High-order realisations of the para-Fermi algebra with parafield operators

Using second-order realisations of Lie algebras by means of creation and annihilation parafield operators the generators of the para-Fermi algebras are expressed as high-order polynomials of para-Bose or para-Fermi creation and annihilation operators.     

Irreducible representations of a parafield and the connection of the parafield with usual fields

All irreducible separable representations of the non-relativistic para-Fermi field of order 3 in the configuration space are considered. The existence of many different irreducible representations of the parafield permits us to interpret the excited states of this field as the states of particles with internal degrees of freedom. These states can be labelled by the Young patterns and the eigenvalues of internal quantum number like baryonic and hypercharges. The parafield theory is shown to be equivalent to the theory of three kinds of ordinary ferminons, like quarks, and one of them, ‘strange’, can be distinguished from the other two by means of its interaction, not only statistically but also dynamically. Thus the parafield theory is shown to be equivalent to some model of the physicalSU (3) symmetry of hadrons when the strong and medium-strong interactions could be switched on but the electromagnetic and weak interactions should be switched off.     

Laser-induced nano-patterning by means of interference subpatterns generated by microspheres

Interference patterns generated by a regular lattice of SiO₂ microspheres on a transparent support are used for the surface patterning of polyimide (PI) foils. Using 248 nm excimer-laser radiation, thousands to millions of holes with a full width at half maximum (FWHM) of 160±40 nm can be generated with a single laser pulse. Received: 1 March 2002 / Accepted: 4 March 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +43-732/2468-9242, E-mail: dieter.baeuerle@jku.at     

Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions

We investigate one-dimensional discrete Schrödinger operators whose potentials are invariant under a substitution rule. The spectral properties of these operators can be obtained from the analysis of a dynamical system, called the trace map. We give a careful derivation of these maps in the general case and exhibit some specific properties. Under an additional, easily verifiable ypothesis concerning the structure of the trace map we present an analysis of their dynamical properties that allows us to prove that the spectrum of the underlying Schrödinger operator is singular and supported on a set of zero Lebesgue measure. A condition allowing to exclude point spectrum is also given. The application of our theorems is explained on a series of examples.     

The nonlinear evolution of rogue waves generated by means of wave focusing technique

Generating the rogue waves in offshore engineering is investigated,first of all,to forecast its occurrence to protect the offshore structure from being attacked,to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design.To achieve these purposes demands an accurate wave generation and calculation.In this paper,we establish a spatial domain model of fourth order nonlinear Schrdinger(NLS) equation for describing deep-wat...     

Efficiently generated rotational and vibrational stimulated raman emission by means of a two-color laser beam

When a two-color laser beam is introduced into pressurized hydrogen, about 40 laser emission lines are generated from the ultraviolet to the visible regions. This phenomenon is ascribed to the stimulated Raman effect due to a combination ofJ=1 J=3 rotational andv=0 v=1 vibrational transitions. By introducing the two-color laser beam, the threshold for generation of the rotational line is substantially reduced. The present phenomenon is attributed to four-wave mixing, which allows efficient generation of higher-order rotational and vibrational Raman lines.     

Hamiltonian structures and Lax equations generated by matrix differential operators with polynomial dependence on a parameter

We investigate a general set of equations which can be studied by the inverse scattering method.     

On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods

Recent results in the study of quantum manifestations in classical chaos raise the problem of computing a very large number of eigenvalues of selfadjoint elliptic operators. The standard numerical methods for large eigenvalue problems cover the range of applications where a few of the leading eigenvalues are needed. They are not appropriate and generally fail to solve problems involving a number of eigenvalues exceeding a few hundreds. Further, the accurate computation of a large number of eigenvalues leads to much larger problem dimension in comparison with the usual case dealing with only a few eigenvalues. A new method is presented which combines multigrid techniques with the Lanczos process. The resulting scheme requires O(mn) arithmetic operations and O(n) storage requirement, where n is the number of unknowns and m, the number of needed eigenvalues. The discretization of the considered differential operators is realized by means of p-finite elements and is applicable on general geometries. Numerical experiments validate the proposed approach and demonstrate that it allows to tackle problems considered to be beyond the range of standard iterative methods, at least on current workstations. The ability to compute more than 9000 eigenvalues of an operator of dimension exceeding 8 million on a PC shows the potential of this method. Practical applications are found, e.g. in the numerical simulation of quantum billiards.     

