . ,  f _s : the geometric degree of the system. With this notion we can show the following effective Nullstellensatz: if δ denotes the geometric degree of the trivial system  f ₁, . . . ,  f _s and d :=max _j  deg( f _j ), then there exist polynomials p ₁, . . . , p _s ∈k[X ₁, . . . , X _n ] such that 1=∑ _j  p _j  f _j and deg p _j   f _j ≦3n ²δd. Since the number δ is always bounded by (d+1) ^n-1 , one deduces a classical single exponential upper bound in terms of d and n, but in some cases our new bound improves the known ones. Received November 24, 1995, revised version January 19, 1996     

Charge Order in (TMTTF)2PF6 Investigated by Infrared Spectroscopy

To explore novel physical phenomena related to strong π-d interaction, we measured the resistivity (ρ) and magnetoresistance of the first organic ferrimagnetic π-d system, (EDT-TTFVO)₂FeBr₄ under high pressures up to 8 GPa, where EDT-TTFVO denotes ethylenedithiotetrathiafulvalenoquinone-1,3-dithiolemethide. At ambient pressure, ρ(T) exhibits resistivity minimum near T_min ∼ 170 K followed by a gradual increase below it. With increasing pressure, T_min abruptly decreases till 4 GPa, beyond which it slightly increases. The increase ofT _min above 4 GPa is discussed in terms of the enhancement of the π-d interaction by applying pressure.