Symmetrizer and Antisymmetrizer of the Birman–Wenzl–Murakami Algebras

Explicit formulas for the symmetrizer and the antisymmetrizer of the Birman–Wenzl–Murakami algebras BWM(r,q) _n are given.     

Thermal Stability of Structure and Properties of Gradient and Gradient-Layered Coatings of the Ti–Al–Si–Cu–N System

Russian Physics Journal - Using the methods of dark-field electron microscopy analysis, energy-dispersive X-ray microanalysis, hardness measurements and scratch testing, the variations of elemental...     

Square Integrability and Uniqueness of the Solutions of the Kadomtsev–Petviashvili-I Equation

We prove that the solution of the Cauchy problem for the Kadomtsev–Petviashvili-I Equation obtained by the inverse spectral method belongs to the Sobolev space H^k(R²) for k 0, under the assumption that the initial datum is a small Schwartz function. This solution is shown to be the unique solution within a class of generalized solutions of the Kadomtsev–Petviashvili-I equation.     

Dynamics of the normal–superconductor phase transition and the puzzle of the Meissner effect

The analysis of Pippard (1950) for the growth of the normal phase into the superconducting phase in the presence of a magnetic field H>H_c$H>H_c$ is applied in reverse to the case H<H_c$H<H_c$ (H_c=$H_c=$ critical magnetic field). We carry out the analysis both for a planar and a cylindrical geometry. As the superconducting phase grows into the normal phase, a supercurrent is generated at the superconductor–normal phase boundary that flows in direction opposite to the Faraday electric field resulting from the moving phase boundary. This supercurrent motion is in direction opposite to what is dictated by the Lorentz force on the current carriers, and in addition requires that mechanical momentum of opposite sign be transferred to the system as a whole to ensure momentum conservation. In the cylindrical geometry case, a macroscopic torque of unknown origin acts on the body as a whole as the magnetic field is expelled. We argue that the conventional BCS-London theory of superconductivity cannot explain these facts, and that as a consequence the Meissner effect remains unexplained within the conventional theory of superconductivity. We propose that the Meissner effect can only be understood by assuming that there is motion of charge in direction perpendicular to the normal–superconductor phase boundary and point out that the unconventional theory of hole superconductivity describes this physics.     

Inversion of the Penrose transform and the Cauchy–Fantappie formula

We discuss the construction of an explicit inversion of the Penrose transform with the focus on connections with the Radon transform, multi-dimensional residues and the Cauchy–Fantappie integral formula following to results [1], [2]. The focus is on the new representation (M) of the inverse Penrose transform as a residue. The proof of this formula can be extracted from [1]. This proof includes an explicit computation of this residue (D). In this formula not the exact values of all coefficients but the existence of a differential operator, inverting the Penrose transform (we call this Leibnitz–Newton’s phenomenon) is important. It is similar to local inversion formulas in integral geometry.     

Effect of the Energy of Krypton Ions on the Structure and Hardening of Ti–Cr–N Coatings

Russian Physics Journal -     

Effect of copper on the structure–phase transformations and the properties of quasi-binary TiNi–TiCu alloys

The effect of copper alloying up to 25 at % on the structure–phase transformations and the physicomechanical properties of ternary alloys from the quasi-binary TiNi–TiCu section is studied by measuring the physicomechanical properties, transmission electron microscopy, scanning electron microscopy, electron diffraction, and X-ray diffraction (XRD). The data of temperature measurements of the electrical resistivity and the magnetic susceptibility and XRD data are used to plot a general diagram for the thermoelastic B2 ? B19', B2 ? B19 ? B19', and B2 ? B19 martensitic transformations, which occur in the alloys upon cooling as the copper content increases in the ranges 0–8, 8–15, and 15–25 at % Cu, respectively. The experimental results are compared to the well-known data, including differential scanning calorimetry data, obtained for these alloys. The changes in the mechanical properties and the microstructure of the alloys in the state of B19 or B19' martensite are discussed.     

Analytical Solution of the Duffin–Kemmer–Petiau Equation for the Sum of Manning–Rosen and Yukawa Class Potentials

Russian Physics Journal - This paper presents an analytical bound-state solution to the Duffin–Kemmer–Petiau equation for the new putative combined Manning–Rosen and Yukawa class...     

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve is calculated. The first mathematical analysis to explain the relation between the transition voltage V_t and the coercive voltage V_c is obtained. The origin of the interrelation between the transition voltage of the I–V curve and the coercive field is that the height of the boundary barrier is inversely proportional to the effective dielectric constant of the near-boundary region, which is dependent on a derivative of polarization on the electric field, ∂P/∂E. The term ξ(eV_t) plus the term (en_b²δ/dN_dP_s)(eV_c) equals a constant. V_t is the function of E_g, P_s, V_c, and E. There is a linear relation between V_c and V_t. This relationship will induce the matchable relations between the I–V curve and the E–P loop. As long as the V_c of the V–P loop exists, the correspondent V_t of I–V curve will certainly exist. It will be the foundation of a new ferroelectric memory, which operates by the I–V characteristics. These relations are the conditions that can enable nonvolatile memory and nondestructive readout.     

Bosonization and Integral Representation of Solutions¶of the Knizhnik–Zamolodchikov–Bernard Equations

We construct an integral representation of solutions of the Knizhnik–Zamolodchikov–Bernard equations, using the Wakimoto modules. Received: 5 October 1998 / Accepted: 8 February 1999     

The monodromy of the Lagrange top and the Picard–Lefschetz formula

The purpose of this paper is to show that the monodromy of action variables of the Lagrange top and its generalizations can be deduced from the monodromy of cycles on a suitable hyperelliptic curve (computed by the Picard–Lefschetz formula).     

