A new bijection between the diagonally convex directed (dai-) polyominoes and ternary trees makes it possible to enumerate the dcd-polyominoes according to several parameters (sources, diagonals, horizontal and vertical edges, target cells). For a part of these results we also give another proof, which is based on Raney’s generalized lemma. Thanks to the fact that the diagonals of a dcd-polyomi...

In 1890 German mathematician and physicist W. Hess found new special case of integrability Euler - Poisson equations motion a heavy rigid body with fixed point. 1892 P. A. Nekrasov proved that the solution problem point under conditions reduces to integrating second order linear differential equation. this paper corresponding equation is derived its coefficients are presented in rational form. ...

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange mu...

Abstract We study a minimisation problem in L p and ∞ for certain cost functionals, where the class of admissible mappings is constrained by Navier–Stokes equations. Problems this type are motivated variational data assimilation atmospheric flows arising weather forecasting. Herein we establish existence PDE-constrained minimisers all , also that converge to as → ∞. further show solve an Euler–...

A lower set of nodes is a subset of a grid that can be indexed by a lower set of indices. In order to apply the Lagrange interpolation formula, it is convenient to express the Lagrange fundamental polynomials as sums of few terms. We present such a formula for the Lagrange interpolation formula in two variables. In the general multidimensional case, we express the Lagrange fundamental polynomia...