Search results for "polynomials"
showing 10 items of 144 documents
*-Graded Capelli polynomials and their asymptotics
2022
Let [Formula: see text] be the free *-superalgebra over a field [Formula: see text] of characteristic zero and let [Formula: see text] be the [Formula: see text]-ideal generated by the set of the *-graded Capelli polynomials [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] alternating on [Formula: see text] symmetric variables of homogeneous degree zero, on [Formula: see text] skew variables of homogeneous degree zero, on [Formula: see text] symmetric variables of homogeneous degree one and on [Formula: see text] skew variables of homogeneous degree one, respectively. We study the asymptotic behavior of the sequence of *-graded codimensions of [Formula: se…
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels
2018
Abstract A Rayleigh-Ritz solution approach for generally restrained multilayered variable angle tow stiffened plates in postbuckling regime is presented. The plate model is based on the first order shear deformation theory and accounts for geometrical nonlinearity through the von Karman’s assumptions. Stiffened plates are modelled as assembly of plate-like elements and penalty techniques are used to join the elements in the assembled structure and to apply the kinematical boundary conditions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to build the trial functions. A computer code was developed to implement the propose…
Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation
2002
Abstract The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order with arbitrarily variable coefficients is reported. The usefulness of the resulting resolutive formula is illustrated by simple applications to the Hermite polynomials and to the Fibonacci sequence.
Novel Stability Criteria for T--S Fuzzy Systems
2014
In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature. Then, new membership-dependent stability conditions are developed by the new Lyapunov function approach. It is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical resul…
Precision of a commercial hartmann-shack aberrometer: limits of total wavefront laser vision correction.
2012
Purpose To assess the intrasession and intersession precision of higher-order aberrations (HOAs) measured using a commercial Hartmann-Shack wavefront sensor (Zywave; Bausch & Lomb) in refractive surgery candidates. Design Prospective, experimental study of a device. Methods To analyze intrasession repeatability, 1 experienced examiner measured 30 healthy eyes 5 times successively. To study intersession reproducibility, the same clinician obtained measurements from another 30 eyes in 2 consecutive sessions at the same time of day 1 week apart. Results For intrasession repeatability, excellent intraclass correlation coefficients (ICCs) were obtained for total ocular aberrations, total HOAs, a…
Accommodative Stimulus-Response Curve with Emoji Symbols
2017
Purpose. To evaluate the static measurement of the accommodative stimulus-response curve with emoji symbols. Methods. The accommodative stimulus-response curve was measured in 18 subjects using a Hartmann-Shack sensor to obtain the objective accommodative response from the Zernike defocus term. Measurements were acquired at different accommodative demands, from 0 to 3 D with a step of 0.5 D. Detailed and nondetailed emoji targets were used with two different sizes, corresponding to the two most common visual angles used in smartphones. Results. A regression analysis was performed to fit the mean results obtained for each target. The determination coefficient was R2≥0.988 for all targets. Fo…
A semi-parametric stochastic generator for bivariate extreme events
2017
The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate extreme events is convenient for end users who need a large number of random replications of extremes as input of a given complex system to test its sensitivity. The simulation of multivariate extremes is often based on the assumption that the dependence structure, the so-called extremal dependence function, is described by a specific parametric model. We propose a simulation method for sampling bivariate extremes, under the assumption that the extremal dependence function is semiparametric. Th…
Study on the Effects of Pseudorandom Generation Quality on the Performance of Differential Evolution
2011
Experiences in the field of Monte Carlo methods indicate that the quality of a random number generator is exceedingly significant for obtaining good results. This result has not been demonstrated in the field of evolutionary optimization, and many practitioners of the field assume that the choice of the generator is superfluous and fail to document this aspect of their algorithm. In this paper, we demonstrate empirically that the requirement of high quality generator does not hold in the case of Differential Evolution.
Creating highly squeezed vacua in hybrid Laguerre-Gauss modes
2009
In this communication we study the above threshold quantum properties of a degenerate optical parametric oscillator (DOPO) tuned to a given transverse mode family at the signal frequency. We will show that under this configuration DOPOs are versatile sources of nonclassical light, in which one could be able to generate highly squeezed vacua with the non trivial shapes of Hybrid Laguerre-Gauss modes.