Holomorphic extension of the logistic sequence

The logistic problem is formulated in terms of the Superfunction and Abelfunction of the quadratic transfer function H(z) = uz(1 − z). The Superfunction F as holomorphic solution of equation H(F(z)) = F(z + 1) generalizes the logistic sequence to the complex values of the argument z. The efficient algorithm for the evaluation of function F and its inverse function, id est, the Abelfunction G are suggested; F(G(z)) = z. The halfiteration h(z) = F(1/2 + G(z)) is constructed; in wide range of values z, the relation h(h(z)) = H(z) holds. For the special case u = 4, the Superfunction F and the Abelfunction G are expressed in terms of elementary functions.     

Magnetism of fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt

The magnetic moments of the fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt were investigated by first-principles calculations based on density functional theory. The magnetic moments in fcc/fcc were larger than those of the bulk fcc, while the variations in the magnetic moment were complicated in hcp/hcp and fcc/hcp. The magnetovolume effect on the magnetic moment at the twin(-like) boundaries was investigated in terms of the local average atomic distance and the average deviation from equilibrium; however, the complicated variations in the magnetic moment could not be explained from the magnetovolume effect. Next, the narrowing (or broadening) of the partial density of states (PDOS) width of 3d orbitals, the number of occupied states for the spin-down channel, and the PDOS around the Fermi level were investigated. The entire variation in the magnetic moment at the twin(-like) boundaries could be understood in terms of these factors. Charge transfer occurred in hcp/hcp. In this case, the contributions of 4s and 4p electrons to the variation in the magnetic moment were relatively large.     

Superconductivity in amorphous thin films of tin–copper

The properties of the superconducting state in the amorphous Sn_1?xCu_x thin films were characterized. The concentration of copper changes in the range from 0.08 to 0.41. The calculations were conducted in the framework of the strong-coupling formalism, wherein the Eliashberg functions determined in the tunnel experiment were used. The value of the Coulomb pseudopotential equal to 0.1 was adopted. It will be shown that the critical temperature (T_C) decreases from 7 to 3.9 K. The ratio, R_Δ = 2Δ(0)/k_BT_C, differs from the BCS value: R_Δ ∈ <4.4, 3.95>, where Δ(0) represents the order parameter. Similarly behave the ratios: R_C = ΔC(T_C)/C^N(T_C) ∈ <2.2, 1.75> and R_H = T_CC^N(T_C)/H²_C(0) ∈ <0.141, 0.154>. The parameter ΔC(T_C) is the specific heat jump, C^N(T_C) denotes the specific heat of the normal state and H_C(0) is the thermodynamic critical field.     

Orientational order parameter studies on 3.Om and 3O.Om liquid crystals

Orientational order parameter S is evaluated in the nematic phase of six liquid crystal compounds, N-(p-n-propyl benzylidene)-p-n-alkoxy anilines, 3.Om and N-(p-n-propyloxy benzylidene)-p-n-alkoxy anilines, 3O.Om compounds with m = 6, 7 and 8, using different methods. The techniques employed are S from birefringence δn, Haller's approximation from (1?T/T_c) ^β, effective geometry parameter α_g and Vuks’ scaling factor S_C. The values of S obtained using the above methods are compared with one another and with the results on a number of liquid crystals; the liquid crystals favor isotropic Vuks’ method.     

Theoretical explanation of electron paramagnetic resonance and optical parameters for Cu<Superscript>2+</Superscript> ion in LiNbO<Subscript>3</Subscript> crystal

The EPR parameters, anisotropic g-factors g _x , g _y and g _z for cu²⁺ ion and hyperfine structure constants A _x , A _y and A _z for Cu²⁺ in LiNbO₃ crystal are calculated by the method of diagonalizing the full Hamiltonian matrix. The crystal-field parameters contact with the crystal structure by the aid of the superposition model. The optical transition parameters are calculated using Zhao crystal-field model. The calculated results are in good agreement with the observed values. The results are discussed.      

