Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Spectroscopy of optical centers of Eu<Superscript>3+</Superscript> ions in partially stabilized and stabilized zirconium crystals

The structure of the optical centers of Eu³⁺ ions in tetragonal (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 2.7–3.6; y = 0.1) and cubic (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 8–38; y = 0.1–0.5) crystals of solid solutions on the basis of zirconium dioxide is studied using the methods of optical and Raman-scattering spectroscopy. Characteristic optical centers of Eu³⁺ ions with different crystalline environments are revealed in the above compounds.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Extreme Electromechanical Characteristics and Microstructural Features of Ferro-Piezoceramics Based on Lead Titanate

Microstructural features and electrophysical parameters of a number of solid solutions based on PbTiO₃ are investigated. Solid solutions (Pb_{1–3/2x + z/2}Nd _x )(Ti_1–y–zMn _y Inz)O₃ and Pb_1–xCa _x Ti_1–y(W_1/2Co_1/2) _y O₃ with extreme values of the mechanical Q-factor and electromechanical anisotropy are chosen as the objects of investigation. The ferro-piezoceramic samples are obtained through conventional sintering and hot pressing. X-ray structural and microstructural studies are performed, and the complex elastic, dielectric, and piezoelectric parameters of experimental samples are measured. The frequency dependences of complex parameters of the experimental samples have been studied at frequencies of up to 40 MHz. It is established that the extreme values of the mechanical Q-factor and piezoelectric anisotropy of the investigated PbTiO₃-based solid solutions are due to microstructural features associated with the technological regimes of ferropiezoceramic fabrication.     

Symmetries of the pseudo-diffusion equation and related topics

We show in details how to determine and identify the algebra g = {A_i} of the infinitesimal symmetry operators of the following pseudo-diffusion equation (PSDE) LQ ≡ \(\left[ {\frac{\partial }{{\partial t}} - \frac{1}{4}\left( {\frac{{{\partial ^2}}}{{\partial {x^2}}} - \frac{1}{{{t^2}}}\frac{{{\partial ^2}}}{{\partial {p^2}}}} \right)} \right]\) Q(x, p, t) = 0. This equation describes the behavior of the Q functions in the (x, p) phase space as a function of a squeeze parameter y, where t = e ^2y. We illustrate how G _i(λ) ≡ exp[λA _i] can be used to obtain interesting solutions. We show that one of the symmetry generators, A ₄, acts in the (x, p) plane like the Lorentz boost in (x, t) plane. We construct the Anti-de-Sitter algebra so(3, 2) from quadratic products of 4 of the A _i, which makes it the invariance algebra of the PSDE. We also discuss the unusual contraction of so(3, 1) to so(1, 1)? h². We show that the spherical Bessel functions I ₀(z) and K ₀(z) yield solutions of the PSDE, where z is scaling and “twist” invariant.     

Correlation of the piezoelectric and dielectric properties of soft ferroelectric ceramics

The dependences of the piezoelectric (g ₃₃) and electrostriction (Q ₃₃) coefficients of nonpolarized soft relaxor ferroelectric ceramics of the PbMg_1/3Nb_2/3O₃-PbTiO₃ system on electric field E ₃ are calculated and interpreted. The nonmonotonic g ₃₃(E ₃) dependence and negative values of Q ₃₃ were revealed in strong electric fields. These features are shown to be the manifestation of correlation between the piezoelectric and dielectric properties.     

Heat capacity of PMN near an electric-field-induced phase transition

The heat capacity of a single crystal of Pb(Mg_1/3Nb_2/3)O₃ (PMN) in an electric filed with E = 3 kV/cm applied along the [111] direction has been measured using adiabatic calorimetry over the temperature range 170–250 K. Anomalies in C _p have been found, which correspond to a field-induced phase transition from a relaxor to a ferroelectric state at 225 K under field cooling conditions or at 235–240 K on the subsequent field heating. The field-induced ferroelectric phase persists in a metastable state at low temperatures and is destroyed on zero-field heating at 210 K. The small entropy change ΔS = 0.028R in the field-induced phase transition suggests an insignificant change in the volume fraction of existing polar nanoregions.     

Multicomponent <Emphasis Type="Italic">n</Emphasis>-(Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions with different atomic substitutions in the Bi and Te sublattices

The thermoelectric properties of n-Bi_{2 ? x} Sb _x Te_{3 ? y ? z} Se _y S _z solid solutions are studied in the temperature range 300–550 K. It is shown that an increase in the parameter β determining the figure-of-merit Z of the material is observed in compositions with the optimally related effective mass of the density of states m/m ₀, the carrier mobility μ₀, and the lattice thermal conductivity κ _L . Within the temperature range 300–350 K, the parameter β and the figure-of-merit Z are found to increase in solid solutions with substitutions in both bismuth telluride sublattices Bi → Sb and Te → Se, S (x = 0.16, y = z = 0.12) for optimum electron concentrations. An increase in the electron concentration and substitutions of atoms only in the tellurium sublattice bring about an increase in the β parameter and the value of Z at higher temperatures. Within the range 350–450 K, the parameters β and Z are observed to increase in a solid solution with a low content of substituted atoms in the tellurium sublattice Te → Se, S for y = z = 0.09 and, at higher temperatures up to 550 K, in compositions with tellurium substituted by selenium only, with increasing content of substituted atoms.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

