Sediment unmixing using detrital geochronology

Science.gov (United States)

Sharman, Glenn R.; Johnstone, Samuel A.

2017-11-01

Sediment mixing within sediment routing systems can exert a strong influence on the preservation of provenance signals that yield insight into the effect of environmental forcing (e.g., tectonism, climate) on the Earth's surface. Here, we discuss two approaches to unmixing detrital geochronologic data in an effort to characterize complex changes in the sedimentary record. First, we summarize 'top-down' mixing, which has been successfully employed in the past to characterize the different fractions of prescribed source distributions ('parents') that characterize a derived sample or set of samples ('daughters'). Second, we propose the use of 'bottom-up' methods, previously used primarily for grain size distributions, to model parent distributions and the abundances of these parents within a set of daughters. We demonstrate the utility of both top-down and bottom-up approaches to unmixing detrital geochronologic data within a well-constrained sediment routing system in central California. Use of a variety of goodness-of-fit metrics in top-down modeling reveals the importance of considering the range of allowable that is well mixed over any single best-fit mixture calculation. Bottom-up modeling of 12 daughter samples from beaches and submarine canyons yields modeled parent distributions that are remarkably similar to those expected from the geologic context of the sediment-routing system. In general, mixture modeling has the potential to supplement more widely applied approaches in comparing detrital geochronologic data by casting differences between samples as differing proportions of geologically meaningful end-member provenance categories.

An uncertainty inclusive un-mixing model to identify tracer non-conservativeness

Science.gov (United States)

Sherriff, Sophie; Rowan, John; Franks, Stewart; Fenton, Owen; Jordan, Phil; hUallacháin, Daire Ó.

2015-04-01

Sediment fingerprinting is being increasingly recognised as an essential tool for catchment soil and water management. Selected physico-chemical properties (tracers) of soils and river sediments are used in a statistically-based 'un-mixing' model to apportion sediment delivered to the catchment outlet (target) to its upstream sediment sources. Development of uncertainty-inclusive approaches, taking into account uncertainties in the sampling, measurement and statistical un-mixing, are improving the robustness of results. However, methodological challenges remain including issues of particle size and organic matter selectivity and non-conservative behaviour of tracers - relating to biogeochemical transformations along the transport pathway. This study builds on our earlier uncertainty-inclusive approach (FR2000) to detect and assess the impact of tracer non-conservativeness using synthetic data before applying these lessons to new field data from Ireland. Un-mixing was conducted on 'pristine' and 'corrupted' synthetic datasets containing three to fifty tracers (in the corrupted dataset one target tracer value was manually corrupted to replicate non-conservative behaviour). Additionally, a smaller corrupted dataset was un-mixed using a permutation version of the algorithm. Field data was collected in an 11 km2 river catchment in Ireland. Source samples were collected from topsoils, subsoils, channel banks, open field drains, damaged road verges and farm tracks. Target samples were collected using time integrated suspended sediment samplers at the catchment outlet at 6-12 week intervals from July 2012 to June 2013. Samples were dried (affected whereas uncertainty was only marginally impacted by the corrupted tracer. Improvement of uncertainty resulted from increasing the number of tracers in both the perfect and corrupted datasets. FR2000 was capable of detecting non-conservative tracer behaviour within the range of mean source values, therefore, it provided a more

Multiplex protein pattern unmixing using a non-linear variable-weighted support vector machine as optimized by a particle swarm optimization algorithm.

Science.gov (United States)

Yang, Qin; Zou, Hong-Yan; Zhang, Yan; Tang, Li-Juan; Shen, Guo-Li; Jiang, Jian-Hui; Yu, Ru-Qin

2016-01-15

Most of the proteins locate more than one organelle in a cell. Unmixing the localization patterns of proteins is critical for understanding the protein functions and other vital cellular processes. Herein, non-linear machine learning technique is proposed for the first time upon protein pattern unmixing. Variable-weighted support vector machine (VW-SVM) is a demonstrated robust modeling technique with flexible and rational variable selection. As optimized by a global stochastic optimization technique, particle swarm optimization (PSO) algorithm, it makes VW-SVM to be an adaptive parameter-free method for automated unmixing of protein subcellular patterns. Results obtained by pattern unmixing of a set of fluorescence microscope images of cells indicate VW-SVM as optimized by PSO is able to extract useful pattern features by optimally rescaling each variable for non-linear SVM modeling, consequently leading to improved performances in multiplex protein pattern unmixing compared with conventional SVM and other exiting pattern unmixing methods. Copyright © 2015 Elsevier B.V. All rights reserved.

Manifold regularization for sparse unmixing of hyperspectral images.

Science.gov (United States)

Liu, Junmin; Zhang, Chunxia; Zhang, Jiangshe; Li, Huirong; Gao, Yuelin

2016-01-01

Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression , ignore the intrinsic geometric structure in the hyperspectral data. In this paper, we propose a novel model, called manifold regularized collaborative sparse regression , by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.

Orthogonal polynomials

CERN Document Server

Freud, Géza

1971-01-01

Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as referenc

Spectral Mixture Analysis: Linear and Semi-parametric Full and Iterated Partial Unmixing in Multi- and Hyperspectral Image Data

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2001-01-01

) and non-negative least squares (NNLS), and the partial unmixing methods orthogonal subspace projection (OSP), constrained energy minimization (CEM) and an eigenvalue formulation alternative are dealt with. The solution to the eigenvalue formulation alternative proves to be identical to the CEM solution....... The matrix inversion involved in CEM can be avoided by working on (a subset of) orthogonally transformed data such as signal maximum autocorrelation factors, MAFs, or signal minimum noise fractions, MNFs. This will also cause the partial unmixing result to be independent of the noise isolated in the MAF....../MNFs not included in the analysis. CEM and the eigenvalue formulation alternative enable us to perform partial unmixing when we know one desired end-member spectrum only and not the full set of end-member spectra. This is an advantage over full unmixing and OSP. The eigenvalue formulation of CEM inspires us...

Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

Science.gov (United States)

Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

2016-02-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Stress-strength reliability for general bivariate distributions

Directory of Open Access Journals (Sweden)

Alaa H. Abdel-Hamid

2016-10-01

Full Text Available An expression for the stress-strength reliability R=P(X1bivariate distribution. Such distribution includes bivariate compound Weibull, bivariate compound Gompertz, bivariate compound Pareto, among others. In the parametric case, the maximum likelihood estimates of the parameters and reliability function R are obtained. In the non-parametric case, point and interval estimates of R are developed using Govindarajulu's asymptotic distribution-free method when X1 and X2 are dependent. An example is given when the population distribution is bivariate compound Weibull. Simulation is performed, based on different sample sizes to study the performance of estimates.

Hyperspectral clustering and unmixing for studying the ecology of state formation and complex societies

Science.gov (United States)

Kwong, Justin D.; Messinger, David W.; Middleton, William D.

2009-08-01

This project is an application of hyperspectral classification and unmixing in support of an ongoing archaeological study. The study region is the Oaxaca Valley located in the state of Oaxaca, Mexico on the southern coast. This was the birthplace of the Zapotec civilization which grew into a complex state level society. Hyperion imagery is being collected over a 30,000 km2 area. Classification maps of regions of interest are generated using K-means clustering and a novel algorithm called Gradient Flow. Gradient Flow departs from conventional stochastic or deterministic approaches, using graph theory to cluster spectral data. Spectral unmixing is conducted using the RIT developed algorithm Max-D to automatically find end members. Stepwise unmixing is performed to better model the data using the end members found be Max-D. Data are efficiently shared between imaging scientists and archaeologists using Google Earth to stream images over the internet rather than downloading them. The overall goal of the project is to provide archaeologists with useful information maps without having to interpret the raw data.

Generalization of binary tensor product schemes depends upon four parameters

International Nuclear Information System (INIS)

Bashir, R.; Bari, M.; Mustafa, G.

2018-01-01

This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes. (author)

Comparing performance of standard and iterative linear unmixing methods for hyperspectral signatures

Science.gov (United States)

Gault, Travis R.; Jansen, Melissa E.; DeCoster, Mallory E.; Jansing, E. David; Rodriguez, Benjamin M.

2016-05-01

Linear unmixing is a method of decomposing a mixed signature to determine the component materials that are present in sensor's field of view, along with the abundances at which they occur. Linear unmixing assumes that energy from the materials in the field of view is mixed in a linear fashion across the spectrum of interest. Traditional unmixing methods can take advantage of adjacent pixels in the decomposition algorithm, but is not the case for point sensors. This paper explores several iterative and non-iterative methods for linear unmixing, and examines their effectiveness at identifying the individual signatures that make up simulated single pixel mixed signatures, along with their corresponding abundances. The major hurdle addressed in the proposed method is that no neighboring pixel information is available for the spectral signature of interest. Testing is performed using two collections of spectral signatures from the Johns Hopkins University Applied Physics Laboratory's Signatures Database software (SigDB): a hand-selected small dataset of 25 distinct signatures from a larger dataset of approximately 1600 pure visible/near-infrared/short-wave-infrared (VIS/NIR/SWIR) spectra. Simulated spectra are created with three and four material mixtures randomly drawn from a dataset originating from SigDB, where the abundance of one material is swept in 10% increments from 10% to 90%with the abundances of the other materials equally divided amongst the remainder. For the smaller dataset of 25 signatures, all combinations of three or four materials are used to create simulated spectra, from which the accuracy of materials returned, as well as the correctness of the abundances, is compared to the inputs. The experiment is expanded to include the signatures from the larger dataset of almost 1600 signatures evaluated using a Monte Carlo scheme with 5000 draws of three or four materials to create the simulated mixed signatures. The spectral similarity of the inputs to the

Generation, Validation, and Application of Abundance Map Reference Data for Spectral Unmixing

Science.gov (United States)

Williams, McKay D.

Reference data ("ground truth") maps traditionally have been used to assess the accuracy of imaging spectrometer classification algorithms. However, these reference data can be prohibitively expensive to produce, often do not include sub-pixel abundance estimates necessary to assess spectral unmixing algorithms, and lack published validation reports. Our research proposes methodologies to efficiently generate, validate, and apply abundance map reference data (AMRD) to airborne remote sensing scenes. We generated scene-wide AMRD for three different remote sensing scenes using our remotely sensed reference data (RSRD) technique, which spatially aggregates unmixing results from fine scale imagery (e.g., 1-m Ground Sample Distance (GSD)) to co-located coarse scale imagery (e.g., 10-m GSD or larger). We validated the accuracy of this methodology by estimating AMRD in 51 randomly-selected 10 m x 10 m plots, using seven independent methods and observers, including field surveys by two observers, imagery analysis by two observers, and RSRD using three algorithms. Results indicated statistically-significant differences between all versions of AMRD, suggesting that all forms of reference data need to be validated. Given these significant differences between the independent versions of AMRD, we proposed that the mean of all (MOA) versions of reference data for each plot and class were most likely to represent true abundances. We then compared each version of AMRD to MOA. Best case accuracy was achieved by a version of imagery analysis, which had a mean coverage area error of 2.0%, with a standard deviation of 5.6%. One of the RSRD algorithms was nearly as accurate, achieving a mean error of 3.0%, with a standard deviation of 6.3%, showing the potential of RSRD-based AMRD generation. Application of validated AMRD to specific coarse scale imagery involved three main parts: 1) spatial alignment of coarse and fine scale imagery, 2) aggregation of fine scale abundances to produce

Target Transformation Constrained Sparse Unmixing (ttcsu) Algorithm for Retrieving Hydrous Minerals on Mars: Application to Southwest Melas Chasma

Science.gov (United States)

Lin, H.; Zhang, X.; Wu, X.; Tarnas, J. D.; Mustard, J. F.

2018-04-01

Quantitative analysis of hydrated minerals from hyperspectral remote sensing data is fundamental for understanding Martian geologic process. Because of the difficulties for selecting endmembers from hyperspectral images, a sparse unmixing algorithm has been proposed to be applied to CRISM data on Mars. However, it's challenge when the endmember library increases dramatically. Here, we proposed a new methodology termed Target Transformation Constrained Sparse Unmixing (TTCSU) to accurately detect hydrous minerals on Mars. A new version of target transformation technique proposed in our recent work was used to obtain the potential detections from CRISM data. Sparse unmixing constrained with these detections as prior information was applied to CRISM single-scattering albedo images, which were calculated using a Hapke radiative transfer model. This methodology increases success rate of the automatic endmember selection of sparse unmixing and could get more accurate abundances. CRISM images with well analyzed in Southwest Melas Chasma was used to validate our methodology in this study. The sulfates jarosite was detected from Southwest Melas Chasma, the distribution is consistent with previous work and the abundance is comparable. More validations will be done in our future work.

Irreducible multivariate polynomials obtained from polynomials in ...

Indian Academy of Sciences (India)

Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: Nicolae. ... Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ..... This shows us that deg ai = (n − i) deg f2 for each i = 0,..., n, so min k>0.

Bivariate discrete beta Kernel graduation of mortality data.

Science.gov (United States)

Mazza, Angelo; Punzo, Antonio

2015-07-01

Various parametric/nonparametric techniques have been proposed in literature to graduate mortality data as a function of age. Nonparametric approaches, as for example kernel smoothing regression, are often preferred because they do not assume any particular mortality law. Among the existing kernel smoothing approaches, the recently proposed (univariate) discrete beta kernel smoother has been shown to provide some benefits. Bivariate graduation, over age and calendar years or durations, is common practice in demography and actuarial sciences. In this paper, we generalize the discrete beta kernel smoother to the bivariate case, and we introduce an adaptive bandwidth variant that may provide additional benefits when data on exposures to the risk of death are available; furthermore, we outline a cross-validation procedure for bandwidths selection. Using simulations studies, we compare the bivariate approach proposed here with its corresponding univariate formulation and with two popular nonparametric bivariate graduation techniques, based on Epanechnikov kernels and on P-splines. To make simulations realistic, a bivariate dataset, based on probabilities of dying recorded for the US males, is used. Simulations have confirmed the gain in performance of the new bivariate approach with respect to both the univariate and the bivariate competitors.

Branched polynomial covering maps

DEFF Research Database (Denmark)

Hansen, Vagn Lundsgaard

2002-01-01

A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch ...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved.......A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...

Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography

Energy Technology Data Exchange (ETDEWEB)

Fujii, Yuka [NASA Goddard Institute for Space Studies, New York, NY 10025 (United States); Lustig-Yaeger, Jacob [Astronomy Department, University of Washington, Box 951580, Seattle, WA 98195 (United States); Cowan, Nicolas B., E-mail: yuka.fujii.ebihara@gmail.com [Department of Earth and Planetary Sciences, McGill University, Montreal, Quebec, H3A 0E8 (Canada)

2017-11-01

Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions like Earth. Although previous work on unmixing the spectra of Earth from disk-integrated multi-band light curves appeared successful, we point out a mathematical degeneracy between the surface colors and their spatial distributions. Nevertheless, useful constraints on the spectral shape of individual surface types may be obtained from the premise that albedo is everywhere between 0 and 1. We demonstrate the degeneracy and the possible constraints using both mock data based on a toy model of Earth, as well as real observations of Earth. Despite the severe degeneracy, we are still able to recover an approximate albedo spectrum for an ocean. In general, we find that surfaces are easier to identify when they cover a large fraction of the planet and when their spectra approach zero or unity in certain bands.

Rotational Spectral Unmixing of Exoplanets: Degeneracies Between Surface Colors and Geography

Science.gov (United States)

Fujii, Yuka; Lustig-Yaeger, Jacob; Cowan, Nicolas B.

2017-01-01

Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions like Earth. Although previous work on unmixing the spectra of Earth from disk-integrated multi-band light curves appeared successful, we point out a mathematical degeneracy between the surface colors and their spatial distributions. Nevertheless, useful constraints on the spectral shape of individual surface types may be obtained from the premise that albedo is everywhere between 0 and 1. We demonstrate the degeneracy and the possible constraints using both mock data based on a toy model of Earth, as well as real observations of Earth. Despite the severe degeneracy, we are still able to recover an approximate albedo spectrum for an ocean. In general, we find that surfaces are easier to identify when they cover a large fraction of the planet and when their spectra approach zero or unity in certain bands.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

Science.gov (United States)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

OpenAIRE

Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie

2011-01-01

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...

[Orthogonal Vector Projection Algorithm for Spectral Unmixing].

Science.gov (United States)

Song, Mei-ping; Xu, Xing-wei; Chang, Chein-I; An, Ju-bai; Yao, Li

2015-12-01

Spectrum unmixing is an important part of hyperspectral technologies, which is essential for material quantity analysis in hyperspectral imagery. Most linear unmixing algorithms require computations of matrix multiplication and matrix inversion or matrix determination. These are difficult for programming, especially hard for realization on hardware. At the same time, the computation costs of the algorithms increase significantly as the number of endmembers grows. Here, based on the traditional algorithm Orthogonal Subspace Projection, a new method called. Orthogonal Vector Projection is prompted using orthogonal principle. It simplifies this process by avoiding matrix multiplication and inversion. It firstly computes the final orthogonal vector via Gram-Schmidt process for each endmember spectrum. And then, these orthogonal vectors are used as projection vector for the pixel signature. The unconstrained abundance can be obtained directly by projecting the signature to the projection vectors, and computing the ratio of projected vector length and orthogonal vector length. Compared to the Orthogonal Subspace Projection and Least Squares Error algorithms, this method does not need matrix inversion, which is much computation costing and hard to implement on hardware. It just completes the orthogonalization process by repeated vector operations, easy for application on both parallel computation and hardware. The reasonability of the algorithm is proved by its relationship with Orthogonal Sub-space Projection and Least Squares Error algorithms. And its computational complexity is also compared with the other two algorithms', which is the lowest one. At last, the experimental results on synthetic image and real image are also provided, giving another evidence for effectiveness of the method.

A new class of generalized polynomials associated with Hermite and Bernoulli polynomials

Directory of Open Access Journals (Sweden)

M. A. Pathan

2015-05-01

Full Text Available In this paper, we introduce a new class of generalized  polynomials associated with  the modified Milne-Thomson's polynomials Φ_{n}^{(α}(x,ν of degree n and order α introduced by  Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials  B_n(x, generalized Bernoulli numbers B_n(a,b, generalized Bernoulli polynomials  B_n(x;a,b,c of Luo et al, Hermite-Bernoulli polynomials  {_HB}_n(x,y of Dattoli et al and {_HB}_n^{(α} (x,y of Pathan  are generalized to the one   {_HB}_n^{(α}(x,y,a,b,c which is called  the generalized  polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x, B_n(a,b, B_n(x;a,b,c and {}_HB_n^{(α}(x,y;a,b,c  are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomials

[Source apportionment of soil heavy metals in Jiapigou goldmine based on the UNMIX model].

Science.gov (United States)

Ai, Jian-chao; Wang, Ning; Yang, Jing

2014-09-01

The paper determines 16 kinds of metal elements' concentration in soil samples which collected in Jipigou goldmine upper the Songhua River. The UNMIX Model which was recommended by US EPA to get the source apportionment results was applied in this study, Cd, Hg, Pb and Ag concentration contour maps were generated by using Kriging interpolation method to verify the results. The main conclusions of this study are: (1)the concentrations of Cd, Hg, Pb and Ag exceeded Jilin Province soil background values and enriched obviously in soil samples; (2)using the UNMIX Model resolved four pollution sources: source 1 represents human activities of transportation, ore mining and garbage, and the source 1's contribution is 39. 1% ; Source 2 represents the contribution of the weathering of rocks and biological effects, and the source 2's contribution is 13. 87% ; Source 3 is a comprehensive source of soil parent material and chemical fertilizer, and the source 3's contribution is 23. 93% ; Source 4 represents iron ore mining and transportation sources, and the source 4's contribution is 22. 89%. (3)the UNMIX Model results are in accordance with the survey of local land-use types, human activities and Cd, Hg and Pb content distributions.

Imaging the distribution of photoswitchable probes with temporally-unmixed multispectral optoacoustic tomography

Science.gov (United States)

Deán-Ben, X. Luís.; Stiel, Andre C.; Jiang, Yuanyuan; Ntziachristos, Vasilis; Westmeyer, Gil G.; Razansky, Daniel

2016-03-01

Synthetic and genetically encoded chromo- and fluorophores have become indispensable tools for biomedical research enabling a myriad of applications in imaging modalities based on biomedical optics. The versatility offered by the optoacoustic (photoacoustic) contrast mechanism enables to detect signals from any substance absorbing light, and hence these probes can be used as optoacoustic contrast agents. While contrast versatility generally represents an advantage of optoacoustics, the strong background signal generated by light absorption in endogeneous chromophores hampers the optoacoustic capacity to detect a photo-absorbing agent of interest. Increasing the optoacoustic sensitivity is then determined by the capability to differentiate specific features of such agent. For example, multispectral optoacoustic tomography (MSOT) exploits illuminating the tissue at multiple optical wavelengths to spectrally resolve (unmix) the contribution of different chromophores. Herein, we present an alternative approach to enhance the sensitivity and specificity in the detection of optoacoustic contrast agents. This is achieved with photoswitchable probes that change optical absorption upon illumination with specific optical wavelengths. Thereby, temporally unmixed MSOT (tuMSOT) is based on photoswitching the compounds according to defined schedules to elicit specific time-varying optoacoustic signals, and then use temporal unmixing algorithms to locate the contrast agent based on their particular temporal profile. The photoswitching kinetics is further affected by light intensity, so that tuMSOT can be employed to estimate the light fluence distribution in a biological sample. The performance of the method is demonstrated herein with the reversibly switchable fluorescent protein Dronpa and its fast-switching fatigue resistant variant Dronpa-M159T.

A novel highly parallel algorithm for linearly unmixing hyperspectral images

Science.gov (United States)

Guerra, Raúl; López, Sebastián.; Callico, Gustavo M.; López, Jose F.; Sarmiento, Roberto

2014-10-01

Endmember extraction and abundances calculation represent critical steps within the process of linearly unmixing a given hyperspectral image because of two main reasons. The first one is due to the need of computing a set of accurate endmembers in order to further obtain confident abundance maps. The second one refers to the huge amount of operations involved in these time-consuming processes. This work proposes an algorithm to estimate the endmembers of a hyperspectral image under analysis and its abundances at the same time. The main advantage of this algorithm is its high parallelization degree and the mathematical simplicity of the operations implemented. This algorithm estimates the endmembers as virtual pixels. In particular, the proposed algorithm performs the descent gradient method to iteratively refine the endmembers and the abundances, reducing the mean square error, according with the linear unmixing model. Some mathematical restrictions must be added so the method converges in a unique and realistic solution. According with the algorithm nature, these restrictions can be easily implemented. The results obtained with synthetic images demonstrate the well behavior of the algorithm proposed. Moreover, the results obtained with the well-known Cuprite dataset also corroborate the benefits of our proposal.

Application of hierarchical Bayesian unmixing models in river sediment source apportionment

Science.gov (United States)

Blake, Will; Smith, Hugh; Navas, Ana; Bodé, Samuel; Goddard, Rupert; Zou Kuzyk, Zou; Lennard, Amy; Lobb, David; Owens, Phil; Palazon, Leticia; Petticrew, Ellen; Gaspar, Leticia; Stock, Brian; Boeckx, Pacsal; Semmens, Brice

2016-04-01

Fingerprinting and unmixing concepts are used widely across environmental disciplines for forensic evaluation of pollutant sources. In aquatic and marine systems, this includes tracking the source of organic and inorganic pollutants in water and linking problem sediment to soil erosion and land use sources. It is, however, the particular complexity of ecological systems that has driven creation of the most sophisticated mixing models, primarily to (i) evaluate diet composition in complex ecological food webs, (ii) inform population structure and (iii) explore animal movement. In the context of the new hierarchical Bayesian unmixing model, MIXSIAR, developed to characterise intra-population niche variation in ecological systems, we evaluate the linkage between ecological 'prey' and 'consumer' concepts and river basin sediment 'source' and sediment 'mixtures' to exemplify the value of ecological modelling tools to river basin science. Recent studies have outlined advantages presented by Bayesian unmixing approaches in handling complex source and mixture datasets while dealing appropriately with uncertainty in parameter probability distributions. MixSIAR is unique in that it allows individual fixed and random effects associated with mixture hierarchy, i.e. factors that might exert an influence on model outcome for mixture groups, to be explored within the source-receptor framework. This offers new and powerful ways of interpreting river basin apportionment data. In this contribution, key components of the model are evaluated in the context of common experimental designs for sediment fingerprinting studies namely simple, nested and distributed catchment sampling programmes. Illustrative examples using geochemical and compound specific stable isotope datasets are presented and used to discuss best practice with specific attention to (1) the tracer selection process, (2) incorporation of fixed effects relating to sample timeframe and sediment type in the modelling

Branched polynomial covering maps

DEFF Research Database (Denmark)

Hansen, Vagn Lundsgaard

1999-01-01

A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere....

Bayesian Nonnegative Matrix Factorization with Volume Prior for Unmixing of Hyperspectral Images

DEFF Research Database (Denmark)

Arngren, Morten; Schmidt, Mikkel Nørgaard; Larsen, Jan

2009-01-01

based unmixing algorithms are based on sparsity regularization encouraging pure spectral endmembers, but this is not optimal for certain applications, such as foods, where abundances are not sparse. The pixels will theoretically lie on a simplex and hence the endmembers can be estimated as the vertices...

On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations

Science.gov (United States)

Cima, A.; Gasull, A.; Mañosas, F.

2017-12-01

In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions. We show that the addressed problems can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then we approach to these equations either applying several tools developed to study extended Fermat problems for polynomial equations, or reducing the question to the computation of the genus of some associated planar algebraic curves.

On generalized Fibonacci and Lucas polynomials

Energy Technology Data Exchange (ETDEWEB)

Nalli, Ayse [Department of Mathematics, Faculty of Sciences, Selcuk University, 42075 Campus-Konya (Turkey)], E-mail: aysenalli@yahoo.com; Haukkanen, Pentti [Department of Mathematics, Statistics and Philosophy, 33014 University of Tampere (Finland)], E-mail: mapehau@uta.fi

2009-12-15

Let h(x) be a polynomial with real coefficients. We introduce h(x)-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these h(x)-Fibonacci polynomials. We also introduce h(x)-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q{sub h}(x) that generalizes the Q-matrix whose powers generate the Fibonacci numbers.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

Science.gov (United States)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Spatial unmixing for environmental impact monitoring of mining using UAS and WV-2

Science.gov (United States)

Delalieux, S.; Livens, S.; Goossens, M.; Reusen, I.; Tote, C.

2012-04-01

The three principal activities of the mineral resources mining industry - mining, mineral processing and metallurgical extraction - all produce waste. The environmental impact of these activities depends on many factors, in particular, the type of mining and the size of the operation. The effects of the mining (extraction) stage tend to be mainly local, associated with surface disturbance, the production of large amounts of solid waste material, and the spread of chemically reactive particulate matter to the atmosphere and hydrosphere. Many studies have shown the potential of remote sensing for environmental impact monitoring, e.g., [1]. However, its applicability has been limited due to the inherent spatial-spectral and temporal trade-off of most sensors. More recently, miniaturization of sensors makes it possible to capture color images from unmanned aerial systems (UAS) with a very high spatial resolution. In addition, the UAS can be deployed in a very flexible manner, allowing high temporal resolution imaging. More detailed spectral information is available from multispectral images, albeit at lower spatial resolution. Combining both types of images using image fusion can help to overcome the spatial-spectral trade-off and provide a new tool for more detailed monitoring of environmental impacts. Within the framework of the ImpactMin project, funded by the Framework Programme 7 of the European Commission, the objective of this study is to implement and apply the spatial unmixing algorithm, as proposed by [2], on images of the 'Vihovici Coal Mine' area, located in the Mostar Valley, Bosnia and Herzegovina. A WorldView2 (WV2) satellite image will be employed, which provides 8-band multispectral data at a spatial resolution of 2m. High spatial resolution images, obtained by a SmartPlanes UAS, will provide RGB data with 0.05m spatial resolution. The spatial unmixing technique is based on the idea that a linear mixing model can be used to perform the downscaling of

Better polynomials for GNFS

OpenAIRE

Bai , Shi; Bouvier , Cyril; Kruppa , Alexander; Zimmermann , Paul

2016-01-01

International audience; The general number field sieve (GNFS) is the most efficient algo-rithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial tha...

