In this paper we present a new quality metric for methods dealing with impulse noise removal. The metric is a modiication of the well-known quadratic distortion measure which takes into account the visibility of impulses for a human viewer by means of a threshold and a saturation characteristic. Based on this metric, which can be considered as a new type of cost function, we propose an adaptati...

We provide an algebraic description for sum-rank metric codes, as quotient space of a skew polynomial ring. This approach generalizes at the same time group algebra setting rank-metric codes and in Hamming metric. allows to construct twisted linearized Reed-Solomon new family maximum distance extending Sheekey's Gabidulin rank Furthermore, we analogue Trombetti-Zhou construction, which also pro...

We correct a partial mistake for a metric presented in the article ”Lattice constellation and codes from quadratic number fields” [IEEE Trans. Inform. Theory, vol. 47, No. 4, May. 2001]. We show that the metric defined in the article is not true, therefore, this brings about to destroy the encoding and decoding procedures. Also, we define a proper metric for some codes defined in the article an...

Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using Killing tensors we obtain an integrability condition for quadratic invariants which involves an arbitrary analytic function S(z). For invariants at arbitrary e...

In this paper, we show that the class of R-quadratic Finsler spaces is a proper subset of the class of generalized Douglas-Weyl spaces. Then we prove that all generalized Douglas-Weyl spaces with vanishing Landsberg curvature have vanishing the non-Riemannian quantity H, generalizing result previously only known in the case of R-quadratic metric. Also, this yields an extension of well-known Num...

We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched.

A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported.