A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is pres...

For every supersingular K3 surface X in characteristic 2, there exists a homogeneous polynomial G of degree 6 such that X is birational to the purely inseparable double cover of P defined by w = G. We present an algorithm to calculate from G a set of generators of the numerical Néron-Severi lattice of X. As an application, we investigate the stratification defined by the Artin invariant on a mo...

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...

The inverse conjecture for the Gowers norms U(V ) for finite-dimensional vector spaces V over a finite field F asserts, roughly speaking, that a bounded function f has large Gowers norm ‖f‖Ud(V ) if and only if it correlates with a phase polynomial φ = eF(P ) of degree at most d− 1, thus P : V → F is a polynomial of degree at most d− 1. In this paper, we develop a variant of the Furstenberg cor...

In this study, four arylazobenzylidene dyes (a-d) were synthesized with excellent yields in two steps using Knoevenagel condensation and azo-coupling reactions. Absorption spectra of these dyes with different substituents were investigated in organic solvents as a function of solvent polarity. The spectral features of synthesized arylazobenzylidene dyes were described according to azo-hydrazone...

Based on an information theory approach we suggest a quantitative characteristic for evaluating the degree of chaotic synchronization. The proposed characteristic is tested for the cases of complete and phase synchronization of chaos. It is shown that this characteristic is stable with respect to the influence of small noise and nonlinear signal distortion.

The paper is concerned with several kinds of stochastic frontier models whose likelihood function is not available in closed form. First, with output-oriented stochastic frontier models whose one-sided errors have a distribution other than the standard ones (exponential or half-normal). The gamma and beta distributions are leading examples. Second, with input-oriented stochastic frontier models...

Using the Hatcher–Oertel algorithm for finding boundary slopes of Montesinos knots, we prove the Slope Conjecture and the Strong Slope Conjecture for a family of 3-tangle pretzel knots. More precisely, we prove that the maximal degrees of the colored Jones polynomial of such a knot determine a boundary slope as predicted by the Slope Conjecture, and that the linear terms in the degrees correspo...

In the present paper we consider Fk(x) = x k − ∑ k−1 t=0 x, the characteristic polynomial of the k-th order Fibonacci sequence, the latter denoted G(k, l). We determine the limits of the real roots of certain odd and even degree polynomials related to the derivatives and integrals of Fk(x), that form infinite sequences of polynomials, of increasing degree. In particular, as k → ∞, the limiting ...

OBJECTIVE To assess the reliability of treatment recommendations based on network meta-analysis (NMA). STUDY DESIGN AND SETTING We consider evidence in an NMA to be potentially biased. Taking each pairwise contrast in turn, we use a structured series of threshold analyses to ask: (1) "How large would the bias in this evidence base have to be before it changed our decision?" and (2) "If the de...