Search results for "Normal"
showing 10 items of 2571 documents
Some local properties defining $\mathcal T_0$-groups and related classes of groups
2016
We call $G$ a $\operatorname{Hall}_{\mathcal X}$-group if there exists a normal nilpotent subgroup $N$ of $G$ for which $G/N'$ is an ${\mathcal X}$-group. We call $G$ a ${\mathcal T}_0$-group provided $G/\Phi(G)$ is a ${\mathcal T}$-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define $\operatorname{Hall}_{\mathcal X}$-groups and ${\mathcal T}_0$-groups where ${\mathcal X}\in\{ {\mathcal T},\mathcal {PT},\mathcal {PST}\}$; the classes $\mathcal {PT}$ and $\mathcal {PST}$ denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.
Ergodic properties of operators in some semi-Hilbertian spaces
2012
This article deals with linear operators T on a complex Hilbert space ℋ, which are bounded with respect to the seminorm induced by a positive operator A on ℋ. The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesaro ergodic, such that T * is not a quasiaff…
Metric operators, generalized hermiticity and partial inner product spaces
2015
A quasi-Hermitian operator is an operator in a Hilbert space that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure of metric operators, bounded or unbounded, in a Hilbert space. We introduce several generalizations of the notion of similarity between operators and explore to what extent they preserve spectral properties. Next we consider canonical lattices of Hilbert spaces generated by unbounded metric operators. Since such lattices constitute the simplest case of a partial inner product space (PIP space), we can exploit the te…
Metric Operators, Generalized Hermiticity and Lattices of Hilbert Spaces
2015
Pseudo-Hermitian quantum mechanics (QM) is a recent, unconventional, approach to QM, based on the use of non-self-adjoint Hamiltonians, whose self-adjointness can be restored by changing the ambient Hilbert space, via a so-called metric operator. The PT-symmetric Hamiltonians are usually pseudo-Hermitian operators, a term introduced a long time ago by Dieudonné for characterizing those bounded operators A that satisfy a relation of the form GA = A G, where G is a metric operator, that is, a strictly positive self-adjoint operator. This chapter explores further the structure of unbounded metric operators, in particular, their incidence on similarity. It examines the notion of similarity betw…
Sylow numbers and nilpotent Hall subgroups
2013
Abstract Let π be a set of primes and G a finite group. We characterize the existence of a nilpotent Hall π-subgroup of G in terms of the number of Sylow subgroups for the primes in π.
Relatively Orthocomplemented Skew Nearlattices in Rickart Rings
2015
AbstractA class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular.The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Ric…
Periodic Spline Wavelets and Wavelet Packets
2014
This chapter presents wavelets and wavelet packets in the spaces of periodic splines of arbitrary order, which, in essence, are the multiple generators for these spaces. The SHA technique provides explicit representation of the wavelets and wavelet packets and fast implementation of the transforms in one and several dimensions.
Trend Analysis Using Discrete Wavelet Transform (DWT) for Non-stationary NDVI Time Series in Tunisia
2021
In this paper, the trends in non-stationary Normalized Difference Vegetation Index (NDVI) Time Series (TS) over different areas in Tunisia are analyzed by applying wavelet transform and statistical tests. In the first step, the Discrete Wavelet Transform (DWT) was applied on three different time series in order to detect changes. Therefore, the different parameters of DWT were tested. In fact, the level of decomposition was calculated. The Maximum Energy to Shannon Entropy Ratio Criterion (MEER) was then investigated to choose the more suitable mother wavelet. Finally, the Mann-Kendall test (MK) was calculated for the last approximation of components to identify the variation in trend. In f…
Is backward disequilibrium in the elderly caused by an abnormal perception of verticality? A pilot study
2007
International audience; OBJECTIVE: We hypothesised that backward disequilibrium (BD), defined by a posterior position of the centre of mass with respect to the base of support, could be caused by a backward tilt in the perception of verticality. METHODS: The relationship between BD, the perception of verticality, and the history of falls in 25 subjects aged 84.5+/-7.4 years was analysed. An original ordinal scale, the BD scale (BDS), was used to quantify BD. Postural (PV) and haptic verticals (HV) were measured in sagittal plane. RESULTS: BDS scores closely correlated with the number of falls (r = 0.81, p =10(-5)). The more the PV was tilted backward, the greater the BDS scores (r = -0.95, …
Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective …
2020
The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution w…