Search results for "Polynomial"
showing 10 items of 566 documents
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.
Analysis of negative-resistance oscillators with piecewise nonlinearity
1977
An iterative method of solution of negative-resistance oscillators with piecewise-analytical characteristics is presented. The method allows the determination of the frequency and the harmonic content of the waveform as a function of the circuit parameters and bias of the nonlinear device. An application of the method, extended to the second order, for a polynomial characteristic limited by two straight lines is also reported. The results are compared with those obtained by numerical integration.
Continuous-Variable Instantaneous Quantum Computing is Hard to Sample
2017
Instantaneous quantum computing is a sub-universal quantum complexity class, whose circuits have proven to be hard to simulate classically in the Discrete-Variable (DV) realm. We extend this proof to the Continuous-Variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of post-selected circuits. In order to treat post-selection in CVs we consider finitely-resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator GKP encoding of quantum information,…
Benchmarking parameter-free AMaLGaM on functions with and without noise.
2013
We describe a parameter-free estimation-of-distribution algorithm (EDA) called the adapted maximum-likelihood Gaussian model iterated density-estimation evolutionary algorithm (AMaLGaM-ID[Formula: see text]A, or AMaLGaM for short) for numerical optimization. AMaLGaM is benchmarked within the 2009 black box optimization benchmarking (BBOB) framework and compared to a variant with incremental model building (iAMaLGaM). We study the implications of factorizing the covariance matrix in the Gaussian distribution, to use only a few or no covariances. Further, AMaLGaM and iAMaLGaM are also evaluated on the noisy BBOB problems and we assess how well multiple evaluations per solution can average ou…