Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

Polynomial functors and polynomial monads

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

An algorithm for semi-infinite polynomial optimization

"Vegeu el resum a l'inici del document del fitxer adjunt."

Fixed rings and strictures in Eosinophilic Esophagitis develop due to continuing inflammation over time

Background and Aims: Two distinct e ndoscopic phenotypes of E osinophilic Esophagitis (EoE) h ave been identified: t he inflammatory (IP) a nd the stenosing (SP) p henotype. I t is not known whether these EoE-associated phenotypes are reflective of different phases during disease course. We aimed to assess the phenotype a t initial EoE p resentation and d iagnosis and to evaluate if SP increases over time. Methods: R etrospective a nalysis of t he Swiss EoE Database (SEED) extended b y a review of p atients charts, endoscopy and pathology records. Results: F orty-four E oE p atients were a nalyzed (33 males, mean age at index visit 41 ± 14 years, all Caucasians). Median follow-up t ime was 3.1 years (IQR 1-4, r ange 1 -18 years). Median diagnostic delay w as 5 y ears (IQR 2-16, range 0-34 years). A t first diagnosis, 3 2% ( 14/44) o f EoE patients h ad already presented w ith a stenosis. T he mean d iameter o f the stenoses w as 1 0 ± 2 mm, and the mean length was 2 .8 ± 2 .9 cm. Peak e osinophil count d id n ot c hange over t ime (48 ± 39 eos/HPF at index visit vs. 59 ± 41 eos/HPF at end of follow-up, n=44). The risk of the presence of a stenosis at index visit was 0% f or a d isease duration of 0 -4 y ears, 37% f or a d isease duration between 5-10 years and 67% f or a d isease duration >10 years (p = 0.0035, trend test). Conclusions: T he frequency of e sophageal stenoses i s proportional to the disease duration, whereas the inflammatory activity does n ot s ignificantly c hange over t ime. O ur f indings underscore the necessity to reduce diagnostic delay in EoE and to control the underlying inflammatory processes to prevent esophageal remodeling.

Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

RadA protein from Archaeoglobus fulgidus forms rings, nucleoprotein filaments and catalyses homologous recombination.

Proteins that catalyse homologous recombination have been identified in all living organisms and are essential for the repair of damaged DNA as well as for the generation of genetic diversity. In bacteria homologous recombination is performed by the RecA protein, whereas in the eukarya a related protein called Rad51 is required to catalyse recombination and repair. More recently, archaeal homologues of RecA/Rad51 (RadA) have been identified and isolated. In this work we have cloned and purified the RadA protein from the hyperthermophilic, sulphate-reducing archaeon Archaeoglobus fulgidus and characterised its in vitro activities. We show that (i) RadA protein forms ring structures in solution and binds single- but not double-stranded DNA to form nucleoprotein filaments, (ii) RadA is a single-stranded DNA-dependent ATPase at elevated temperatures, and (iii) RadA catalyses efficient D-loop formation and strand exchange at temperatures of 60-70 degrees C. Finally, we have used electron microscopy to visualise RadA-mediated joint molecules, the intermediates of homologous recombination. Intriguingly, RadA shares properties of both the bacterial RecA and eukaryotic Rad51 recombinases.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Genetic parameters for growth traits in pigs estimated using third degree polynomial functions

Selostus: Sian kasvuominaisuuksien perinnölliset tunnusluvut arvioituna kolmannen asteen polynomifunktion avulla

Density-functional calculations of magnetoplasmons in quantum rings

We have studied the structure and dipole charge-density response of nanorings as a function of the magnetic field using local-spin-density-functional theory. Two small rings consisting of 12 and 22 electrons confined by a positively charged background are used to represent the cases of narrow and wide rings. The results are qualitatively compared with experimental data existing on microrings and on antidots. A smaller ring containing five electrons is also analyzed to allow for a closer comparison with a recent experiment on a two-electron quantum ring.

Far-infrared spectroscopy of nanoscopic InAs rings

We have employed time-dependent local-spin-density theory to analyze the far-infrared transmission spectrum of InAs self-assembled nanoscopic rings recently reported [A. Lorke et al., Phys. Rev. Lett. (to be published)]. The overall agreement between theory and experiment is fairly good, which on the one hand confirms that the experimental peaks indeed reflect the ringlike structure of the sample, and on the other hand, asseses the suitability of the theoretical method to describe such nanostructures. The addition energies of one- and two-electron rings are also reported and compared with the corresponding capacitance spectra