Experimental implementation of ultrashort laser pulses in the von Neumann picture

The characterization and interpretation of ultrashort laser pulses is most intuitive in the joint time–frequency domain, where structures like multiple pulses become immediately apparent. For practical reasons, ultrafast femtosecond laser pulse shaping, however, is commonly carried out in the frequency domain. Here we implement pulse shaping of optical fields defined in the von Neumann representation, which is a joint time–frequency distribution with complex-valued Gaussian basis functions. We discuss the feasibility as well as the principal limitations of this technique, show illustrative examples, and propose possible applications in coherent control.     

Ultraweak Continuity of σ-derivations on von Neumann Algebras

Let σ be a surjective ultraweakly continuous ∗-linear mapping and d be a σ-derivation on a von Neumann algebra . We show that there are a surjective ultraweakly continuous ∗-homomorphism and a Σ-derivation such that D is ultraweakly continuous if and only if so is d. We use this fact to show that the σ-derivation d is automatically ultraweakly continuous. We also prove the converse in the sense that if σ is a linear mapping and d is an ultraweakly continuous ∗-σ-derivation on , then there is an ultraweakly continuous linear mapping such that d is a ∗-Σ-derivation.      

Subspace Structures in Inner Product Spaces and von Neumann Algebras

We study subspaces of inner product spaces that are invariant with respect to a given von Neumann algebra. The interplay between order properties of the poset of affiliated subspaces and the structure of a von Neumann algebra is investigated. We extend results on nonexistence of measures on incomplete structures to invariant subspaces. Results on inner product spaces as well as on the structure of affiliated subspaces are reviewed.     

The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ _c =0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ _c , the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ _c , the τ restrains that.     

Norton's Trace Formulae for the Griess Algebra¶of a Vertex Operator Algebra with Larger Symmetry

Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They coincide, when applied to the moonshine module V , with the trace formulae obtained in a different way by S. Norton, and the spectrum of some idempotents related to 2A, 2B, 3A and 4A elements of the Monster is determined by the representation theory of the Virasoro algebra at c= 1/2, the W ₃ algebra at c= 4/5 or the W ₄ algebra at c= 1. The generalization to the trace function on the whole space is also given for the composition of two adjoint actions, which can be used to compute the McKay-Thompson series for a 2A involution of the Monster. Received: 24 July 2000 / Accepted: 15 June 2001     

Constraint Algebra for Regge-Teitelboim Formulation of Gravity

We consider the formulation of the gravity theory first suggested by Regge and Teitelboim where the space-time is a four-dimensional surface in a flat ten-dimensional space. We investigate a canonical formalism for this theory following the approach suggested by Regge and Teitelboim. Under constructing the canonical formalism we impose additional constraints agreed with the equations of motion. We obtain the exact form of the first-class constraint algebra. We show that this algebra contains four constraints which form a subalgebra (the ideal), and if these constraints are fulfilled, the algebra becomes the constraint algebra of the Arnowitt-Deser-Misner formalism of Einstein’s gravity. The reasons for the existence of additional first-class constraints in the canonical formalism are discussed.     

On the Hausdorff Dimension of Invariant Measures of Weakly Contracting on Average Measurable IFS

We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.     

Measurements of cavitation bubble dynamics based on a beam-deflection probe

We present an optodynamic measurement of a laser-induced cavitation bubble and its oscillations based on a scanning technique using a laser beam-deflection probe. The deflection of the beam was detected with a fast quadrant photodiode which was built into the optical probe. The applied experimental setup enabled us to carry out one- or two-dimensional scanning of the cavitation bubble, automatic control of the experiment, data acquisition and data processing. Shadow photography was used as a comparative method during the experiments.     

Breaking of Global Gauge Symmetries on a Spatial-temporal Subdomain

It is generally considered that global gauge symmetry of an action integral over a finite spatial-temporal domain as a whole holds in any subdomain of this domain. However, in this paper we demonstrate that when the so-called localized assumption is no longer valid, the global gauge symmetry will break in the subdomain of this spatial-temporal domain, due to occurrence of a new source called the nonlocal residual. The nonlocal residual is correlated with a gauge field and satisfies the zero mean condition with respect to whole spatial-temporal domain. An example is given to support this conclusion.     

