Three-dimensional stationary cyclic symmetric Einstein–Maxwell solutions; black holes

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2 + 1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants F_μνF^μν and T_μνT^μν, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein–Maxwell equations, reducible to three nonlinear equations for the three unknown functions, two new classes of solutions – having anti-de Sitter spinning metric limit – are derived. The relationship of various families with those reported by different authors’ solutions has been established. Among the classes of solutions with cosmological constant a relevant place is occupied by the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata–Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via SL(2,R)-transformations where the Clement spinning charged solution, the Martinez–Teitelboim–Zanelli black hole solution, and Dias–Lemos metric merit mention.     

The electronic structure of bcc-based random solid solutions of transition metals

The electronic structure of Nb _x Zr_1–x , V _x Nb_1–x and Mo _x V_1–x random solid solutions with the bcc lattice structure is investigated in the frame of the first-principles tight-binding muffin-tin orbital method and the coherent potential approximation. The total and component densities of states as well as the Bloch spectral densities are determined over a broad concentration range.     

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

Graded algebras of the second rank and integration of nonlinear equations Y zz =exp (2Y)−2Y,Y zz =2 exp (Y)−exp (−2Y)

In the terms of the notions of the theory of infinite-dimensional algebras of finite growth of the second rank, we have derived solutions to the equations; Y _zz =exp (2Y)–2Y, Y _zz =2 exp (Y)–exp (–2Y) dependent on two arbitrary functions.     

Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes,II

This paper is a continuation of an earlier study on the generalized Yang–Mills instantons over 4m-dimensional spheres. We will first present a discussion on the generalized Yang–Mills equations, the higher-order Chern–Pontryagin classes, c _2m , and the self-dual or anti-self-dual equations. We will then obtain some sharp asymptotic estimates for the self-dual or anti-self-dual equations within the Witten–Tchrakian framework which relates the integer value of c _2m to the number of vortices of the solution to a reduced 2-dimensional Abelian Higgs system over the Poincaré half-plane. We will prove that, indeed, for any integer N, there exists a 2|N|-parameter family of the generalized self-dual or anti-self-dual instantons realizing the topology c _2m =N. Furthermore, for the purpose of accommodating more general solutions, we establish a removable singularity theorem which enables us to extend the solutions obtained on a 4m-dimensional Euclidean space with an integral bound to the Hölder continuous solutions on a 4m-dimensional sphere.Research supported in part by PSC-CUNY Research Award 32Research supported in part by NSF under grants DMS–9972300 and DMS–9729992 through IAS     

The superconductive properties and crystal structure of Ba2(Y1−x Pr x )Cu3O9−y solid solutions

A series of Ba₂(Y_1–x Pr _x )Cu₃O_9–y solid solutions were prepared with the orthorhombic distorted perovskite structure. The compound Ba₂PrCu₃O_9–y belonging to tetragonal system is a good semiconductor. The superconductivity is observed for samples withx<0.6. With the increase of Y content, the distortion of crystal structure is greater and the superconductive transition temperature of zero resistanceTc(0) raises.     

Concentration Phase Transitions and Structural Disordering in the System of Solid Solutions LixNa1?xTa0.1Nb0.9O3

Concentration phase transitions and structural disordering in the system of solid solutions Li _x Na_1–x Ta_0.1Nb_0.9O₃ (x = 0–0.16) are investigated by the methods of Raman scattering, x–ray structural analysis, and electrophysical measurements. Points of disruption of the translational order in the arrangement of cations at x = 0.05–0.06, 0.09, 0.11, 0.135, and 0.14 that correspond to the boundaries of morphotropic regions and concentration structural anomalies are detected. At points x = 0.11; 0.135, and 0.14, the Raman spectrum in the region of vibrations of the cations located in octahedral and cubooctahedral holes (0–400 cm^–1) consists of two wide maxima and is practically smeared into the wing of the Rayleigh line, and on the concentration dependences of the electrophysical properties one observes sharp anomalies. The oxygen ochahedrons are distorted less significantly as x changes: the corresponding lines broaden, and new lines demonstrating a symmetry change of the oxygen octahedrons appear only for x 0.14. It is shown that the system of solid solutions Li _x Na_1–x Ta_0.1Nb_0.9O₃ for x < 0.015 is characterized by the antiferroelectric type of dipole ordering, and for x 0.015 the structure of a solid solution becomes noncentrosymmetric.     

The infrared spectra of solid solutions of some iron and chromium oxides

Oxides Fe_2–x Cr _x O₃ (corundum-type) and Fe_3–y ,Cr _y O₄ (spinel-type) were studied by transmission IR spectroscopy. The wavenumbers corresponding to characteristic absorption maxima depend linearly on the composition of both types of solid solutions, i.e. onx andy. The results show that IR spectroscopy can contribute to the analysis of solid solutions of iron and chromium oxides and of the oxidation products of Fe-Cr alloys.The authors are indebted to Ing. P. Holba for the preparation of synthetic oxide samples. The cooperation of Yu. Borodkin and I. Zuika (Riga) who made the measurements in the far IR region is gratefully acknowledged.     