q-Sigma-algebra generated by balls

The q--algebra, i.e., the system of sets closed under complementation, countable disjoint unions, and containing the empty set, generated by the system of open balls coincides with the -field of Borel sets inR sun forn=1,2, and 3. A first step to extend the proof forn=4, 5, 6, and 7 is indicated.     

Noises generated by nonlinear autoregression

A nonlinear generalization of autoregressive scheme of first order is suggested as approximate model for 1/f^k noises. The iterative generation makes use of reducing function instead of a constant. Computer simulations – carried out over three decades of frequency – have demonstrated that there is such a family of these functions that to any function of the family there exists a unique value of standard deviation of white noise source such that the noise generated by the iterative scheme has the spectral factor k ≈ 1. Implications of the results for understanding the origin, structural stability and ubiquity of 1/f noise are discussed.     

Anomalies generated by extrinsic curvature

On the classical level, the embedding of a two-dimensional string in ad-dimensional space induces a natural Weyl operator. It is shown, however, that ford≧4 the corresponding quantum theory is ill-defined. The anomalies of the effective action require the presence of additional degrees of freedom—the theory cannot be specified exclusively in terms of the embedding.     

Reparable sonoporation generated by microstreaming

Reparable sonoporation was observed in Jurkat lymphocytes in suspension exposed to a vibrating Mason horn tuned to 21.4 KHz. The diameter of the horn tip was 400 microm and its transverse displacement amplitude was 7.8 microm. It was found that the shear stress associated with microstreaming surrounding the Mason-horn tip was the primary reason for the cell reparable sonoporation. The threshold shear stress was determined to be 12 +/- 4 Pa for exposure time up to 7 min. It was also found that the shorter the exposure time, the greater the threshold.     

Turbulence spectra generated by singularities

The problem of turbulence spectra generated by the singularities located on lines and planes is considered. It is shown that the frequency spectrum of fluid-surface displacements due to whitecaps (linear singularities) is scaled like a weakly turbulent Zakharov-Filonenko spectrum. The corresponding wave-vector spectrum may be highly anisotropic with a decrease in maximum, as in the Phillips spectrum. However, in the isotropic situation, the spectrum differs markedly from the Phillips form. For a highly anisotropic two-dimensional turbulence, the vorticity jumps can generate the Kraichnan power-law distribution in the region of maximal angular peak. For the isotropic distribution, the turbulence spectrum coincides with the Saffman spectrum. For the shock-generated acoustic turbulence, the spectrum has the form of the Kadomtsev-Petviashvili spectrum Eω～ ω^?2 for all spatial dimensionalities.     

Arithmetical and geometrical means of generalized logarithmic and exponential functions: Generalized sum and product operators

One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on several values of a variable are obtained here. Applications of the above formalism are considered.     

SimpleC*-algebra generated by isometries

We consider theC*-algebra generated byn2 isometriesS ₁,...,S _n on an infinite-dimensional Hilbert space, with the property thatS ₁ S*₁+...+S _n S* _n =1. It turns out that has the structure of a crossed product of a finite simpleC*-algebra by a single endomorphism scaling the trace of by 1/n. Thus, is a separableC*-algebra sharing many of the properties of a factor of typeIII with =1/n. As a consequence we show that is simple and that its isomorphism type does not depend on the choice ofS ₁,...,S _n .     

Three-dimensional images generated by quadrature interferometry

Quadrature detection techniques have been applied to images obtained from a Mach-Zehnder interferometer with differently polarized beams to yield the real and the imaginary parts of the diffracted fields simultaneously. This approach eliminates the need for phase retrieval by providing complete information on the complex amplitude of the diffracted signal. We present results in which we demonstrate our ability to reconstruct two- and three-dimensional microscopic objects from their complex diffraction patterns.