Nonnegativity of uncertain polynomials

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Šiljak Dragoslav D.

1998-01-01

Full Text Available The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

On Multiple Polynomials of Capelli Type

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S.Y. Antonov

2016-03-01

Full Text Available This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.

Chromatic polynomials for simplicial complexes

DEFF Research Database (Denmark)

Møller, Jesper Michael; Nord, Gesche

2016-01-01

In this note we consider s s -chromatic polynomials for finite simplicial complexes. When s=1 s=1 , the 1 1 -chromatic polynomial is just the usual graph chromatic polynomial of the 1 1 -skeleton. In general, the s s -chromatic polynomial depends on the s s -skeleton and its value at r...

Bivariate Kumaraswamy Models via Modified FGM Copulas: Properties and Applications

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Indranil Ghosh

2017-11-01

Full Text Available A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of FGM (Farlie–Gumbel–Morgenstern bivariate copula for constructing several different bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions by this method allows for greater flexibility in the values of Spearman’s correlation coefficient, ρ and Kendall’s τ .

An Affine Invariant Bivariate Version of the Sign Test.

Science.gov (United States)

1987-06-01

words: affine invariance, bivariate quantile, bivariate symmetry, model,. generalized median, influence function , permutation test, normal efficiency...calculate a bivariate version of the influence function , and the resulting form is bounded, as is the case for the univartate sign test, and shows the...terms of a blvariate analogue of IHmpel’s (1974) influence function . The latter, though usually defined as a von-Mises derivative of certain

Roots of the Chromatic Polynomial

DEFF Research Database (Denmark)

Perrett, Thomas

The chromatic polynomial of a graph G is a univariate polynomial whose evaluation at any positive integer q enumerates the proper q-colourings of G. It was introduced in connection with the famous four colour theorem but has recently found other applications in the field of statistical physics...... extend Thomassen’s technique to the Tutte polynomial and as a consequence, deduce a density result for roots of the Tutte polynomial. This partially answers a conjecture of Jackson and Sokal. Finally, we refocus our attention on the chromatic polynomial and investigate the density of chromatic roots...

General Reducibility and Solvability of Polynomial Equations ...

African Journals Online (AJOL)

General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...

Certain non-linear differential polynomials sharing a non zero polynomial

Directory of Open Access Journals (Sweden)

Majumder Sujoy

2015-10-01

functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008, 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011, 23-32.].

STUDI PERBANDINGAN ANTARA ALGORITMA BIVARIATE MARGINAL DISTRIBUTION DENGAN ALGORITMA GENETIKA

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Chastine Fatichah

2006-01-01

Full Text Available Bivariate Marginal Distribution Algorithm is extended from Estimation of Distribution Algorithm. This heuristic algorithm proposes the new approach for recombination of generate new individual that without crossover and mutation process such as genetic algorithm. Bivariate Marginal Distribution Algorithm uses connectivity variable the pair gene for recombination of generate new individual. Connectivity between variable is doing along optimization process. In this research, genetic algorithm performance with one point crossover is compared with Bivariate Marginal Distribution Algorithm performance in case Onemax, De Jong F2 function, and Traveling Salesman Problem. In this research, experimental results have shown performance the both algorithm is dependence of parameter respectively and also population size that used. For Onemax case with size small problem, Genetic Algorithm perform better with small number of iteration and more fast for get optimum result. However, Bivariate Marginal Distribution Algorithm perform better of result optimization for case Onemax with huge size problem. For De Jong F2 function, Genetic Algorithm perform better from Bivariate Marginal Distribution Algorithm of a number of iteration and time. For case Traveling Salesman Problem, Bivariate Marginal Distribution Algorithm have shown perform better from Genetic Algorithm of optimization result. Abstract in Bahasa Indonesia : Bivariate Marginal Distribution Algorithm merupakan perkembangan lebih lanjut dari Estimation of Distribution Algorithm. Algoritma heuristik ini mengenalkan pendekatan baru dalam melakukan rekombinasi untuk membentuk individu baru, yaitu tidak menggunakan proses crossover dan mutasi seperti pada Genetic Algorithm. Bivariate Marginal Distribution Algorithm menggunakan keterkaitan pasangan variabel dalam melakukan rekombinasi untuk membentuk individu baru. Keterkaitan antar variabel tersebut ditemukan selama proses optimasi berlangsung. Aplikasi yang

Arctic lead detection using a waveform unmixing algorithm from CryoSat-2 data

Science.gov (United States)

Lee, S.; Im, J.

2016-12-01

Arctic areas consist of ice floes, leads, and polynyas. While leads and polynyas account for small parts in the Arctic Ocean, they play a key role in exchanging heat flux, moisture, and momentum between the atmosphere and ocean in wintertime because of their huge temperature difference In this study, a linear waveform unmixing approach was proposed to detect lead fraction. CryoSat-2 waveforms for pure leads, sea ice, and ocean were used as end-members based on visual interpretation of MODIS images coincident with CryoSat-2 data. The unmixing model produced lead, sea ice, and ocean abundances and a threshold (> 0.7) was applied to make a binary classification between lead and sea ice. The unmixing model produced better results than the existing models in the literature, which are based on simple thresholding approaches. The results were also comparable with our previous research using machine learning based models (i.e., decision trees and random forest). A monthly lead fraction was calculated, dividing the number of detected leads by the total number of measurements. The lead fraction around Beaufort Sea and Fram strait was high due to the anti-cyclonic rotation of Beaufort Gyre and the outflows of sea ice to the Atlantic. The lead fraction maps produced in this study were matched well with monthly lead fraction maps in the literature. The areas with thin sea ice identified from our previous research correspond to the high lead fraction areas in the present study. Furthermore, sea ice roughness from ASCAT scatterometer was compared to a lead fraction map to see the relationship between surface roughness and lead distribution.

Polynomial Heisenberg algebras

International Nuclear Information System (INIS)

Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M

2004-01-01

Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively

Polynomial optimization : Error analysis and applications

NARCIS (Netherlands)

Sun, Zhao

2015-01-01

Polynomial optimization is the problem of minimizing a polynomial function subject to polynomial inequality constraints. In this thesis we investigate several hierarchies of relaxations for polynomial optimization problems. Our main interest lies in understanding their performance, in particular how

Encoding Strategy Changes and Spacing Effects in the Free Recall of Unmixed Lists

Science.gov (United States)

Delaney, P.F.; Knowles, M.E.

2005-01-01

Memory for repeated items often improves when repetitions are separated by other items-a phenomenon called the spacing effect. In two experiments, we explored the complex interaction between study strategies, serial position, and spacing effects. When people studied several unmixed lists, they initially used mainly rote rehearsal, but some people…

Comparison of Model Reliabilities from Single-Step and Bivariate Blending Methods

DEFF Research Database (Denmark)

Taskinen, Matti; Mäntysaari, Esa; Lidauer, Martin

2013-01-01

Model based reliabilities in genetic evaluation are compared between three methods: animal model BLUP, single-step BLUP, and bivariate blending after genomic BLUP. The original bivariate blending is revised in this work to better account animal models. The study data is extracted from...... be calculated. Model reliabilities by the single-step and the bivariate blending methods were higher than by animal model due to genomic information. Compared to the single-step method, the bivariate blending method reliability estimates were, in general, lower. Computationally bivariate blending method was......, on the other hand, lighter than the single-step method....

Birth-death processes and associated polynomials

NARCIS (Netherlands)

van Doorn, Erik A.

2003-01-01

We consider birth-death processes on the nonnegative integers and the corresponding sequences of orthogonal polynomials called birth-death polynomials. The sequence of associated polynomials linked with a sequence of birth-death polynomials and its orthogonalizing measure can be used in the analysis

Extended biorthogonal matrix polynomials

Directory of Open Access Journals (Sweden)

Ayman Shehata

2017-01-01

Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.

Bannai-Ito polynomials and dressing chains

OpenAIRE

Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei

2012-01-01

Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by quadratic algebras. The Bannai-Ito polynomials and their kernel polynomials -- the complementary Bannai-Ito polynomials -- are shown to arise in the framework of the SDG maps.

Multi-tissue partial volume quantification in multi-contrast MRI using an optimised spectral unmixing approach.

Science.gov (United States)

Collewet, Guylaine; Moussaoui, Saïd; Deligny, Cécile; Lucas, Tiphaine; Idier, Jérôme

2018-06-01

Multi-tissue partial volume estimation in MRI images is investigated with a viewpoint related to spectral unmixing as used in hyperspectral imaging. The main contribution of this paper is twofold. It firstly proposes a theoretical analysis of the statistical optimality conditions of the proportion estimation problem, which in the context of multi-contrast MRI data acquisition allows to appropriately set the imaging sequence parameters. Secondly, an efficient proportion quantification algorithm based on the minimisation of a penalised least-square criterion incorporating a regularity constraint on the spatial distribution of the proportions is proposed. Furthermore, the resulting developments are discussed using empirical simulations. The practical usefulness of the spectral unmixing approach for partial volume quantification in MRI is illustrated through an application to food analysis on the proving of a Danish pastry. Copyright © 2018 Elsevier Inc. All rights reserved.

Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation

International Nuclear Information System (INIS)

Demina, Maria V; Kudryashov, Nikolai A

2012-01-01

Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of any system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is also obtained that translating relative equilibria of point vortices with arbitrary circulations can be constructed using a generalization of the Tkachenko equation. Roots of any pair of polynomials solving the Tkachenko equation and the generalized Tkachenko equation are proved to give positions of point vortices in stationary and translating relative equilibria accordingly. These results are valid even if the polynomials in a pair have multiple or common roots. It is obtained that the Adler–Moser polynomial provides non-unique polynomial solutions of the Tkachenko equation. It is shown that the generalized Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers. (paper)

Covariate analysis of bivariate survival data

Energy Technology Data Exchange (ETDEWEB)

Bennett, L.E.

1992-01-01

The methods developed are used to analyze the effects of covariates on bivariate survival data when censoring and ties are present. The proposed method provides models for bivariate survival data that include differential covariate effects and censored observations. The proposed models are based on an extension of the univariate Buckley-James estimators which replace censored data points by their expected values, conditional on the censoring time and the covariates. For the bivariate situation, it is necessary to determine the expectation of the failure times for one component conditional on the failure or censoring time of the other component. Two different methods have been developed to estimate these expectations. In the semiparametric approach these expectations are determined from a modification of Burke's estimate of the bivariate empirical survival function. In the parametric approach censored data points are also replaced by their conditional expected values where the expected values are determined from a specified parametric distribution. The model estimation will be based on the revised data set, comprised of uncensored components and expected values for the censored components. The variance-covariance matrix for the estimated covariate parameters has also been derived for both the semiparametric and parametric methods. Data from the Demographic and Health Survey was analyzed by these methods. The two outcome variables are post-partum amenorrhea and breastfeeding; education and parity were used as the covariates. Both the covariate parameter estimates and the variance-covariance estimates for the semiparametric and parametric models will be compared. In addition, a multivariate test statistic was used in the semiparametric model to examine contrasts. The significance of the statistic was determined from a bootstrap distribution of the test statistic.

Reliability for some bivariate beta distributions

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Nadarajah Saralees

2005-01-01

Full Text Available In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R=Pr( Xbivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate beta. The calculations involve the use of special functions.

Reliability for some bivariate gamma distributions

Directory of Open Access Journals (Sweden)

Nadarajah Saralees

2005-01-01

Full Text Available In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R=Pr( Xbivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate gamma. The calculations involve the use of special functions.

Generalizations of orthogonal polynomials

Science.gov (United States)

Bultheel, A.; Cuyt, A.; van Assche, W.; van Barel, M.; Verdonk, B.

2005-07-01

We give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of these applications, which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, and random matrices.

Stochastic Estimation via Polynomial Chaos

Science.gov (United States)

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

A New Generalisation of Macdonald Polynomials

Science.gov (United States)

Garbali, Alexandr; de Gier, Jan; Wheeler, Michael

2017-06-01

We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters ( q, t) and polynomial in a further two parameters ( u, v). We evaluate these polynomials explicitly as a matrix product. At u = v = 0 they reduce to Macdonald polynomials, while at q = 0, u = v = s they recover a family of inhomogeneous symmetric functions originally introduced by Borodin.

Special polynomials associated with some hierarchies

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2008-01-01

Special polynomials associated with rational solutions of a hierarchy of equations of Painleve type are introduced. The hierarchy arises by similarity reduction from the Fordy-Gibbons hierarchy of partial differential equations. Some relations for these special polynomials are given. Differential-difference hierarchies for finding special polynomials are presented. These formulae allow us to obtain special polynomials associated with the hierarchy studied. It is shown that rational solutions of members of the Schwarz-Sawada-Kotera, the Schwarz-Kaup-Kupershmidt, the Fordy-Gibbons, the Sawada-Kotera and the Kaup-Kupershmidt hierarchies can be expressed through special polynomials of the hierarchy studied

A Summation Formula for Macdonald Polynomials

Science.gov (United States)

de Gier, Jan; Wheeler, Michael

2016-03-01

We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.

Ordinal bivariate inequality

DEFF Research Database (Denmark)

Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter Raahave

This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlationincreasing switches and/or median......-preserving spreads. For the canonical 2x2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique....

Terahertz spectral unmixing based method for identifying gastric cancer

Science.gov (United States)

Cao, Yuqi; Huang, Pingjie; Li, Xian; Ge, Weiting; Hou, Dibo; Zhang, Guangxin

2018-02-01

At present, many researchers are exploring biological tissue inspection using terahertz time-domain spectroscopy (THz-TDS) techniques. In this study, based on a modified hard modeling factor analysis method, terahertz spectral unmixing was applied to investigate the relationships between the absorption spectra in THz-TDS and certain biomarkers of gastric cancer in order to systematically identify gastric cancer. A probability distribution and box plot were used to extract the distinctive peaks that indicate carcinogenesis, and the corresponding weight distributions were used to discriminate the tissue types. The results of this work indicate that terahertz techniques have the potential to detect different levels of cancer, including benign tumors and polyps.

A comparison of STARFM and an unmixing-based algorithm for Landsat and MODIS data fusion

NARCIS (Netherlands)

Gevaert, C.M.; Garcia-Haro, F.J.

2015-01-01

The focus of the current study is to compare data fusion methods applied to sensors with medium- and high-spatial resolutions. Two documented methods are applied, the spatial and temporal adaptive reflectance fusion model (STARFM) and an unmixing-based method which proposes a Bayesian formulation to

Weierstrass polynomials for links

DEFF Research Database (Denmark)

Hansen, Vagn Lundsgaard

1997-01-01

There is a natural way of identifying links in3-space with polynomial covering spaces over thecircle. Thereby any link in 3-space can be definedby a Weierstrass polynomial over the circle. Theequivalence relation for covering spaces over thecircle is, however, completely different from...

On Symmetric Polynomials

OpenAIRE

Golden, Ryan; Cho, Ilwoo

2015-01-01

In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...

Associated polynomials and birth-death processes

NARCIS (Netherlands)

van Doorn, Erik A.

2001-01-01

We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to

The impact of initialization procedures on unsupervised unmixing of hyperspectral imagery using the constrained positive matrix factorization

Science.gov (United States)

Masalmah, Yahya M.; Vélez-Reyes, Miguel

2007-04-01

The authors proposed in previous papers the use of the constrained Positive Matrix Factorization (cPMF) to perform unsupervised unmixing of hyperspectral imagery. Two iterative algorithms were proposed to compute the cPMF based on the Gauss-Seidel and penalty approaches to solve optimization problems. Results presented in previous papers have shown the potential of the proposed method to perform unsupervised unmixing in HYPERION and AVIRIS imagery. The performance of iterative methods is highly dependent on the initialization scheme. Good initialization schemes can improve convergence speed, whether or not a global minimum is found, and whether or not spectra with physical relevance are retrieved as endmembers. In this paper, different initializations using random selection, longest norm pixels, and standard endmembers selection routines are studied and compared using simulated and real data.

UNMIX Methods Applied to Characterize Sources of Volatile Organic Compounds in Toronto, Ontario

Directory of Open Access Journals (Sweden)

Eugeniusz Porada

2016-06-01

Full Text Available UNMIX, a sensor modeling routine from the U.S. Environmental Protection Agency (EPA, was used to model volatile organic compound (VOC receptors in four urban sites in Toronto, Ontario. VOC ambient concentration data acquired in 2000–2009 for 175 VOC species in four air quality monitoring stations were analyzed. UNMIX, by performing multiple modeling attempts upon varying VOC menus—while rejecting the results that were not reliable—allowed for discriminating sources by their most consistent chemical characteristics. The method assessed occurrences of VOCs in sources typical of the urban environment (traffic, evaporative emissions of fuels, banks of fugitive inert gases, industrial point sources (plastic-, polymer-, and metalworking manufactures, and in secondary sources (releases from water, sediments, and contaminated urban soil. The remote sensing and robust modeling used here produces chemical profiles of putative VOC sources that, if combined with known environmental fates of VOCs, can be used to assign physical sources’ shares of VOCs emissions into the atmosphere. This in turn provides a means of assessing the impact of environmental policies on one hand, and industrial activities on the other hand, on VOC air pollution.

Ordinal Bivariate Inequality

DEFF Research Database (Denmark)

Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter Raahave

2016-01-01

This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlation-increasing switches and....../or median-preserving spreads. For the canonical 2 × 2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique....

Improving Land Use/Land Cover Classification by Integrating Pixel Unmixing and Decision Tree Methods

Directory of Open Access Journals (Sweden)

Chao Yang

2017-11-01

Full Text Available Decision tree classification is one of the most efficient methods for obtaining land use/land cover (LULC information from remotely sensed imageries. However, traditional decision tree classification methods cannot effectively eliminate the influence of mixed pixels. This study aimed to integrate pixel unmixing and decision tree to improve LULC classification by removing mixed pixel influence. The abundance and minimum noise fraction (MNF results that were obtained from mixed pixel decomposition were added to decision tree multi-features using a three-dimensional (3D Terrain model, which was created using an image fusion digital elevation model (DEM, to select training samples (ROIs, and improve ROI separability. A Landsat-8 OLI image of the Yunlong Reservoir Basin in Kunming was used to test this proposed method. Study results showed that the Kappa coefficient and the overall accuracy of integrated pixel unmixing and decision tree method increased by 0.093% and 10%, respectively, as compared with the original decision tree method. This proposed method could effectively eliminate the influence of mixed pixels and improve the accuracy in complex LULC classifications.

Scattering theory and orthogonal polynomials

International Nuclear Information System (INIS)

Geronimo, J.S.

1977-01-01

The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms

Bivariate copula in fitting rainfall data

Science.gov (United States)

Yee, Kong Ching; Suhaila, Jamaludin; Yusof, Fadhilah; Mean, Foo Hui

2014-07-01

The usage of copula to determine the joint distribution between two variables is widely used in various areas. The joint distribution of rainfall characteristic obtained using the copula model is more ideal than the standard bivariate modelling where copula is belief to have overcome some limitation. Six copula models will be applied to obtain the most suitable bivariate distribution between two rain gauge stations. The copula models are Ali-Mikhail-Haq (AMH), Clayton, Frank, Galambos, Gumbel-Hoogaurd (GH) and Plackett. The rainfall data used in the study is selected from rain gauge stations which are located in the southern part of Peninsular Malaysia, during the period from 1980 to 2011. The goodness-of-fit test in this study is based on the Akaike information criterion (AIC).

Fermionic formula for double Kostka polynomials

OpenAIRE

Liu, Shiyuan

2016-01-01

The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\\Bla,\\Bmu}(t),$ indexed by two double partitions $\\Bla,\\Bmu,$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{\\Bla,\\Bmu}(t)$ in the special case where $\\Bmu=(-,\\mu'').$ We formula...

Relations between Möbius and coboundary polynomials

NARCIS (Netherlands)

Jurrius, R.P.M.J.

2012-01-01

It is known that, in general, the coboundary polynomial and the Möbius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will investigate if it is possible that the Möbius polynomial of a matroid, together with the Möbius polynomial of

Matrix product formula for Macdonald polynomials

Science.gov (United States)

Cantini, Luigi; de Gier, Jan; Wheeler, Michael

2015-09-01

We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik-Zamolodchikov equations, which arise by considering representations of the Zamolodchikov-Faddeev and Yang-Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1.

Matrix product formula for Macdonald polynomials

International Nuclear Information System (INIS)

Cantini, Luigi; Gier, Jan de; Michael Wheeler

2015-01-01

We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik–Zamolodchikov equations, which arise by considering representations of the Zamolodchikov–Faddeev and Yang–Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1. (paper)

Arabic text classification using Polynomial Networks

Directory of Open Access Journals (Sweden)

Mayy M. Al-Tahrawi

2015-10-01

Full Text Available In this paper, an Arabic statistical learning-based text classification system has been developed using Polynomial Neural Networks. Polynomial Networks have been recently applied to English text classification, but they were never used for Arabic text classification. In this research, we investigate the performance of Polynomial Networks in classifying Arabic texts. Experiments are conducted on a widely used Arabic dataset in text classification: Al-Jazeera News dataset. We chose this dataset to enable direct comparisons of the performance of Polynomial Networks classifier versus other well-known classifiers on this dataset in the literature of Arabic text classification. Results of experiments show that Polynomial Networks classifier is a competitive algorithm to the state-of-the-art ones in the field of Arabic text classification.

Bivariable analysis of ventricular late potentials in high resolution ECG records

International Nuclear Information System (INIS)

Orosco, L; Laciar, E

2007-01-01

In this study the bivariable analysis for ventricular late potentials detection in high-resolution electrocardiographic records is proposed. The standard time-domain analysis and the application of the time-frequency technique to high-resolution ECG records are briefly described as well as their corresponding results. In the proposed technique the time-domain parameter, QRSD and the most significant time-frequency index, EN QRS are used like variables. A bivariable index is defined, that combines the previous parameters. The propose technique allows evaluating the risk of ventricular tachycardia in post-myocardial infarct patients. The results show that the used bivariable index allows discriminating between the patient's population with ventricular tachycardia and the subjects of the control group. Also, it was found that the bivariable technique obtains a good valuation as diagnostic test. It is concluded that comparatively, the valuation of the bivariable technique as diagnostic test is superior to that of the time-domain method and the time-frequency technique evaluated individually

(LMRG): Microscope Resolution, Objective Quality, Spectral Accuracy and Spectral Un-mixing

Science.gov (United States)

Bayles, Carol J.; Cole, Richard W.; Eason, Brady; Girard, Anne-Marie; Jinadasa, Tushare; Martin, Karen; McNamara, George; Opansky, Cynthia; Schulz, Katherine; Thibault, Marc; Brown, Claire M.

2012-01-01

The second study by the LMRG focuses on measuring confocal laser scanning microscope (CLSM) resolution, objective lens quality, spectral imaging accuracy and spectral un-mixing. Affordable test samples for each aspect of the study were designed, prepared and sent to 116 labs from 23 countries across the globe. Detailed protocols were designed for the three tests and customized for most of the major confocal instruments being used by the study participants. One protocol developed for measuring resolution and objective quality was recently published in Nature Protocols (Cole, R. W., T. Jinadasa, et al. (2011). Nature Protocols 6(12): 1929–1941). The first study involved 3D imaging of sub-resolution fluorescent microspheres to determine the microscope point spread function. Results of the resolution studies as well as point spread function quality (i.e. objective lens quality) from 140 different objective lenses will be presented. The second study of spectral accuracy looked at the reflection of the laser excitation lines into the spectral detection in order to determine the accuracy of these systems to report back the accurate laser emission wavelengths. Results will be presented from 42 different spectral confocal systems. Finally, samples with double orange beads (orange core and orange coating) were imaged spectrally and the imaging software was used to un-mix fluorescence signals from the two orange dyes. Results from 26 different confocal systems will be summarized. Time will be left to discuss possibilities for the next LMRG study.

Many-body orthogonal polynomial systems

International Nuclear Information System (INIS)

Witte, N.S.

1997-03-01

The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)

Top local cohomology and the catenary of the unmixed part of support of a finitely generated module

International Nuclear Information System (INIS)

Nguyen Tu Cuong; Nguyen Thi Dung; Le Thanh Nhan

2005-09-01

Let (R,m) be a Noetherian local ring and M a finitely generated R-module with dim M = d. This paper is concerned with the following property for the top local cohomology H m d (M): Ann R (0: H m d (M) p) = p for all prime ideals p is a subset of Ann R H m d ( M). It is shown that this property is equivalent to the catenary of the unmixed part Supp M/U M (0) of the support of M, where U M (0) is the largest submodule of M of dimension less than d. Some characterizations of this property in terms of systems of parameters and relations between the unmixed parts of Supp M and Supp M-circumflex are given. A connection to the so-called co-localization is discussed. (author)

Vertex models, TASEP and Grothendieck polynomials

International Nuclear Information System (INIS)

Motegi, Kohei; Sakai, Kazumitsu

2013-01-01

We examine the wavefunctions and their scalar products of a one-parameter family of integrable five-vertex models. At a special point of the parameter, the model investigated is related to an irreversible interacting stochastic particle system—the so-called totally asymmetric simple exclusion process (TASEP). By combining the quantum inverse scattering method with a matrix product representation of the wavefunctions, the on-/off-shell wavefunctions of the five-vertex models are represented as a certain determinant form. Up to some normalization factors, we find that the wavefunctions are given by Grothendieck polynomials, which are a one-parameter deformation of Schur polynomials. Introducing a dual version of the Grothendieck polynomials, and utilizing the determinant representation for the scalar products of the wavefunctions, we derive a generalized Cauchy identity satisfied by the Grothendieck polynomials and their duals. Several representation theoretical formulae for the Grothendieck polynomials are also presented. As a byproduct, the relaxation dynamics such as Green functions for the periodic TASEP are found to be described in terms of the Grothendieck polynomials. (paper)

On the Laurent polynomial rings

International Nuclear Information System (INIS)

Stefanescu, D.

1985-02-01

We describe some properties of the Laurent polynomial rings in a finite number of indeterminates over a commutative unitary ring. We study some subrings of the Laurent polynomial rings. We finally obtain two cancellation properties. (author)

Building Bivariate Tables: The compareGroups Package for R

Directory of Open Access Journals (Sweden)

Isaac Subirana

2014-05-01

Full Text Available The R package compareGroups provides functions meant to facilitate the construction of bivariate tables (descriptives of several variables for comparison between groups and generates reports in several formats (LATEX, HTML or plain text CSV. Moreover, bivariate tables can be viewed directly on the R console in a nice format. A graphical user interface (GUI has been implemented to build the bivariate tables more easily for those users who are not familiar with the R software. Some new functions and methods have been incorporated in the newest version of the compareGroups package (version 1.x to deal with time-to-event variables, stratifying tables, merging several tables, and revising the statistical methods used. The GUI interface also has been improved, making it much easier and more intuitive to set the inputs for building the bivariate tables. The ?rst version (version 0.x and this version were presented at the 2010 useR! conference (Sanz, Subirana, and Vila 2010 and the 2011 useR! conference (Sanz, Subirana, and Vila 2011, respectively. Package compareGroups is available from the Comprehensive R Archive Network at http://CRAN.R-project.org/package=compareGroups.

The relative performance of bivariate causality tests in small samples

NARCIS (Netherlands)

Bult, J..R.; Leeflang, P.S.H.; Wittink, D.R.

1997-01-01

Causality tests have been applied to establish directional effects and to reduce the set of potential predictors, For the latter type of application only bivariate tests can be used, In this study we compare bivariate causality tests. Although the problem addressed is general and could benefit

Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

KAUST Repository

Ait-Haddou, Rachid

2015-06-07

We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.

Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

KAUST Repository

Ait-Haddou, Rachid; Goldman, Ron

2015-01-01

We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.

Computing the Alexander Polynomial Numerically

DEFF Research Database (Denmark)

Hansen, Mikael Sonne

2006-01-01

Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically.......Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically....

Direct comparison of Fe-Cr unmixing characterization by atom probe tomography and small angle scattering

Energy Technology Data Exchange (ETDEWEB)

Couturier, Laurent, E-mail: laurent.couturier55@hotmail.fr [Univ. Grenoble Alpes, SIMAP, F-38000 Grenoble (France); CNRS, SIMAP, F-38000 Grenoble (France); Department of Materials Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4 (Canada); De Geuser, Frédéric; Deschamps, Alexis [Univ. Grenoble Alpes, SIMAP, F-38000 Grenoble (France); CNRS, SIMAP, F-38000 Grenoble (France)

2016-11-15

The fine microstructure obtained by unmixing of a solid solution either by classical precipitation or spinodal decomposition is often characterized either by small angle scattering or atom probe tomography. This article shows that a common data analysis framework can be used to analyze data obtained from these two techniques. An example of the application of this common analysis is given for characterization of the unmixing of the Fe-Cr matrix of a 15-5 PH stainless steel during long-term ageing at 350 °C and 400 °C. A direct comparison of the Cr composition fluctuations amplitudes and characteristic lengths obtained with both techniques is made showing a quantitative agreement for the fluctuation amplitudes. The origin of the discrepancy remaining for the characteristic lengths is discussed. - Highlights: •Common analysis framework for atom probe tomography and small angle scattering •Comparison of same microstructural characteristics obtained using both techniques •Good correlation of Cr composition fluctuations amplitudes from both techniques •Good correlation of Cr composition fluctuations amplitudes with classic V parameter.

Density of Real Zeros of the Tutte Polynomial

DEFF Research Database (Denmark)

Ok, Seongmin; Perrett, Thomas

2018-01-01

The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...

Density of Real Zeros of the Tutte Polynomial

DEFF Research Database (Denmark)

Ok, Seongmin; Perrett, Thomas

2017-01-01

The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...

Parallel Construction of Irreducible Polynomials

DEFF Research Database (Denmark)

Frandsen, Gudmund Skovbjerg

Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....

Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

Science.gov (United States)

Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

2011-01-01

Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

Optimization over polynomials : Selected topics

NARCIS (Netherlands)

Laurent, M.; Jang, Sun Young; Kim, Young Rock; Lee, Dae-Woong; Yie, Ikkwon

2014-01-01

Minimizing a polynomial function over a region defined by polynomial inequalities models broad classes of hard problems from combinatorics, geometry and optimization. New algorithmic approaches have emerged recently for computing the global minimum, by combining tools from real algebra (sums of

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

International Nuclear Information System (INIS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-01-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

Science.gov (United States)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Efficient computation of Laguerre polynomials

NARCIS (Netherlands)

A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

2017-01-01

textabstractAn efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials . Ln(α)(z) are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for . n large and . α small, are used

Orthogonal polynomials in transport theories

International Nuclear Information System (INIS)

Dehesa, J.S.

1981-01-01

The asymptotical (k→infinity) behaviour of zeros of the polynomials gsub(k)sup((m)(ν)) encountered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude antiwsub(k) of the kth Legendre polynomial needed in the expansion of the scattering function. The parameters antiwsub(k) describe the anisotropy of scattering of the medium considered. In particular, it is shown that the asymptotical density of zeros of the polynomials gsub(k)sup(m)(ν) is an inverted semicircle for the anisotropic non-multiplying scattering medium

Chromatic polynomials of random graphs

International Nuclear Information System (INIS)

Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian

2010-01-01

Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

New polynomial-based molecular descriptors with low degeneracy.

Directory of Open Access Journals (Sweden)

Matthias Dehmer

Full Text Available In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power.

Need for higher order polynomial basis for polynomial nodal methods employed in LWR calculations

International Nuclear Information System (INIS)

Taiwo, T.A.; Palmiotti, G.

1997-01-01

The paper evaluates the accuracy and efficiency of sixth order polynomial solutions and the use of one radial node per core assembly for pressurized water reactor (PWR) core power distributions and reactivities. The computer code VARIANT was modified to calculate sixth order polynomial solutions for a hot zero power benchmark problem in which a control assembly along a core axis is assumed to be out of the core. Results are presented for the VARIANT, DIF3D-NODAL, and DIF3D-finite difference codes. The VARIANT results indicate that second order expansion of the within-node source and linear representation of the node surface currents are adequate for this problem. The results also demonstrate the improvement in the VARIANT solution when the order of the polynomial expansion of the within-node flux is increased from fourth to sixth order. There is a substantial saving in computational time for using one radial node per assembly with the sixth order expansion compared to using four or more nodes per assembly and fourth order polynomial solutions. 11 refs., 1 tab

Sheffer and Non-Sheffer Polynomial Families

Directory of Open Access Journals (Sweden)

G. Dattoli

2012-01-01

Full Text Available By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.

Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

Directory of Open Access Journals (Sweden)

Oksana Bihun

2018-01-01

Full Text Available Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x=qν(xpν(x, where A is a linear differential operator and each qν(x is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.

On the Connection Coefficients of the Chebyshev-Boubaker Polynomials

Directory of Open Access Journals (Sweden)

Paul Barry

2013-01-01

Full Text Available The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.

Non-invasive monitoring of cytokine-based regenerative treatment of cartilage by hyperspectral unmixing (Conference Presentation)

Science.gov (United States)

Mahbub, Saabah B.; Succer, Peter; Gosnell, Martin E.; Anwaer, Ayad G.; Herbert, Benjamin; Vesey, Graham; Goldys, Ewa M.

2016-03-01

Extracting biochemical information from tissue autofluorescence is a promising approach to non-invasively monitor disease treatments at a cellular level, without using any external biomarkers. Our recently developed unsupervised hyperspectral unmixing by Dependent Component Analysis (DECA) provides robust and detailed metabolic information with proper account of intrinsic cellular heterogeneity. Moreover this method is compatible with established methods of fluorescent biomarker labelling. Recently adipose-derived stem cell (ADSC) - based therapies have been introduced for treating different diseases in animals and humans. ADSC have been shown promise in regenerative treatments for osteoarthritis and other bone and joint disorders. One of the mechanism of their action is their anti-inflammatory effects within osteoarthritic joints which aid the regeneration of cartilage. These therapeutic effects are known to be driven by secretions of different cytokines from the ADSCs. We have been using the hyperspectral unmixing techniques to study in-vitro the effects of ADSC-derived cytokine-rich secretions with the cartilage chip in both human and bovine samples. The study of metabolic effects of different cytokine treatment on different cartilage layers makes it possible to compare the merits of those treatments for repairing cartilage.

Polynomial sequences generated by infinite Hessenberg matrices

Directory of Open Access Journals (Sweden)

Verde-Star Luis

2017-01-01

Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

Special polynomials associated with rational solutions of some hierarchies

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2009-01-01

New special polynomials associated with rational solutions of the Painleve hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials associated with the hierarchies. It is shown that rational solutions of the Caudrey-Dodd-Gibbon, the Kaup-Kupershmidt and the modified hierarchy for these ones can be obtained using new special polynomials.

Cosmographic analysis with Chebyshev polynomials

Science.gov (United States)

Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

2018-05-01

The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

Multilevel weighted least squares polynomial approximation

KAUST Repository

Haji-Ali, Abdul-Lateef

2017-06-30

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

Relations between zeros of special polynomials associated with the Painleve equations

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding relations of roots of polynomials is presented. Our approach allows us to get a number of relations between the zeros of the classical polynomials as well as the roots of special polynomials associated with rational solutions of the Painleve equations. We apply the method to obtain the relations for the zeros of several polynomials. These are: the Hermite polynomials, the Laguerre polynomials, the Yablonskii-Vorob'ev polynomials, the generalized Okamoto polynomials, and the generalized Hermite polynomials. All the relations found can be considered as analogues of generalized Stieltjes relations

On polynomial solutions of the Heun equation

International Nuclear Information System (INIS)

Gurappa, N; Panigrahi, Prasanta K

2004-01-01

By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)

A new Arnoldi approach for polynomial eigenproblems

Energy Technology Data Exchange (ETDEWEB)

Raeven, F.A.

1996-12-31

In this paper we introduce a new generalization of the method of Arnoldi for matrix polynomials. The new approach is compared with the approach of rewriting the polynomial problem into a linear eigenproblem and applying the standard method of Arnoldi to the linearised problem. The algorithm that can be applied directly to the polynomial eigenproblem turns out to be more efficient, both in storage and in computation.

Orthogonal Polynomials and Special Functions

CERN Document Server

Assche, Walter

2003-01-01

The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.

Unmixing demonstration with a twist: A photochromic Taylor-Couette device

Science.gov (United States)

Fonda, Enrico; Sreenivasan, Katepalli R.

2017-10-01

10.1119/1.4996901.1 This article describes an updated version of the famous Taylor-Couette flow reversibility demonstration. The viscous fluid confined between two concentric cylinders is forced to move by the rotating inner cylinder and visualized through the transparent outer cylinder. After a few rotations, a colored blob of fluid appears well mixed. Yet, after reversing the motion for the same number of turns, the blob reappears in the original location as if the fluid has just been unmixed. The use of household supplies makes the device inexpensive and easy to build without specific technical skills. The device can be used for demonstrations in fluid dynamics courses and outreach activities to discuss the concepts of viscosity, creeping flows, the absence of inertia, and time-reversibility.

Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

International Nuclear Information System (INIS)

Ndayiragije, F; Van Assche, W

2013-01-01

Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind. (paper)

Colouring and knot polynomials

International Nuclear Information System (INIS)

Welsh, D.J.A.

1991-01-01

These lectures will attempt to explain a connection between the recent advances in knot theory using the Jones and related knot polynomials with classical problems in combinatorics and statistical mechanics. The difficulty of some of these problems will be analysed in the context of their computational complexity. In particular we shall discuss colourings and groups valued flows in graphs, knots and the Jones and Kauffman polynomials, the Ising, Potts and percolation problems of statistical physics, computational complexity of the above problems. (author). 20 refs, 9 figs

Uniqueness and zeros of q-shift difference polynomials

Indian Academy of Sciences (India)

In this paper, we consider the zero distributions of -shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical Hayman results on the zeros of differential polynomials to -shift difference polynomials. We also investigate the uniqueness problem of -shift ...

Factoring polynomials over arbitrary finite fields

NARCIS (Netherlands)

Lange, T.; Winterhof, A.

2000-01-01

We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of

Additive and polynomial representations

CERN Document Server

Krantz, David H; Suppes, Patrick

1971-01-01

Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz

A generalized right truncated bivariate Poisson regression model with applications to health data.

Science.gov (United States)

Islam, M Ataharul; Chowdhury, Rafiqul I

2017-01-01

A generalized right truncated bivariate Poisson regression model is proposed in this paper. Estimation and tests for goodness of fit and over or under dispersion are illustrated for both untruncated and right truncated bivariate Poisson regression models using marginal-conditional approach. Estimation and test procedures are illustrated for bivariate Poisson regression models with applications to Health and Retirement Study data on number of health conditions and the number of health care services utilized. The proposed test statistics are easy to compute and it is evident from the results that the models fit the data very well. A comparison between the right truncated and untruncated bivariate Poisson regression models using the test for nonnested models clearly shows that the truncated model performs significantly better than the untruncated model.

PAN-SHARPENING APPROACHES BASED ON UNMIXING OF MULTISPECTRAL REMOTE SENSING IMAGERY

Directory of Open Access Journals (Sweden)

G. Palubinskas

2016-06-01

Full Text Available Model based analysis or explicit definition/listing of all models/assumptions used in the derivation of a pan-sharpening method allows us to understand the rationale or properties of existing methods and shows a way for a proper usage or proposal/selection of new methods ‘better’ satisfying the needs of a particular application. Most existing pan-sharpening methods are based mainly on the two models/assumptions: spectral consistency for high resolution multispectral data (physical relationship between multispectral and panchromatic data in a high resolution scale and spatial consistency for multispectral data (so-called Wald’s protocol first property or relationship between multispectral data in different resolution scales. Two methods, one based on a linear unmixing model and another one based on spatial unmixing, are described/proposed/modified which respect models assumed and thus can produce correct or physically justified fusion results. Earlier mentioned property ‘better’ should be measurable quantitatively, e.g. by means of so-called quality measures. The difficulty of a quality assessment task in multi-resolution image fusion or pan-sharpening is that a reference image is missing. Existing measures or so-called protocols are still not satisfactory because quite often the rationale or assumptions used are not valid or not fulfilled. From a model based view it follows naturally that a quality assessment measure can be defined as a combination of error model residuals using common or general models assumed in all fusion methods. Thus in this paper a comparison of the two earlier proposed/modified pan-sharpening methods is performed. Preliminary experiments based on visual analysis are carried out in the urban area of Munich city for optical remote sensing multispectral data and panchromatic imagery of the WorldView-2 satellite sensor.

A Determinant Expression for the Generalized Bessel Polynomials

Directory of Open Access Journals (Sweden)

Sheng-liang Yang

2013-01-01

Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

A generalization of the Bernoulli polynomials

Directory of Open Access Journals (Sweden)

Pierpaolo Natalini

2003-01-01

Full Text Available A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the factorization method introduced by Infeld and Hull (1951.

Information-theoretic lengths of Jacobi polynomials

Energy Technology Data Exchange (ETDEWEB)

Guerrero, A; Dehesa, J S [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, Granada (Spain); Sanchez-Moreno, P, E-mail: agmartinez@ugr.e, E-mail: pablos@ugr.e, E-mail: dehesa@ugr.e [Instituto ' Carlos I' de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain)

2010-07-30

The information-theoretic lengths of the Jacobi polynomials P{sup ({alpha}, {beta})}{sub n}(x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are investigated. They quantify the spreading of the polynomials along the orthogonality interval [- 1, 1] in a complementary but different way as the root-mean-square or standard deviation because, contrary to this measure, they do not refer to any specific point of the interval. The explicit expressions of the Fisher length are given. The Renyi lengths are found by the use of the combinatorial multivariable Bell polynomials in terms of the polynomial degree n and the parameters ({alpha}, {beta}). The Shannon length, which cannot be exactly calculated because of its logarithmic functional form, is bounded from below by using sharp upper bounds to general densities on [- 1, +1] given in terms of various expectation values; moreover, its asymptotics is also pointed out. Finally, several computational issues relative to these three quantities are carefully analyzed.

Transversals of Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

Dias, Kealey

Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...

On Multiple Interpolation Functions of the -Genocchi Polynomials

Directory of Open Access Journals (Sweden)

Jin Jeong-Hee

2010-01-01

Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.

Polynomial regression analysis and significance test of the regression function

International Nuclear Information System (INIS)

Gao Zhengming; Zhao Juan; He Shengping

2012-01-01

In order to analyze the decay heating power of a certain radioactive isotope per kilogram with polynomial regression method, the paper firstly demonstrated the broad usage of polynomial function and deduced its parameters with ordinary least squares estimate. Then significance test method of polynomial regression function is derived considering the similarity between the polynomial regression model and the multivariable linear regression model. Finally, polynomial regression analysis and significance test of the polynomial function are done to the decay heating power of the iso tope per kilogram in accord with the authors' real work. (authors)

The modified Gauss diagonalization of polynomial matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-10-01

The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

Science.gov (United States)

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Numerical Simulation of Polynomial-Speed Convergence Phenomenon

Science.gov (United States)

Li, Yao; Xu, Hui

2017-11-01

We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on the coupling technique and renewal theory. We propose to replace some estimates in classical results about the ergodicity of Markov processes by numerical simulations when the corresponding analytical proof is difficult. After that, all remaining conclusions can be derived from rigorous analysis. Then we apply our results to seek numerical justification for the ergodicity of two 1D microscopic heat conduction models. The mixing rate of these two models are expected to be polynomial but very difficult to prove. In both examples, our numerical results match the expected polynomial mixing rate well.

Exceptional polynomials and SUSY quantum mechanics

Indian Academy of Sciences (India)

Abstract. We show that for the quantum mechanical problem which admit classical Laguerre/. Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional. Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the ...

A companion matrix for 2-D polynomials

International Nuclear Information System (INIS)

Boudellioua, M.S.

1995-08-01

In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

Global sensitivity analysis by polynomial dimensional decomposition

Energy Technology Data Exchange (ETDEWEB)

Rahman, Sharif, E-mail: rahman@engineering.uiowa.ed [College of Engineering, The University of Iowa, Iowa City, IA 52242 (United States)

2011-07-15

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.

Polynomial asymptotic stability of damped stochastic differential equations

Directory of Open Access Journals (Sweden)

John Appleby

2004-08-01

Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

International Nuclear Information System (INIS)

Konakli, Katerina; Sudret, Bruno

2016-01-01

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

Energy Technology Data Exchange (ETDEWEB)

Konakli, Katerina, E-mail: konakli@ibk.baug.ethz.ch; Sudret, Bruno

2016-09-15

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input

A comparison of bivariate and univariate QTL mapping in livestock populations

Directory of Open Access Journals (Sweden)

Sorensen Daniel

2003-11-01

Full Text Available Abstract This study presents a multivariate, variance component-based QTL mapping model implemented via restricted maximum likelihood (REML. The method was applied to investigate bivariate and univariate QTL mapping analyses, using simulated data. Specifically, we report results on the statistical power to detect a QTL and on the precision of parameter estimates using univariate and bivariate approaches. The model and methodology were also applied to study the effectiveness of partitioning the overall genetic correlation between two traits into a component due to many genes of small effect, and one due to the QTL. It is shown that when the QTL has a pleiotropic effect on two traits, a bivariate analysis leads to a higher statistical power of detecting the QTL and to a more precise estimate of the QTL's map position, in particular in the case when the QTL has a small effect on the trait. The increase in power is most marked in cases where the contributions of the QTL and of the polygenic components to the genetic correlation have opposite signs. The bivariate REML analysis can successfully partition the two components contributing to the genetic correlation between traits.

Degenerate r-Stirling Numbers and r-Bell Polynomials

Science.gov (United States)

Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.

2018-01-01

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

Commutators with idempotent values on multilinear polynomials in ...

Indian Academy of Sciences (India)

Multilinear polynomial; derivations; generalized polynomial identity; prime ring; right ideal. Abstract. Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R , f ( x 1 , … , x n ) a multilinear polynomial over C , ϱ a nonzero right ideal of R and m > 1 a fixed integer such that.

Polynomial weights and code constructions

DEFF Research Database (Denmark)

Massey, J; Costello, D; Justesen, Jørn

1973-01-01

polynomial included. This fundamental property is then used as the key to a variety of code constructions including 1) a simplified derivation of the binary Reed-Muller codes and, for any primepgreater than 2, a new extensive class ofp-ary "Reed-Muller codes," 2) a new class of "repeated-root" cyclic codes...... of long constraint length binary convolutional codes derived from2^r-ary Reed-Solomon codes, and 6) a new class ofq-ary "repeated-root" constacyclic codes with an algebraic decoding algorithm.......For any nonzero elementcof a general finite fieldGF(q), it is shown that the polynomials(x - c)^i, i = 0,1,2,cdots, have the "weight-retaining" property that any linear combination of these polynomials with coefficients inGF(q)has Hamming weight at least as great as that of the minimum degree...

The generalized Yablonskii-Vorob'ev polynomials and their properties

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2008-01-01

Rational solutions of the generalized second Painleve hierarchy are classified. Representation of the rational solutions in terms of special polynomials, the generalized Yablonskii-Vorob'ev polynomials, is introduced. Differential-difference relations satisfied by the polynomials are found. Hierarchies of differential equations related to the generalized second Painleve hierarchy are derived. One of these hierarchies is a sequence of differential equations satisfied by the generalized Yablonskii-Vorob'ev polynomials

2-variable Laguerre matrix polynomials and Lie-algebraic techniques

International Nuclear Information System (INIS)

Khan, Subuhi; Hassan, Nader Ali Makboul

2010-01-01

The authors introduce 2-variable forms of Laguerre and modified Laguerre matrix polynomials and derive their special properties. Further, the representations of the special linear Lie algebra sl(2) and the harmonic oscillator Lie algebra G(0,1) are used to derive certain results involving these polynomials. Furthermore, the generating relations for the ordinary as well as matrix polynomials related to these matrix polynomials are derived as applications.

Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

DEFF Research Database (Denmark)

Sørensen, Dan Erik Krarup

1996-01-01

We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

Orthogonal polynomials derived from the tridiagonal representation approach

Science.gov (United States)

Alhaidari, A. D.

2018-01-01

The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose properties give the structure and dynamics of the corresponding physical system. For a certain range of parameters, one of these polynomials has a mix of continuous and discrete spectra making it suitable for describing physical systems with both scattering and bound states. In this work, we define these polynomials by their recursion relations and highlight some of their properties using numerical means. Due to the prime significance of these polynomials in physics, we hope that our short expose will encourage experts in the field of orthogonal polynomials to study them and derive their properties (weight functions, generating functions, asymptotics, orthogonality relations, zeros, etc.) analytically.

A note on some identities of derangement polynomials.

Science.gov (United States)

Kim, Taekyun; Kim, Dae San; Jang, Gwan-Woo; Kwon, Jongkyum

2018-01-01

The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255-258, 1978, Clarke and Sved in Math. Mag. 66(5):299-303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1-11 2018. A derangement is a permutation that has no fixed points, and the derangement number [Formula: see text] is the number of fixed-point-free permutations on an n element set. In this paper, we study the derangement polynomials and investigate some interesting properties which are related to derangement numbers. Also, we study two generalizations of derangement polynomials, namely higher-order and r -derangement polynomials, and show some relations between them. In addition, we express several special polynomials in terms of the higher-order derangement polynomials by using umbral calculus.

Topological quantum information, virtual Jones polynomials and Khovanov homology

International Nuclear Information System (INIS)

Kauffman, Louis H

2011-01-01

In this paper, we give a quantum statistical interpretation of the bracket polynomial state sum 〈K〉, the Jones polynomial V K (t) and virtual knot theory versions of the Jones polynomial, including the arrow polynomial. We use these quantum mechanical interpretations to give new quantum algorithms for these Jones polynomials. In those cases where the Khovanov homology is defined, the Hilbert space C(K) of our model is isomorphic with the chain complex for Khovanov homology with coefficients in the complex numbers. There is a natural unitary transformation U:C(K) → C(K) such that 〈K〉 = Trace(U), where 〈K〉 denotes the evaluation of the state sum model for the corresponding polynomial. We show that for the Khovanov boundary operator ∂:C(K) → C(K), we have the relationship ∂U + U∂ = 0. Consequently, the operator U acts on the Khovanov homology, and we obtain a direct relationship between the Khovanov homology and this quantum algorithm for the Jones polynomial. (paper)

Polynomial solutions of the Monge-Ampère equation

Energy Technology Data Exchange (ETDEWEB)

Aminov, Yu A [B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar' kov (Ukraine)

2014-11-30

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.

Comparison between two bivariate Poisson distributions through the ...

African Journals Online (AJOL)

These two models express themselves by their probability mass function. ... To remedy this problem, Berkhout and Plug proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive.

Bivariate value-at-risk

Directory of Open Access Journals (Sweden)

Giuseppe Arbia

2007-10-01

Full Text Available In this paper we extend the concept of Value-at-risk (VaR to bivariate return distributions in order to obtain measures of the market risk of an asset taking into account additional features linked to downside risk exposure. We first present a general definition of risk as the probability of an adverse event over a random distribution and we then introduce a measure of market risk (b-VaR that admits the traditional b of an asset in portfolio management as a special case when asset returns are normally distributed. Empirical evidences are provided by using Italian stock market data.

Zeros and uniqueness of Q-difference polynomials of meromorphic ...

Indian Academy of Sciences (India)

Meromorphic functions; Nevanlinna theory; logarithmic order; uniqueness problem; difference-differential polynomial. Abstract. In this paper, we investigate the value distribution of -difference polynomials of meromorphic function of finite logarithmic order, and study the zero distribution of difference-differential polynomials ...

Laguerre polynomials by a harmonic oscillator

Science.gov (United States)

Baykal, Melek; Baykal, Ahmet

2014-09-01

The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Directory of Open Access Journals (Sweden)

Chi Zhang

2015-05-01

Full Text Available To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP distributions by incorporating a multiplicative factor (or dependency parameter λ, named as Type I and Type II bivariate ZIGP distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over- or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.

Julia Sets of Orthogonal Polynomials

DEFF Research Database (Denmark)

Christiansen, Jacob Stordal; Henriksen, Christian; Petersen, Henrik Laurberg

2018-01-01

For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials fPng to properties of the support. More precisely we relate the Julia set of Pn to the outer boundary of the support, the lled Julia...... set to the polynomial convex hull K of the support, and the Green's function associated with Pn to the Green's function for the complement of K....

An introduction to orthogonal polynomials

CERN Document Server

Chihara, Theodore S

1978-01-01

Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some

Imaging characteristics of Zernike and annular polynomial aberrations.

Science.gov (United States)

Mahajan, Virendra N; Díaz, José Antonio

2013-04-01

The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

Simultaneous measurement of quantum yield ratio and absorption ratio between acceptor and donor by linearly unmixing excitation-emission spectra.

Science.gov (United States)

Zhang, C; Lin, F; DU, M; Qu, W; Mai, Z; Qu, J; Chen, T

2018-02-13

Quantum yield ratio (Q A /Q D ) and absorption ratio (K A /K D ) in all excitation wavelengths used between acceptor and donor are indispensable to quantitative fluorescence resonance energy transfer (FRET) measurement based on linearly unmixing excitation-emission spectra (ExEm-spFRET). We here describe an approach to simultaneously measure Q A /Q D and K A /K D values by linearly unmixing the excitation-emission spectra of at least two different donor-acceptor tandem constructs with unknown FRET efficiency. To measure the Q A /Q D and K A /K D values of Venus (V) to Cerulean (C), we used a wide-field fluorescence microscope to image living HepG2 cells separately expressing each of four different C-V tandem constructs at different emission wavelengths with 435 nm and 470 nm excitation respectively to obtain the corresponding excitation-emission spectrum (S DA ). Every S DA was linearly unmixed into the contributions (weights) of three excitation-emission spectra of donor (W D ) and acceptor (W A ) as well as donor-acceptor sensitisation (W S ). Plot of W S /W D versus W A /W D for the four C-V plasmids from at least 40 cells indicated a linear relationship with 1.865 of absolute intercept (Q A /Q D ) and 0.273 of the reciprocal of slope (K A /K D ), which was validated by quantitative FRET measurements adopting 1.865 of Q A /Q D and 0.273 of K A /K D for C32V, C5V, CVC and VCV constructs respectively in living HepG2 cells. © 2018 The Authors Journal of Microscopy © 2018 Royal Microscopical Society.

Spectral Unmixing of Forest Crown Components at Close Range, Airborne and Simulated Sentinel-2 and EnMAP Spectral Imaging Scale

Directory of Open Access Journals (Sweden)

Anne Clasen

2015-11-01

Full Text Available Forest biochemical and biophysical variables and their spatial and temporal distribution are essential inputs to process-orientated ecosystem models. To provide this information, imaging spectroscopy appears to be a promising tool. In this context, the present study investigates the potential of spectral unmixing to derive sub-pixel crown component fractions in a temperate deciduous forest ecosystem. However, the high proportion of foliage in this complex vegetation structure leads to the problem of saturation effects, when applying broadband vegetation indices. This study illustrates that multiple endmember spectral mixture analysis (MESMA can contribute to overcoming this challenge. Reference fractional abundances, as well as spectral measurements of the canopy components, could be precisely determined from a crane measurement platform situated in a deciduous forest in North-East Germany. In contrast to most other studies, which only use leaf and soil endmembers, this experimental setup allowed for the inclusion of a bark endmember for the unmixing of components within the canopy. This study demonstrates that the inclusion of additional endmembers markedly improves the accuracy. A mean absolute error of 7.9% could be achieved for the fractional occurrence of the leaf endmember and 5.9% for the bark endmember. In order to evaluate the results of this field-based study for airborne and satellite-based remote sensing applications, a transfer to Airborne Imaging Spectrometer for Applications (AISA and simulated Environmental Mapping and Analysis Program (EnMAP and Sentinel-2 imagery was carried out. All sensors were capable of unmixing crown components with a mean absolute error ranging between 3% and 21%.