Letter: Solutions of All One-Dimensional Wave Equations with Time Independent Potential and Separable Variables

Solutions, in terms of special functions, of all wave equations u _xx – u _tt = V(x) u(t,x), characterised by eight inequivalent time independent potentials and by variables separation, have been found. The real valueness and the properties of the solutions produced by computer algebra programs are not always manifest and in this work we provide ready to use solutions. We discuss especially the potential (m ₁ + m ₂ sinh x)cosh^–2x. Such potential approximates the Schwarzschild black hole potential and its use for determining black holes quasi-normal modes is hinted to.     

Irreversible cis-trans-Photoisomerization of Porphyrin Dimers with an Ethylene Bridge

On the basis of a comparison of the stationary absorption, fluorescence, and fluorescence excitation spectra of solutions of synthetic dimers of octaethylporphyrin (H₂OEP) and its zinc complex (ZnOEP) of composition ZnOEP–ZnOEP and ZnOEP–H₂OEP linked by an ethylene bridge in cis- and trans-geometry, we conclude that the cis-isomers of the above dimers, when illuminated, irreversibly change to their corresponding trans-isomers.     

Magnetic and magnetotransport properties of Co-doped manganites with perovskite structure

A systematic study of the doping of the Mn-sites by cobalt in three series of manganites — La_0.76Ba_0.24(Mn_1−xCo_x)O₃ single crystals, La_2/3Ba_1/3(Mn_1−xCo_x)O₃ and La(Mn_1−xCo_x)O₃ ceramics has been performed. It was found that La(Mn_1−xCo_x)O₃ annealed at 800°C in the range 0.4x0.9 is a mixture of ferromagnetic domains with ordered Mn and Co ions and ionically disordered spin-glass domains. In the quenched samples the fraction of spin-glass-type component increases strongly. The La_2/3Ba_1/3(Mn_1−xCo_x)O₃ solid solutions exhibit also an evidence for phase separation in the range 0.5x0.8. All the La(Mn_1−xCo_x)O₃ samples show an insulating behavior, however, magnetoresistance reduces strongly when the cobalt content rises to x=0.5. The La_0.76Ba_0.24(Mn_1−xCo_x)O₃ single crystals show first-order phase transition below their Curie points associated with a change of ground state of the Co²⁺ ions. The magnetic phase diagrams are depicted. The results are discussed in terms of positive Mn³⁺–O–Mn⁴⁺, Mn³⁺–O–Mn³⁺, Mn⁴⁺–O–Co²⁺ and negative Mn⁴⁺–O–Mn⁴⁺, Co²⁺–O–Co²⁺, Co²⁺–O–Mn³⁺ superexchange interactions as well as Co²⁺ and Mn⁴⁺ ionic ordering.     

Optical Properties of the (CuInSe2) x ·(2ZnSe)1−x and (CuInTe2) x (·2ZnTe)1−x Solid Solutions

Crystals of the compounds CuInSe₂, CuInTe₂, ZnSe, and ZnTe, and the solid solutions (CuInSe₂) _x ·(2ZnSe)_1–x and (CuInTe₂) _x ·(2ZnTe)_1–x were grown by the Bridgman and chemical transport reactions methods. Their transmission and reflection spectra in the region of the main absorption line edge were studied. The forbidden band gap of the indicated materials was determined and its concentration dependences were built for the solid solutions. It is established that the forbidden band gap changes linearly with the x composition and is satisfactorily described by the square-law dependence.     

Spectrophotometric Study of Luminol in Dimethyl Sulfoxide–Potassium Hydroxide

The spectrophotometric study of luminol (LH₂) in dimethyl sulfoxide (DMSO), DMSO-water solutions, and alkaline DMSO and DMSO-water solutions has been done, focusing on the effect of the KOH additon on LH₂ absorption and fluorescence properties. The absorption spectra indicate an acid-base equilibrium, and the luminol dianion (L^2–) formation at 3 × 10^–4 – 2.4 × 10^–3 M KOH. The decrease of the fluorescence intensity and the variation of the excitation spectra of LH₂-DMSO-KOH solutions with KOH concentration have been similarly explained. The acid-base process is reversible. The addition of HCl to the solution with 3.0 × 10^–3 M KOH leads to an increase of the fluorescence intensity to its highest value, observed in pure DMSO. The addition of HCl to the LH₂-DMSO solution leads to the decrease of the fluorescence intensity as a result of the LH⁺ ₃ cation formation. In LH₂-DMSO-water, the fluorescence band is shifted from 405 nm to 424 nm and increased in the intensity. In the presence of KOH (in LH₂-DMSO-water-KOH solution) a new band appears, with the maximum at 485 nm and the band at 405 nm decreased. The changes in fluorescence lifetimes also evidence the different chemical species formed.     