Effects of Fe doping on ac susceptibility of Pr0.75Na0.25MnO3

Ac susceptibility at low temperatures of Pr_0.75Na_0.25Mn_1-xFe_xO₃ (0 ≤ x ≤ 0.30) is investigated. The peak value of the real component of ac susceptibility χ' at the freezing temperature T_f is suppressed with the increasing frequency. The peak value of χ' shows a linear relation between T_f and the logarithm of the frequency ω. The normalized slope P = ΔT_f/T_fΔlgω, which is much lower than canonical insulating spin glass systems in which 0.06 ≤ P ≤ 0.08. The peak value of the imaginary component of the ac susceptibility χ' at T_f for the x = 0, 0.02, 0.30 samples increases with increasing frequency, suggesting a cluster glass ground state with a coexistence of charge-ordered phase and correlated ferromagnetic clusters in spin glass matrix. The peak value of χ' at T_f for the x = 0.10 sample decreases with increasing frequency, suggesting a phase separation ground state. The peak value of χ' at T_f for the x = 0.05 sample decreases with increasing frequency for ω ≤ 52 Hz and increases subsequently till 701 Hz, and then decreases with further increasing frequency for ω ≥ 1501 Hz. This complex behaviour is ascribed to the competition between the effects of large and little ferromagnetic clusters in the sample. The ground state of x = 0.05 sample is a transition state from cluster glass to phase separation.     

改进的全矢量有效折射率方法分析光子晶体光纤的色散特性

得到了全矢量有效折射率方法中归一化等效纤芯半径(p/Λ)随归一化空气孔直径(d/Λ)和归一化频率(Λ/λ)的变化关系，修正了p/Λ为固定值的不合理取法，得到了改进的全矢量有效折射率方法(IFVEIM).用IFVEIM计算的基模有效折射率和总色散等模式特性与多极法的结果和试验值相比较都具有很好的一致性，将基模有效折射率的误差减小了2—3个数量级.用IFVEIM详细地分析了光子晶体光纤的色散特性，得到了色散值、波长、孔间距、d/Λ之间的相互变化关系. 关键词： 光子晶体光纤 有效折射率方法 等效纤芯半径 色散     

PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

The Matrix Algebras of Continuous Groups with Antilinear Operations

The corepresentation theory of continuous groups is presented without the assumption that the subgroup G of the group with antilinear operations is unitary. Continuous groups of the form: G+a ₀ G are defined, where G denotes a linear Lie group and a ₀ denotes an antilinear operation which fulfils the condition a²₀=±1a^{2}_{0}=\pm1. The matrix algebras connected with the groups G+a ₀ G are defined. The structural constants of these algebras fulfill the conditions following from the Jacobi identities. Applications are presented to the groups G=SU(d), d=1,2,… , for a ₀=K, the complex conjugation operation, and to the group SL(2,C) for a ₀=K or Θ, the time-reversal operation.     

Drinfeld-Sokolov gravity

A lagrangian euclidean model of Drinfeld-Sokolov (DS) reduction leading to generalW-algebras on a Riemann surface of any genus is presented. The background geometry is given by the DS principal bundleK associated to a complex Lie groupG and anSL(2,) subgroupS. The basic fields are a hermitian fiber metricH ofK and a (0, 1) Koszul gauge fieldA ^* ofK valued in a certain negative graded subalgebrar ofg related tos. The action governing theH andA ^* dynamics is the effective action of a DS field theory in the geometric background specified byH andA ^*. Quantization ofH andA ^* implements on one hand the DS reduction and on the other defines a novel model of 2d gravity, DS gravity. The gauge fixing of the DS gauge symmetry yields an integration on a moduli space of DS gauge equivalence classes ofA ^* configurations, the DS moduli space. The model has a residual gauge symmetry associated to the DS gauge transformations leaving a given fieldA ^* invariant. This is the DS counterpart of conformal symmetry. Conformal invariance and certain non-perturbative features of the model are discussed in detail.     

Study of the pion trajectory in the photoproduction of leading neutrons at HERA

Energetic neutrons produced in ep collisions at HERA have been studied with the ZEUS detector in the photoproduction regime at a mean photon–proton center-of-mass energy of 220 GeV. The neutrons carry a large fraction 0.64<x_L<0.925 of the incoming proton energy, and the four-momentum transfer squared at the proton–neutron vertex is small, |t|<0.425 GeV². The x_L distribution of the neutrons is measured in bins of t. The (1−x_L) distributions in the t bins studied satisfy a power law dN/dx_L∝(1−x_L)^a(t), with the powers a(t) following a linear function of t: . This result is consistent with the expectations of pion-exchange models, in which the incoming proton fluctuates to a neutron–pion state, and the electron interacts with the pion.     