Polynomial selection in number field sieve for integer factorization

Directory of Open Access Journals (Sweden)

Gireesh Pandey

2016-09-01

Full Text Available The general number field sieve (GNFS is the fastest algorithm for factoring large composite integers which is made up by two prime numbers. Polynomial selection is an important step of GNFS. The asymptotic runtime depends on choice of good polynomial pairs. In this paper, we present polynomial selection algorithm that will be modelled with size and root properties. The correlations between polynomial coefficient and number of relations have been explored with experimental findings.

Polynomial solutions of nonlinear integral equations

International Nuclear Information System (INIS)

Dominici, Diego

2009-01-01

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials

Polynomial solutions of nonlinear integral equations

Energy Technology Data Exchange (ETDEWEB)

Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu

2009-05-22

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

Laguerre polynomials by a harmonic oscillator

International Nuclear Information System (INIS)

Baykal, Melek; Baykal, Ahmet

2014-01-01

The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)

Remarks on determinants and the classical polynomials

International Nuclear Information System (INIS)

Henning, J.J.; Kranold, H.U.; Louw, D.F.B.

1986-01-01

As motivation for this formal analysis the problem of Landau damping of Bernstein modes is discussed. It is shown that in the case of a weak but finite constant external magnetic field, the analytical structure of the dispersion relations is of such a nature that longitudinal waves propagating orthogonal to the external magnetic field are also damped, contrary to normal belief. In the treatment of the linearized Vlasov equation it is found convenient to generate certain polynomials by the problem at hand and to explicitly write down expressions for these polynomials. In the course of this study methods are used that relate to elementary but fairly unknown functional relationships between power sums and coefficients of polynomials. These relationships, also called Waring functions, are derived. They are then used in other applications to give explicit expressions for the generalized Laguerre polynomials in terms of determinant functions. The properties of polynomials generated by a wide class of generating functions are investigated. These relationships are also used to obtain explicit forms for the cumulants of a distribution in terms of its moments. It is pointed out that cumulants (or moments, for that matter) do not determine a distribution function

General quantum polynomials: irreducible modules and Morita equivalence

International Nuclear Information System (INIS)

Artamonov, V A

1999-01-01

In this paper we continue the investigation of the structure of finitely generated modules over rings of general quantum (Laurent) polynomials. We obtain a description of the lattice of submodules of periodic finitely generated modules and describe the irreducible modules. We investigate the problem of Morita equivalence of rings of general quantum polynomials, consider properties of division rings of fractions, and solve Zariski's problem for quantum polynomials

Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

OpenAIRE

Ndayiragije, François; Van Assche, Walter

2013-01-01

Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to $r>1$ different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Followi...

Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials

International Nuclear Information System (INIS)

Tratnik, M.V.

1990-01-01

Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials

Primitive polynomials selection method for pseudo-random number generator

Science.gov (United States)

Anikin, I. V.; Alnajjar, Kh

2018-01-01

In this paper we suggested the method for primitive polynomials selection of special type. This kind of polynomials can be efficiently used as a characteristic polynomials for linear feedback shift registers in pseudo-random number generators. The proposed method consists of two basic steps: finding minimum-cost irreducible polynomials of the desired degree and applying primitivity tests to get the primitive ones. Finally two primitive polynomials, which was found by the proposed method, used in pseudorandom number generator based on fuzzy logic (FRNG) which had been suggested before by the authors. The sequences generated by new version of FRNG have low correlation magnitude, high linear complexity, less power consumption, is more balanced and have better statistical properties.

Neck curve polynomials in neck rupture model

International Nuclear Information System (INIS)

Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul

2012-01-01

The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of 280 X 90 with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.

The finite Fourier transform of classical polynomials

OpenAIRE

Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

2014-01-01

The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

Causal networks clarify productivity-richness interrelations, bivariate plots do not

Science.gov (United States)

Grace, James B.; Adler, Peter B.; Harpole, W. Stanley; Borer, Elizabeth T.; Seabloom, Eric W.

2014-01-01

Perhaps no other pair of variables in ecology has generated as much discussion as species richness and ecosystem productivity, as illustrated by the reactions by Pierce (2013) and others to Adler et al.'s (2011) report that empirical patterns are weak and inconsistent. Adler et al. (2011) argued we need to move beyond a focus on simplistic bivariate relationships and test mechanistic, multivariate causal hypotheses. We feel the continuing debate over productivity–richness relationships (PRRs) provides a focused context for illustrating the fundamental difficulties of using bivariate relationships to gain scientific understanding.

Algebraic limit cycles in polynomial systems of differential equations

International Nuclear Information System (INIS)

Llibre, Jaume; Zhao Yulin

2007-01-01

Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4

From sequences to polynomials and back, via operator orderings

Energy Technology Data Exchange (ETDEWEB)

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 (United States); De Angelis, Valerio, E-mail: vdeangel@xula.edu [Department of Mathematics, Xavier University of Louisiana, New Orleans, Louisiana 70125 (United States); Vignat, Christophe, E-mail: vignat@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d' Orsay (France)

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Connection coefficients between Boas-Buck polynomial sets

Science.gov (United States)

Cheikh, Y. Ben; Chaggara, H.

2006-07-01

In this paper, a general method to express explicitly connection coefficients between two Boas-Buck polynomial sets is presented. As application, we consider some generalized hypergeometric polynomials, from which we derive some well-known results including duplication and inversion formulas.

Least squares orthogonal polynomial approximation in several independent variables

International Nuclear Information System (INIS)

Caprari, R.S.

1992-06-01

This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab

A bivariate model for analyzing recurrent multi-type automobile failures

Science.gov (United States)

Sunethra, A. A.; Sooriyarachchi, M. R.

2017-09-01

The failure mechanism in an automobile can be defined as a system of multi-type recurrent failures where failures can occur due to various multi-type failure modes and these failures are repetitive such that more than one failure can occur from each failure mode. In analysing such automobile failures, both the time and type of the failure serve as response variables. However, these two response variables are highly correlated with each other since the timing of failures has an association with the mode of the failure. When there are more than one correlated response variables, the fitting of a multivariate model is more preferable than separate univariate models. Therefore, a bivariate model of time and type of failure becomes appealing for such automobile failure data. When there are multiple failure observations pertaining to a single automobile, such data cannot be treated as independent data because failure instances of a single automobile are correlated with each other while failures among different automobiles can be treated as independent. Therefore, this study proposes a bivariate model consisting time and type of failure as responses adjusted for correlated data. The proposed model was formulated following the approaches of shared parameter models and random effects models for joining the responses and for representing the correlated data respectively. The proposed model is applied to a sample of automobile failures with three types of failure modes and up to five failure recurrences. The parametric distributions that were suitable for the two responses of time to failure and type of failure were Weibull distribution and multinomial distribution respectively. The proposed bivariate model was programmed in SAS Procedure Proc NLMIXED by user programming appropriate likelihood functions. The performance of the bivariate model was compared with separate univariate models fitted for the two responses and it was identified that better performance is secured by

Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

International Nuclear Information System (INIS)

Yasa, F.; Anli, F.; Guengoer, S.

2007-01-01

We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

On Roots of Polynomials and Algebraically Closed Fields

Directory of Open Access Journals (Sweden)

Schwarzweller Christoph

2017-10-01

Full Text Available In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].

Topological string partition functions as polynomials

International Nuclear Information System (INIS)

Yamaguchi, Satoshi; Yau Shingtung

2004-01-01

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus. (author)

Rotation of 2D orthogonal polynomials

Czech Academy of Sciences Publication Activity Database

Yang, B.; Flusser, Jan; Kautský, J.

2018-01-01

Roč. 102, č. 1 (2018), s. 44-49 ISSN 0167-8655 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal polynomials * Recurrent relation * Hermite-like polynomials * Hermite moments Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.995, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0483250.pdf

Approximation of bivariate copulas by patched bivariate Fréchet copulas

KAUST Repository

Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.

2011-01-01

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

Approximation of bivariate copulas by patched bivariate Fréchet copulas

KAUST Repository

Zheng, Yanting

2011-03-01

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

q-analogue of the Krawtchouk and Meixner orthogonal polynomials

International Nuclear Information System (INIS)

Campigotto, C.; Smirnov, Yu.F.; Enikeev, S.G.

1993-06-01

The comparative analysis of Krawtchouk polynomials on a uniform grid with Wigner D-functions for the SU(2) group is presented. As a result the partnership between corresponding properties of the polynomials and D-functions is established giving the group-theoretical interpretation of the Krawtchouk polynomials properties. In order to extend such an analysis on the quantum groups SU q (2) and SU q (1,1), q-analogues of Krawtchouk and Meixner polynomials of a discrete variable are studied. The total set of characteristics of these polynomials is calculated, including the orthogonality condition, normalization factor, recurrent relation, the explicit analytic expression, the Rodrigues formula, the difference derivative formula and various particular cases and values. (R.P.) 22 refs.; 2 tabs

Skew-orthogonal polynomials and random matrix theory

CERN Document Server

Ghosh, Saugata

2009-01-01

Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the ...

Some properties of generalized self-reciprocal polynomials over finite fields

Directory of Open Access Journals (Sweden)

Ryul Kim

2014-07-01

Full Text Available Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal polynomials and characterize the parity of the number of irreducible factors for a-self reciprocal polynomials over finite fields of odd characteristic.

on the performance of Autoregressive Moving Average Polynomial

African Journals Online (AJOL)

Timothy Ademakinwa

Distributed Lag (PDL) model, Autoregressive Polynomial Distributed Lag ... Moving Average Polynomial Distributed Lag (ARMAPDL) model. ..... Global Journal of Mathematics and Statistics. Vol. 1. ... Business and Economic Research Center.

Application of polynomial preconditioners to conservation laws

NARCIS (Netherlands)

Geurts, Bernardus J.; van Buuren, R.; Lu, H.

2000-01-01

Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of

Symmetric functions and orthogonal polynomials

CERN Document Server

Macdonald, I G

1997-01-01

One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

Applications of polynomial optimization in financial risk investment

Science.gov (United States)

Zeng, Meilan; Fu, Hongwei

2017-09-01

Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.

Polynomially Riesz elements | Živković-Zlatanović | Quaestiones ...

African Journals Online (AJOL)

A Banach algebra element ɑ ∈ A is said to be "polynomially Riesz", relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image Tp ∈ B is quasinilpotent. Keywords: Homomorphism of Banach algebras, polynomially Riesz element, Fredholm spectrum, Browder element, ...

Symmetric integrable-polynomial factorization for symplectic one-turn-map tracking

International Nuclear Information System (INIS)

Shi, Jicong

1993-01-01

It was found that any homogeneous polynomial can be written as a sum of integrable polynomials of the same degree which Lie transformations can be evaluated exactly. By utilizing symplectic integrators, an integrable-polynomial factorization is developed to convert a symplectic map in the form of Dragt-Finn factorization into a product of Lie transformations associated with integrable polynomials. A small number of factorization bases of integrable polynomials enable one to use high order symplectic integrators so that the high-order spurious terms can be greatly suppressed. A symplectic map can thus be evaluated with desired accuracy

Polynomial fuzzy model-based approach for underactuated surface vessels

DEFF Research Database (Denmark)

Khooban, Mohammad Hassan; Vafamand, Navid; Dragicevic, Tomislav

2018-01-01

The main goal of this study is to introduce a new polynomial fuzzy model-based structure for a class of marine systems with non-linear and polynomial dynamics. The suggested technique relies on a polynomial Takagi–Sugeno (T–S) fuzzy modelling, a polynomial dynamic parallel distributed compensation...... surface vessel (USV). Additionally, in order to overcome the USV control challenges, including the USV un-modelled dynamics, complex nonlinear dynamics, external disturbances and parameter uncertainties, the polynomial fuzzy model representation is adopted. Moreover, the USV-based control structure...... and a sum-of-squares (SOS) decomposition. The new proposed approach is a generalisation of the standard T–S fuzzy models and linear matrix inequality which indicated its effectiveness in decreasing the tracking time and increasing the efficiency of the robust tracking control problem for an underactuated...

Connections between the matching and chromatic polynomials

Directory of Open Access Journals (Sweden)

E. J. Farrell

1992-01-01

Full Text Available The main results established are (i a connection between the matching and chromatic polynomials and (ii a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.

On Generalisation of Polynomials in Complex Plane

Directory of Open Access Journals (Sweden)

Maslina Darus

2010-01-01

Full Text Available The generalised Bell and Laguerre polynomials of fractional-order in complex z-plane are defined. Some properties are studied. Moreover, we proved that these polynomials are univalent solutions for second order differential equations. Also, the Laguerre-type of some special functions are introduced.

Technique for image interpolation using polynomial transforms

NARCIS (Netherlands)

Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.

1993-01-01

We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is

Okounkov's BC-Type Interpolation Macdonald Polynomials and Their q=1 Limit

NARCIS (Netherlands)

Koornwinder, T.H.

2015-01-01

This paper surveys eight classes of polynomials associated with A-type and BC-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or shifted) Jack and Macdonald polynomials and their BC-type extensions. Among these the BC-type interpolation Jack polynomials were

Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

Dias, Kealey

vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...

Interlacing of zeros of quasi-orthogonal meixner polynomials | Driver ...

African Journals Online (AJOL)

... interlacing of zeros of quasi-orthogonal Meixner polynomials Mn(x;β; c) with the zeros of their nearest orthogonal counterparts Mt(x;β + k; c), l; n ∈ ℕ, k ∈ {1; 2}; is also discussed. Mathematics Subject Classication (2010): 33C45, 42C05. Key words: Discrete orthogonal polynomials, quasi-orthogonal polynomials, Meixner

Discriminants and functional equations for polynomials orthogonal on the unit circle

International Nuclear Information System (INIS)

Ismail, M.E.H.; Witte, N.S.

2000-01-01

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle

Contributions to fuzzy polynomial techniques for stability analysis and control

OpenAIRE

Pitarch Pérez, José Luis

2014-01-01

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees...

On the Lorentz degree of a product of polynomials

KAUST Repository

Ait-Haddou, Rachid

2015-01-01

In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.

Strong result for real zeros of random algebraic polynomials

Directory of Open Access Journals (Sweden)

T. Uno

2001-01-01

Full Text Available An estimate is given for the lower bound of real zeros of random algebraic polynomials whose coefficients are non-identically distributed dependent Gaussian random variables. Moreover, our estimated measure of the exceptional set, which is independent of the degree of the polynomials, tends to zero as the degree of the polynomial tends to infinity.

Large degree asymptotics of generalized Bessel polynomials

NARCIS (Netherlands)

J.L. López; N.M. Temme (Nico)

2011-01-01

textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the

Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials

International Nuclear Information System (INIS)

Gruenbaum, F A; Vinet, Luc; Zhedanov, Alexei

2004-01-01

We study operator pencils on generators of the Lie algebras sl 2 and the oscillator algebra. These pencils are linear in a spectral parameter λ. The corresponding generalized eigenvalue problem gives rise to some sets of orthogonal polynomials and Laurent biorthogonal polynomials (LBP) expressed in terms of the Gauss 2 F 1 and degenerate 1 F 1 hypergeometric functions. For special choices of the parameters of the pencils, we identify the resulting polynomials with the Hendriksen-van Rossum LBP which are widely believed to be the biorthogonal analogues of the classical orthogonal polynomials. This places these examples under the umbrella of the generalized bispectral problem which is considered here. Other (non-bispectral) cases give rise to some 'nonclassical' orthogonal polynomials including Tricomi-Carlitz and random-walk polynomials. An application to solutions of relativistic Toda chain is considered

Probability distributions with truncated, log and bivariate extensions

CERN Document Server

Thomopoulos, Nick T

2018-01-01

This volume presents a concise and practical overview of statistical methods and tables not readily available in other publications. It begins with a review of the commonly used continuous and discrete probability distributions. Several useful distributions that are not so common and less understood are described with examples and applications in full detail: discrete normal, left-partial, right-partial, left-truncated normal, right-truncated normal, lognormal, bivariate normal, and bivariate lognormal. Table values are provided with examples that enable researchers to easily apply the distributions to real applications and sample data. The left- and right-truncated normal distributions offer a wide variety of shapes in contrast to the symmetrically shaped normal distribution, and a newly developed spread ratio enables analysts to determine which of the three distributions best fits a particular set of sample data. The book will be highly useful to anyone who does statistical and probability analysis. This in...

Higher order branching of periodic orbits from polynomial isochrones

Directory of Open Access Journals (Sweden)

B. Toni

1999-09-01

Full Text Available We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary $n$ degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.

On the estimation of the degree of regression polynomial

International Nuclear Information System (INIS)

Toeroek, Cs.

1997-01-01

The mathematical functions most commonly used to model curvature in plots are polynomials. Generally, the higher the degree of the polynomial, the more complex is the trend that its graph can represent. We propose a new statistical-graphical approach based on the discrete projective transformation (DPT) to estimating the degree of polynomial that adequately describes the trend in the plot

On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

Directory of Open Access Journals (Sweden)

Sezgin Sucu

2012-01-01

Full Text Available This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

On associated polynomials and decay rates for birth-death processes

NARCIS (Netherlands)

van Doorn, Erik A.

2001-01-01

We consider sequences of orthogonal polynomials and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials. In particular, we relate the supports of the

On associated polynomials and decay rates for birth-death processes

NARCIS (Netherlands)

van Doorn, Erik A.

2003-01-01

We consider sequences of orthogonal polynomials and pursue the question of how (partial) knowledge of the orthogonalizing measure for the associated polynomials can lead to information about the orthogonalizing measure for the original polynomials. In particular, we relate the supports of the two

Some Polynomials Associated with the r-Whitney Numbers

Indian Academy of Sciences (India)

26

Abstract. In the present article we study three families of polynomials associated with ... [29, 39] for their relations with the Bernoulli and generalized Bernoulli polynomials and ... generating functions in a similar way as in the classical cases.

The Bessel polynomials and their differential operators

International Nuclear Information System (INIS)

Onyango Otieno, V.P.

1987-10-01

Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs

Conference on Commutative rings, integer-valued polynomials and polynomial functions

CERN Document Server

Frisch, Sophie; Glaz, Sarah; Commutative Algebra : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions

2014-01-01

This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: ·    Homological dimensions of Prüfer-like rings ·    Quasi complete rings ·    Total graphs of rings ·    Properties of prime ideals over various rings ·    Bases for integer-valued polynomials ·    Boolean subrings ·    The portable property of domains ·    Probabilistic topics in Intn(D) ·    Closure operations in Zariski-Riemann spaces of valuation domains ·    Stability of do...

Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

African Journals Online (AJOL)

Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

Dual exponential polynomials and linear differential equations

Science.gov (United States)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

Generalized Freud's equation and level densities with polynomial

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.

Polynomial fuzzy observer designs: a sum-of-squares approach.

Science.gov (United States)

Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O

2012-10-01

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

GIS-Based bivariate statistical techniques for groundwater potential ...

Indian Academy of Sciences (India)

24

This study shows the potency of two GIS-based data driven bivariate techniques namely ... In the view of these weaknesses , there is a strong requirement for reassessment of .... Font color: Text 1, Not Expanded by / Condensed by , ...... West Bengal (India) using remote sensing, geographical information system and multi-.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

Science.gov (United States)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Unmixing hyperspectral images using Markov random fields

International Nuclear Information System (INIS)

Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves

2011-01-01

This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.

An overview on polynomial approximation of NP-hard problems

Directory of Open Access Journals (Sweden)

Paschos Vangelis Th.

2009-01-01

Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

Constructing general partial differential equations using polynomial and neural networks.

Science.gov (United States)

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

A note on the zeros of Freud-Sobolev orthogonal polynomials

Science.gov (United States)

Moreno-Balcazar, Juan J.

2007-10-01

We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

About the solvability of matrix polynomial equations

OpenAIRE

Netzer, Tim; Thom, Andreas

2016-01-01

We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

Two polynomial representations of experimental design

OpenAIRE

Notari, Roberto; Riccomagno, Eva; Rogantin, Maria-Piera

2007-01-01

In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Groebner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch between them. Examples include fractions of full factorial designs and designs for mixture experiments.

Assessing the copula selection for bivariate frequency analysis ...

Indian Academy of Sciences (India)

58

Copulas are applied to overcome the restriction of traditional bivariate frequency ... frequency analysis methods cannot describe the random variable properties that ... In order to overcome the limitation of multivariate distributions, a copula is a ..... The Mann-Kendall (M-K) test is a non-parametric statistical test which is used ...

Stable piecewise polynomial vector fields

Directory of Open Access Journals (Sweden)

Claudio Pessoa

2012-09-01

Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

q-Bernoulli numbers and q-Bernoulli polynomials revisited

Directory of Open Access Journals (Sweden)

Kim Taekyun

2011-01-01

Full Text Available Abstract This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010, some incorrect properties are revised. It is point out that the generating function for the q-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math 48, 73-86, 1994 (see Equation 9, some new generating functions for the q-Bernoulli numbers and polynomials are shown. Mathematics Subject Classification (2000 11B68, 11S40, 11S80

Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

Science.gov (United States)

Milstead, Jonathan

The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

Fast beampattern evaluation by polynomial rooting

Science.gov (United States)

Häcker, P.; Uhlich, S.; Yang, B.

2011-07-01

Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.

Guts of surfaces and the colored Jones polynomial

CERN Document Server

Futer, David; Purcell, Jessica

2013-01-01

This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the  complement to the combinatorics of certain surface spines (state graphs). Since state graphs have p...

Computing Tutte polynomials of contact networks in classrooms

Science.gov (United States)

Hincapié, Doracelly; Ospina, Juan

2013-05-01

Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network

About some properties of bivariate splines with shape parameters

Science.gov (United States)

Caliò, F.; Marchetti, E.

2017-07-01

The paper presents and proves geometrical properties of a particular bivariate function spline, built and algorithmically implemented in previous papers. The properties typical of this family of splines impact the field of computer graphics in particular that of the reverse engineering.

Evaluating the Performance of Polynomial Regression Method with Different Parameters during Color Characterization

Directory of Open Access Journals (Sweden)

Bangyong Sun

2014-01-01

Full Text Available The polynomial regression method is employed to calculate the relationship of device color space and CIE color space for color characterization, and the performance of different expressions with specific parameters is evaluated. Firstly, the polynomial equation for color conversion is established and the computation of polynomial coefficients is analysed. And then different forms of polynomial equations are used to calculate the RGB and CMYK’s CIE color values, while the corresponding color errors are compared. At last, an optimal polynomial expression is obtained by analysing several related parameters during color conversion, including polynomial numbers, the degree of polynomial terms, the selection of CIE visual spaces, and the linearization.

Exponential time paradigms through the polynomial time lens

NARCIS (Netherlands)

Drucker, A.; Nederlof, J.; Santhanam, R.; Sankowski, P.; Zaroliagis, C.

2016-01-01

We propose a general approach to modelling algorithmic paradigms for the exact solution of NP-hard problems. Our approach is based on polynomial time reductions to succinct versions of problems solvable in polynomial time. We use this viewpoint to explore and compare the power of paradigms such as

Root and Critical Point Behaviors of Certain Sums of Polynomials

Indian Academy of Sciences (India)

13

There is an extensive literature concerning roots of sums of polynomials. Many papers and books([5], [6],. [7]) have written about these polynomials. Perhaps the most immediate question of sums of polynomials,. A + B = C, is “given bounds for the roots of A and B, what bounds can be given for the roots of C?” By. Fell [3], if ...

Optimizing an objective function under a bivariate probability model

NARCIS (Netherlands)

X. Brusset; N.M. Temme (Nico)

2007-01-01

htmlabstractThe motivation of this paper is to obtain an analytical closed form of a quadratic objective function arising from a stochastic decision process with bivariate exponential probability distribution functions that may be dependent. This method is applicable when results need to be

A New Measure Of Bivariate Asymmetry And Its Evaluation

International Nuclear Information System (INIS)

Ferreira, Flavio Henn; Kolev, Nikolai Valtchev

2008-01-01

In this paper we propose a new measure of bivariate asymmetry, based on conditional correlation coefficients. A decomposition of the Pearson correlation coefficient in terms of its conditional versions is studied and an example of application of the proposed measure is given.

The chromatic polynomial and list colorings

DEFF Research Database (Denmark)

Thomassen, Carsten

2009-01-01

We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph.......We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph....

BSDEs with polynomial growth generators

Directory of Open Access Journals (Sweden)

Philippe Briand

2000-01-01

Full Text Available In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Spectrum-based estimators of the bivariate Hurst exponent

Czech Academy of Sciences Publication Activity Database

Krištoufek, Ladislav

2014-01-01

Roč. 90, č. 6 (2014), art. 062802 ISSN 1539-3755 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : bivariate Hurst exponent * power- law cross-correlations * estimation Subject RIV: AH - Economics Impact factor: 2.288, year: 2014 http://library.utia.cas.cz/separaty/2014/E/kristoufek-0436818.pdf

Polynomial chaos functions and stochastic differential equations

International Nuclear Information System (INIS)

Williams, M.M.R.

2006-01-01

The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory

Minimal residual method stronger than polynomial preconditioning

Energy Technology Data Exchange (ETDEWEB)

Faber, V.; Joubert, W.; Knill, E. [Los Alamos National Lab., NM (United States)] [and others

1994-12-31

Two popular methods for solving symmetric and nonsymmetric systems of equations are the minimal residual method, implemented by algorithms such as GMRES, and polynomial preconditioning methods. In this study results are given on the convergence rates of these methods for various classes of matrices. It is shown that for some matrices, such as normal matrices, the convergence rates for GMRES and for the optimal polynomial preconditioning are the same, and for other matrices such as the upper triangular Toeplitz matrices, it is at least assured that if one method converges then the other must converge. On the other hand, it is shown that matrices exist for which restarted GMRES always converges but any polynomial preconditioning of corresponding degree makes no progress toward the solution for some initial error. The implications of these results for these and other iterative methods are discussed.

Bernoulli numbers and polynomials from a more general point of view

International Nuclear Information System (INIS)

Dattoli, G.; Cesarano, C.; Lorenzutta, S.

2000-01-01

In this work it is applied the method of generating function, to introduce new forms of Bernoulli numbers and polynomials, which are exploited to derive further classes of partial sums involving generalized many index many variable polynomials. Analogous considerations are developed for the Euler numbers and polynomials [it

Generalizations of an integral for Legendre polynomials by Persson and Strang

NARCIS (Netherlands)

Diekema, E.; Koornwinder, T.H.

2012-01-01

Persson and Strang (2003) evaluated the integral over [−1,1] of a squared odd degree Legendre polynomial divided by x2 as being equal to 2. We consider a similar integral for orthogonal polynomials with respect to a general even orthogonality measure, with Gegenbauer and Hermite polynomials as

Eye aberration analysis with Zernike polynomials

Science.gov (United States)

Molebny, Vasyl V.; Chyzh, Igor H.; Sokurenko, Vyacheslav M.; Pallikaris, Ioannis G.; Naoumidis, Leonidas P.

1998-06-01

New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberration, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.

Animating Nested Taylor Polynomials to Approximate a Function

Science.gov (United States)

Mazzone, Eric F.; Piper, Bruce R.