EPR study of the spin dynamics of the (La<Subscript>1−<Emphasis Type="Italic">y</Emphasis></Subscript>Pr<Subscript>y</Subscript>)<Subscript>0.7</Subscript>Ca<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> system

The EPR of Mn ions in the (La_1?yPr_y)_0.7Ca_0.3MnO₃ system has been studied within a broad range of temperatures (4<T<600 K) and Pr concentrations (0≤y≤1), as well as under isotope substitution of ¹⁸O for ¹⁶O. All compositions were shown to undergo transitions to a magnetically ordered state with decreasing temperature. Magnetic phase diagrams were constructed for systems with different oxygen isotopes. The diagrams include paramagnetic, ferromagnetic, and antiferromagnetic regions. In the paramagnetic region, at temperatures not too close to the phase transition points, the Mn ion linewidth ΔH _pp (T) is related to the magnetic susceptibility χ(T) through the relation ΔH _pp (T) = [χ₀/χ(T)]ΔH _pp (∞) + ΔH₀, where ΔH _pp (∞) is the width of the exchange-narrowed line in the high-temperature approximation, χ₀ ∝ 1/T is the susceptibility of noninteracting ions, and ΔH₀ is the residual width originating from the sample porosity and resonance-field scatter in unoriented grains of a powder sample. An analysis of the data on ΔH _pp (∞), ΔH₀, and χ(T) made it possible to estimate the symmetric and antisymmetric exchange interaction of Mn ions and of the noncubic crystal-field component of the oxygen ions. These parameters were found to be independent of the oxygen isotope species to within experimental error.     

Kinetics of nucleation of thermodynamically ordered ferroelectric phases in PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>–<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> crystals with different compositions

The kinetics of electric field-induced nucleation of ordered ferroelectric phases from a mixed glassy relaxor state has been studied in a number of single-crystal (1–x)PbMg_1/3Nb_2/3O₃–xPbTiO₃ (PMN–xPT) solid solutions (x = 29, 33, 35%) lying in a morphotropic phase region. It is shown that the formation of these phases and fast establishment of a macroscopic polarization are preceded by some delay time, depending on the electric field strength and temperature. It is found that the monoclinic phase is thermodynamically stable at room temperature in all the compounds in the time (~3000 s) and electric field (~1 kV/cm) ranges under study, whereas the monoclinic phase of the compound with x = 35% transforms, at temperatures near the temperature of the morphotropic phase transition after insignificant time interval of ~100 s, to another stable ferroelectric tetragonal phase.     

Colossal room-temperature magnetoresistance in thin La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>y</Subscript>MnO<Subscript>3</Subscript> epitaxial films

The first thin La_1?xAg_yMnO₃ epitaxial films (_y ≤ x) were grown on SrTiO₃ (110) substrates with silver present in the ionized state (Ag⁺) only. The Curie temperatures T_C of the compositions with x = y = 0.05, x = y = 0.1, and x = 0.3 and y = 0.27 crystallizing in the hexagonal structure \(R\bar 3c\) above or close to room temperature. The temperature dependences of electrical resistivity ρ and of magnetoresistance ¦Δρ/ρ/¦ = ¦(ρ_H ? ρ _H = 0)/ρ_H=0¦ pass through maxima near T_C, with the magnetoresistance being negative and reaching colossal values of ～7–20% in a magnetic field H = 8.2 kOe not only at T_C but also at room temperature. The magnetic moment per formula unit as derived from the saturation magnetization at T = 5 K is substantially smaller than expected for complete ferromagnetic ordering. The magnetization in fields of up to 6 kOe depends on the actual sample cooling conditions, and the hysteresis loop of a field-cooled sample is displaced along the H axis by ΔH. The above properties can be accounted for by the fact that the films are in a two-phase magnetic (ferromagnetic-antiferromagnetic) state induced by strong s-d exchange. The maximum value of Δ H was used to calculate the energy of exchange coupling between the ferromagnetic and antiferromagnetic parts of a sample.     

Enhancement of pseudogap anomalies induced by nanoscale structural inhomogeneity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductor

The magnetization M(H) in the superconducting state, dc magnetic susceptibility χ(T) in the normal state, and specific heat C(T) near the superconducting transition temperature T _c have been measured for a series of fine-crystalline YBa₂Cu₃O _y samples having nearly optimum values of y = 6.93 ± 0.3 and T _c = (91.5 ± 0.5) K. The samples differ only in the degree of nanoscale structural inhomogeneity. The characteristic parameters of superconductors (the London penetration depth and the Ginzburg–Landau parameter) and the thermodynamic critical field H _c are determined by the analysis of the magnetization curves M(H). It is found that the increase in the degree of nanoscale structural inhomogeneity leads to an increase in the characteristic parameters of superconductors and a decrease in H _c(T) and the jump of the specific heat ΔC/T _c. It is shown that the changes in the physical characteristics are caused by the suppression of the density of states near the Fermi level. The pseudogap is estimated by analyzing χ(T). It is found that the nanoscale structural inhomogeneity significantly enhances and probably even creates the pseudogap regime in the optimally doped high-T _c superconductors.     

