Search results for "Quadratic function"
showing 10 items of 10 documents
Updating the orbital ephemeris of the dipping source XB 1254-690 and the distance to the source
2017
XB 1254-690 is a dipping low mass X-ray binary system hosting a neutron star and showing type I X-ray bursts. We aim at obtaining more accurate orbital ephemeris and at constraining the orbital period derivative of the system for the first time. In addition, we want to better constrain the distance to the source in order to locate the system in a well defined evolutive scenario. We apply for the first time an orbital timing technique to XB 1254-690, using the arrival times of the dips present in the light curves that have been collected during 26 years of X-ray pointed observations performed from different space missions. We estimate the dip arrival times using a statistical method that wei…
Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term
2001
Abstract Our aim in this article is to study the following nonlinear elliptic Dirichlet problem: − div [a(x,u)·∇u]+b(x,u,∇u)=f, in Ω; u=0, on ∂Ω; where Ω is a bounded open subset of RN, with N>2, f∈L m (Ω) . Under wide conditions on functions a and b, we prove that there exists a type of solution for this problem; this is a bounded weak solution for m>N/2, and an unbounded entropy solution for N/2>m⩾2N/(N+2). Moreover, we show when this entropy solution is a weak one and when can be taken as test function in the weak formulation. We also study the summability of the solutions.
Quadratic characters in groups of odd order
2009
Abstract We prove that in a finite group of odd order, the number of irreducible quadratic characters is the number of quadratic conjugacy classes.
Signature of the presence of a third body orbiting around XB 1916-053
2015
The ultra-compact dipping source \object{XB 1916-053} has an orbital period of close to 50 min and a companion star with a very low mass (less than 0.1 M$_{\odot}$). The orbital period derivative of the source was estimated to be $1.5(3) \times 10^{-11}$ s/s through analysing the delays associated with the dip arrival times obtained from observations spanning 25 years, from 1978 to 2002. The known orbital period derivative is extremely large and can be explained by invoking an extreme, non-conservative mass transfer rate that is not easily justifiable. We extended the analysed data from 1978 to 2014, by spanning 37 years, to verify whether a larger sample of data can be fitted with a quadra…
Generalized Conformal Symmetry and Extended Objects from the Free Particle
1998
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphi…
Spectrum of composition operators on S(R) with polynomial symbols
2020
Abstract We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.
Separation of representations with quadratic overgroups
2011
AbstractAny unitary irreducible representation π of a Lie group G defines a moment set Iπ, subset of the dual g⁎ of the Lie algebra of G. Unfortunately, Iπ does not characterize π. If G is exponential, there exists an overgroup G+ of G, built using real-analytic functions on g⁎, and extensions π+ of any generic representation π to G+ such that Iπ+ characterizes π.In this paper, we prove that, for many different classes of group G, G admits a quadratic overgroup: such an overgroup is built with the only use of linear and quadratic functions.
Using Modelling and Tablets in the Classroom to Learn Quadratic Functions
2017
In this chapter, we present teaching material to work with a quadratic function and the meaning of its parameters through the mathematical modelling of a real-life phenomenon: the relation between the time and the height of a ball during a complete vertical rebound and fall. The teaching material uses electronic tablets to collect and process real data in the classroom. After analysing a year 11 implementation, we note that a qualitative analysis of the phenomenon and the families of functions and the students’ prior knowledge about these functions are key elements to manage and control the modelling process, especially, to choose the model and to interpret the results in terms of the pheno…
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…
Electromagnetic wave propagation in non-homogeneous waveguides
2015
We investigate an electromagnetic waveguide, having several cylindrical ends. The waveguide is assumed to be empty and to have a perfectly conductive boundary. We study the electromagnetic field, excited in the waveguide in the presence of charges and currents. The field can be described as a solution of the stationary Maxwell system with conductive boundary conditions and “intrinsic” radiation conditions at infinity. We prove the problem to be well-posed. Electromagnetic waves propagation in the waveguide can be described by means of a scattering matrix. We introduce such a matrix for all values of the spectral parameter k in the waveguide continuous spectrum and study its properties. Moreove…