2010-01-01

The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…

Learning Read-constant Polynomials of Constant Degree modulo Composites

DEFF Research Database (Denmark)

Chattopadhyay, Arkadev; Gavaldá, Richard; Hansen, Kristoffer Arnsfelt

2011-01-01

Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class \\textACC0ACC0. They are also precisely the functions computable efficiently by programs over fixed and finite nilpotent groups. This class...... is not known to be learnable in any reasonable learning model. In this paper, we provide a deterministic polynomial time algorithm for learning Boolean functions represented by polynomials of constant degree over arbitrary finite rings from membership queries, with the additional constraint that each variable...

Bivariate generalized Pareto distribution for extreme atmospheric particulate matter

Science.gov (United States)

Amin, Nor Azrita Mohd; Adam, Mohd Bakri; Ibrahim, Noor Akma; Aris, Ahmad Zaharin

2015-02-01

The high particulate matter (PM10) level is the prominent issue causing various impacts to human health and seriously affecting the economics. The asymptotic theory of extreme value is apply for analyzing the relation of extreme PM10 data from two nearby air quality monitoring stations. The series of daily maxima PM10 for Johor Bahru and Pasir Gudang stations are consider for year 2001 to 2010 databases. The 85% and 95% marginal quantile apply to determine the threshold values and hence construct the series of exceedances over the chosen threshold. The logistic, asymmetric logistic, negative logistic and asymmetric negative logistic models areconsidered as the dependence function to the joint distribution of a bivariate observation. Maximum likelihood estimation is employed for parameter estimations. The best fitted model is chosen based on the Akaike Information Criterion and the quantile plots. It is found that the asymmetric logistic model gives the best fitted model for bivariate extreme PM10 data and shows the weak dependence between two stations.

Bivariational calculations for radiation transfer in an inhomogeneous participating media

International Nuclear Information System (INIS)

El Wakil, S.A.; Machali, H.M.; Haggag, M.H.; Attia, M.T.

1986-07-01

Equations for radiation transfer are obtained for dispersive media with space dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared. (author)

Complex centers of polynomial differential equations

Directory of Open Access Journals (Sweden)

Mohamad Ali M. Alwash

2007-07-01

Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

Differential recurrence formulae for orthogonal polynomials

Directory of Open Access Journals (Sweden)

Anton L. W. von Bachhaus

1995-11-01

Full Text Available Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(xY'n(x=fn(xYn(x+Yn-1(x. Part II - A recurrence formula of the form: rn(xY'n(x+sn(xY'n+1(x+tn(xY'n-1(x=0, is derived using the result of Part I.

Considering a non-polynomial basis for local kernel regression problem

Science.gov (United States)

Silalahi, Divo Dharma; Midi, Habshah

2017-01-01

A common used as solution for local kernel nonparametric regression problem is given using polynomial regression. In this study, we demonstrated the estimator and properties using maximum likelihood estimator for a non-polynomial basis such B-spline to replacing the polynomial basis. This estimator allows for flexibility in the selection of a bandwidth and a knot. The best estimator was selected by finding an optimal bandwidth and knot through minimizing the famous generalized validation function.

Open Problems Related to the Hurwitz Stability of Polynomials Segments

Directory of Open Access Journals (Sweden)

Baltazar Aguirre-Hernández

2018-01-01

Full Text Available In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.

Spectral density regression for bivariate extremes

KAUST Repository

Castro Camilo, Daniela

2016-05-11

We introduce a density regression model for the spectral density of a bivariate extreme value distribution, that allows us to assess how extremal dependence can change over a covariate. Inference is performed through a double kernel estimator, which can be seen as an extension of the Nadaraya–Watson estimator where the usual scalar responses are replaced by mean constrained densities on the unit interval. Numerical experiments with the methods illustrate their resilience in a variety of contexts of practical interest. An extreme temperature dataset is used to illustrate our methods. © 2016 Springer-Verlag Berlin Heidelberg

The computation of bond percolation critical polynomials by the deletion–contraction algorithm

International Nuclear Information System (INIS)

Scullard, Christian R

2012-01-01

Although every exactly known bond percolation critical threshold is the root in [0,1] of a lattice-dependent polynomial, it has recently been shown that the notion of a critical polynomial can be extended to any periodic lattice. The polynomial is computed on a finite subgraph, called the base, of an infinite lattice. For any problem with exactly known solution, the prediction of the bond threshold is always correct for any base containing an arbitrary number of unit cells. For unsolved problems, the polynomial is referred to as the generalized critical polynomial and provides an approximation that becomes more accurate with increasing number of bonds in the base, appearing to approach the exact answer. The polynomials are computed using the deletion–contraction algorithm, which quickly becomes intractable by hand for more than about 18 bonds. Here, I present generalized critical polynomials calculated with a computer program for bases of up to 36 bonds for all the unsolved Archimedean lattices, except the kagome lattice, which was considered in an earlier work. The polynomial estimates are generally within 10 −5 –10 −7 of the numerical values, but the prediction for the (4,8 2 ) lattice, though not exact, is not ruled out by simulations. (paper)

Solving the interval type-2 fuzzy polynomial equation using the ranking method

Science.gov (United States)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

A high-order q-difference equation for q-Hahn multiple orthogonal polynomials

DEFF Research Database (Denmark)

Arvesú, J.; Esposito, Chiara

2012-01-01

A high-order linear q-difference equation with polynomial coefficients having q-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation coincides with the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when are studie....... Indeed, the difference equation for Hahn multiple orthogonal polynomials given in Lee [J. Approx. Theory (2007), ), doi: 10.1016/j.jat.2007.06.002] is obtained as a limiting case....

On the Lorentz degree of a product of polynomials

KAUST Repository

Ait-Haddou, Rachid

2015-01-01

In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence

Generalized Freud's equation and level densities with polynomial potential

Science.gov (United States)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach

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Bomo W. Sanjaya

2014-07-01

Full Text Available This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simulation study is presented to show the effectiveness of the SOS-based H∞ control designfor nonlinear polynomial fuzzy systems.

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

Science.gov (United States)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Some Results on the Independence Polynomial of Unicyclic Graphs

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Oboudi Mohammad Reza

2018-05-01

Full Text Available Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x=∑k=0ns(G,kxk$I(G,x = \\sum\

Bivariate extreme value with application to PM10 concentration analysis

Science.gov (United States)

Amin, Nor Azrita Mohd; Adam, Mohd Bakri; Ibrahim, Noor Akma; Aris, Ahmad Zaharin

2015-05-01

This study is focus on a bivariate extreme of renormalized componentwise maxima with generalized extreme value distribution as a marginal function. The limiting joint distribution of several parametric models are presented. Maximum likelihood estimation is employed for parameter estimations and the best model is selected based on the Akaike Information Criterion. The weekly and monthly componentwise maxima series are extracted from the original observations of daily maxima PM10 data for two air quality monitoring stations located in Pasir Gudang and Johor Bahru. The 10 years data are considered for both stations from year 2001 to 2010. The asymmetric negative logistic model is found as the best fit bivariate extreme model for both weekly and monthly maxima componentwise series. However the dependence parameters show that the variables for weekly maxima series is more dependence to each other compared to the monthly maxima.

Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers

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Jaume Llibre

2015-10-01

Full Text Available We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of any cubic homogeneous polynomial center when it is perturbed inside the class of all polynomial differential systems of degree n.

An Improved STARFM with Help of an Unmixing-Based Method to Generate High Spatial and Temporal Resolution Remote Sensing Data in Complex Heterogeneous Regions.

Science.gov (United States)

Xie, Dengfeng; Zhang, Jinshui; Zhu, Xiufang; Pan, Yaozhong; Liu, Hongli; Yuan, Zhoumiqi; Yun, Ya

2016-02-05

Remote sensing technology plays an important role in monitoring rapid changes of the Earth's surface. However, sensors that can simultaneously provide satellite images with both high temporal and spatial resolution haven't been designed yet. This paper proposes an improved spatial and temporal adaptive reflectance fusion model (STARFM) with the help of an Unmixing-based method (USTARFM) to generate the high spatial and temporal data needed for the study of heterogeneous areas. The results showed that the USTARFM had higher accuracy than STARFM methods in two aspects of analysis: individual bands and of heterogeneity analysis. Taking the predicted NIR band as an example, the correlation coefficients (r) for the USTARFM, STARFM and unmixing methods were 0.96, 0.95, 0.90, respectively (p-value data fusion problems faced when using STARFM. Additionally, the USTARFM method could help researchers achieve better performance than STARFM at a smaller window size from its heterogeneous land surface quantitative representation.

Polynomial Poisson algebras: Gel'fand-Kirillov problem and Poisson spectra

OpenAIRE

Lecoutre, César

2014-01-01

We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras.\\ud \\ud First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to...

On an Inequality Concerning the Polar Derivative of a Polynomial

Indian Academy of Sciences (India)

Abstract. In this paper, we present a correct proof of an -inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.

Classification of complex polynomial vector fields in one complex variable

DEFF Research Database (Denmark)

Branner, Bodil; Dias, Kealey

2010-01-01

This paper classifies the global structure of monic and centred one-variable complex polynomial vector fields. The classification is achieved by means of combinatorial and analytic data. More specifically, given a polynomial vector field, we construct a combinatorial invariant, describing...... the topology, and a set of analytic invariants, describing the geometry. Conversely, given admissible combinatorial and analytic data sets, we show using surgery the existence of a unique monic and centred polynomial vector field realizing the given invariants. This is the content of the Structure Theorem......, the main result of the paper. This result is an extension and refinement of Douady et al. (Champs de vecteurs polynomiaux sur C. Unpublished manuscript) classification of the structurally stable polynomial vector fields. We further review some general concepts for completeness and show that vector fields...

Bivariate Rayleigh Distribution and its Properties

Directory of Open Access Journals (Sweden)

Ahmad Saeed Akhter

2007-01-01

Full Text Available Rayleigh (1880 observed that the sea waves follow no law because of the complexities of the sea, but it has been seen that the probability distributions of wave heights, wave length, wave induce pitch, wave and heave motions of the ships follow the Rayleigh distribution. At present, several different quantities are in use for describing the state of the sea; for example, the mean height of the waves, the root mean square height, the height of the “significant waves” (the mean height of the highest one-third of all the waves the maximum height over a given interval of the time, and so on. At present, the ship building industry knows less than any other construction industry about the service conditions under which it must operate. Only small efforts have been made to establish the stresses and motions and to incorporate the result of such studies in to design. This is due to the complexity of the problem caused by the extensive variability of the sea and the corresponding response of the ships. Although the problem appears feasible, yet it is possible to predict service conditions for ships in an orderly and relatively simple manner Rayleigh (1980 derived it from the amplitude of sound resulting from many independent sources. This distribution is also connected with one or two dimensions and is sometimes referred to as “random walk” frequency distribution. The Rayleigh distribution can be derived from the bivariate normal distribution when the variate are independent and random with equal variances. We try to construct bivariate Rayleigh distribution with marginal Rayleigh distribution function and discuss its fundamental properties.

Random polynomials and expected complexity of bisection methods for real solving

DEFF Research Database (Denmark)

Emiris, Ioannis Z.; Galligo, André; Tsigaridas, Elias

2010-01-01

, and by Edelman and Kostlan in order to estimate the real root separation of degree d polynomials with i.i.d. coefficients that follow two zero-mean normal distributions: for SO(2) polynomials, the i-th coefficient has variance (d/i), whereas for Weyl polynomials its variance is 1/i!. By applying results from....... The second part of the paper shows that the expected number of real roots of a degree d polynomial in the Bernstein basis is √2d ± O(1), when the coefficients are i.i.d. variables with moderate standard deviation. Our paper concludes with experimental results which corroborate our analysis....

O(N) symmetries, sum rules for generalized Hermite polynomials and squeezed states

International Nuclear Information System (INIS)

Daboul, Jamil; Mizrahi, Salomon S

2005-01-01

Quantum optics has been dealing with coherent states, squeezed states and many other non-classical states. The associated mathematical framework makes use of special functions as Hermite polynomials, Laguerre polynomials and others. In this connection we here present some formal results that follow directly from the group O(N) of complex transformations. Motivated by the squeezed states structure, we introduce the generalized Hermite polynomials (GHP), which include as particular cases, the Hermite polynomials as well as the heat polynomials. Using generalized raising operators, we derive new sum rules for the GHP, which are covariant under O(N) transformations. The GHP and the associated sum rules become useful for evaluating Wigner functions in a straightforward manner. As a byproduct, we use one of these sum rules, on the operator level, to obtain raising and lowering operators for the Laguerre polynomials and show that they generate an sl(2, R) ≅ su(1, 1) algebra

Euler polynomials and identities for non-commutative operators

Science.gov (United States)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach.

Science.gov (United States)

Chen, Yong; Hong, Chuan; Ning, Yang; Su, Xiao

2016-01-15

When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration. Copyright © 2015 John Wiley & Sons, Ltd.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach.

Science.gov (United States)

Mohammadi, Tayeb; Kheiri, Soleiman; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.

Parameter estimation and statistical test of geographically weighted bivariate Poisson inverse Gaussian regression models

Science.gov (United States)

Amalia, Junita; Purhadi, Otok, Bambang Widjanarko

2017-11-01

Poisson distribution is a discrete distribution with count data as the random variables and it has one parameter defines both mean and variance. Poisson regression assumes mean and variance should be same (equidispersion). Nonetheless, some case of the count data unsatisfied this assumption because variance exceeds mean (over-dispersion). The ignorance of over-dispersion causes underestimates in standard error. Furthermore, it causes incorrect decision in the statistical test. Previously, paired count data has a correlation and it has bivariate Poisson distribution. If there is over-dispersion, modeling paired count data is not sufficient with simple bivariate Poisson regression. Bivariate Poisson Inverse Gaussian Regression (BPIGR) model is mix Poisson regression for modeling paired count data within over-dispersion. BPIGR model produces a global model for all locations. In another hand, each location has different geographic conditions, social, cultural and economic so that Geographically Weighted Regression (GWR) is needed. The weighting function of each location in GWR generates a different local model. Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) model is used to solve over-dispersion and to generate local models. Parameter estimation of GWBPIGR model obtained by Maximum Likelihood Estimation (MLE) method. Meanwhile, hypothesis testing of GWBPIGR model acquired by Maximum Likelihood Ratio Test (MLRT) method.

On integral and finite Fourier transforms of continuous q-Hermite polynomials

International Nuclear Information System (INIS)

Atakishiyeva, M. K.; Atakishiyev, N. M.

2009-01-01

We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

On polynomial selection for the general number field sieve

Science.gov (United States)

Kleinjung, Thorsten

2006-12-01

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials

Science.gov (United States)

Horozov, Emil

2016-05-01

We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.

Families of superintegrable Hamiltonians constructed from exceptional polynomials

International Nuclear Information System (INIS)

Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc

2012-01-01

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)

Raising and Lowering Operators for Askey-Wilson Polynomials

Directory of Open Access Journals (Sweden)

Siddhartha Sahi

2007-01-01

Full Text Available In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

Science.gov (United States)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2008-10-01

We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.

Mathematical Use Of Polynomials Of Different End Periods Of ...

African Journals Online (AJOL)

This paper focused on how polynomials of different end period of random numbers can be used in the application of encryption and decryption of a message. Eight steps were used in generating information on how polynomials of different end periods of random numbers in the application of encryption and decryption of a ...

Computing derivative-based global sensitivity measures using polynomial chaos expansions

International Nuclear Information System (INIS)

Sudret, B.; Mai, C.V.

2015-01-01

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSMs) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis. - Highlights: • Derivative-based global sensitivity measures (DGSM) have been developed for screening purpose. • Polynomial chaos expansions (PC) are used as a surrogate model of the original computational model. • From a PC expansion the DGSM can be computed analytically. • The paper provides the derivatives of Hermite, Legendre and Laguerre polynomials for this purpose

Univariate and Bivariate Empirical Mode Decomposition for Postural Stability Analysis

Directory of Open Access Journals (Sweden)

Jacques Duchêne

2008-05-01

Full Text Available The aim of this paper was to compare empirical mode decomposition (EMD and two new extended methods of  EMD named complex empirical mode decomposition (complex-EMD and bivariate empirical mode decomposition (bivariate-EMD. All methods were used to analyze stabilogram center of pressure (COP time series. The two new methods are suitable to be applied to complex time series to extract complex intrinsic mode functions (IMFs before the Hilbert transform is subsequently applied on the IMFs. The trace of the analytic IMF in the complex plane has a circular form, with each IMF having its own rotation frequency. The area of the circle and the average rotation frequency of IMFs represent efficient indicators of the postural stability status of subjects. Experimental results show the effectiveness of these indicators to identify differences in standing posture between groups.

Genetics of Obesity Traits: A Bivariate Genome-Wide Association Analysis

DEFF Research Database (Denmark)

Wu, Yili; Duan, Haiping; Tian, Xiaocao

2018-01-01

Previous genome-wide association studies on anthropometric measurements have identified more than 100 related loci, but only a small portion of heritability in obesity was explained. Here we present a bivariate twin study to look for the genetic variants associated with body mass index and waist......-hip ratio, and to explore the obesity-related pathways in Northern Han Chinese. Cholesky decompositionmodel for 242monozygotic and 140 dizygotic twin pairs indicated a moderate genetic correlation (r = 0.53, 95%CI: 0.42–0.64) between body mass index and waist-hip ratio. Bivariate genome-wide association.......05. Expression quantitative trait loci analysis identified rs2242044 as a significant cis-eQTL in both the normal adipose-subcutaneous (P = 1.7 × 10−9) and adipose-visceral (P = 4.4 × 10−15) tissue. These findings may provide an important entry point to unravel genetic pleiotropy in obesity traits....

Exact polynomial solutions of second order differential equations and their applications

International Nuclear Information System (INIS)

Zhang Yaozhong

2012-01-01

We find all polynomials Z(z) such that the differential equation where X(z), Y(z), Z(z) are polynomials of degree at most 4, 3, 2, respectively, has polynomial solutions S(z) = ∏ n i=1 (z − z i ) of degree n with distinct roots z i . We derive a set of n algebraic equations which determine these roots. We also find all polynomials Z(z) which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schrödinger-type differential equations describing: (1) two Coulombically repelling electrons on a sphere; (2) Schrödinger equation from the kink stability analysis of φ 6 -type field theory; (3) static perturbations for the non-extremal Reissner–Nordström solution; (4) planar Dirac electron in Coulomb and magnetic fields; and (5) O(N) invariant decatic anharmonic oscillator. (paper)

The Jones polynomial as a new invariant of topological fluid dynamics

International Nuclear Information System (INIS)

Ricca, Renzo L; Liu, Xin

2014-01-01

A new method based on the use of the Jones polynomial, a well-known topological invariant of knot theory, is introduced to tackle and quantify topological aspects of structural complexity of vortex tangles in ideal fluids. By re-writing the Jones polynomial in terms of helicity, the resulting polynomial becomes then function of knot topology and vortex circulation, providing thus a new invariant of topological fluid dynamics. Explicit computations of the Jones polynomial for some standard configurations, including the Whitehead link and the Borromean rings (whose linking numbers are zero), are presented for illustration. In the case of a homogeneous, isotropic tangle of vortex filaments with same circulation, the new Jones polynomial reduces to some simple algebraic expression, that can be easily computed by numerical methods. This shows that this technique may offer a new setting and a powerful tool to detect and compute topological complexity and to investigate relations with energy, by tackling fundamental aspects of turbulence research. (paper)

PLOTNFIT.4TH, Data Plotting and Curve Fitting by Polynomials

International Nuclear Information System (INIS)

Schiffgens, J.O.

1990-01-01

1 - Description of program or function: PLOTnFIT is used for plotting and analyzing data by fitting nth degree polynomials of basis functions to the data interactively and printing graphs of the data and the polynomial functions. It can be used to generate linear, semi-log, and log-log graphs and can automatically scale the coordinate axes to suit the data. Multiple data sets may be plotted on a single graph. An auxiliary program, READ1ST, is included which produces an on-line summary of the information contained in the PLOTnFIT reference report. 2 - Method of solution: PLOTnFIT uses the least squares method to calculate the coefficients of nth-degree (up to 10. degree) polynomials of 11 selected basis functions such that each polynomial fits the data in a least squares sense. The procedure incorporated in the code uses a linear combination of orthogonal polynomials to avoid 'i11-conditioning' and to perform the curve fitting task with single-precision arithmetic. 3 - Restrictions on the complexity of the problem - Maxima of: 225 data points per job (or graph) including all data sets 8 data sets (or tasks) per job (or graph)

Twisted Polynomials and Forgery Attacks on GCM

DEFF Research Database (Denmark)

Abdelraheem, Mohamed Ahmed A. M. A.; Beelen, Peter; Bogdanov, Andrey

2015-01-01

Polynomial hashing as an instantiation of universal hashing is a widely employed method for the construction of MACs and authenticated encryption (AE) schemes, the ubiquitous GCM being a prominent example. It is also used in recent AE proposals within the CAESAR competition which aim at providing...... in an improved key recovery algorithm. As cryptanalytic applications of our twisted polynomials, we develop the first universal forgery attacks on GCM in the weak-key model that do not require nonce reuse. Moreover, we present universal weak-key forgeries for the nonce-misuse resistant AE scheme POET, which...

A polynomial based model for cell fate prediction in human diseases.

Science.gov (United States)

Ma, Lichun; Zheng, Jie

2017-12-21

Cell fate regulation directly affects tissue homeostasis and human health. Research on cell fate decision sheds light on key regulators, facilitates understanding the mechanisms, and suggests novel strategies to treat human diseases that are related to abnormal cell development. In this study, we proposed a polynomial based model to predict cell fate. This model was derived from Taylor series. As a case study, gene expression data of pancreatic cells were adopted to test and verify the model. As numerous features (genes) are available, we employed two kinds of feature selection methods, i.e. correlation based and apoptosis pathway based. Then polynomials of different degrees were used to refine the cell fate prediction function. 10-fold cross-validation was carried out to evaluate the performance of our model. In addition, we analyzed the stability of the resultant cell fate prediction model by evaluating the ranges of the parameters, as well as assessing the variances of the predicted values at randomly selected points. Results show that, within both the two considered gene selection methods, the prediction accuracies of polynomials of different degrees show little differences. Interestingly, the linear polynomial (degree 1 polynomial) is more stable than others. When comparing the linear polynomials based on the two gene selection methods, it shows that although the accuracy of the linear polynomial that uses correlation analysis outcomes is a little higher (achieves 86.62%), the one within genes of the apoptosis pathway is much more stable. Considering both the prediction accuracy and the stability of polynomial models of different degrees, the linear model is a preferred choice for cell fate prediction with gene expression data of pancreatic cells. The presented cell fate prediction model can be extended to other cells, which may be important for basic research as well as clinical study of cell development related diseases.

Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan

2012-12-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

Synchronization of generalized Henon map using polynomial controller

International Nuclear Information System (INIS)

Lam, H.K.

2010-01-01

This Letter presents the chaos synchronization of two discrete-time generalized Henon map, namely the drive and response systems. A polynomial controller is proposed to drive the system states of the response system to follow those of the drive system. The system stability of the error system formed by the drive and response systems and the synthesis of the polynomial controller are investigated using the sum-of-squares (SOS) technique. Based on the Lyapunov stability theory, stability conditions in terms of SOS are derived to guarantee the system stability and facilitate the controller synthesis. By satisfying the SOS-based stability conditions, chaotic synchronization is achieved. The solution of the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. A simulation example is given to illustrate the merits of the proposed polynomial control approach.

Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem

2012-01-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

Semi-automated detection of aberrant chromosomes in bivariate flow karyotypes

NARCIS (Netherlands)

Boschman, G. A.; Manders, E. M.; Rens, W.; Slater, R.; Aten, J. A.

1992-01-01

A method is described that is designed to compare, in a standardized procedure, bivariate flow karyotypes of Hoechst 33258 (HO)/Chromomycin A3 (CA) stained human chromosomes from cells with aberrations with a reference flow karyotype of normal chromosomes. In addition to uniform normalization of

Non-existence criteria for Laurent polynomial first integrals

Directory of Open Access Journals (Sweden)

Shaoyun Shi

2003-01-01

Full Text Available In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations $\\dot x = f(x$, $x \\in \\mathbb{R}^n$ with $f(0 = 0$. We show that if the eigenvalues of the Jacobi matrix of the vector field $f(x$ are $\\mathbb{Z}$-independent, then the system has no nontrivial Laurent polynomial integrals.

Vanishing of Littlewood-Richardson polynomials is in P

OpenAIRE

Adve, Anshul; Robichaux, Colleen; Yong, Alexander

2017-01-01

J. DeLoera-T. McAllister and K. D. Mulmuley-H. Narayanan-M. Sohoni independently proved that determining the vanishing of Littlewood-Richardson coefficients has strongly polynomial time computational complexity. Viewing these as Schubert calculus numbers, we prove the generalization to the Littlewood-Richardson polynomials that control equivariant cohomology of Grassmannians. We construct a polytope using the edge-labeled tableau rule of H. Thomas-A. Yong. Our proof then combines a saturation...

Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations

International Nuclear Information System (INIS)

Clarkson, Peter A

2013-01-01

We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations can be expressed in terms of Wronskians of modified Bessel functions and confluent hypergeometric functions, respectively for the generalized Charlier and generalized Meixner polynomials. These Wronskians arise in the description of special function solutions of the third and fifth Painlevé equations. (paper)

Design and Use of a Learning Object for Finding Complex Polynomial Roots

Science.gov (United States)

Benitez, Julio; Gimenez, Marcos H.; Hueso, Jose L.; Martinez, Eulalia; Riera, Jaime

2013-01-01

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

Applied Statistics: From Bivariate through Multivariate Techniques [with CD-ROM

Science.gov (United States)

Warner, Rebecca M.

2007-01-01

This book provides a clear introduction to widely used topics in bivariate and multivariate statistics, including multiple regression, discriminant analysis, MANOVA, factor analysis, and binary logistic regression. The approach is applied and does not require formal mathematics; equations are accompanied by verbal explanations. Students are asked…

Two polynomial division inequalities in

Directory of Open Access Journals (Sweden)

Goetgheluck P

1998-01-01

Full Text Available This paper is a first attempt to give numerical values for constants and , in classical estimates and where is an algebraic polynomial of degree at most and denotes the -metric on . The basic tools are Markov and Bernstein inequalities.

Asymptotics for the ratio and the zeros of multiple Charlier polynomials

OpenAIRE

Ndayiragije, François; Van Assche, Walter

2011-01-01

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depend on the degree of the polynomial, in which case we obtain another asymptotic distributio...

H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach

OpenAIRE

Bomo W. Sanjaya; Bambang Riyanto Trilaksono; Arief Syaichu-Rohman

2014-01-01

This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simul...

Catalytic Unmixed Combustion of Coal with Zero Pollution

Energy Technology Data Exchange (ETDEWEB)

George Rizeq; Parag Kulkarni; Raul Subia; Wei Wei

2005-12-01

GE Global Research is developing an innovative energy-based technology for coal combustion with high efficiency and near-zero pollution. This Unmixed Combustion of coal (UMC-Coal) technology simultaneously converts coal, steam and air into two separate streams of high pressure CO{sub 2}-rich gas for sequestration, and high-temperature, high-pressure vitiated air for producing electricity in gas turbine expanders. The UMC process utilizes an oxygen transfer material (OTM) and eliminates the need for an air separation unit (ASU) and a CO{sub 2} separation unit as compared to conventional gasification based processes. This is the final report for the two-year DOE-funded program (DE-FC26-03NT41842) on this technology that ended in September 30, 2005. The UMC technology development program encompassed lab- and pilot-scale studies to demonstrate the UMC concept. The chemical feasibility of the individual UMC steps was established via lab-scale testing. A pilot plant, designed in a related DOE funded program (DE-FC26-00FT40974), was reconstructed and operated to demonstrate the chemistry of UMC process in a pilot-scale system. The risks associated with this promising technology including cost, lifetime and durability OTM and the impact of contaminants on turbine performance are currently being addressed in detail in a related ongoing DOE funded program (DE-FC26-00FT40974, Phase II). Results obtained to date suggest that this technology has the potential to economically meet future efficiency and environmental performance goals.

