On wavelets interpolated from a pair of wavelet sets

We show that any wavelet, with the support of its Fourier transform small enough, can be interpolated from a pair of wavelet sets. In particular, the support of the Fourier transform of such wavelets must contain a wavelet set, answering a special case of an open problem of Larson. The interpolation procedure, which was introduced by X. Dai and D. Larson, allows us also to prove the extension property.

     

The matrix Lax representation of the generalized Riemann equations and its conservation laws

It is shown that the generalized Riemann equation is equivalent with the multicomponent generalization of the Hunter-Saxton equation. New matrix and scalar Lax representation are presented for this generalization. New class of the conserved densities, which depends explicitly on the time are obtained directly from the Lax operator. The algorithm, which allows us to generate a big class of the non-polynomial conservation laws of the generalized Riemann equation is presented. Due to this new series of conservation laws of the Hunter-Saxton equation is obtained.     

The Painleve Ping-Pong P IV

We construct a transformation which generates new solutions for a one-parameter family of the fourth Painlevé equations. We obtain solutions with the same parameter values as in the given equation. Also we obtain new relations between two Painlevé transcendents of the fourth kind with different free parameters.     

The gauge field copies through the Bäcklund transformation for the Liouville equation

It is shown that the gauge field copies for the field strength tensor associated with the Lax pair of the Liouville equation are generated through the non-auto Bäcklund transformations.     

Flat minimal quantizations of Stäckel systems and quantum separability

In this paper, we consider the problem of quantization of classical Stäckel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stäckel transform, natural Hamiltonian systems from a given Riemann space are expressed by some flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stäckel systems which remains separable after any of admissible flat minimal quantizations.     

Identification of the stick and slip motion between contact surfaces using artificial neural networks

Nonlinear Dynamics - The paper presents work related to nonlinear system parameters identification. The research is focused on systems with hysteretic stiffness characteristics. The identification...     

Convergence Analysis of the Finite Section Method and Banach Algebras of Matrices

The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. Based on an axiomatic framework we present a convergence analysis of the finite section method for unstructured matrices on weighted ℓ ^p -spaces. In particular, the stability of the finite section method on ℓ ² implies its stability on weighted ℓ ^p -spaces. Our approach uses recent results from the theory of Banach algebras of matrices with off-diagonal decay. Furthermore, we demonstrate that Banach algebra theory provides a natural framework for deriving a finite section method that is applicable to large classes of unstructured non-hermitian matrices as well as to least squares problems.     

Representations of the CAR generated by the representations of the CCR III. non-Fock extension

An idea to construct a representation of the CAR algebra in a representation of the CCR algebra, which succeeded in the Fock case, is verified for the simplest non-Fock extensions of the formalism.