Intrinsic <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> factors of odd-mass <Superscript>167–179</Superscript>Lu isotopes

In this paper, g _K -factors of the intrinsic magnetic moments and effective spin gyromagnetic factors (g _s^eff) of the ^167–179Lu isotopes have been studied within the Tamm-Dancoff approximation (TDA) (Kuliev et al, Sov. J. Nucl. Phys. 9, 185 (1969)) by using a realistic potential such as Woods-Saxon potential for the first time. The effects of the spin-spin and spin-isospin interactions on magnetic moments were investigated. The results of the theoretical calculations are compared with the experimental data for related nuclei. The experimental values of g _K and g _s^eff were computed from the observed magnetic moments (Georg et al, Eur. Phys. J. A3, 225 (1998)) using the spin matrix elements. The theoretical predictions for the g _K factors exhibit good agreement with the experimental g _K factors with increasing mass number A of the lutetium isotopes. The strongest influence of the neutron-proton spin interaction occurs at q = −1. Sufficient agreement between the calculated and the experimental values of g _K is obtained for κ = (45/A) MeV and q = −1.     

Variation of the temperature‐dependent substituent effects with solvent in alkaline hydrolysis of substituted phenyl and alkyl benzoates and phenyl tosylates

The second‐order rate constants k for the alkaline hydrolysis of eight substituted alkyl benzoates have been measured spectrophotometrically in aqueous 5.3 M NaClO₄ and 0.5 M n‐Bu₄NBr at various temperatures. Variation of the substituent effect with temperature in alkaline hydrolysis of ortho‐, meta‐, and para‐substituted phenyl benzoates, phenyl tosylates, and alkyl benzoates in various solvents (water, aqueous 0.5 M Bu₄NBr, 80% (v/v) DMSO, 2.25 M Bu₄NBr, and 5.3 M NaClO₄) was studied. The susceptibility to temperature variation of the meta and para polar substituent effect, the ortho inductive effect, and the alkyl polar effect for various media showed good correlation with the solvent electrophilicity, E_S, which characterizes the hydrogen‐bond donating power of the solvent. The variation of the temperature‐dependent ortho inductive effect with solvent hydrogen‐bond donor capacity (electrophilicity) was found to be nearly twice smaller than that for meta and para polar effect. The temperature‐dependent alkyl polar substituent effect was found to vary with E_S nearly by the same extent as the polar effect of meta and para substituents. The dependences of the ρ values (altogether 109 values of ρ) on the (1/T) term for various media were found to cross nearly at the same isosolvent temperature (1/β_isosolv ≈ 2 × 10^?3) for meta‐, para‐, ortho‐, and alkyl‐substituted esters. At T = β_isosolv the difference (ρ)_S ? (ρ)_Water becomes zero for all polar substituent effects in all media considered and the additional inductive effect from the ortho position (compared with para derivatives) disappears for all solvents studied. Copyright © 2007 John Wiley & Sons, Ltd.     

First-principles prediction of crystal structure and physical properties of ScB3

The crystal structure of ScB₃ is seeked by combining the developed particle swarm optimisation algorithm for crystal structure prediction with first-principles calculations. A new monoclinic phase with the C2/m symmetry is predicted successfully, which is energetically more superior to the early reported R-3m-, P2₁/m-, P6₃/mmc-, P-6m2-, Pnma-, and Pm-3m-type structures in the pressure range from 0 to 100?GPa. The obtained elastic constants and phonon dispersion curve reveal that the C2/m-ScB₃ is mechanically and dynamically stable. The predicted large bulk module, high shear modulus, small Poisson’s ratio as well as the considerable hardness indicate that the C2/m-ScB₃ has outstanding mechanical property. Meanwhile, the dependences of the bulk modulus and Young’s modulus of ScB₃ on the crystal orientation are investigated theoretically. Through applying the strain–stress method, the ideal tensile and shear strengths along different crystal directions are also estimated, and the obtained results confirm that the shear mode dominates the failure mode in the C2/m-ScB₃ structure and it is intrinsically a hard material. The electronic structure calculation and chemical bonding analysis illustrate that the strong covalent B-B and Sc-B bonds are responsible for its structural stability and high hardness.     