Euler Polynomials and Identities for Non-Commutative Operators

OpenAIRE

De Angelis, V.; Vignat, C.

2015-01-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...

Local polynomial Whittle estimation of perturbed fractional processes

DEFF Research Database (Denmark)

Frederiksen, Per; Nielsen, Frank; Nielsen, Morten Ørregaard

We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the spectrum of the perturbation as well as that of the short-memory component...... of the signal by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptotic variance of the long memory estimate by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal...... for d ε (0, 3/4), and if the spectral density is infinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, pn. A Monte Carlo study reveals that the LPWN estimator performs well in the presence of a serially correlated perturbation term...

Polynomial algebra of discrete models in systems biology.

Science.gov (United States)

Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2010-07-01

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

Polynomial chaos expansion with random and fuzzy variables

Science.gov (United States)

Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.

2016-06-01

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.

Polynomial Vector Fields in One Complex Variable

DEFF Research Database (Denmark)

Branner, Bodil

In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....

Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices

Directory of Open Access Journals (Sweden)

Hjalmar Rosengren

2006-12-01

Full Text Available We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux and number theory (representation of integers as sums of squares.

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type.

Science.gov (United States)

Sidharth, Manjari; Agrawal, P N; Araci, Serkan

2017-01-01

The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012). We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with the help of Lipschitz type space and weighted modulus of continuity. Next, we obtain a direct approximation theorem with the aid of unified Ditzian-Totik modulus of smoothness. Furthermore, we study the approximation of functions whose derivatives are locally of bounded variation.

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type

Directory of Open Access Journals (Sweden)

Manjari Sidharth

2017-05-01

Full Text Available Abstract The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012. We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with the help of Lipschitz type space and weighted modulus of continuity. Next, we obtain a direct approximation theorem with the aid of unified Ditzian-Totik modulus of smoothness. Furthermore, we study the approximation of functions whose derivatives are locally of bounded variation.

An extension of Krawtchouk\\'s polynomials to the contstruction of ...

African Journals Online (AJOL)

A simple method is described for the construction of a set of orthogonal polynomials for any case where the proportions of observations follow a binomial distribution. The least squares equation which fits the data is determined using the properties of orthogonal polynomials and the analysis of variance technique.

Geometry of polynomials and root-finding via path-lifting

Science.gov (United States)

Kim, Myong-Hi; Martens, Marco; Sutherland, Scott

2018-02-01

Using the interplay between topological, combinatorial, and geometric properties of polynomials and analytic results (primarily the covering structure and distortion estimates), we analyze a path-lifting method for finding approximate zeros, similar to those studied by Smale, Shub, Kim, and others. Given any polynomial, this simple algorithm always converges to a root, except on a finite set of initial points lying on a circle of a given radius. Specifically, the algorithm we analyze consists of iterating where the t k form a decreasing sequence of real numbers and z 0 is chosen on a circle containing all the roots. We show that the number of iterates required to locate an approximate zero of a polynomial f depends only on log\\vert f(z_0)/ρ_\\zeta\\vert (where ρ_\\zeta is the radius of convergence of the branch of f-1 taking 0 to a root ζ) and the logarithm of the angle between f(z_0) and certain critical values. Previous complexity results for related algorithms depend linearly on the reciprocals of these angles. Note that the complexity of the algorithm does not depend directly on the degree of f, but only on the geometry of the critical values. Furthermore, for any polynomial f with distinct roots, the average number of steps required over all starting points taken on a circle containing all the roots is bounded by a constant times the average of log(1/ρ_\\zeta) . The average of log(1/ρ_\\zeta) over all polynomials f with d roots in the unit disk is \

On the matched pairs sign test using bivariate ranked set sampling ...

African Journals Online (AJOL)

BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived.

The Combinatorial Rigidity Conjecture is False for Cubic Polynomials

DEFF Research Database (Denmark)

Henriksen, Christian

2003-01-01

We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995.......We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995....

Ratio asymptotics of Hermite-Pade polynomials for Nikishin systems

International Nuclear Information System (INIS)

Aptekarev, A I; Lopez, Guillermo L; Rocha, I A

2005-01-01

The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.

Asymptotic behaviour of the zeros of the Jacobi polynomials Psub(n)(chi)sup(at,bt) as t→infinity and limit relations of these polynomials with Hermite polynomials

International Nuclear Information System (INIS)

Calogero, F.

1978-01-01

Let zsub(j)(α, β) be the jth zero of the Jacobi polynomial J sub(n)sup(α,β)(z), and xsub(j) the jth zero of the Hermite polynomial Hsub(n)(x). Then, as t→infinity, zsub(j)(at,bt)=(b-a)/(b+a)+t sup(-1/2)c x sub(j)+t -1 4/3(n+1/2+xsub(j) 2 )(a-b)/(a+b) 2 +0(t sup(-3/2)), with c=(ab)sup(1/2) [(a+b)/2]sup(-3/2) a>0, b>0. This formula implies the limit relation n exclamation mark lim sub(t→infinity) [t sup(-n/2)J sub(n)sup(at,bt) ((b-a)/(b+a)+t sup(-1/2)x)] = [(a+b)c/4]sup(n) Hsub(n)(chi/c). (author)

Congruences concerning Legendre polynomials III

OpenAIRE

Sun, Zhi-Hong

2010-01-01

Let $p>3$ be a prime, and let $R_p$ be the set of rational numbers whose denominator is coprime to $p$. Let $\\{P_n(x)\\}$ be the Legendre polynomials. In this paper we mainly show that for $m,n,t\\in R_p$ with $m\

Global Polynomial Kernel Hazard Estimation

DEFF Research Database (Denmark)

Hiabu, Munir; Miranda, Maria Dolores Martínez; Nielsen, Jens Perch

2015-01-01

This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically redu...

Optimal Conformal Polynomial Projections for Croatia According to the Airy/Jordan Criterion

Directory of Open Access Journals (Sweden)

Dražen Tutić

2009-05-01

Full Text Available The paper describes optimal conformal polynomial projections for Croatia according to the Airy/Jordan criterion. A brief introduction of history and theory of conformal mapping is followed by descriptions of conformal polynomial projections and their current application. The paper considers polynomials of degrees 1 to 10. Since there are conditions in which the 1st degree polynomial becomes the famous Mercator projection, it was not considered specifically for Croatian territory. The area of Croatia was defined as a union of national territory and the continental shelf. Area definition data were taken from the Euro Global Map 1:1 000 000 for Croatia, as well as from two maritime delimitation treaties. Such an irregular area was approximated with a regular grid consisting of 11 934 ellipsoidal trapezoids 2' large. The Airy/Jordan criterion for the optimal projection is defined as minimum of weighted mean of Airy/Jordan measure of distortion in points. The value of the Airy/Jordan criterion is calculated from all 11 934 centres of ellipsoidal trapezoids, while the weights are equal to areas of corresponding ellipsoidal trapezoids. The minimum is obtained by Nelder and Mead’s method, as implemented in the fminsearch function of the MATLAB package. Maps of Croatia representing the distribution of distortions are given for polynomial degrees 2 to 6 and 10. Increasing the polynomial degree results in better projections considering the criterion, and the 6th degree polynomial provides a good ratio of formula complexity and criterion value.

Polynomial realization of the Uq (sl(3)) Gel'fand-(Weyl)-Zetlin basis

International Nuclear Information System (INIS)

Dobrev, V.K.; Truini, P.

1996-01-01

We give an explicit realization of the U ≡ U q (sl(3)) Gel'fand-(Weyl)-Zetlin (GWZ) basis as polynomial functions in three variables. This realization is obtained in two complementary ways. First we establish a 1-to-1 correspondence between the abstract GWZ basis and explicit polynomials in the quantum subgroup U + of the raising generators. We then use an explicit construction of arbitrary lowest weight (holomorphic) representations of U in terms of three variables on which the generators of U are realized as q-difference operators. Applying the GWZ corresponding polynomials in this realization to the lowest weight vector (the function 1) produces one realization of our GWZ basis. Another realization of the GWZ polynomial basis is found by the explicit diagonalization of the operators of isospin I-circumflex 2 , third component of isospin I-circumflex z , and hypercharge Y-circumflex, in the same realization as q-difference operators. The result is that the eigenvectors can be written in terms of q-hypergeometric polynomials in our three variables. Finally we construct an explicit scalar product (adapting the Shapovalov form to our setting). Using it we prove the orthogonality of our GWZ polynomials for which we use both realizations. This provides a polynomial construction for the orthonormal GWZ basis. We work for generic q, leaving the root of unity case for a following paper. It seems that our results are new also in the classical situation (q=1). (author). 20 refs

Real zeros of classes of random algebraic polynomials

Directory of Open Access Journals (Sweden)

K. Farahmand

2003-01-01

Full Text Available There are many known asymptotic estimates for the expected number of real zeros of an algebraic polynomial a0+a1x+a2x2+⋯+an−1xn−1 with identically distributed random coefficients. Under different assumptions for the distribution of the coefficients {aj}j=0n−1 it is shown that the above expected number is asymptotic to O(logn. This order for the expected number of zeros remains valid for the case when the coefficients are grouped into two, each group with a different variance. However, it was recently shown that if the coefficients are non-identically distributed such that the variance of the jth term is (nj the expected number of zeros of the polynomial increases to O(n. The present paper provides the value for this asymptotic formula for the polynomials with the latter variances when they are grouped into three with different patterns for their variances.

a Unified Matrix Polynomial Approach to Modal Identification

Science.gov (United States)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks

Czech Academy of Sciences Publication Activity Database

Knížek, J.; Tichý, Petr; Beránek, L.; Šindelář, Jan; Vojtěšek, B.; Bouchal, P.; Nenutil, R.; Dedík, O.

2010-01-01

Roč. 7, č. 10 (2010), s. 48-60 ISSN 0974-5718 Grant - others:GA MZd(CZ) NS9812; GA ČR(CZ) GAP304/10/0868 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10750506 Keywords : polynomial regression * orthogonalization * numerical methods * markers * biomarkers Subject RIV: BA - General Mathematics

Quantum entanglement via nilpotent polynomials

International Nuclear Information System (INIS)

Mandilara, Aikaterini; Akulin, Vladimir M.; Smilga, Andrei V.; Viola, Lorenza

2006-01-01

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed

Nuclear-magnetic-resonance quantum calculations of the Jones polynomial

International Nuclear Information System (INIS)

Marx, Raimund; Spoerl, Andreas; Pomplun, Nikolas; Schulte-Herbrueggen, Thomas; Glaser, Steffen J.; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Myers, John M.

2010-01-01

The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for a small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots.

Weierstrass method for quaternionic polynomial root-finding

Science.gov (United States)

Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana

2018-01-01

Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.

A set of sums for continuous dual q-2-Hahn polynomials

International Nuclear Information System (INIS)

Gade, R. M.

2009-01-01

An infinite set {τ (l) (y;r,z)} r,lisanelementofN 0 of linear sums of continuous dual q -2 -Hahn polynomials with prefactors depending on a complex parameter z is studied. The sums τ (l) (y;r,z) have an interpretation in context with tensor product representations of the quantum affine algebra U q ' (sl(2)) involving both a positive and a negative discrete series representation. For each l>0, the sum τ (l) (y;r,z) can be expressed in terms of the sum τ (0) (y;r,z), continuous dual q 2 -Hahn polynomials, and their associated polynomials. The sum τ (0) (y;r,z) is obtained as a combination of eight basic hypergeometric series. Moreover, an integral representation is provided for the sums τ (l) (y;r,z) with the complex parameter restricted by |zq| -2 -Hahn polynomials.

Fibonacci-like Differential Equations with a Polynomial Non-Homogeneous Part

NARCIS (Netherlands)

Asveld, P.R.J.

1989-01-01

We investigate non-homogeneous linear differential equations of the form $x''(t) + x'(t) - x(t) = p(t)$ where $p(t)$ is either a polynomial or a factorial polynomial in $t$. We express the solution of these differential equations in terms of the coefficients of $p(t)$, in the initial conditions, and

Sparse DOA estimation with polynomial rooting

DEFF Research Database (Denmark)

Xenaki, Angeliki; Gerstoft, Peter; Fernandez Grande, Efren

2015-01-01

Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve highresol......Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve...... highresolution imaging. Utilizing the dual optimal variables of the CS optimization problem, it is shown with Monte Carlo simulations that the DOAs are accurately reconstructed through polynomial rooting (Root-CS). Polynomial rooting is known to improve the resolution in several other DOA estimation methods...

Smoothing of the bivariate LOD score for non-normal quantitative traits.

Science.gov (United States)

Buil, Alfonso; Dyer, Thomas D; Almasy, Laura; Blangero, John

2005-12-30

Variance component analysis provides an efficient method for performing linkage analysis for quantitative traits. However, type I error of variance components-based likelihood ratio testing may be affected when phenotypic data are non-normally distributed (especially with high values of kurtosis). This results in inflated LOD scores when the normality assumption does not hold. Even though different solutions have been proposed to deal with this problem with univariate phenotypes, little work has been done in the multivariate case. We present an empirical approach to adjust the inflated LOD scores obtained from a bivariate phenotype that violates the assumption of normality. Using the Collaborative Study on the Genetics of Alcoholism data available for the Genetic Analysis Workshop 14, we show how bivariate linkage analysis with leptokurtotic traits gives an inflated type I error. We perform a novel correction that achieves acceptable levels of type I error.

Increasing the Accuracy of Mapping Urban Forest Carbon Density by Combining Spatial Modeling and Spectral Unmixing Analysis

Directory of Open Access Journals (Sweden)

Hua Sun

2015-11-01

Full Text Available Accurately mapping urban vegetation carbon density is challenging because of complex landscapes and mixed pixels. In this study, a novel methodology was proposed that combines a linear spectral unmixing analysis (LSUA with a linear stepwise regression (LSR, a logistic model-based stepwise regression (LMSR and k-Nearest Neighbors (kNN, to map the forest carbon density of Shenzhen City of China, using Landsat 8 imagery and sample plot data collected in 2014. The independent variables that contributed to statistically significantly improving the fit of a model to data and reducing the sum of squared errors were first selected from a total of 284 spectral variables derived from the image bands. The vegetation fraction from LSUA was then added as an independent variable. The results obtained using cross-validation showed that: (1 Compared to the methods without the vegetation information, adding the vegetation fraction increased the accuracy of mapping carbon density by 1%–9.3%; (2 As the observed values increased, the LSR and kNN residuals showed overestimates and underestimates for the smaller and larger observations, respectively, while LMSR improved the systematical over and underestimations; (3 LSR resulted in illogically negative and unreasonably large estimates, while KNN produced the greatest values of root mean square error (RMSE. The results indicate that combining the spatial modeling method LMSR and the spectral unmixing analysis LUSA, coupled with Landsat imagery, is most promising for increasing the accuracy of urban forest carbon density maps. In addition, this method has considerable potential for accurate, rapid and nondestructive prediction of urban and peri-urban forest carbon stocks with an acceptable level of error and low cost.

Polynomials in finite geometries and combinatorics

NARCIS (Netherlands)

Blokhuis, A.; Walker, K.

1993-01-01

It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.

Dirichlet polynomials, majorization, and trumping

International Nuclear Information System (INIS)

Pereira, Rajesh; Plosker, Sarah

2013-01-01

Majorization and trumping are two partial orders which have proved useful in quantum information theory. We show some relations between these two partial orders and generalized Dirichlet polynomials, Mellin transforms, and completely monotone functions. These relations are used to prove a succinct generalization of Turgut’s characterization of trumping. (paper)

The neighbourhood polynomial of some families of dendrimers

Science.gov (United States)

Nazri Husin, Mohamad; Hasni, Roslan

2018-04-01

The neighbourhood polynomial N(G,x) is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph and it is defined as (G,x)={\\sum }U\\in N(G){x}|U|, where N(G) is neighbourhood complex of a graph, whose vertices of the graph and faces are subsets of vertices that have a common neighbour. A dendrimers is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, we compute this polynomial for some families of dendrimer.

A new derivation of the highest-weight polynomial of a unitary lie algebra

International Nuclear Information System (INIS)

P Chau, Huu-Tai; P Van, Isacker

2000-01-01

A new method is presented to derive the expression of the highest-weight polynomial used to build the basis of an irreducible representation (IR) of the unitary algebra U(2J+1). After a brief reminder of Moshinsky's method to arrive at the set of equations defining the highest-weight polynomial of U(2J+1), an alternative derivation of the polynomial from these equations is presented. The method is less general than the one proposed by Moshinsky but has the advantage that the determinantal expression of the highest-weight polynomial is arrived at in a direct way using matrix inversions. (authors)

A probabilistic approach of sum rules for heat polynomials

International Nuclear Information System (INIS)

Vignat, C; Lévêque, O

2012-01-01

In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. http://dx.doi.org/10.1088/0305-4470/38/2/010) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered using a probabilistic moment representation of these polynomials. The covariance property of the raising operator of the harmonic oscillator, which is at the origin of the identities proved in Daboul and Mizrahi and the dimension reduction effect expressed in the main result of Graczyk and Nowak are both interpreted in terms of the rotational invariance of the Gaussian distributions. As an application of these results, we uncover a probabilistic moment interpretation of two classical integrals of the Wigner function that involve the associated Laguerre polynomials. (paper)

GEMAS: Unmixing magnetic properties of European agricultural soil

Science.gov (United States)

Fabian, Karl; Reimann, Clemens; Kuzina, Dilyara; Kosareva, Lina; Fattakhova, Leysan; Nurgaliev, Danis

2016-04-01

High resolution magnetic measurements provide new methods for world-wide characterization and monitoring of agricultural soil which is essential for quantifying geologic and human impact on the critical zone environment and consequences of climatic change, for planning economic and ecological land use, and for forensic applications. Hysteresis measurements of all Ap samples from the GEMAS survey yield a comprehensive overview of mineral magnetic properties in European agricultural soil on a continental scale. Low (460 Hz), and high frequency (4600 Hz) magnetic susceptibility k were measured using a Bartington MS2B sensor. Hysteresis properties were determined by a J-coercivity spectrometer, built at the paleomagnetic laboratory of Kazan University, providing for each sample a modified hysteresis loop, backfield curve, acquisition curve of isothermal remanent magnetization, and a viscous IRM decay spectrum. Each measurement set is obtained in a single run from zero field up to 1.5 T and back to -1.5 T. The resulting data are used to create the first continental-scale maps of magnetic soil parameters. Because the GEMAS geochemical atlas contains a comprehensive set of geochemical data for the same soil samples, the new data can be used to map magnetic parameters in relation to chemical and geological parameters. The data set also provides a unique opportunity to analyze the magnetic mineral fraction of the soil samples by unmixing their IRM acquisition curves. The endmember coefficients are interpreted by linear inversion for other magnetic, physical and chemical properties which results in an unprecedented and detailed view of the mineral magnetic composition of European agricultural soils.

A Combinatorial Proof of a Result on Generalized Lucas Polynomials

Directory of Open Access Journals (Sweden)

Laugier Alexandre

2016-09-01

Full Text Available We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.

A Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials

Directory of Open Access Journals (Sweden)

Fatma Taşdelen

2012-01-01

convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials.

Lower bounds for the circuit size of partially homogeneous polynomials

Czech Academy of Sciences Publication Activity Database

Le, Hong-Van

2017-01-01

Roč. 225, č. 4 (2017), s. 639-657 ISSN 1072-3374 Institutional support: RVO:67985840 Keywords : partially homogeneous polynomials * polynomials Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) https://link.springer.com/article/10.1007/s10958-017-3483-4

Generalized catalan numbers, sequences and polynomials

OpenAIRE

KOÇ, Cemal; GÜLOĞLU, İsmail; ESİN, Songül

2010-01-01

In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.

Multilevel weighted least squares polynomial approximation

KAUST Repository

Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren

2017-01-01

, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose

An algorithmic approach to solving polynomial equations associated with quantum circuits

International Nuclear Information System (INIS)

Gerdt, V.P.; Zinin, M.V.

2009-01-01

In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Groebner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Groebner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Groebner bases over F 2

Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

Science.gov (United States)

Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

2018-05-01

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

Canonical basis for type A4 (II) - Polynomial elements in one variable

International Nuclear Information System (INIS)

Hu Yuwang; Ye Jiachen

2003-12-01

All the 62 monomial elements in the canonical basis B of the quantized enveloping algebra for type A 4 have been determined. According to Lusztig's idea, the elements in the canonical basis B consist of monomials and linear combinations of monomials (for convenience, we call them polynomials). In this note, we compute all the 144 polynomial elements in one variable in the canonical basis B of the quantized enveloping algebra for type A 4 based on our joint note. We conjecture that there are other polynomial elements in two or three variables in the canonical basis B, which include independent variables and dependent variables. Moreover, it is conjectured that there are no polynomial elements in the canonical basis B with four or more variables. (author)

Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials

OpenAIRE

N. Stojanovic; N. Stamenkovic; I. Krstic

2016-01-01

A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approx...

Bounds and asymptotics for orthogonal polynomials for varying weights

CERN Document Server

Levin, Eli

2018-01-01

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.  Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics.  This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .

On Linear Combinations of Two Orthogonal Polynomial Sequences on the Unit Circle

Directory of Open Access Journals (Sweden)

Suárez C

2010-01-01

Full Text Available Let be a monic orthogonal polynomial sequence on the unit circle. We define recursively a new sequence of polynomials by the following linear combination: , , . In this paper, we give necessary and sufficient conditions in order to make be an orthogonal polynomial sequence too. Moreover, we obtain an explicit representation for the Verblunsky coefficients and in terms of and . Finally, we show the relation between their corresponding Carathéodory functions and their associated linear functionals.

On the existence of polynomial Lyapunov functions for rationally stable vector fields

DEFF Research Database (Denmark)

Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer

2018-01-01

This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....

Testing independence of bivariate interval-censored data using modified Kendall's tau statistic.

Science.gov (United States)

Kim, Yuneung; Lim, Johan; Park, DoHwan

2015-11-01

In this paper, we study a nonparametric procedure to test independence of bivariate interval censored data; for both current status data (case 1 interval-censored data) and case 2 interval-censored data. To do it, we propose a score-based modification of the Kendall's tau statistic for bivariate interval-censored data. Our modification defines the Kendall's tau statistic with expected numbers of concordant and disconcordant pairs of data. The performance of the modified approach is illustrated by simulation studies and application to the AIDS study. We compare our method to alternative approaches such as the two-stage estimation method by Sun et al. (Scandinavian Journal of Statistics, 2006) and the multiple imputation method by Betensky and Finkelstein (Statistics in Medicine, 1999b). © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Unmixing of spectral components affecting AVIRIS imagery of Tampa Bay

Science.gov (United States)

Carder, Kendall L.; Lee, Z. P.; Chen, Robert F.; Davis, Curtiss O.

1993-09-01

According to Kirk's as well as Morel and Gentili's Monte Carlo simulations, the popular simple expression, R approximately equals 0.33 bb/a, relating subsurface irradiance reflectance (R) to the ratio of the backscattering coefficient (bb) to absorption coefficient (a), is not valid for bb/a > 0.25. This means that it may no longer be valid for values of remote-sensing reflectance (above-surface ratio of water-leaving radiance to downwelling irradiance) where Rrs4/ > 0.01. Since there has been no simple Rrs expression developed for very turbid waters, we developed one based in part on Monte Carlo simulations and empirical adjustments to an Rrs model and applied it to rather turbid coastal waters near Tampa Bay to evaluate its utility for unmixing the optical components affecting the water- leaving radiance. With the high spectral (10 nm) and spatial (20 m2) resolution of Airborne Visible-InfraRed Imaging Spectrometer (AVIRIS) data, the water depth and bottom type were deduced using the model for shallow waters. This research demonstrates the necessity of further research to improve interpretations of scenes with highly variable turbid waters, and it emphasizes the utility of high spectral-resolution data as from AVIRIS for better understanding complicated coastal environments such as the west Florida shelf.

On Modular Counting with Polynomials

DEFF Research Database (Denmark)

Hansen, Kristoffer Arnsfelt

2006-01-01

For any integers m and l, where m has r sufficiently large (depending on l) factors, that are powers of r distinct primes, we give a construction of a (symmetric) polynomial over Z_m of degree O(\\sqrt n) that is a generalized representation (commonly also called weak representation) of the MODl f...

A Bivariate return period for levee failure monitoring

Science.gov (United States)

Isola, M.; Caporali, E.

2017-12-01

Levee breaches are strongly linked with the interaction processes among water, soil and structure, thus many are the factors that affect the breach development. One of the main is the hydraulic load, characterized by intensity and duration, i.e. by the flood event hydrograph. On the magnitude of the hydraulic load is based the levee design, generally without considering the fatigue failure due to the load duration. Moreover, many are the cases in which the levee breach are characterized by flood of magnitude lower than the design one. In order to implement the strategies of flood risk management, we built here a procedure based on a multivariate statistical analysis of flood peak and volume together with the analysis of the past levee failure events. Particularly, in order to define the probability of occurrence of the hydraulic load on a levee, a bivariate copula model is used to obtain the bivariate joint distribution of flood peak and volume. Flood peak is the expression of the load magnitude, while the volume is the expression of the stress over time. We consider the annual flood peak and the relative volume. The volume is given by the hydrograph area between the beginning and the end of event. The beginning of the event is identified as an abrupt rise of the discharge by more than 20%. The end is identified as the point from which the receding limb is characterized by the baseflow, using a nonlinear reservoir algorithm as baseflow separation technique. By this, with the aim to define warning thresholds we consider the past levee failure events and the relative bivariate return period (BTr) compared with the estimation of a traditional univariate model. The discharge data of 30 hydrometric stations of Arno River in Tuscany, Italy, in the period 1995-2016 are analysed. The database of levee failure events, considering for each event the location as well as the failure mode, is also created. The events were registered in the period 2000-2014 by EEA

Bernoulli numbers and polynomials from a more general point of view

Energy Technology Data Exchange (ETDEWEB)

Dattoli, G. [ENEA, Centro Ricerche Frascati, Frascati, RM(Italy). Div. Fisica Applicata; Cesarano, C. [Ulm Univ., Ulm (Germany). Dept. of Mathematics; Lonzellutta, S. [ENEA, Centro Ricerche E. Clementel, Bologna (Italy). Div. Fisica Applicata

2000-07-01

In this work it is applied the method of generating function, to introduce new forms of Bernoulli numbers and polynomials, which are exploited to derive further classes of partial sums involving generalized many index many variable polynomials. Analogous considerations are developed for the Euler numbers and polynomials. [Italian] Si applica il metodo della funzione generatrice per introdurre nuove forme di numeri e polinomi di Bernoulli che vengono utilizzati per sviluppare e per calcolare somme parziali che coinvolgono polinomi a piu' indici ed a piu' variabili. Si sviluppano considerazioni analoghe per i polinomi ed i numeri di Eulero.

Quantum Hurwitz numbers and Macdonald polynomials

Science.gov (United States)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

International Nuclear Information System (INIS)

Hampton, Jerrad; Doostan, Alireza

2015-01-01

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ 1 -minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

Science.gov (United States)

Hampton, Jerrad; Doostan, Alireza

2015-01-01

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ1-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

Science.gov (United States)

Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan

2012-01-01

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. © 2012 Acoustical Society of America.

Tensor calculus in polar coordinates using Jacobi polynomials

Science.gov (United States)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems

Science.gov (United States)

Chen, Zhijie; Kuo, Ting-Jung; Lin, Chang-Shou; Takemura, Kouichi

2018-04-01

We study the spectral polynomial of the Treibich-Verdier potential. Such spectral polynomial, which is a generalization of the classical Lamé polynomial, plays fundamental roles in both the finite-gap theory and the ODE theory of Heun's equation. In this paper, we prove that all the roots of such spectral polynomial are real and distinct under some assumptions. The proof uses the classical concept of Sturm sequence and isomonodromic theories. We also prove an analogous result for a polynomial associated with a generalized Lamé equation, where we apply a new approach based on the viewpoint of the monodromy data.

