Search results for "LYN"
showing 10 items of 910 documents
More limit cycles than expected in Liénard equations
2007
The paper deals with classical polynomial Lienard equations, i.e. planar vector fields associated to scalar second order differential equations x"+ f(x)x' + x = 0 where f is a polynomial. We prove that for a well-chosen polynomial f of degree 6, the equation exhibits 4 limit cycles. It induces that for n ≥ 3 there exist polynomials f of degree 2n such that the related equations exhibit more than n limit cycles. This contradicts the conjecture of Lins, de Melo and Pugh stating that for Lienard equations as above, with f of degree 2n, the maximum number of limit cycles is n. The limit cycles that we found are relaxation oscillations which appear in slow-fast systems at the boundary of classic…
A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
2021
<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…
A Novel Computational Approach for Harmonic Mitigation in PV Systems with Single-Phase Five-Level CHBMI
2018
In this paper, a novel approach to low order harmonic mitigation in fundamental switching frequency modulation is proposed for high power photovoltaic (PV) applications, without trying to solve the cumbersome non-linear transcendental equations. The proposed method allows for mitigation of the first-five harmonics (third, fifth, seventh, ninth, and eleventh harmonics), to reduce the complexity of the required procedure and to allocate few computational resource in the Field Programmable Gate Array (FPGA) based control board. Therefore, the voltage waveform taken into account is different respect traditional voltage waveform. The same concept, known as “voltage cancelation”, used for single-…
Infinite orbit depth and length of Melnikov functions
2019
Abstract In this paper we study polynomial Hamiltonian systems d F = 0 in the plane and their small perturbations: d F + ϵ ω = 0 . The first nonzero Melnikov function M μ = M μ ( F , γ , ω ) of the Poincare map along a loop γ of d F = 0 is given by an iterated integral [3] . In [7] , we bounded the length of the iterated integral M μ by a geometric number k = k ( F , γ ) which we call orbit depth. We conjectured that the bound is optimal. Here, we give a simple example of a Hamiltonian system F and its orbit γ having infinite orbit depth. If our conjecture is true, for this example there should exist deformations d F + ϵ ω with arbitrary high length first nonzero Melnikov function M μ along…
Relative efficiency revealed: Equations for k<inf>1</inf>&#x2013;k<inf>6</inf> of the PVGIS model
2014
The European PV Geographical Information System (PVGIS) describes module performance in terms of the relative efficiency with respect to Standard Testing Conditions (STC). The efficiency's dependence on irradiance and operating temperature is modeled with a bi-quadratic polynomial with respect to the relative temperature and the logarithm of relative irradiance. In earlier works, the present author derived relations between two model coefficients describing the irradiance dependence at 25°C, k 1 and k 2 , and I–V curve model parameters such as the series resistance RS and the ideality factor n. There was good agreement between the theoretical and fitted values of k 1 , but the fitted values…
Blenders near polynomial product maps of $\mathbb C^2$
2021
In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types : repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets : the bifurcation locus of $H_d(\mathbb P^2)$ and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of H\'enon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets.
Learning of regular expressions by pattern matching
1995
We consider the problem of restoring regular expressions from good examples. We describe a natural learning algorithm for obtaining a “plausible” regular expression from one example. The algorithm is based on finding the longest substring which can be matched by some part of the so far obtained expression. We believe that the algorithm to a certain extent mimics humans guessing regular expressions from the same sort of examples. We show that for regular expressions of bounded length successful learning takes time linear in the length of the example, provided that the example is “good”. Under certain natural restrictions the run-time of the learning algorithm is polynomial also in unsuccessf…
Zeroes of real polynomials on C(K) spaces
2007
AbstractFor a compact Hausdorff topological space K, we show that the function space C(K) must satisfy the following dichotomy: (i) either it admits a positive definite continuous 2-homogeneous real-valued polynomial, (ii) or every continuous 2-homogeneous real-valued polynomial vanishes in a non-separable closed linear subspace. Moreover, if K does not have the Countable Chain Condition, then every continuous polynomial, not necessarily homogeneous and with arbitrary degree, has constant value in an isometric copy of c0(Γ), for some uncountable Γ.
The Plateau-Bézier Problem
2003
We study the Plateau problem restricted to polynomial surfaces using techniques coming from the theory of Computer Aided Geometric Design. The results can be used to obtain polynomial approximations to minimal surfaces. The relationship between harmonic Bezier surfaces and minimal surfaces with free boundaries is shown.
GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD
2003
We consider the algebra Un(K) of n×n upper triangular matrices over an infinite field K equipped with its usual ℤn-grading. We describe a basis of the ideal of the graded polynomial identities for this algebra.