On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

Trace element concentrations from São Francisco River - PR analyzed with PIXE technique

Summary Kulcsszavak (angolul, ha nem azonos az elozovel)     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

Highly polarized dithiafulvenes: synthesis and nonlinear optical properties

Push-pull dithiafulvenes with reduced bond length alternation (BLA) and high optical nonlinearities have been prepared. The interplay between the proaromaticity of the donor and the structural and optical properties of these merocyanines is discussed. The donor ability of dithiafulvenes can reach that of ferrocene or dialkylaminophenyl groups.     

The Polyakov path integral over bordered surfaces

Following the general scheme of the convariant path integral quantization of gauge systems, two alternative formulations of the first quantized closed bosonic string in a position representation are presented. In both approaches the covariant path integral representations of the propagator and of the higher order off-shell amplitudes are constructed. For a wide class of gauges the explicit formulae for off-shell amplitudes are obtained. This paper is the continuation of our previous work where the corresponding problems in the open string case were considered [20].     

On bulk-service MAP/PH L,N /1/N G-Queues with repeated attempts

We consider a retrial queue with a finite buffer of size N, with arrivals of ordinary units and of negative units (which cancel one ordinary unit), both assumed to be Markovian arrival processes. The service requirements are of phase type. In addition, a PH^L,N bulk service discipline is assumed. This means that the units are served in groups of size at least L, where 1≤ L≤ N. If at the completion of a service fewer than L units are present at the buffer, the server switches off and waits until the buffer length reaches the threshold L. Then it switches on and initiates service for such a group of units. On the contrary, if at the completion of a service L or more units are present at the buffer, all units enter service as a group. Units arriving when the buffer is full are not lost, but they join a group of unsatisfied units called “orbit”. Our interest is in the continuous-time Markov chain describing the state of the queue at arbitrary times, which constitutes a level dependent quasi-birth-and-death process. We start by analyzing a simplified version of our queueing model, which is amenable to numerical calculation and is based on spatially homogeneous quasi-birth-and-death processes. This leads to modified matrix-geometric formulas that reveal the basic qualitative properties of our algorithmic approach for computing performance measures. AMS Subject Classification: Primary 60K25 Secondary 68M20 90B22.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

On the polarization of non-paraxial transverse fields

On the basis of a plane-wave spectrum representation, the polarization features of a transverse quasimonochromatic non-paraxial field have been studied. A relationship has been established between the polarization characteristics in the near field and the coherence and symmetry properties of the beam in the far field.