Progressive coding is an important feature of compression schemes. Wavelet coders are well suited for this purpose because the wavelet coefficients can be naturally ordered according to decreasing importance. Progressive fractal coding is feasible, but it was proposed only for hybrid fractal-wavelet schemes. We introduce a progressive fractal image coder in the spatial domain. A Lagrange optimi...

We use the Lagrange-Bürmann inversion theorem to characterize the generating function of the central coefficients of the elements of the Riordan group of matrices. We apply this result to calculate the generating function of the central elements of a number of explicit Riordan arrays, defined by rational expressions, and in two cases we use the generating functions thus found to calculate the H...

The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentzand CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete c...

The aim of the present paper is to show how the Lagrange Inversion Formula (LIF) can be applied in a straight-forward way i) to find the generating function of many combinatorial sequences, ii) to extract the coefficients of a formal power series, iii) to compute combinatorial sums, and iv) to perform the inversion of combinatorial identities. Particular forms of the LIF are studied, in order t...

Simplified analytic expressions are derived for the optical propagation matrix of magnetic anisotropic Kerr media using the Lagrange–Sylvester interpolation polynomial. This expression is used to investigate magnetic Kerr films in Fabry–Pérot configurations, magneto-optic recording quadrilayers and alternating periodic stacks. It is found that the magneto-optic reflection coefficients are enhan...

The paper deals with the numerical solution of initial-boundary value problems for diffusion equation with variable coefficients by using a local weak formulation and a meshless approximation of spatial variations of the field variable. The time variation is treated either by the Laplace transform technique or by the linear Lagrange interpolation in the time stepping approach. Advanced formulat...

The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentzand CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete c...

the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...

A Lagrangian for strongly nonlinear unsteady water waves ~including overturning waves! is obtained. It is shown that the system of quadratic equations for the Stokes coefficients, which determine the shape of a steady wave ~discovered by Longuet-Higgins 100 years after Stokes derived his system of cubic equations! directly follows from the canonical system of Lagrange equations. Applications to...

The maximum entropy method is a theoretically sound approach to construct an analytical form for the probability density function (pdf) given a sample of random events. In practice, numerical methods employed to determine the appropriate Lagrange multipliers associated with a set of moments are generally unstable in the presence of noise due to limited sampling. A robust method is presented tha...