Factoriality of Boejko–Speicher von Neumann Algebras

We study the von Neumann algebra generated by q–deformed Gaussian elements l_i+l^*_i, where operators l_i fulfill the q–deformed canonical commutation relations l_il^*_j–ql^*_jli=_ij for –1<q<1. We show that if the number of generators is finite, greater than some constant depending on q, it is a II₁ factor which does not have the property . Our technique can be used for proving factoriality of many examples of von Neumann algebras arising from some generalized Brownian motions, both for the type II₁ and type III case.Research supported by State Committee for Scientific Research (KBN) grant 2 P03A 007 23.     

Realization of the Spectrum Generating Algebra for the Generalized Kratzer Potentials

The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions satisfying quantum dynamical algebra SU(1,1) are established. Factorization method is a very simple method of calculating the matrix elements from these ladder operators. The matrix elements of different functions of r, r\fracddrr\frac{d}{dr}, their sum Γ₁ and difference Γ₂ are evaluated in a closed form. The exact bound state energy eigenvalues E _n,ℓ and matrix elements of r, r\fracddrr\frac{d}{dr}, their sum Γ₁ and difference Γ₂ are calculated for various values of n and ℓ quantum numbers for CO and NO diatomic molecules for the two potentials. The results obtained are in very good agreement with those obtained by other methods.     

Entropy and Entanglement of a Single-mode Vacuum Field Interacting with a Ξ-type Three-level Atom with Detuning

The evolution of the field entropy and the entanglement between the atom and the field for the system of a single-mode vacuum field interacting with a Ξ-type three-level atom have been studied by using the reduced quantum entropy. The influences of the detuning of the light field and the setting of the initial state of the atom on the field entropy and entanglement of the system under consideration are discussed emphatically. It is showed that the detuning of the light field and the setting of the initial state of the atom play an important role for the evolution of the field entropy and the entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.     

New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in general, inhomogeneous metrics, defined with respect to anholonomic frames and their main geometric properties. Such spacetimes contain as particular cases certain conformal and/or frame transforms of the well known Friedman-Robertson-Walker, Bianchi, Kasner and Gödel universes and define a great variety of cosmological models with generic off-diagonal metrics, local anisotropy and inhomogeneity. It is shown that certain nonholonomic gravitational configurations may mimic de Sitter like inflation scenarios and different anisotropic modifications without satisfying any classical false-vacuum equation of state. Finally, we speculate on perspectives when such off-diagonal solutions can be related to dark energy and dark matter problems in modern cosmology.     

Perfect Simulation of Infinite Range Gibbs Measures and Coupling with Their Finite Range Approximations

In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a perfect simulation algorithm for the measure and for the coupled measures. The algorithm works for general Gibbsian interaction under requirements on the tails of the interaction. As a consequence we obtain an upper bound for the error we make when sampling from a finite range approximation instead of the true infinite range measure.     

A Basic Algebra Is an MV-Algebra If and Only If It Is a BCC-Algebra

The aim of the paper is to show that every lattice with section antitone involutions, i.e. a lattice having antitone involutions on its principal filters, is an MV-algebra if and only if it is a BCC-algebra. Research is supported by the Research and Development Council of Czech Government via project MSM 6198959214.     

Some Remarks on a Generalization of the Superintegrable Chiral Potts Model

The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function W of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superintegrable case of the chiral Potts model with cylindrical boundary conditions, W can be expressed in terms of reduced Hamiltonians H and a central spin operator S. We conjectured in a previous paper that W can be written as a determinant, similar to that of the Ising model. Here we generalize this conjecture to any Hamiltonians that satisfy a more general Onsager algebra, and give a conjecture for the elements of S.     

Laplace–Beltrami Operator on a Riemann Surface¶and Equidistribution of Measures

We consider the Laplace–Beltrami operator on a compact Riemann surface of a constant negative curvature. For any eigenvalue of the Laplace–Beltrami operator there is an associated sequence of measures on the Riemann surface. These measures naturally appear in Quantum Chaos type questions in the theory of electro-magnetic flow on a Riemann surface. The main result of the paper is the claim that this sequence of measures has the Liouville measure as the (weak^*) limit. We prove a quantitative version of this equidistribution claim. Received: 12 March 2001 / Accepted: 23 April 2001     

Accelerating Universe with a Special Form of Decelerating Parameter

In this article, we try to investigate the quintessence model with a minimally coupled scalar field by taking a special form of decelerating parameter q in such a way that which provides an early deceleration and late time acceleration for barotropic fluid and Chaplygin gas dominated models. We have shown that the potential function V(φ) is always decreases with the scalar field φ for barotropic and Chaplygin both models. The {r,s} diagram shows the behaviour of the universe in different stages during the evolution.