Search results for "Polynomial"
showing 10 items of 566 documents
Optical Quality Comparison between Spherical and Aspheric Toric Intraocular Lenses
2014
Purpose To measure and compare the optical quality of spherical and aspheric toric intraocular lenses (IOLs). Methods Wavefront aberrations of AcrySof Toric and IQ Toric IOLs (Alcon Laboratories) for different powers were measured at 3- and 5-mm pupils by Nimo TR0805 instrument. The Zernike coefficients of trefoil, coma, tetrafoil, secondary astigmatism, and spherical aberration were evaluated. The point spread functions (PSFs) of each IOL evaluated were calculated from the wavefront aberrations. The PSF images also were calculated from the IOL wavefront aberrations, adding the cornea's aberrations to simulate the optical quality after their implantation. Results Spherical toric IOLs showed…
Innovative straight formulation for plate in bending
2017
In this paper it has been introduced an innovative formulation for evaluating the deflection function of a simply supported plate loaded by uniformly distributed edge moments. Framed into Line Element-less Method, this formulation allows the evaluation of solution in terms of deflection, through few lines of algorithm implemented by Mathematica software without resorting to any discretization neither in the domain nor in the boundary. Interesting savings in terms of time and computational costs are achieved. Results obtained by the proposed method are well contrasted by ones obtained by classical methods and Finite Element Method.
Steiner systems and configurations of points
2020
AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…
Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee
2020
In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted wi…
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…
Chaos Synchronization Based on Unknown Input Proportional Multiple-Integral Fuzzy Observer
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/670878 Open Access This paper presents an unknown input Proportional Multiple-Integral Observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input with kth derivative zero. Using Lyapunov stability theory…
On eleven-dimensional supergravity and chern?SIMONS Theory
2012
We probe in some depth into the structure of eleven-dimensional, osp(32|1)-based Chern-Simons supergravity, as put forward by Troncoso and Zanelli (TZ) in 1997. We find that the TZ Lagrangian may be cast as a polynomial in 1/l, where l is a length, and compute explicitly the first three dominant terms. The term proportional to 1/l^9 turns out to be essentially the Lagrangian of the standard 1978 supergravity theory of Cremmer, Julia and Scherk, thus establishing a previously unknown relation between the two theories. The computation is nontrivial because, when written in a sufficiently explicit way, the TZ Lagrangian has roughly one thousand non-explicitly Lorentz-covariant terms. Specially…
Removing Batch Effects from Longitudinal Gene Expression - Quantile Normalization Plus ComBat as Best Approach for Microarray Transcriptome Data
2016
International audience; Technical variation plays an important role in microarray-based gene expression studies, and batch effects explain a large proportion of this noise. It is therefore mandatory to eliminate technical variation while maintaining biological variability. Several strategies have been proposed for the removal of batch effects, although they have not been evaluated in large-scale longitudinal gene expression data. In this study, we aimed at identifying a suitable method for batch effect removal in a large study of microarray-based longitudinal gene expression. Monocytic gene expression was measured in 1092 participants of the Gutenberg Health Study at baseline and 5-year fol…
Influence of trifocal intraocular lenses on standard autorefraction and aberrometer-based autorefraction.
2019
To study the agreement between manifest refraction and objective refraction measured with two autorefractor models and an aberrometer in eyes implanted with a trifocal diffractive intraocular lens (IOL).IOA Madrid Innova Ocular, Madrid, Spain.Prospective comparative cohort study.An autorefractor keratometer (KR-8800), based on a Scheiner double pinhole, and a 3-dimension wavefront topography aberrometer system (OPD-Scan III), based on the scanning-slit retinoscopy principle, were used to obtain objective refraction readings. In addition, lower-order Zernike coefficients (Z) were used to calculate objective refraction. A set of 7 different results was obtained in power vector notation (spher…
Three-Dimensional Reconstruction of the Bony Nasolacrimal Canal by Automated Segmentation of Computed Tomography Images.
2016
Objective To apply a fully automated method to quantify the 3D structure of the bony nasolacrimal canal (NLC) from CT scans whereby the size and main morphometric characteristics of the canal can be determined. Design Cross-sectional study. Subjects 36 eyes of 18 healthy individuals. Methods Using software designed to detect the boundaries of the NLC on CT images, 36 NLC reconstructions were prepared. These reconstructions were then used to calculate NLC volume. The NLC axis in each case was determined according to a polygonal model and to 2nd, 3rd and 4th degree polynomials. From these models, NLC sectional areas and length were determined. For each variable, descriptive statistics and nor…