Some Remarks on the Cohomology of Krichever–Novikov Algebras

We calculate the continuous cohomology of the Lie algebra of meromorphic vector fields on a compact Riemann surface from the cohomology of the holomorphic vector fields on the open Riemann surface pointed in the poles. This cohomology has been given by Kawazumi. Our result shows the Feigin–Novikov conjecture.     

Invariant Solutions of the Yang–Mills Field Equations Coupled to a Scalar Doublet

The Yang–Mills system of field equations which includes coupling to an SU(2) scalar matter doublet is developed. It is shown that an SU(2) current for a scalar matter doublet can be developed. The basic structure which fits the Yang–Mills system is somewhat different from the case of the scalar triplet. Using this form for the scalar current, it is possible to write down the Yang–Mills system which couples to the scalar matter doublet. It is shown that several sets of solutions to this system of equations can be obtained.     

Gaussian,non-Gaussian critical fluctuations in the Curie-Weiss model

It is known that at the critical temperature the Curie-Weiss mean-field model has non-Gaussian fluctuations and that internal fluctuations can be Gaussian. Here we compute the distribution of theq-mode magnetization fluctuations as a function of the temperature, the wave vectorq, and a fading out external field. We obtain new classes of probability distributions generated by this external field as well as new critical behavior in terms of its rate of fading out. We discuss also the susceptibility as the limitq tending to zero.     

Statistical analyses of electromyographic activity in spasmodic dysphonic and normal control subjects

Heterogeneity in the quality and task sensitivity of vocal symptoms in the spasmodic dysphonia (SD) population contributes to controversy as to whether this is a single disorder or two disorders with different etiologies (neurogenic versus psychogenic). Perceptual and acoustic assessments of vocal symptoms are inadequate to resolve this controversy. However, myoelectric events are intimately proximal to the source of vocal disruption and may be informative. The present report employs statistical modeling of quantitative amplitude measures of electromyographic activity recorded from thyroarytenoid to examine neuromotor bases of vocal symptoms in SD. Consideration of perceptual ratings of the quality and task sensitivity of vocal symptoms in the context of statistical models provides support for the conclusion that the range of vocal symptoms identified as SD represents a single, neurogenic disorder.     

The effect of oxygen vacancy on the oxide ion mobility in LaAlO3-based oxides

The electrical property of (La_1−xSr_x)_1−z(Al_1−yMg_y)O_3−δ (LSAM; x≤0.3, y≤0.15 and z≤0.1) was measured using the DC four-probe method as a function of temperature (500–1000°C) and oxygen partial pressure (1–10⁻²² atm). Among LSAMs, (La_0.9Sr_0.1)AlO_3−δ showed the highest ionic conductivity, σ_i=1.3×10⁻² S cm⁻¹ at 900°C. A simultaneous substitution at A and B sites or A site deficiency is expected to create larger oxygen vacancy and higher ionic conductivity. However, it showed a negative effect. The effect of the vacancy increase did not effect monotonously the ionic conductivity. It was found that the concentration of oxygen vacancy, [V_O], influences not only the oxide ion conductivity, σ_i, but also the mobility, μ_v, of [V_O]. These properties exhibit a maximum at around [V_O]=0.05. With the increase in [V_O], the activation energy, E_a, of the ionic conduction dropped from 1.8 to ca. 1.0 eV at [V_O]=0.05 and became almost constant at [V_O]>0.05. The dependency of the pre-exponential term, μ⁰_v, and E_a on [V_O] was analyzed and their effect on μ_v and σ_i was discussed with respect to crystal structure and defect association. It was estimated that the crystal structure mainly governs these properties. The effect of defect association could not be ignored but is considered to be a complicated correlation.     

Differential operators in terms of Clebsch-Gordon (C-G) coefficients and the wave equation of massless tensor fields

The quantum theory of angular momentum affords a treatment of tensors and vectors in a spherical basis. By using this theory we define the tensor differential operators: divergence, curl and gradient which act on a tensor of any rank, in terms of C-G coefficients. With these definitions we obtain a matrix representation and useful properties for those operators. An interesting application of this formalism is to find the wave equation of a tensor of any rank in a linear theory. This provides a new common way to look at the wave equations associated with both Maxwell's equations and the Maxwell-like equations for the linearized Weyl curvature tensor in gravitoelectromagnetism describing gravitational radiation on a Minkowski spacetime background.     

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios. AMS Subject Classifications: 60G60, 60G15, 62M15, 60H15     

Atom waveguide and 1D optical lattice using a two-color evanescent light field around an optical micro/nano-fiber

We propose a two-color scheme of atom waveguides and one-dimensional （1D） optical lattices using evanescent wave fields of different transverse modes around an optical micro/nano-fiber. The atom guide potential can be produced when the optical fiber carries a red-detuned light with TE01 mode and a blue-detuned light with HEll mode, and the 1D optical lattice potential can be produced when the red-detuned light is transformed to the superposition of the TE01 mode and HE11 mode. The two trapping potentials can be transformed to each other for accurately controlling mode transformation for the red-detuned light. This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.     

Electron holography of biological samples

In this paper, we summarise the development of off-axis electron holography on biological samples starting in 1986 with the first results on ferritin from the group of Tonomura. In the middle of the 1990s strong interest was evoked, but then stagnation took place because the results obtained at that stage did not reach the contrast and the resolution achieved by conventional electron microscopy.

To date, there exist only a few (12) publications on electron holography of biological objects, thus this topic is quite small and concise. The reason for this could be that holography is mostly established in materials science by physicists. Therefore, applications for off-axis holography were powerfully pushed forward in the area of imaging, e.g. electric or magnetic micro- and nanofields. Unstained biological systems investigated by means of off-axis electron holography up to now are ferritin, tobacco mosaic virus, a bacterial flagellum, T5 bacteriophage virus, hexagonal packed intermediate layer of bacteria and the Semliki Forest virus. New results of the authors on collagen fibres and surface layer of bacteria, the so-called S-layer 2D crystal lattice are presented in this review. For the sake of completeness, we will shortly discuss in-line holography of biological samples and off-axis holography of materials related to biological systems, such as biomaterial composites or magnetotactic bacteria.     

The interaction of three fields in ECE theory: The inverse Faraday effect

The simultaneous interaction of three fundamental fields is illustrated in Einstein Cartan Evans (ECE) theory with reference to the effect of gravitation on the inverse Faraday effect. The three-field interaction in this case is that of the fermionic, electromagnetic and gravitational fields. The interaction of the first two is developed in a well-defined semi-classical approximation of the ECE wave equation and the effect of gravitation incorporated through the index reduced canonical energy momentum density T. The exercise is repeated using the ECE wave equations and a general rule developed for the effect of gravitation on the fermionic, electromagnetic weak and strong fields.