The super-heat-kernel expansion and the renormalization of the pion–nucleon interaction

A recently proposed super-heat-kernel technique is applied to heavy baryon chiral perturbation theory. A previous result for the one-loop divergences of the pion–nucleon system to is confirmed, giving at the same time an impressive demonstration of the efficiency of the new method. The cumbersome and tedious calculations of the conventional approach are now reduced to a few simple algebraic manipulations. The present computational scheme is not restricted to chiral perturbation theory, but can easily be applied or extended to any (in general non-renormalizable) theory with boson–fermion interactions. Received: 21 July 1998 / Published online: 5 October 1998     

Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations

In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).     

The conservation of energy–momentum and the mass for the graviton

In this work we give special attention to the bimetric theory of gravitation with massive gravitons proposed by Visser in 1998. In his theory, a prior background metric is necessary to take in account the massive term. Although in the great part of the astrophysical studies the Minkowski metric is the best choice to the background metric, it is not possible to consider this metric in cosmology. In order to keep the Minkowski metric as background in this case, we suggest an interpretation of the energy–momentum conservation in Visser’s theory, which is in accordance with the equivalence principle and recovers naturally the special relativity in the absence of gravitational sources. Although we do not present a general proof of our hypothesis we show its validity in the simple case of a plane and dust-dominated universe, in which the “massive term” appears like an extra contribution for the energy density.     

Specific Features of the Structure and the Dielectric Properties of Sodium–Bismuth Titanate-Based Ceramics

The phase formation, specific features, and the dielectric properties of the ceramics of compositions from the region of morphotropic interface in the (Na_0.5Bi_0.5)TiO₃–BaTiO₃ system modified by Bi(Mg_0.5Ti_0.5)O₃ and also low-melting additions KCl, NaCl–LiF, CuO, and MnO₂ that favor the control of the stoichiometry and the properties of the ceramics have been studied. The ceramics are characterized by ferroelectric phase transitions that are observed as jumps at temperatures near 400 K and maxima at T_m ~ 600 K in the temperature dependences of the dielectric permittivity. The phase transitions at ~400 K demonstrate the relaxor behavior indicating the existence of polar domains in the nonpolar matrix. An increase in the content of Bi(Mg_0.5Ti_0.5)O₃ favor a decrease in the electrical conductivity and dielectric losses of the samples, and the relative dielectric permittivity at room temperature ε_rt is retained quite high, achieving the highest values ε_rt = 1080–1350 in the ceramics modified with KCl.     

On the equivalence of the Einstein–Hilbert and the Einstein–Palatini formulations of general relativity for an arbitrary connection

In the framework of the Einstein–Palatini formalism, even though the projective transformation connecting the arbitrary connection with the Levi-Civita connection has been floating in the literature for a long time and perhaps the result was implicitly known in the affine gravity community, yet as far as we know Julia and Silva were the first to realise its gauge character. We rederive this result by using the Rosenfeld–Dirac–Bergmann approach to constrained Hamiltonian systems and do a comprehensive self contained analysis establishing the equivalence of the Einstein–Palatini and the metric formulations without having to impose the gauge choice that the connection is symmetric. We also make contact with the the Einstein–Cartan theory when the matter Lagrangian has fermions.     

Evaluation of the Intensities of Spectral Lines under the Influence of Interferences and the Determination of Global Maxima of the Mass–Spectrum Peaks

We describe the technique by which the intensity of spectral lines can be evaluated and the global maxima of the mass–spectrum peaks under the influence of pulse interferences can be defined using an experimental setup based on a commercial MX–7304A mass spectrometer, IBM personal computer (PC), and a digital extremum regulator that allows one to ignore local extrema and bring about automatic search for a global maximum of the mass–spectrum peak and its tracking with an accuracy of 0.0012% at a speed of response of 50 kHz, elevated speeds of the scanning of masses 500 amu/sec, and stability of regulation.     

Influence of CuO and sintering temperature on the microstructure and magnetic properties of Mg–Cu–Zn ferrites

The synthesis of a series of Mg–Cu–Zn ferrites with the substitution of Cu for Mg has been obtained by solid-state reaction method. Microstuctural and structural analyses were carried out using a scanning electron microscope and X-ray diffraction (XRD), respectively. The lattice parameter is found to increase with increasing copper content. A remarkable densification is observed with the addition of Cu ions in the ferrites. Microstructural analyses indicate that CuO influences the microstructure of the ferrites by the formation of liquid phase during sintering. The grain size significantly increases with increasing copper content. Exaggerated grain growth is observed for the samples of x=0.25–0.35. The initial magnetic permeability (μ′) increases sharply with increasing concentration of Cu ions. This increase in μ′ is explained with the grain growth mechanism and enhanced densification of the ferrites. The resonance frequency of all the samples shifts toward the lower frequency as the permeability increases with Cu content. Sintering temperature T_s also affects the densification, grain growth and initial magnetic permeability of the samples.     

The Baker–Akhiezer Function and Factorization of the Chebotarev–Khrapkov Matrix

A new technique is proposed for the solution of the Riemann–Hilbert problem with the Chebotarev–Khrapkov matrix coefficient \({G(t) = \alpha_{1}(t)I + \alpha_{2}(t)Q(t)}\) , \({\alpha_{1}(t), \alpha_{2}(t) \in H(L)}\) , I = diag{1, 1}, Q(t) is a \({2\times2}\) zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann–Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker–Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann–Hilbert problem requires the finding of the \({\rho}\) zeros of the Baker–Akhiezer function ( \({\rho}\) is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree- \({\rho}\) polynomial and solution of a certain linear algebraic system of \({\rho}\) equations.