We estimate the expected number of limit cycles situated in a neighbourhood of the origin of a planar polynomial vector field. Our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter. We obtain this inequality by methods of Pluripotential Theory. This inequality also implies versions of a str...

We describe Poincaré–Birkhoff–Witt bases for the two-parameter quantum groups U = Ur,s(sln) following Kharchenko and show that the positive part of U has the structure of an iterated skew polynomial ring. We define an ad-invariant bilinear form on U , which plays an important role in the construction of central elements. We introduce an analogue of the Harish-Chandra homomorphism and use it to ...

This paper considers the robust stability problem for state space models via homogeneous polynomially parameter-dependent Lyapunov functions. The suggested approach is based on a quadratic in the vector of parametric monomials matrix representation of the time derivative of the Lyapunov function. At each step, sufficiency is provided by a set of relaxed linear matrix inequalities and check for ...

In this paper, aircraft with control surface impairment faults is modelled as a set of affine parameter-dependent nonlinear systems with polynomial vector fields. Based on the Lyapunov stability theorem, sufficient conditions to test the stability of the closed-loop system are presented. The synthesis problem of stabilizing feedback controllers to enlarge the region of attraction is converted t...

In the adaptive step primal dual interior point method for linear programming polynomial algorithms are obtained by computing Newton directions towards targets on the central path and restricting the iterates to a neighborhood of this central path In this paper the adaptive step methodology is extended by considering targets in a certain central region which contains the usual central path and ...

We trace a systematic and consistent method to precisely numerate the magnitude range for various structural isospin compositional properties of neutron star. Incompressibility, symmetry energy, slope parameter, curvature star are investigated using relativistic energy density functional within framework coherent fluctuation model. The analytical expression matter is motivated from Br\"uckner a...

Conventional generalized polynomial chaos is known to fail for long time integration, loosing its optimal convergence behaviour and developing unacceptable error levels. The reason for this loss of convergence is the assumption that the probability density function is constant in time. By allowing a probability density function to evolve in time the optimal properties of polynomial chaos are re...

Muttalib–Borodin determinants are generalizations of Hankel and depend on a parameter $$\theta >0$$ . In this paper, we obtain large n asymptotics for $$n \times n$$ whose weight possesses an arbitrary number Fisher–Hartwig singularities. As corollary, the expectation variance real imaginary parts logarithm underlying characteristic polynomial, several central limit theorems, some global bulk r...