An extremal nonnegative sine polynomial

For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed in such a way that {Kn(θ)} is a summability kernel. Thus, for each Pi 1 ≤ P ≤ ∞ and for any 27π-periodic function f ∈ Lp [-π, π], the sequence of convolutions Kn * f is proved to converge to f in Lp[-ππ]. The pointwise and almost everywhere convergences are also consequences of our construction.

Nonnegative trigonometric polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.

On some Extremal Problems of Landau

2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.

Model-order selection in Zernike polynomial expansion of corneal surfaces using the efficient detection criterion

Corneal-height data are typically measured with videokeratoscopes and modeled using a set of orthogonal Zernike polynomials. We address the estimation of the number of Zernike polynomials, which is formalized as a model-order selection problem in linear regression. Classical information-theoretic criteria tend to overestimate the corneal surface due to the weakness of their penalty functions, while bootstrap-based techniques tend to underestimate the surface or require extensive processing. In this paper, we propose to use the efficient detection criterion (EDC), which has the same general form of information-theoretic-based criteria, as an alternative to estimating the optimal number of Zernike polynomials. We first show, via simulations, that the EDC outperforms a large number of information-theoretic criteria and resampling-based techniques. We then illustrate that using the EDC for real corneas results in models that are in closer agreement with clinical expectations and provides means for distinguishing normal corneal surfaces from astigmatic and keratoconic surfaces.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

Decomposition construction for secret sharing schemes with graph access structures in polynomial time

The purpose of this paper is to describe a new decomposition construction for perfect secret sharing schemes with graph access structures. The previous decomposition construction proposed by Stinson is a recursive method that uses small secret sharing schemes as building blocks in the construction of larger schemes. When the Stinson method is applied to the graph access structures, the number of such “small” schemes is typically exponential in the number of the participants, resulting in an exponential algorithm. Our method has the same flavor as the Stinson decomposition construction; however, the linear programming problem involved in the construction is formulated in such a way that the number of “small” schemes is polynomial in the size of the participants, which in turn gives rise to a polynomial time construction. We also show that if we apply the Stinson construction to the “small” schemes arising from our new construction, both have the same information rate.

Tandem B1 SINE retro-elements may provide a basis for natural antisense transcription in the Magi1 locus of the mouse (Mus musculus)

Transposable elements, which are DNA sequences that can move between different sites in genomes, comprise approximately 40% of the genome of mammals and are emerging as important contributors to biological diversity. Here we report a transcription unit lying within intron 1 of the murine Magi1 (membrane associated guanylate kinase inverted 1) gene that codes for a cell-cell junction scaffolding protein. The transcription unit, termed Magi1OS (Magi1 Opposite Strand), originates from a region with tandem B1 short interspersed nuclear elements (SINEs) and is an antisense gene to Magi1. Mag1OS transcription initiates in a proximal B1 element that shows only 4% divergence from the consensus sequence, indicating that it has been recently inserted into the mouse genome and could be replication competent. Moreover, a chimaeric transcript may result from intra-chromosomal interaction and trans-splicing of the Magi1 antisense transcript (Magi1OS) and Ghrl, which codes for the multifunctional peptide hormone ghrelin. These two genes are 20 megabases apart on chromosome 6 and are transcribed in opposite directions. We propose that the Magi1OS locus may serve as a useful model system to study exaptation and retrotransposition of B1 SINEs, as well as to examine the mechanisms of intra-chromosomal trans-splicing.

Pulsed dc- and sine-wave-excited cold atmospheric plasma plumes: A comparative analysis

Cold atmospheric-pressure plasma plumes are generated in the ambient air by a single-electrode plasma jet device powered by pulsed dc and ac sine-wave excitation sources. Comprehensive comparisons of the plasma characteristics, including electrical properties, optical emission spectra, gas temperatures, plasma dynamics, and bacterial inactivation ability of the two plasmas are carried out. It is shown that the dc pulse excited plasma features a much larger discharge current and stronger optical emission than the sine-wave excited plasma. The gas temperature in the former discharge remains very close to the room temperature across the entire plume length; the sine-wave driven discharge also shows a uniform temperature profile, which is 20-30 degrees higher than the room temperature. The dc pulse excited plasma also shows a better performance in the inactivation of gram-positive staphylococcus aureus bacteria. These results suggest that the pulsed dc electric field is more effective for the generation of nonequilibrium atmospheric pressure plasma plumes for advanced plasma health care applications.

An accuracy assessment of ASTER stereo images-derived digital elevation model by using rational polynomial coefficient model

The along-track stereo images of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor with 15 m resolution were used to generate Digital Elevation Model (DEM) on an area with low and near Mean Sea Level (MSL) elevation in Johor, Malaysia. The absolute DEM was generated by using the Rational Polynomial Coefficient (RPC) model which was run on ENVI 4.8 software. In order to generate the absolute DEM, 60 Ground Control Pointes (GCPs) with almost vertical accuracy less than 10 meter extracted from topographic map of the study area. The assessment was carried out on uncorrected and corrected DEM by utilizing dozens of Independent Check Points (ICPs). Consequently, the uncorrected DEM showed the RMSEz of ± 26.43 meter which was decreased to the RMSEz of ± 16.49 meter for the corrected DEM after post-processing. Overall, the corrected DEM of ASTER stereo images met the expectations.

Reproducibility of fatmax and fat oxidation rates during exercise in recreationally trained males

Aerobic exercise training performed at the intensity eliciting maximal fat oxidation (Fatmax) has been shown to improve the metabolic profile of obese patients. However, limited information is available on the reproducibility of Fatmax and related physiological measures. The aim of this study was to assess the intra-individual variability of: a) Fatmax measurements determined using three different data analysis approaches and b) fat and carbohydrate oxidation rates at rest and at each stage of an individualized graded test. Fifteen healthy males [body mass index 23.1±0.6 kg/m2, maximal oxygen consumption () 52.0±2.0 ml/kg/min] completed a maximal test and two identical submaximal incremental tests on ergocycle (30-min rest followed by 5-min stages with increments of 7.5% of the maximal power output). Fat and carbohydrate oxidation rates were determined using indirect calorimetry. Fatmax was determined with three approaches: the sine model (SIN), measured values (MV) and 3rd polynomial curve (P3). Intra-individual coefficients of variation (CVs) and limits of agreement were calculated. CV for Fatmax determined with SIN was 16.4% and tended to be lower than with P3 and MV (18.6% and 20.8%, respectively). Limits of agreement for Fatmax were −2±27% of with SIN, −4±32 with P3 and −4±28 with MV. CVs of oxygen uptake, carbon dioxide production and respiratory exchange rate were <10% at rest and <5% during exercise. Conversely, CVs of fat oxidation rates (20% at rest and 24–49% during exercise) and carbohydrate oxidation rates (33.5% at rest, 8.5–12.9% during exercise) were higher. The intra-individual variability of Fatmax and fat oxidation rates was high (CV>15%), regardless of the data analysis approach employed. Further research on the determinants of the variability of Fatmax and fat oxidation rates is required.