On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

Directory of Open Access Journals (Sweden)

Tian-Xiao He

2009-01-01

Full Text Available Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

Directory of Open Access Journals (Sweden)

Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure

Directory of Open Access Journals (Sweden)

S. Vukotic

2016-08-01

Full Text Available Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.

Robust bivariate error detection in skewed data with application to historical radiosonde winds

KAUST Repository

Sun, Ying

2017-01-18

The global historical radiosonde archives date back to the 1920s and contain the only directly observed measurements of temperature, wind, and moisture in the upper atmosphere, but they contain many random errors. Most of the focus on cleaning these large datasets has been on temperatures, but winds are important inputs to climate models and in studies of wind climatology. The bivariate distribution of the wind vector does not have elliptical contours but is skewed and heavy-tailed, so we develop two methods for outlier detection based on the bivariate skew-t (BST) distribution, using either distance-based or contour-based approaches to flag observations as potential outliers. We develop a framework to robustly estimate the parameters of the BST and then show how the tuning parameter to get these estimates is chosen. In simulation, we compare our methods with one based on a bivariate normal distribution and a nonparametric approach based on the bagplot. We then apply all four methods to the winds observed for over 35,000 radiosonde launches at a single station and demonstrate differences in the number of observations flagged across eight pressure levels and through time. In this pilot study, the method based on the BST contours performs very well.

Robust bivariate error detection in skewed data with application to historical radiosonde winds

KAUST Repository

Sun, Ying; Hering, Amanda S.; Browning, Joshua M.

2017-01-01

The global historical radiosonde archives date back to the 1920s and contain the only directly observed measurements of temperature, wind, and moisture in the upper atmosphere, but they contain many random errors. Most of the focus on cleaning these large datasets has been on temperatures, but winds are important inputs to climate models and in studies of wind climatology. The bivariate distribution of the wind vector does not have elliptical contours but is skewed and heavy-tailed, so we develop two methods for outlier detection based on the bivariate skew-t (BST) distribution, using either distance-based or contour-based approaches to flag observations as potential outliers. We develop a framework to robustly estimate the parameters of the BST and then show how the tuning parameter to get these estimates is chosen. In simulation, we compare our methods with one based on a bivariate normal distribution and a nonparametric approach based on the bagplot. We then apply all four methods to the winds observed for over 35,000 radiosonde launches at a single station and demonstrate differences in the number of observations flagged across eight pressure levels and through time. In this pilot study, the method based on the BST contours performs very well.

Invariant hyperplanes and Darboux integrability of polynomial vector fields

International Nuclear Information System (INIS)

Zhang Xiang

2002-01-01

This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables. This result generalizes those given in Artes et al (1998 Pac. J. Math. 184 207-30) and Llibre and Rodriguez (2000 Bull. Sci. Math. 124 599-619). The second part gives an extension of the Darboux theory of integrability to polynomial vector fields on algebraic varieties

Chain Plot: A Tool for Exploiting Bivariate Temporal Structures

OpenAIRE

Taylor, CC; Zempeni, A

2004-01-01

In this paper we present a graphical tool useful for visualizing the cyclic behaviour of bivariate time series. We investigate its properties and link it to the asymmetry of the two variables concerned. We also suggest adding approximate confidence bounds to the points on the plot and investigate the effect of lagging to the chain plot. We conclude our paper by some standard Fourier analysis, relating and comparing this to the chain plot.

A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

Science.gov (United States)

Narkawicz, Anthony; Munoz, Cesar

2015-01-01

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.

On selfadjoint functors satisfying polynomial relations

DEFF Research Database (Denmark)

Agerholm, Troels; Mazorchuk, Volodomyr

2011-01-01

We study selfadjoint functors acting on categories of finite dimen- sional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint func- tors satisfying several easy relations, in particular, idempotents and square roots of a sum...

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

Energy Technology Data Exchange (ETDEWEB)

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

International Nuclear Information System (INIS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-01-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10

Bivariate tensor product ( p , q $(p, q$ -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators

Directory of Open Access Journals (Sweden)

Qing-Bo Cai

2017-11-01

Full Text Available Abstract In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of ( p , q $(p, q$ -integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions.

Bayer Demosaicking with Polynomial Interpolation.

Science.gov (United States)

Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil

2016-08-30

Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.

Polynomials in algebraic analysis

OpenAIRE

Multarzyński, Piotr

2012-01-01

The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \\cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear ...

Estimating the formation age distribution of continental crust by unmixing zircon ages

Science.gov (United States)

Korenaga, Jun

2018-01-01

Continental crust provides first-order control on Earth's surface environment, enabling the presence of stable dry landmasses surrounded by deep oceans. The evolution of continental crust is important for atmospheric evolution, because continental crust is an essential component of deep carbon cycle and is likely to have played a critical role in the oxygenation of the atmosphere. Geochemical information stored in the mineral zircon, known for its resilience to diagenesis and metamorphism, has been central to ongoing debates on the genesis and evolution of continental crust. However, correction for crustal reworking, which is the most critical step when estimating original formation ages, has been incorrectly formulated, undermining the significance of previous estimates. Here I suggest a simple yet promising approach for reworking correction using the global compilation of zircon data. The present-day distribution of crustal formation age estimated by the new "unmixing" method serves as the lower bound to the true crustal growth, and large deviations from growth models based on mantle depletion imply the important role of crustal recycling through the Earth history.

Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement

International Nuclear Information System (INIS)

van Diejen, J.F.

1997-01-01

Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl. (orig.)

Global sensitivity analysis using sparse grid interpolation and polynomial chaos

International Nuclear Information System (INIS)

Buzzard, Gregery T.

2012-01-01

Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evaluations to estimate several types of sensitivity coefficients and to provide estimates on local minima and maxima. First, we provide a good estimate of the variance-based sensitivity coefficients of Sobol' (1990) [1] and then use the gradient of the gPC representation to give good approximations to the derivative-based sensitivity coefficients described by Kucherenko and Sobol' (2009) [2]. Finally, we use the package HOM4PS-2.0 given in Lee et al. (2008) [3] to determine the critical points of the interpolating polynomial and use these to determine the local minima and maxima of this polynomial. - Highlights: ► Efficient estimation of variance-based sensitivity coefficients. ► Efficient estimation of derivative-based sensitivity coefficients. ► Use of homotopy methods for approximation of local maxima and minima.

Application of Chybeshev Polynomials in Factorizations of Balancing and Lucas-Balancing Numbers

Directory of Open Access Journals (Sweden)

Prasanta Kumar Ray

2012-01-01

Full Text Available In this paper, with the help of orthogonal polynomial especially Chybeshev polynomials of first and second kind, number theory and linear algebra intertwined to yield factorization of the balancing and Lucas-balancing numbers.

STABILITY SYSTEMS VIA HURWITZ POLYNOMIALS

Directory of Open Access Journals (Sweden)

BALTAZAR AGUIRRE HERNÁNDEZ

2017-01-01

Full Text Available To analyze the stability of a linear system of differential equations  ẋ = Ax we can study the location of the roots of the characteristic polynomial pA(t associated with the matrix A. We present various criteria - algebraic and geometric - that help us to determine where the roots are located without calculating them directly.

Space complexity in polynomial calculus

Czech Academy of Sciences Publication Activity Database

Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil

2015-01-01

Roč. 44, č. 4 (2015), s. 1119-1153 ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/10.1137/120895950

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

Directory of Open Access Journals (Sweden)

Hamed Kharrati

2012-01-01

Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

Science.gov (United States)

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Convergence acceleration of quasi-periodic and quasi-periodic-rational interpolations by polynomial corrections

OpenAIRE

Lusine Poghosyan

2014-01-01

The paper considers convergence acceleration of the quasi-periodic and the quasi-periodic-rational interpolations by application of polynomial corrections. We investigate convergence of the resultant quasi-periodic-polynomial and quasi-periodic-rational-polynomial interpolations and derive exact constants of the main terms of asymptotic errors in the regions away from the endpoints. Results of numerical experiments clarify behavior of the corresponding interpolations for moderate number of in...

Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror

CSIR Research Space (South Africa)

Long, CS

2012-04-01

Full Text Available , are routinely and conveniently described using Zernike polynomials. A Rayleigh-Ritz structural model, which uses Zernike polynomials directly to describe the displacements, is proposed in this paper. The proposed formulation produces a numerically inexpensive...

Polynomial structures in one-loop amplitudes

International Nuclear Information System (INIS)

Britto, Ruth; Feng Bo; Yang Gang

2008-01-01

A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2ε)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2ε)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.

Optimization of polynomials in non-commuting variables

CERN Document Server

Burgdorf, Sabine; Povh, Janez

2016-01-01

This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

Computation of the Likelihood in Biallelic Diffusion Models Using Orthogonal Polynomials

Directory of Open Access Journals (Sweden)

Claus Vogl

2014-11-01

Full Text Available In population genetics, parameters describing forces such as mutation, migration and drift are generally inferred from molecular data. Lately, approximate methods based on simulations and summary statistics have been widely applied for such inference, even though these methods waste information. In contrast, probabilistic methods of inference can be shown to be optimal, if their assumptions are met. In genomic regions where recombination rates are high relative to mutation rates, polymorphic nucleotide sites can be assumed to evolve independently from each other. The distribution of allele frequencies at a large number of such sites has been called “allele-frequency spectrum” or “site-frequency spectrum” (SFS. Conditional on the allelic proportions, the likelihoods of such data can be modeled as binomial. A simple model representing the evolution of allelic proportions is the biallelic mutation-drift or mutation-directional selection-drift diffusion model. With series of orthogonal polynomials, specifically Jacobi and Gegenbauer polynomials, or the related spheroidal wave function, the diffusion equations can be solved efficiently. In the neutral case, the product of the binomial likelihoods with the sum of such polynomials leads to finite series of polynomials, i.e., relatively simple equations, from which the exact likelihoods can be calculated. In this article, the use of orthogonal polynomials for inferring population genetic parameters is investigated.

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

Science.gov (United States)

Attorps, Iiris; Björk, Kjell; Radic, Mirko

2016-01-01

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students' learning opportunities in the study group compared with the control group.

A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce

Directory of Open Access Journals (Sweden)

Stefano Chinaglia

2017-09-01

Full Text Available Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.

M-Polynomials and Topological Indices of Dominating David Derived Networks

Directory of Open Access Journals (Sweden)

Kang Shin Min

2018-03-01

Full Text Available There is a strong relationship between the chemical characteristics of chemical compounds and their molecular structures. Topological indices are numerical values associated with the chemical molecular graphs that help to understand the physical features, chemical reactivity, and biological activity of chemical compound. Thus, the study of the topological indices is important. M-polynomial helps to recover many degree-based topological indices for example Zagreb indices, Randic index, symmetric division idex, inverse sum index etc. In this article we compute M-polynomials of dominating David derived networks of the first type, second type and third type of dimension n and find some topological properties by using these M-polynomials. The results are plotted using Maple to see the dependence of topological indices on the involved parameters.

Nonclassical Orthogonal Polynomials and Corresponding Quadratures

CERN Document Server

Fukuda, H; Alt, E O; Matveenko, A V

2004-01-01

We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

OpenAIRE

Hamed Kharrati; Sohrab Khanmohammadi; Witold Pedrycz; Ghasem Alizadeh

2012-01-01

This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy m...

A general U-block model-based design procedure for nonlinear polynomial control systems

Science.gov (United States)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Schur Stability Regions for Complex Quadratic Polynomials

Science.gov (United States)

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

A novel stabilization condition for T-S polynomial fuzzy system with time-delay:A sum-of-squares approach

OpenAIRE

Tsai, Shun Hung; Chen, Yu-An; Chen, Yu-Wen; Lo, Ji-Chang; Lam, Hak-Keung

2017-01-01

A novel stabilization problem for T-S polynomial fuzzy system with time-delay is investigated in this paper. Firstly, a polynomial fuzzy controller for T-S polynomial fuzzy system with time-delay is proposed. In addition, based on polynomial Lyapunov-Krasovskii function and the developed polynomial slack variable matrices, a novel stabilization condition for T-S polynomial fuzzy system with time-delay is presented in terms of sum-of-square (SOS) form. Lastly, nonlinear system with time-delay ...

M-Polynomial and Related Topological Indices of Nanostar Dendrimers

Directory of Open Access Journals (Sweden)

Mobeen Munir

2016-09-01

Full Text Available Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

Coexistence of critical orbit types in sub-hyperbolic polynomial maps

OpenAIRE

Poirier, Alfredo

1994-01-01

We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\\bf C} to itself which have degree two or more in each copy. As a consequence of these results we prove a transitivity relation between hyperbolic components in parameter space which was conjectured by Milnor.

Gaussian polynomials and content ideal in trivial extensions

International Nuclear Information System (INIS)

Bakkari, C.; Mahdou, N.

2006-12-01

The goal of this paper is to exhibit a class of Gaussian non-coherent rings R (with zero-divisors) such that wdim(R) = ∞ and fPdim(R) is always at most one and also exhibits a new class of rings (with zerodivisors) which are neither locally Noetherian nor locally domain where Gaussian polynomials have a locally principal content. For this purpose, we study the possible transfer of the 'Gaussian' property and the property 'the content ideal of a Gaussian polynomial is locally principal' to various trivial extension contexts. This article includes a brief discussion of the scopes and limits of our result. (author)

A simple approximation to the bivariate normal distribution with large correlation coefficient

NARCIS (Netherlands)

Albers, Willem/Wim; Kallenberg, W.C.M.

1994-01-01

The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the

Algebraic polynomial system solving and applications

NARCIS (Netherlands)

Bleylevens, I.W.M.

2010-01-01

The problem of computing the solutions of a system of multivariate polynomial equations can be approached by the Stetter-Möller matrix method which casts the problem into a large eigenvalue problem. This Stetter-Möller matrix method forms the starting point for the development of computational

Function approximation with polynomial regression slines

International Nuclear Information System (INIS)

Urbanski, P.

1996-01-01

Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author)

Stability Analysis of Positive Polynomial Fuzzy-Model-Based Control Systems with Time Delay under Imperfect Premise Matching

OpenAIRE

Li, Xiaomiao; Lam, Hak Keung; Song, Ge; Liu, Fucai

2017-01-01

This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based ({PFMB}) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares (SOS)-based stability ana...

Global assessment of predictability of water availability: A bivariate probabilistic Budyko analysis

Science.gov (United States)

Wang, Weiguang; Fu, Jianyu

2018-02-01

Estimating continental water availability is of great importance for water resources management, in terms of maintaining ecosystem integrity and sustaining society development. To more accurately quantify the predictability of water availability, on the basis of univariate probabilistic Budyko framework, a bivariate probabilistic Budyko approach was developed using copula-based joint distribution model for considering the dependence between parameter ω of Wang-Tang's equation and the Normalized Difference Vegetation Index (NDVI), and was applied globally. The results indicate the predictive performance in global water availability is conditional on the climatic condition. In comparison with simple univariate distribution, the bivariate one produces the lower interquartile range under the same global dataset, especially in the regions with higher NDVI values, highlighting the importance of developing the joint distribution by taking into account the dependence structure of parameter ω and NDVI, which can provide more accurate probabilistic evaluation of water availability.

On factorization of generalized Macdonald polynomials

International Nuclear Information System (INIS)

Kononov, Ya.; Morozov, A.

2016-01-01

A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W ∞ - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U q (SL N ) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)

On factorization of generalized Macdonald polynomials

Science.gov (United States)

Kononov, Ya.; Morozov, A.

2016-08-01

A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from W_∞ —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U_q(SL_N) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.

On factorization of generalized Macdonald polynomials

Energy Technology Data Exchange (ETDEWEB)

Kononov, Ya. [Landau Institute for Theoretical Physics, Chernogolovka (Russian Federation); HSE, Math Department, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation)

2016-08-15

A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W{sub ∞} - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U{sub q}(SL{sub N}) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)

Weighted Polynomial Approximation for Automated Detection of Inspiratory Flow Limitation

Directory of Open Access Journals (Sweden)

Sheng-Cheng Huang

2017-01-01

Full Text Available Inspiratory flow limitation (IFL is a critical symptom of sleep breathing disorders. A characteristic flattened flow-time curve indicates the presence of highest resistance flow limitation. This study involved investigating a real-time algorithm for detecting IFL during sleep. Three categories of inspiratory flow shape were collected from previous studies for use as a development set. Of these, 16 cases were labeled as non-IFL and 78 as IFL which were further categorized into minor level (20 cases and severe level (58 cases of obstruction. In this study, algorithms using polynomial functions were proposed for extracting the features of IFL. Methods using first- to third-order polynomial approximations were applied to calculate the fitting curve to obtain the mean absolute error. The proposed algorithm is described by the weighted third-order (w.3rd-order polynomial function. For validation, a total of 1,093 inspiratory breaths were acquired as a test set. The accuracy levels of the classifications produced by the presented feature detection methods were analyzed, and the performance levels were compared using a misclassification cobweb. According to the results, the algorithm using the w.3rd-order polynomial approximation achieved an accuracy of 94.14% for IFL classification. We concluded that this algorithm achieved effective automatic IFL detection during sleep.

Computer programme for the derivation of transfer functions for multivariable systems (solutions of determinants with polynomial elements)

International Nuclear Information System (INIS)

Guppy, C.B.

1962-03-01

In the methods adopted in this report transfer functions in the form of the ratio of two polynomials of the complex variable s are derived from sets of laplace transformed simultaneous differential equations. The set of algebraic simultaneous equations are solved using Cramer's Rule and this gives rise to determinants having polynomial elements. It is shown how the determinants are formed when transfer functions are specified. The procedure for finding the polynomial coefficients from a given determinant is fully described. The first method adopted is a direct one and reduces a determinant with first degree polynomial elements to secular form and follows this by an application of the similarity transformation to reduce the determinant to a form from which the polynomial coefficients can be read out directly. The programme is able to solve a single determinant with polynomial elements and this can be used to reduce an eigenvalue problem in the form of a secular determinant to polynomial form if the need arises. A description is given of the way in which the data is to be set out for solution by the programme. A description is also given of a method used in an earlier programme for solving polynomial determinants by curve fitting techniques using Chebyshev Polynomials. In this method determinants with polynomial elements of any degree can be solved. (author)

Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics

Science.gov (United States)

Engliš, Miroslav; Ali, S. Twareque

2015-07-01

Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.

Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials

Directory of Open Access Journals (Sweden)

N. Stojanovic

2016-09-01

Full Text Available A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approximations(Chebyshev, Legendre, Butterworth are shown to be a special cases of proposed approximation method.

Local polynomial Whittle estimation covering non-stationary fractional processes

DEFF Research Database (Denmark)

Nielsen, Frank

to the non-stationary region. By approximating the short-run component of the spectrum by a polynomial, instead of a constant, in a shrinking neighborhood of zero we alleviate some of the bias that the classical local Whittle estimators is prone to. This bias reduction comes at a cost as the variance is in...... study illustrates the performance of the proposed estimator compared to the classical local Whittle estimator and the local polynomial Whittle estimator. The empirical justi.cation of the proposed estimator is shown through an analysis of credit spreads....

Interpretation of stream programs: characterizing type 2 polynomial time complexity

OpenAIRE

Férée , Hugo; Hainry , Emmanuel; Hoyrup , Mathieu; Péchoux , Romain

2010-01-01

International audience; We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These charac- terizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over th...

Exponential-Polynomial Families and the Term Structure of Interest Rates

OpenAIRE

Filipovic, Damir

2000-01-01

Exponential-polynomial families like the Nelson-Siegel or Svensson family are widely used to estimate the current forward rate curve. We investigate whether these methods go well with inter-temporal modelling. We characterize the consistent Ito processes which have the property to provide an arbitrage free interest rate model when representing the parameters of some bounded exponential-polynomial type function. This includes in particular diffusion processes. We show that there is a strong li...

Handbook on semidefinite, conic and polynomial optimization

CERN Document Server

Anjos, Miguel F

2012-01-01

This book offers the reader a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization and polynomial optimization. It covers theory, algorithms, software and applications.

Polynomial Variables and the Jacobian Problem

Indian Academy of Sciences (India)

algebra and algebraic geometry, and ... algebraically, to making the change of variables (X, Y) r--t. (X +p, Y ... aX + bY + p and eX + dY + q are linear polynomials in X, Y. ..... [5] T T Moh, On the Jacobian conjecture and the confipration of roots,.

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...

Indecomposability of polynomials via Jacobian matrix

International Nuclear Information System (INIS)

Cheze, G.; Najib, S.

2007-12-01

Uni-multivariate decomposition of polynomials is a special case of absolute factorization. Recently, thanks to the Ruppert's matrix some effective results about absolute factorization have been improved. Here we show that with a jacobian matrix we can get sharper bounds for the special case of uni-multivariate decomposition. (author)

Spectral properties of birth-death polynomials

NARCIS (Netherlands)

van Doorn, Erik A.

2015-01-01

We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by

Spectral properties of birth-death polynomials

NARCIS (Netherlands)

van Doorn, Erik A.

We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by

Integral Inequalities for Self-Reciprocal Polynomials

Indian Academy of Sciences (India)

Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. Integral Inequalities for Self-Reciprocal Polynomials. Horst Alzer. Volume 120 Issue 2 April 2010 ...

Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

International Nuclear Information System (INIS)

Yahiaoui, S.-A.; Bentaiba, M.

2011-01-01

We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)

Discrimination of Sedimentary Lithologies Through Unmixing of EO-1 Hyperion Data: Melville Island, Canadian High Arctic

Science.gov (United States)

Leverington, D. W.

2008-12-01

The use of remote-sensing techniques in the discrimination of rock and soil classes in northern regions can help support a diverse range of activities including environmental characterization, mineral exploration, and the study of Quaternary paleoenvironments. Images of low spectral resolution can commonly be used in the mapping of lithological classes possessing distinct spectral characteristics, but hyperspectral databases offer greater potential for discrimination of materials distinguished by more subtle reflectance properties. Orbiting sensors offer an especially flexible and cost-effective means for acquisition of data to workers unable to conduct airborne surveys. In an effort to better constrain the utility of hyperspectral datasets in northern research, this study undertook to investigate the effectiveness of EO-1 Hyperion data in the discrimination and mapping of surface classes at a study area on Melville Island, Nunavut. Bedrock units in the immediate study area consist of late-Paleozoic clastic and carbonate sequences of the Sverdrup Basin. Weathered and frost-shattered felsenmeer, predominantly taking the form of boulder- to pebble-sized clasts that have accumulated in place and that mantle parent bedrock units, is the most common surface material in the study area. Hyperion data were converted from at-sensor radiance to reflectance, and were then linearly unmixed on the basis of end-member spectra measured from field samples. Hyperion unmixing results effectively portray the general fractional cover of six end members, although the fraction images of several materials contain background values that in some areas overestimate surface exposure. The best separated end members include the snow, green vegetation, and red-weathering sandstone classes, whereas the classes most negatively affected by elevated fraction values include the mudstone, limestone, and 'other' sandstone classes. Local overestimates of fractional cover are likely related to the

Polynomial intelligent states

International Nuclear Information System (INIS)

Milks, Matthew M; Guise, Hubert de

2005-01-01

The construction of su(2) intelligent states is simplified using a polynomial representation of su(2). The cornerstone of the new construction is the diagonalization of a 2 x 2 matrix. The method is sufficiently simple to be easily extended to su(3), where one is required to diagonalize a single 3 x 3 matrix. For two perfectly general su(3) operators, this diagonalization is technically possible but the procedure loses much of its simplicity owing to the algebraic form of the roots of a cubic equation. Simplified expressions can be obtained by specializing the choice of su(3) operators. This simpler construction will be discussed in detail

Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights

KAUST Repository

Ait-Haddou, Rachid

2016-03-02

We show that the weighted least squares approximation of Bézier coefficients with Hahn weights provides the best polynomial degree reduction in the Jacobi L2L2-norm. A discrete analogue of this result is also provided. Applications to Jacobi and Hahn orthogonal polynomials are presented.

A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

Directory of Open Access Journals (Sweden)

Rabia Aktaş

2013-01-01

Full Text Available We introduce a Kantorovich-Stancu type modification of a generalization of Szasz operators defined by means of the Brenke type polynomials and obtain approximation properties of these operators. Also, we give a Voronovskaya type theorem for Kantorovich-Stancu type operators including Gould-Hopper polynomials.

On minimum divergence adaptation of discrete bivariate distributions to given marginals

Czech Academy of Sciences Publication Activity Database

Vajda, Igor; van der Meulen, E. C.

2005-01-01

Roč. 51, č. 1 (2005), s. 313-320 ISSN 0018-9448 R&D Projects: GA ČR GA201/02/1391; GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : approximation of contingency tables * bivariate discrete distributions * minimization of divergences Subject RIV: BD - Theory of Information Impact factor: 2.183, year: 2005

Infinite families of (non)-Hermitian Hamiltonians associated with exceptional Xm Jacobi polynomials

International Nuclear Information System (INIS)

Midya, Bikashkali; Roy, Barnana

2013-01-01

Using an appropriate change of variable, the Schrödinger equation is transformed into a second-order differential equation satisfied by recently discovered Jacobi-type X m exceptional orthogonal polynomials. This facilitates the derivation of infinite families of exactly solvable Hermitian as well as non-Hermitian trigonometric Scarf potentials and a finite number of Hermitian and an infinite number of non-Hermitian PT-symmetric hyperbolic Scarf potentials. The bound state solutions of all these potentials are associated with the aforesaid exceptional orthogonal polynomials. These infinite families of potentials are shown to be extensions of the conventional trigonometric and hyperbolic Scarf potentials by the addition of some rational terms characterized by the presence of classical Jacobi polynomials. All the members of a particular family of these ‘rationally extended polynomial-dependent’ potentials have the same energy spectrum and possess translational shape-invariant symmetry. The obtained non-Hermitian trigonometric Scarf potentials are shown to be quasi-Hermitian in nature ensuring the reality of the associated energy spectra. (paper)

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

Science.gov (United States)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

New realisation of Preisach model using adaptive polynomial approximation

Science.gov (United States)

Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young

2012-09-01

Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.

Recognition of Arabic Sign Language Alphabet Using Polynomial Classifiers

Directory of Open Access Journals (Sweden)

M. Al-Rousan

2005-08-01

Full Text Available Building an accurate automatic sign language recognition system is of great importance in facilitating efficient communication with deaf people. In this paper, we propose the use of polynomial classifiers as a classification engine for the recognition of Arabic sign language (ArSL alphabet. Polynomial classifiers have several advantages over other classifiers in that they do not require iterative training, and that they are highly computationally scalable with the number of classes. Based on polynomial classifiers, we have built an ArSL system and measured its performance using real ArSL data collected from deaf people. We show that the proposed system provides superior recognition results when compared with previously published results using ANFIS-based classification on the same dataset and feature extraction methodology. The comparison is shown in terms of the number of misclassified test patterns. The reduction in the rate of misclassified patterns was very significant. In particular, we have achieved a 36% reduction of misclassifications on the training data and 57% on the test data.

Spectral unmixing of urban land cover using a generic library approach

Science.gov (United States)

Degerickx, Jeroen; Lordache, Marian-Daniel; Okujeni, Akpona; Hermy, Martin; van der Linden, Sebastian; Somers, Ben

2016-10-01

Remote sensing based land cover classification in urban areas generally requires the use of subpixel classification algorithms to take into account the high spatial heterogeneity. These spectral unmixing techniques often rely on spectral libraries, i.e. collections of pure material spectra (endmembers, EM), which ideally cover the large EM variability typically present in urban scenes. Despite the advent of several (semi-) automated EM detection algorithms, the collection of such image-specific libraries remains a tedious and time-consuming task. As an alternative, we suggest the use of a generic urban EM library, containing material spectra under varying conditions, acquired from different locations and sensors. This approach requires an efficient EM selection technique, capable of only selecting those spectra relevant for a specific image. In this paper, we evaluate and compare the potential of different existing library pruning algorithms (Iterative Endmember Selection and MUSIC) using simulated hyperspectral (APEX) data of the Brussels metropolitan area. In addition, we develop a new hybrid EM selection method which is shown to be highly efficient in dealing with both imagespecific and generic libraries, subsequently yielding more robust land cover classification results compared to existing methods. Future research will include further optimization of the proposed algorithm and additional tests on both simulated and real hyperspectral data.