Mechanism for Conversion of the Conductivity Type in Arsenic-Doped p-CdxHg1–xTe Subject to Ionic Etching

Based on an analysis of chemical diffusion of mercury in p-Cd _x Hg_1–x Te:As narrow-band solid solutions, a mechanism for conversion of the conductivity type upon ionic etching is suggested. It is shown that the n–p conversion of the conductivity in this case is due to the formation of a donor complex between arsenic in the Te sublattice and an interstitial Hg atom. Moreover, the electron concentration in the converted layer corresponds to the concentration of the implanted arsenic impurity. The theoretical results are confirmed by the experimental investigation of the electron concentration distribution over the n-layer of a p-Cd _x Hg_1–x Te:As epistructure converted upon ionic etching.     

On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations

Recently, considerable progress has been made in understanding the nature of the algebro-geometrical superposition principles for the solutions of nonlinear completely integrable evolution equations, and mainly for the equations related to hyperelliptic Riemann surfaces. Here we find such a superposition formula for particular real solutions of the KP and Boussinesq equations related to the nonhyperelliptic curve ⁴ = ( – E ₁) ( – E ₂) ( – E ₃) ( – E ₄). It is shown that the associated Riemann theta function may be decomposed into a sum containing two terms, each term being the product of three one-dimensional theta functions. The space and time variables of the KP and Boussinesq equations enter into the arguments of these one-dimensional theta functions in a linear way.On leave from Leningrad State University and Leningrad Institute of Aviation Instrumentation.     

Solutions of the reflection equation for the vertex model

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the fundamental U_q[G₂] vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half are non-diagonal. The latter are parameterized by two continuous parameters but only one solution has all entries non-null. The non-diagonal solutions do not reduce to diagonal ones at any special limit of the free-parameters.     

Extraordinary Magnetic Properties of Ca1–xEuxS and Sr1–xEuxS Solid Solutions

The electron paramagnetic resonance (EPR) spectra and the stationary magnetic susceptibility are investigated for Ca_1–x Eu _x S and Sr_1–x Eu _x S solid solutions (0.00005 < x < 0.0032). The EPR spectrum of Eu²⁺ in both matrices contains a wide structureless line in addition to the narrow lines of the superfine structure characteristic of ions with high local symmetry. Because of the extraordinary temperature dependence of this line in CaS:Eu, it is associated with strongly interacting magnetic centers, namely, exchange-coupling pairs and chains or more complex clusters of magnetic ions. At the same time, the dependence of the stationary magnetic susceptibility in the temperature range 4.2–50 K has no peculiarities for CaS:Eu and SrS:Eu and obeys the Curie law.     

Vanadium-iron mixed trifluorides investigated by Mössbauer spectroscopy

Several solid solutions of the mixed crystalline Fe_1–x V _x F₃ series, synthesized by the solid-state reaction, are investigated by Mössbauer spectroscopy. The evolution of the hyperfine structure as a function of temperature suggests that the Fe_0.50V_0.50F₃ compound exhibits a spin-clustering phenomenon over the temperature range 70–175 K. We report here some preliminary high field Mössbauer spectra in order to discuss the magnetic behaviour.     

S-d Exchange Interaction and the Invar Anomaly of Thermal Expansion of Weak Band Magnets (on the Example of Fe1–x Co x Si Solid Solutions)

In the present paper, the temperature dependence of the linear thermal expansion coefficient (LTEC) of weak band magnets is studied both theoretically and experimentally on the example of Fe_1–x Co _x Si solid solutions. The contributions of electron and magnetic components are also analyzed. It is demonstrated that the experimental data obtained cannot be explained within the framework of the well-known single-particle models. A theoretical approach describing contributions of electrons and fluctuations to the LTEC of weak band magnets is developed based on the spd-model which, in addition to the interatomic exchange interaction of d-electrons, considers the spd-interaction resulting in a noticeable shift of the chemical electron potential along the energy axis. It is demonstrated that the exchange interaction of magnetic moments of s,p- and d-electrons plays the important role in the formation of the Invar LTEC anomaly in Fe_1–x Co _x Si solid solutions.     

Vortex pinning properties of –Ba–Cu–O and –Ba–Cu–O superconducting bulks

We have studied the effect of a small amount of Y-site substitution by La or Pr ions on the vortex pinning in the Y–Ba–Cu–O system. (Y_1-xLa_x)–Ba–Cu–O and (Y_1-xPr_x)–Ba–Cu–O bulks were fabricated by the melt-textured growth, in which x was varied from 0 to 0.01. The critical current density J_c at 77 K is improved in magnetic fields parallel to the c-axis above 2–4.5 T and the corresponding irreversibility field, H_irr, shifts to the higher value in both bulks.