Search results for "Polynomial"
showing 10 items of 566 documents
Growth of Differential Identities
2020
In this paper we study the growth of the differential identities of some algebras with derivations, i.e., associative algebras where a Lie algebra L (and its universal enveloping algebra U(L)) acts on them by derivations. In particular, we study in detail the differential identities and the cocharacter sequences of some algebras whose sequence of differential codimensions has polynomial growth. Moreover, we shall give a complete description of the differential identities of the algebra UT2 of 2 × 2 upper triangular matrices endowed with all possible action of a Lie algebra by derivations. Finally, we present the structure of the differential identities of the infinite dimensional Grassmann …
A note on zeroes of real polynomials in $C(K)$ spaces
2008
For real C(K) spaces, we show that being injected in a Hilbert space is a 3-space property. As a consequence, we obtain that, when K does not carry a strictly positive Radon measure, every quadratic continuous homogeneous real-valued polynomial on C(K) admits a linear zero subspace enjoying a property which implies non-separability.
On distinguished polynomials and their projections
2012
We study projections and injections between projective tensor products spaces or spaces of polynomials and we show that the example of a polynomial constructed in (4), that is neither p-dominated nor compact, can be identified with the projection map of the symmetric tensor product onto the space. Also we give a characterization of the weak and quasi approximation properties on symmetric tensor products.
Trace Identities on Diagonal Matrix Algebras
2020
Let Dn be the algebra of n × n diagonal matrices. On such an algebra it is possible to define very many trace functions. The purpose of this paper is to present several results concerning trace identities satisfied by this kind of algebras.
Some algebras of symmetric analytic functions and their spectra
2011
AbstractIn the spectrum of the algebra of symmetric analytic functions of bounded type on ℓp, 1 ≤ p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the ‘radius’ function. It is also proved that the algebra of analytic functions of bounded type on ℓ1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of ℓ1. We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.
An annihilator-based strategy for the automatic detection of exponential polynomial spaces in subdivision
2021
Abstract Exponential polynomials are essential in subdivision for the reconstruction of specific families of curves and surfaces, such as conic sections and quadric surfaces. It is well known that if a linear subdivision scheme is able to reproduce a certain space of exponential polynomials, then it must be level-dependent, with rules depending on the frequencies (and eventual multiplicities) defining the considered space. This work discusses a general strategy that exploits annihilating operators to locally detect those frequencies directly from the given data and therefore to choose the correct subdivision rule to be applied. This is intended as a first step towards the construction of se…
Generation of stimulus features for analysis of FMRI during natural auditory experiences
2014
In contrast to block and event-related designs for fMRI experiments, it becomes much more difficult to extract events of interest in the complex continuous stimulus for finding corresponding blood-oxygen-level dependent (BOLD) responses. Recently, in a free music listening fMRI experiment, acoustic features of the naturalistic music stimulus were first extracted, and then principal component analysis (PCA) was applied to select the features of interest acting as the stimulus sequences. For feature generation, kernel PCA has shown its superiority over PCA in various applications, since it can implicitly exploit nonlinear relationship among features and such relationship seems to exist genera…
Chiral condensates from tau decay: a critical reappraisal
2006
The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion, with the results: {O}_{6}=-(0.00226 \pm 0.00055) GeV^6, and O_8=-(0.0053 \pm 0.0033) GeV^8 from pinched FESR, and compatible values from the minimizing polynomial FESR. Som…
Type I optical parametric oscillators above threshold are perfect squeezers for empty gauss-hermite modes at any pumping level
2007
A type I optical parametric oscillator pumped by a Gaussian beam above threshold and tuned to its first transverse mode family is shown to yield a perfectly squeezed, empty Gauss-Hermite mode at any pumping level.
Rational Solutions to the KdV Equation in Terms of Particular Polynomials
2022
Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order n for any positive integer n, and we call these solutions, solutions of the order n. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order 10.