Eigenvalues of PT-symmetric oscillators with polynomial potentials

International Nuclear Information System (INIS)

Shin, Kwang C

2005-01-01

We study the eigenvalue problem -u''(z) - [(iz) m + P m-1 (iz)]u(z) λu(z) with the boundary condition that u(z) decays to zero as z tends to infinity along the rays arg z = -π/2 ± 2π/(m+2) in the complex plane, where P m-1 (z) = a 1 z m-1 + a 2 z m-2 + . . . + a m-1 z is a polynomial and integers m ≥ 3. We provide an asymptotic expansion of the eigenvalues λ n as n → +∞, and prove that for each real polynomial P m-1 , the eigenvalues are all real and positive, with only finitely many exceptions

A bivariate space-time downscaler under space and time misalignment.

Science.gov (United States)

Berrocal, Veronica J; Gelfand, Alan E; Holland, David M

2010-12-01

Ozone and particulate matter PM(2.5) are co-pollutants that have long been associated with increased public health risks. Information on concentration levels for both pollutants come from two sources: monitoring sites and output from complex numerical models that produce concentration surfaces over large spatial regions. In this paper, we offer a fully-model based approach for fusing these two sources of information for the pair of co-pollutants which is computationally feasible over large spatial regions and long periods of time. Due to the association between concentration levels of the two environmental contaminants, it is expected that information regarding one will help to improve prediction of the other. Misalignment is an obvious issue since the monitoring networks for the two contaminants only partly intersect and because the collection rate for PM(2.5) is typically less frequent than that for ozone.Extending previous work in Berrocal et al. (2009), we introduce a bivariate downscaler that provides a flexible class of bivariate space-time assimilation models. We discuss computational issues for model fitting and analyze a dataset for ozone and PM(2.5) for the ozone season during year 2002. We show a modest improvement in predictive performance, not surprising in a setting where we can anticipate only a small gain.

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

Science.gov (United States)

Kulkarni, Rishikesh; Rastogi, Pramod

2018-02-01

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Large level crossings of a random polynomial

Directory of Open Access Journals (Sweden)

Kambiz Farahmand

1987-01-01

Full Text Available We know the expected number of times that a polynomial of degree n with independent random real coefficients asymptotically crosses the level K, when K is any real value such that (K2/n→0 as n→∞. The present paper shows that, when K is allowed to be large, this expected number of crossings reduces to only one. The coefficients of the polynomial are assumed to be normally distributed. It is shown that it is sufficient to let K≥exp(nf where f is any function of n such that f→∞ as n→∞.

Polynomial chaos representation of databases on manifolds

Energy Technology Data Exchange (ETDEWEB)

Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

Design of a Polynomial Fuzzy Observer Controller With Sampled-Output Measurements for Nonlinear Systems Considering Unmeasurable Premise Variables

OpenAIRE

Liu, Chuang; Lam, H. K.

2015-01-01

In this paper, we propose a polynomial fuzzy observer controller for nonlinear systems, where the design is achieved through the stability analysis of polynomial-fuzzy-model-based (PFMB) observer-control system. The polynomial fuzzy observer estimates the system states using estimated premise variables. The estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model. The system stability of the P...

Unadjusted Bivariate Two-Group Comparisons: When Simpler is Better.

Science.gov (United States)

Vetter, Thomas R; Mascha, Edward J

2018-01-01

Hypothesis testing involves posing both a null hypothesis and an alternative hypothesis. This basic statistical tutorial discusses the appropriate use, including their so-called assumptions, of the common unadjusted bivariate tests for hypothesis testing and thus comparing study sample data for a difference or association. The appropriate choice of a statistical test is predicated on the type of data being analyzed and compared. The unpaired or independent samples t test is used to test the null hypothesis that the 2 population means are equal, thereby accepting the alternative hypothesis that the 2 population means are not equal. The unpaired t test is intended for comparing dependent continuous (interval or ratio) data from 2 study groups. A common mistake is to apply several unpaired t tests when comparing data from 3 or more study groups. In this situation, an analysis of variance with post hoc (posttest) intragroup comparisons should instead be applied. Another common mistake is to apply a series of unpaired t tests when comparing sequentially collected data from 2 study groups. In this situation, a repeated-measures analysis of variance, with tests for group-by-time interaction, and post hoc comparisons, as appropriate, should instead be applied in analyzing data from sequential collection points. The paired t test is used to assess the difference in the means of 2 study groups when the sample observations have been obtained in pairs, often before and after an intervention in each study subject. The Pearson chi-square test is widely used to test the null hypothesis that 2 unpaired categorical variables, each with 2 or more nominal levels (values), are independent of each other. When the null hypothesis is rejected, 1 concludes that there is a probable association between the 2 unpaired categorical variables. When comparing 2 groups on an ordinal or nonnormally distributed continuous outcome variable, the 2-sample t test is usually not appropriate. The

Evidence for bivariate linkage of obesity and HDL-C levels in the Framingham Heart Study.

Science.gov (United States)

Arya, Rector; Lehman, Donna; Hunt, Kelly J; Schneider, Jennifer; Almasy, Laura; Blangero, John; Stern, Michael P; Duggirala, Ravindranath

2003-12-31

Epidemiological studies have indicated that obesity and low high-density lipoprotein (HDL) levels are strong cardiovascular risk factors, and that these traits are inversely correlated. Despite the belief that these traits are correlated in part due to pleiotropy, knowledge on specific genes commonly affecting obesity and dyslipidemia is very limited. To address this issue, we first conducted univariate multipoint linkage analysis for body mass index (BMI) and HDL-C to identify loci influencing variation in these phenotypes using Framingham Heart Study data relating to 1702 subjects distributed across 330 pedigrees. Subsequently, we performed bivariate multipoint linkage analysis to detect common loci influencing covariation between these two traits. We scanned the genome and identified a major locus near marker D6S1009 influencing variation in BMI (LOD = 3.9) using the program SOLAR. We also identified a major locus for HDL-C near marker D2S1334 on chromosome 2 (LOD = 3.5) and another region near marker D6S1009 on chromosome 6 with suggestive evidence for linkage (LOD = 2.7). Since these two phenotypes have been independently mapped to the same region on chromosome 6q, we used the bivariate multipoint linkage approach using SOLAR. The bivariate linkage analysis of BMI and HDL-C implicated the genetic region near marker D6S1009 as harboring a major gene commonly influencing these phenotypes (bivariate LOD = 6.2; LODeq = 5.5) and appears to improve power to map the correlated traits to a region, precisely. We found substantial evidence for a quantitative trait locus with pleiotropic effects, which appears to influence both BMI and HDL-C phenotypes in the Framingham data.

The bivariate probit model of uncomplicated control of tumor: a heuristic exposition of the methodology

International Nuclear Information System (INIS)

Herbert, Donald

1997-01-01

Purpose: To describe the concept, models, and methods for the construction of estimates of joint probability of uncomplicated control of tumors in radiation oncology. Interpolations using this model can lead to the identification of more efficient treatment regimens for an individual patient. The requirement to find the treatment regimen that will maximize the joint probability of uncomplicated control of tumors suggests a new class of evolutionary experimental designs--Response Surface Methods--for clinical trials in radiation oncology. Methods and Materials: The software developed by Lesaffre and Molenberghs is used to construct bivariate probit models of the joint probability of uncomplicated control of cancer of the oropharynx from a set of 45 patients for each of whom the presence/absence of recurrent tumor (the binary event E-bar 1 /E 1 ) and the presence/absence of necrosis (the binary event E 2 /E-bar 2 ) of the normal tissues of the target volume is recorded, together with the treatment variables dose, time, and fractionation. Results: The bivariate probit model can be used to select a treatment regime that will give a specified probability, say P(S) = 0.60, of uncomplicated control of tumor by interpolation within a set of treatment regimes with known outcomes of recurrence and necrosis. The bivariate probit model can be used to guide a sequence of clinical trials to find the maximum probability of uncomplicated control of tumor for patients in a given prognostic stratum using Response Surface methods by extrapolation from an initial set of treatment regimens. Conclusions: The design of treatments for individual patients and the design of clinical trials might be improved by use of a bivariate probit model and Response Surface Methods

Mirror symmetry, toric branes and topological string amplitudes as polynomials

Energy Technology Data Exchange (ETDEWEB)

Alim, Murad

2009-07-13

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

Computation of rectangular source integral by rational parameter polynomial method

International Nuclear Information System (INIS)

Prabha, Hem

2001-01-01

Hubbell et al. (J. Res. Nat Bureau Standards 64C, (1960) 121) have obtained a series expansion for the calculation of the radiation field generated by a plane isotropic rectangular source (plaque), in which leading term is the integral H(a,b). In this paper another integral I(a,b), which is related with the integral H(a,b) has been solved by the rational parameter polynomial method. From I(a,b), we compute H(a,b). Using this method the integral I(a,b) is expressed in the form of a polynomial of a rational parameter. Generally, a function f (x) is expressed in terms of x. In this method this is expressed in terms of x/(1+x). In this way, the accuracy of the expression is good over a wide range of x as compared to the earlier approach. The results for I(a,b) and H(a,b) are given for a sixth degree polynomial and are found to be in good agreement with the results obtained by numerically integrating the integral. Accuracy could be increased either by increasing the degree of the polynomial or by dividing the range of integration. The results of H(a,b) and I(a,b) are given for values of b and a up to 2.0 and 20.0, respectively

Mirror symmetry, toric branes and topological string amplitudes as polynomials

International Nuclear Information System (INIS)

Alim, Murad

2009-01-01

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

Polynomial analysis of ambulatory blood pressure measurements

NARCIS (Netherlands)

Zwinderman, A. H.; Cleophas, T. A.; Cleophas, T. J.; van der Wall, E. E.

2001-01-01

In normotensive subjects blood pressures follow a circadian rhythm. A circadian rhythm in hypertensive patients is less well established, and may be clinically important, particularly with rigorous treatments of daytime blood pressures. Polynomial analysis of ambulatory blood pressure monitoring

Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2001-01-01

The Hessian topology has just begun to be developed (in connection with the study of parabolic curves on smooth surfaces in Euclidean or projective space), in contrast to the symplectic and contact topologies related to it. For instance, it is not known how many (compact) parabolic curves can belong to the graph of a polynomial of a given (even of the fourth) degree in two variables or to a smooth algebraic surface of a given degree. The astroid is a hypocycloid with four cusp points. A hyperbolic polynomial is a homogeneous polynomial whose second differential has the signature (+,-) at any non-zero point. Hyperbolic polynomials and functions are connected with Morse theory and Sturm theory and with hypocycloids via caustics (and wave fronts) of periodic functions. The astroid is the caustic of the cosine of a double angle. The caustic of any periodic function has at least four cusp points, and if there are four of them, as is the case for the astroid, then these points form a parallelogram. The theory developed in this paper, based on the study of envelopes and inequalities between derivatives of smooth functions, proves that hyperbolic polynomials of degree four form a connected set and those of degree six form a disconnected set. These topological generalizations of the Sturm and Hurwitz theorems about the zeros of Fourier series give algebraic-geometric results on caustics and wave fronts as well and also establish relationships between these results and the Morse theory of anti-Rolle functions (whose zeros alternate with those of their derivatives)

Skew-orthogonal polynomials, differential systems and random matrix theory

International Nuclear Information System (INIS)

Ghosh, S.

2007-01-01

We study skew-orthogonal polynomials with respect to the weight function exp[-2V (x)], with V (x) = Σ K=1 2d (u K /K)x K , u 2d > 0, d > 0. A finite subsequence of such skew-orthogonal polynomials arising in the study of Orthogonal and Symplectic ensembles of random matrices, satisfy a system of differential-difference-deformation equation. The vectors formed by such subsequence has the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions. (author)

On the Lojasiewicz exponent at infinity of real polynomials

International Nuclear Information System (INIS)

Ha Huy Vui; Pham Tien Son

2007-07-01

Let f : R n → R be a nonconstant polynomial function. In this paper, using the information from 'the curve of tangency' of f, we provide a method to determine the Lojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Lojasiewicz exponent at infinity is finite or not. Then, we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Lojasiewicz exponent at infinity of f with the problem of computing the global optimum of f is also established. (author)

Codimensions of generalized polynomial identities

International Nuclear Information System (INIS)

Gordienko, Aleksei S

2010-01-01

It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q + and t element of Z + such that gc n (A)∼Cn t d n as n→∞, where d=PI exp(A) element of Z + . Thus, Amitsur's and Regev's conjectures hold for the codimensions gc n (A) of the generalized polynomial identities. Bibliography: 6 titles.

On the non-hyperbolicity of a class of exponential polynomials

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Gaspar Mora

2017-10-01

Full Text Available In this paper we have constructed a class of non-hyperbolic exponential polynomials that contains all the partial sums of the Riemann zeta function. An exponential polynomial been also defined to illustrate the complexity of the structure of the set defined by the closure of the real projections of its zeros. The sensitivity of this set, when the vector of delays is perturbed, has been analysed. These results have immediate implications in the theory of the neutral differential equations.

Polynomial approximation on polytopes

CERN Document Server

Totik, Vilmos

2014-01-01

Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

Polynomial Asymptotes of the Second Kind

Science.gov (United States)

Dobbs, David E.

2011-01-01

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

The Kauffman bracket and the Jones polynomial in quantum gravity

International Nuclear Information System (INIS)

Griego, J.

1996-01-01

In the loop representation the quantum states of gravity are given by knot invariants. From general arguments concerning the loop transform of the exponential of the Chern-Simons form, a certain expansion of the Kauffman bracket knot polynomial can be formally viewed as a solution of the Hamiltonian constraint with a cosmological constant in the loop representation. The Kauffman bracket is closely related to the Jones polynomial. In this paper the operation of the Hamiltonian on the power expansions of the Kauffman bracket and Jones polynomials is analyzed. It is explicitly shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint to third order in the cosmological constant. We make use of the extended loop representation of quantum gravity where the analytic calculation can be thoroughly accomplished. Some peculiarities of the extended loop calculus are considered and the significance of the results to the case of the conventional loop representation is discussed. (orig.)

Technical note: Towards a continuous classification of climate using bivariate colour mapping

NARCIS (Netherlands)

Teuling, A.J.

2011-01-01

Climate is often defined in terms of discrete classes. Here I use bivariate colour mapping to show that the global distribution of K¨oppen-Geiger climate classes can largely be reproduced by combining the simple means of two key states of the climate system 5 (i.e., air temperature and relative

Quadratic polynomial interpolation on triangular domain

Science.gov (United States)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

A summation procedure for expansions in orthogonal polynomials

International Nuclear Information System (INIS)

Garibotti, C.R.; Grinstein, F.F.

1977-01-01

Approximants to functions defined by formal series expansions in orthogonal polynomials are introduced. They are shown to be convergent even out of the elliptical domain where the original expansion converges

On the Lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems

NARCIS (Netherlands)

de Klerk, E.; Laurent, M.

2011-01-01

The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J. B. Lasserre, Convexity in semialgebraic geometry and polynomial optimization, SIAM J. Optim., 19 (2009), pp. 1995–2014]. We give a

Image Compression Based On Wavelet, Polynomial and Quadtree

Directory of Open Access Journals (Sweden)

Bushra A. SULTAN

2011-01-01

Full Text Available In this paper a simple and fast image compression scheme is proposed, it is based on using wavelet transform to decompose the image signal and then using polynomial approximation to prune the smoothing component of the image band. The architect of proposed coding scheme is high synthetic where the error produced due to polynomial approximation in addition to the detail sub-band data are coded using both quantization and Quadtree spatial coding. As a last stage of the encoding process shift encoding is used as a simple and efficient entropy encoder to compress the outcomes of the previous stage.The test results indicate that the proposed system can produce a promising compression performance while preserving the image quality level.

Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula

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Marlowe Thomas J.

1998-01-01

Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants. We illustrate this approach using threshhold graphs, and show that any computation of reliability using Gilbert's formula will be polynomial-time if and only if the number of invariants considered is polynomial; we then show families of graphs with polynomial-time, and non-polynomial reliability computation, and show that these encompass most previously known results. We then codify our approach to indicate how it can be used for other classes of graphs, and suggest several classes to which the technique can be applied.

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

KAUST Repository

Migliorati, Giovanni; Nobile, Fabio; von Schwerin, Erik; Tempone, Raul

2014-01-01

We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points are sampled in a bounded domain from a probability density function bounded away from zero and bounded from above, provided the number of samples scales quadratically with the dimension of the polynomial space. Optimality is meant in the sense that the weighted L2 norm of the error committed by the random discrete projection is bounded with high probability from above by the best L∞ error achievable in the given polynomial space, up to logarithmic factors. Several numerical tests are presented in both the univariate and multivariate cases, confirming our theoretical estimates. The numerical tests also clarify how the convergence rate depends on the number of sampling points, on the polynomial degree, and on the smoothness of the target function. © 2014 SFoCM.

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

KAUST Repository

Migliorati, Giovanni

2014-03-05

We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points are sampled in a bounded domain from a probability density function bounded away from zero and bounded from above, provided the number of samples scales quadratically with the dimension of the polynomial space. Optimality is meant in the sense that the weighted L2 norm of the error committed by the random discrete projection is bounded with high probability from above by the best L∞ error achievable in the given polynomial space, up to logarithmic factors. Several numerical tests are presented in both the univariate and multivariate cases, confirming our theoretical estimates. The numerical tests also clarify how the convergence rate depends on the number of sampling points, on the polynomial degree, and on the smoothness of the target function. © 2014 SFoCM.

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

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Bolandtalat A.

2016-01-01

Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

International Nuclear Information System (INIS)

Doha, E H; Ahmed, H M

2004-01-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed

Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials

International Nuclear Information System (INIS)

Tierz, Miguel

2016-01-01

We solve for finite N the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N f fundamental and N f anti-fundamental chiral multiplets of R-charge 1/2 and of mass m, by identifying it with an average of inverse characteristic polynomials in a Stieltjes-Wigert ensemble. This requires the computation of the Cauchy transform of the Stieltjes-Wigert polynomials, which we carry out, finding a relationship with Mordell integrals, and hence with previous analytical results on the matrix model. The semiclassical limit of the model is expressed, for arbitrary N f , in terms of a single Hermite polynomial. This result also holds for more general matter content, involving matrix models with double-sine functions.

On characteristic polynomials for a generalized chiral random matrix ensemble with a source

Science.gov (United States)

Fyodorov, Yan V.; Grela, Jacek; Strahov, Eugene

2018-04-01

We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a N× N random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

Sparse grid-based polynomial chaos expansion for aerodynamics of an airfoil with uncertainties

Directory of Open Access Journals (Sweden)

Xiaojing WU

2018-05-01

Full Text Available The uncertainties can generate fluctuations with aerodynamic characteristics. Uncertainty Quantification (UQ is applied to compute its impact on the aerodynamic characteristics. In addition, the contribution of each uncertainty to aerodynamic characteristics should be computed by uncertainty sensitivity analysis. Non-Intrusive Polynomial Chaos (NIPC has been successfully applied to uncertainty quantification and uncertainty sensitivity analysis. However, the non-intrusive polynomial chaos method becomes inefficient as the number of random variables adopted to describe uncertainties increases. This deficiency becomes significant in stochastic aerodynamic analysis considering the geometric uncertainty because the description of geometric uncertainty generally needs many parameters. To solve the deficiency, a Sparse Grid-based Polynomial Chaos (SGPC expansion is used to do uncertainty quantification and sensitivity analysis for stochastic aerodynamic analysis considering geometric and operational uncertainties. It is proved that the method is more efficient than non-intrusive polynomial chaos and Monte Carlo Simulation (MSC method for the stochastic aerodynamic analysis. By uncertainty quantification, it can be learnt that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region. The uncertainty sensitivity analysis reveals the individual and coupled effects among the uncertainty parameters. Keywords: Non-intrusive polynomial chaos, Sparse grid, Stochastic aerodynamic analysis, Uncertainty sensitivity analysis, Uncertainty quantification

Intrinsic Diophantine approximation on general polynomial surfaces

DEFF Research Database (Denmark)

Tiljeset, Morten Hein

2017-01-01

We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...

On rational classical orthogonal polynomials and their application for explicit computation of inverse Laplace transforms

Directory of Open Access Journals (Sweden)

Masjed-Jamei Mohammad

2005-01-01

Full Text Available From the main equation ( a x 2 +bx+c y ″ n ( x +( dx+e y ′ n ( x −n( ( n−1 a+d y n ( x =0 , n∈ ℤ + , six finite and infinite classes of orthogonal polynomials can be extracted. In this work, first we have a survey on these classes, particularly on finite classes, and their corresponding rational orthogonal polynomials, which are generated by Mobius transform x=p z −1 +q , p≠0 , q∈ℝ . Some new integral relations are also given in this section for the Jacobi, Laguerre, and Bessel orthogonal polynomials. Then we show that the rational orthogonal polynomials can be a very suitable tool to compute the inverse Laplace transform directly, with no additional calculation for finding their roots. In this way, by applying infinite and finite rational classical orthogonal polynomials, we give three basic expansions of six ones as a sample for computation of inverse Laplace transform.

An efficient coupled polynomial interpolation scheme for shear mode sandwich beam finite element

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Litesh N. Sulbhewar

Full Text Available An efficient piezoelectric sandwich beam finite element is presented here. It employs the coupled polynomial field interpolation scheme for field variables which incorporates electromechanical coupling at interpolation level itself; unlike conventional sandwich beam theory (SBT based formulations available in the literature. A variational formulation is used to derive the governing equations, which are used to establish the relationships between field variables. These relations lead to the coupled polynomial field descriptions of variables, unlike conventional SBT formulations which use assumed independent polynomials. The relative axial displacement is expressed only by coupled terms containing contributions from other mechanical and electrical variables, thus eliminating use of the transverse displacement derivative as a degree of freedom. A set of coupled shape function based on these polynomials has shown the improvement in the convergence characteristics of the SBT based formulation. This improvement in the performance is achieved with one nodal degree of freedom lesser than the conventional SBT formulations.

Orthogonal polynomials on the unit circle part 2 spectral theory

CERN Document Server

Simon, Barry

2013-01-01

This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal po

Orthogonal polynomials on the unit circle part 1 classical theory

CERN Document Server

2009-01-01

This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal po

M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes

Directory of Open Access Journals (Sweden)

Mobeen Munir

2016-12-01

Full Text Available The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.

SOLUTION OF SINGULAR INTEGRAL EQUATION FOR ELASTICITY THEORY WITH THE HELP OF ASYMPTOTIC POLYNOMIAL FUNCTION

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V. P. Gribkova

2014-01-01

Full Text Available The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points using a method of mechanical quadrature  and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation, which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

Science.gov (United States)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

A method of moments to estimate bivariate survival functions: the copula approach

Directory of Open Access Journals (Sweden)

Silvia Angela Osmetti

2013-05-01

Full Text Available In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. We generalize this model by the copula and different marginal distributions to construct several bivariate survival functions. The cumulative distribution functions are not absolutely continuous and they unknown parameters are often not be obtained in explicit form. In order to estimate the parameters we propose an easy procedure based on the moments. This method consist in two steps: in the first step we estimate only the parameters of marginal distributions and in the second step we estimate only the copula parameter. This procedure can be used to estimate the parameters of complex survival functions in which it is difficult to find an explicit expression of the mixed moments. Moreover it is preferred to the maximum likelihood one for its simplex mathematic form; in particular for distributions whose maximum likelihood parameters estimators can not be obtained in explicit form.

Maximum Power Point Tracking Control of Photovoltaic Systems: A Polynomial Fuzzy Model-Based Approach

DEFF Research Database (Denmark)

Rakhshan, Mohsen; Vafamand, Navid; Khooban, Mohammad Hassan

2018-01-01

This paper introduces a polynomial fuzzy model (PFM)-based maximum power point tracking (MPPT) control approach to increase the performance and efficiency of the solar photovoltaic (PV) electricity generation. The proposed method relies on a polynomial fuzzy modeling, a polynomial parallel......, a direct maximum power (DMP)-based control structure is considered for MPPT. Using the PFM representation, the DMP-based control structure is formulated in terms of SOS conditions. Unlike the conventional approaches, the proposed approach does not require exploring the maximum power operational point...

2D-Zernike Polynomials and Coherent State Quantization of the Unit Disc

Energy Technology Data Exchange (ETDEWEB)

Thirulogasanthar, K., E-mail: santhar@gmail.com [Concordia University, Department of Comuter Science and Software Engineering (Canada); Saad, Nasser, E-mail: nsaad@upei.ca [University of Prince Edward Island, Department of mathematics and Statistics (Canada); Honnouvo, G., E-mail: g-honnouvo@yahoo.fr [McGill University, Department of Mathematics and Statistics (Canada)

2015-12-15

Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized Berezin transforms also obtained. A number of necessary summation formulas for the 2D-Zernike polynomials proved.

Bernoulli Polynomials, Fourier Series and Zeta Numbers

DEFF Research Database (Denmark)

Scheufens, Ernst E

2013-01-01

Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...

M-Polynomials and Topological Indices of Titania Nanotubes

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Mobeen Munir

2016-10-01

Full Text Available Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO2 nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO2 nanotubes.

Spectral Unmixing Modeling of the Aristarchus Pyroclastic Deposit: Assessing the Eruptive History of Glass-Rich Regional Lunar Pyroclastic Deposits

Science.gov (United States)

Jawin, E. R.; Head, J. W., III; Cannon, K.

2017-12-01

The Aristarchus pyroclastic deposit in central Oceanus Procellarum is understood to have formed in a gas-rich explosive volcanic eruption, and has been observed to contain abundant volcanic glass. However, the interpreted color (and therefore composition) of the glass has been debated. In addition, previous analyses of the pyroclastic deposit have been performed using lower resolution data than are currently available. In this work, a nonlinear spectral unmixing model was applied to Moon Mineralogy Mapper (M3) data of the Aristarchus plateau to investigate the detailed mineralogic and crystalline nature of the Aristarchus pyroclastic deposit by using spectra of laboratory endmembers including a suite of volcanic glasses returned from the Apollo 15 and 17 missions (green, orange, black beads), as well as synthetic lunar glasses (orange, green, red, yellow). Preliminary results of the M3 unmixing model suggest that spectra of the pyroclastic deposit can be modeled by a mixture composed predominantly of a featureless endmember approximating space weathering and a smaller component of glass. The modeled spectra were most accurate with a synthetic orange glass endmember, relative to the other glasses analyzed in this work. The results confirm that there is a detectable component of glass in the Aristarchus pyroclastic deposit which may be similar to the high-Ti orange glass seen in other regional pyroclastic deposits, with only minimal contributions of other crystalline minerals. The presence of volcanic glass in the pyroclastic deposit, with the low abundance of crystalline material, would support the model that the Aristarchus pyroclastic deposit formed in a long-duration, hawaiian-style fire fountain eruption. No significant detection of devitrified black beads in the spectral modeling results (as was observed at the Apollo 17 landing site in the Taurus-Littrow pyroclastic deposit), suggests the optical density of the eruptive plume remained low throughout the

Completeness of the ring of polynomials

DEFF Research Database (Denmark)

Thorup, Anders

2015-01-01

Consider the polynomial ring R:=k[X1,…,Xn]R:=k[X1,…,Xn] in n≥2n≥2 variables over an uncountable field k. We prove that R   is complete in its adic topology, that is, the translation invariant topology in which the non-zero ideals form a fundamental system of neighborhoods of 0. In addition we pro...