Extremal points for fractional boundary value problems

This article is concerned with characterizing the first extremal point, b₀, for a Riemann–Liouville fractional boundary value problem, D^α₀₊y + p(t)y = 0, 0 < t < b, y(0) = y′(0) = y″(b) = 0, 2 < α ≤ 3, by applying the theory of u₀-positive operators with respect to a suitable cone in a Banach space. The key argument is that a mapping, which maps a linear, compact operator, depending on b to its spectral radius, is continuous and strictly increasing as a function of b. Furthermore, an application to a nonlinear case is given.     

The Nernst-Ettingshausen coefficient in the normal phase of doped HTSCs of the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>y</Subscript> system

The temperature dependence of the Nernst-Ettingshausen coefficient Q(T) in the normal phase of doped HTSCs of the yttrium system was studied. The main features characterizing the behavior of this coefficient were revealed, and the character and mechanism of the effect that various nonisovalent substituents exert on the Q(T) dependence were analyzed. It is shown that the narrow-band model permits one not only to describe all the specific features observed in the Q(T) curves but also to perform a simultaneous quantitative analysis of the temperature dependences of four kinetic coefficients (the electrical resistivity and the Seebeck, Hall, and Nernst-Ettingshausen coefficients) with the use of a common set of model parameters characterizing the band structure and carrier system in the normal phase of an HTSC. This approach was employed to determine the carrier mobilities and the asymmetry of the dispersion curve in the systems studied (YBa₂Cu₃O_y, y = 6.37–6.91; YBa₂Cu_3?xCo_xO_y, x = 0–0.3; Y_1?xCa_xBa₂Cu₃O_y, x = 0–0.25; Y_1?xCa_xBa_2?xLa_xCu₃O_y, x = 0–0.5) and to analyze the effect of the substitutions involved on the variation of these parameters.     

Low-frequency dielectric relaxation (1/<Emphasis Type="Italic">f</Emphasis> noise) in relaxors of the (1 − <Emphasis Type="Italic">x</Emphasis>)PMN-(<Emphasis Type="Italic">x</Emphasis>)PZT system

The dielectric properties of relaxor ferroelectric ceramics (1 ? x)PbMg_1/3Nb_2/3O₃-(x)PbZr_0.53Ti_0.47O₃ (PMN-PZT) have been studied at frequencies from 40 Hz to 1 MHz in the temperature range of the diffuse phase transition. It is established that the dielectric relaxation generates 1/f noise, whose spectral density depends on the relaxor composition and temperature.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Josephson effects in unconventional heavy fermion superconductors

We discuss the Josephson effect for pairing states which break crystal symmetries in addition to gauge symmetry. We consider theE _1g andE _2u models for the low-temperature phase ofUPt ₃, with order parameters Δ(E _1g )～p _z (p _x +ip _y ) and Δ(E _2u )～p _z (p _x +ip _y )². We report calculations of Josephson critical currents, taking into account the effects of depairing at the interface. For singlet-triplet junctions the critical current is non-zero only for spin-orbit, spin-flip tunneling, and is found to be much smaller than the Ambegaokar-Baratoff value even when the spin-orbit tunneling amplitude is comparable to the spin-independent amplitude.     

Conductivity and anomalous Hall effect in film magnetic nanocomposites based on nonstoichiometric oxides

The transport properties of film nanocomposites (Co₄₀Fe₄₀B₂₀) _x (AlO _y )_{100 ? x} and (Co₈₄Nb₁₄Ta₂) _x (AlO _y )_{100 ? x} based on AlO _y oxide (y ~ 1), containing a ferromagnetic metal, are studied in the region of the metal–insulator transition (57 > x > 47 at %). It is found that at x > 49 at %, the conductivity of nanocomposites is well described by a logarithmic law of σ(T) = a + b ln T, which can be explained by the peculiarities of the Coulomb interaction in nanogranular systems with metallic conductivity near the metal—insulator transition. It is shown that parameter b is determined by the characteristic size of the percolation cluster cell, which in nanocomposites of both types happen to be the same (~8 nm) and correlates well with the results of electron microscopy studies. The temperature dependence of the anomalous Hall effect at the logarithmic dependence of conductivity is studied for the first time. In the immediate vicinity of the transition, a power-law scaling between the anomalous Hall resistance and longitudinal resistance ρ _H ^a ∝ ρ^0.4, is detected, which can be explained by the suppression of its own mechanism of the anomalous Hall effect under the strong scattering of charge carriers.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.