Search results for "group theory"
showing 10 items of 703 documents
The Peregrine breather of order nine and its deformations with sixteen parameters solutions to the NLS equation
2015
Abstract We construct new deformations of the Peregrine breather ( P 9 ) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P 9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.
The Pauli Principle and Systems Consisting of Composite Particles
1993
In nature we often deal with many-body systems that are described in terms of particles that are not elementary but themselves composite. Examples of such composite particles are hadrons, atoms, phonons, and Cooper pairs. For the description of systems consisting of such composite particles in terms of the underlying degrees of freedom group theory plays an important role, in particular the symmetric group to describe the permutational symmetry of the wave function of the system, and unitary groups to describe the symmetry forced on the system by the interaction between the particles.
Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas
2011
Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of strongly correlated systems. Here we derive exact conditions for the suitability of RDMFT to describe the two-dimensional homogeneous electron gas, which is the base system for semiconductor quantum dots and quantum Hall devices, for example. Following the method of Cioslowski and Pernal [J. Chem. Phys. 111, 3396 (1999)] we focus on the properties of power functionals of the form $f(n,{n}^{\ensuremath{'}})={(n{n}^{\ensuremath{'}})}^{\ensuremath{\alpha}}$ for the scaling function in the exchange-correlation energy. We show that in order to hav…
Eye movements when reading sentences with handwritten words.
2016
The examination of how we read handwritten words (i.e., the original form of writing) has typically been disregarded in the literature on reading. Previous research using word recognition tasks has shown that lexical effects (e.g., the word-frequency effect) are magnified when reading difficult handwritten words. To examine this issue in a more ecological scenario, we registered the participants’ eye movements when reading handwritten sentences that varied in the degree of legibility (i.e., sentences composed of words in easy vs. difficult handwritten style). For comparison purposes, we included a condition with printed sentences. Results showed a larger reading cost for sentences with dif…
Homeomorphisms of the Sierpinski curve with periodic properties
2013
In this paper, we study the three following types of homeomorphisms of the Sierpinski curve of the two sphere : pointwise periodic, periodic, and almost periodic, and we prove that they are equivalent. We show that a subgroup of homeomorphisms whose orbits are all finite, is a finite subgroup.
Upper bounds for the zeros of ultraspherical polynomials
1990
AbstractFor k = 1, 2, …, [n2] let xnk(λ) denote the Kth positive zero in decreasing order of the ultraspherical polynomial Pn(λ)(x). We establish upper bounds for xnk(λ). All the bounds become exact when λ = 0 and, in some cases (see case (iii) of Theorem 3.1), also when λ = 1. As a consequence of our results, we obtain for the largest zero xn1(λ)0.. We point out that our results remain useful for large values of λ. Numerical examples show that our upper bounds are quite sharp.
Darboux Linearization and Isochronous Centers with a Rational First Integral
1997
Abstract In this paper we study isochronous centers of polynomial systems. It is known that a center is isochronous if and only if it is linearizable. We introduce the notion of Darboux linearizability of a center and give an effective criterion for verifying Darboux linearizability. If a center is Darboux linearizable, the method produces a linearizing change of coordinates. Most of the known polynomial isochronous centers are Darboux linearizable. Moreover, using this criterion we find a new two-parameter family of cubic isochronous centers and give the linearizing changes of coordinates for centers belonging to that family. We also determine all Hamiltonian cubic systems which are Darbou…
POLYNOMIAL NUMERICAL INDEX FOR SOME COMPLEX VECTOR-VALUED FUNCTION SPACES
2007
We study in this paper the relation between the polynomial numerical indices of a complex vector-valued function space and the ones of its range space. It is proved that the spaces C(K,X), and L∞(μ,X) have the same polynomial numerical index as the complex Banach space X for every compact Hausdorff space K and every σ-finite measure μ, which does not hold any more in the real case. We give an example of a complex Banach space X such that, for every k > 2, the polynomial numerical index of order k of X is the greatest possible, namely 1, while the one of X∗∗ is the least possible, namely k k 1−k . We also give new examples of Banach spaces with the polynomial Daugavet property, namely L∞(μ,X…
A new representation of power spectral density and correlation function by means of fractional spectral moments
2009
In this paper, a new perspective for the representation of both the power spectral density and the correlation function by a unique class of function is introduced. We define the moments of order gamma (gamma being a complex number) of the one sided power spectral density and we call them Fractional Spectral Moments (FSM). These complex quantities remain finite also in the case in which the ordinary spectral moments diverge, and are able to represent the whole Power Spectral Density and the corresponding correlation function.
On the number of different prime divisors of element orders
2005
We prove that the number of different prime divisors of the order of a finite group is bounded by a polynomial function of the maximum of the number of different prime divisors of the element orders. This improves a result of J. Zhang.