Hermitean Oscillator-like Realizations of Classical Algebras and Superalgebras in Hilbert Space with Positive Definite Metric

The hermitean oscillator-like realizations of classical algebras in terms of bosonic and fermionic creation and annihilation operators are given. The hermitean realizations of classical superalgebras using boson-fermion oscillators are explicitely described. The assumption of positive definite metric in a Hilbert space of the oscillators states is exploited. Due to this fact, the realizations of superalgebras in the Hilbert space can be constructed only for: the real orthosymplectic superalgebra osp (N; 2M; R); the unitary compact superalgebra su (N; M); the unitary noncompact one SU(N; K, M); and the quaternionic unitary superalgebra uu_α(N; M; H).     

Pressure and temperature variation of the depolarized light scattering spectra of the fragile glass-former liquid salol

The pressure and temperature dependences of the depolarized light scattering spectra of salol have been measured at isobaric condition P = 1 bar for T between 328 and 393 K, and at isothermal condition T = 343 K for P between 1 and 625 bar, i.e. outside the metastable liquid region. The experimental results for both the α- and β-relaxations can be well described by the Mode Coupling Theory. The independence of the power-law parameters a, and consequently b and γ, from the thermodynamic variables T and P is demonstrated.The critical temperature T _c at 1 bar and the critical pressure P _c at T = 343 K have been determined from the normal liquid state. Received 2 May 2000     

Photoelectrical Characteristics of MIS Structures on the Basis of Heteroepitaxial HgCdTe

The voltage dependence of photo-emf in the HgCdTe/SiO ₂ /Si ₃ N ₄ and HgCdTe/AOF MIS structures is experimentally studied. The heteroepitaxial graded-band films Hg _0.78 Cd _0.22 Te were produced on the GaAs substrates by molecular-beam epitaxy. It was found that the type of field dependence of photo-emf is related to the conduction type of the semiconductor used and to the presence of near-surface graded-band layers.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 35–39, February, 2005.     

A model for the metal-to-insulator transition in V2O3

The metal-to-insulator transition in V₂O₃ is described by a model that is based on the electronic band structure of this material. The vanadium 3d-t _2g band decomposes in the trigonal symmetry into two bands, a _1g and e _π. The a _1g band consists of orbitals connecting pairs of c-axis neighbouring atoms, while the e _π band consists of orbitals in the plane perpendicular to the c-axis. The change in distance between c-axis neighbours changes the nature of the a _1g band from molecular (delocalized) to atomic (localized). The localization of the a _1g electrons causes through the atomic exchange interaction also the localization of the e _π electrons, and this localization creates a gap in the e _π band which causes the material to become insulating. This model is treated in the Hartree-Fock approximation (the ‘Excitonic’ model) at zero and finite temperatures, and various aspects of the transition, such as changes in the c/a ratio, the creation of magnetic moments, changes in covalency, the effect of pressure and the order of the transition, are investigated.     

Theory of sparse random matrices and vibrational spectra of amorphous solids

The random matrix theory has been used for analyzing vibrational spectra of amorphous solids. The random dynamical matrix M = AA ^T with nonnegative eigenvalues ɛ = ω² has been investigated. The matrix A is an arbitrary square (N-by-N) real sparse random matrix with n nonzero elements in each row, mean values 〈A _ij 〉 = 0, and finite variance 〈A _ij ²〉 = V ². It has been demonstrated that the density of vibrational states g(ω) of this matrix at N, n ≫ 1 is described by the Wigner quarter-circle law with the radius independent of N. For n ≪ N, this representation of the dynamical matrix M = AA ^T makes it possible in a number of cases to adequately describe the interaction of atoms in amorphous solids. The statistics of levels (eigenfrequencies) of the matrix M is adequately described by the Wigner surmise formula and indicates the repulsion of vibrational terms. The participation ratio of the vibrational modes is approximately equal to 0.2–0.3 almost over the entire range of frequencies. The conclusions are in qualitative and, frequently, quantitative agreement with the results of numerical calculations performed by molecular dynamics methods for real amorphous systems.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002