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.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

Fractional Integration of the Price-Dividend Ratio in a Present-Value Model of Stock Prices

We re-examine the dynamics of returns and dividend growth within the present-value framework of stock prices. We find that the finite sample order of integration of returns is approximately equal to the order of integration of the first-differenced price-dividend ratio. As such, the traditional return forecasting regressions based on the price-dividend ratio are invalid. Moreover, the nonstationary long memory behaviour of the price-dividend ratio induces antipersistence in returns. This suggests that expected returns should be modelled as an AFIRMA process and we show this improves the forecast ability of the present-value model in-sample and out-of-sample.

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Fractional hepatic de novo lipogenesis in healthy subjects during near-continuous oral nutrition and bed rest: a comparison with published data in artificially fed, critically ill patients.

BACKGROUND AND AIMS: In critically ill patients, fractional hepatic de novo lipogenesis increases in proportion to carbohydrate administration during isoenergetic nutrition. In this study, we sought to determine whether this increase may be the consequence of continuous enteral nutrition and bed rest. We, therefore, measured fractional hepatic de novo lipogenesis in a group of 12 healthy subjects during near-continuous oral feeding (hourly isoenergetic meals with a liquid formula containing 55% carbohydrate). In eight subjects, near-continuous enteral nutrition and bed rest were applied over a 10 h period. In the other four subjects, it was extended to 34 h. Fractional hepatic de novo lipogenesis was measured by infusing(13) C-labeled acetate and monitoring VLDL-(13)C palmitate enrichment with mass isotopomer distribution analysis. Fractional hepatic de novo lipogenesis was 3.2% (range 1.5-7.5%) in the eight subjects after 10 h of near continuous nutrition and 1.6% (range 1.3-2.0%) in the four subjects after 34 h of near-continuous nutrition and bed rest. This indicates that continuous nutrition and physical inactivity do not increase hepatic de novo lipogenesis. Fractional hepatic de novo lipogenesis previously reported in critically ill patients under similar nutritional conditions (9.3%) (range 5.3-15.8%) was markedly higher than in healthy subjects (P<0.001). These data from healthy subjects indicate that fractional hepatic de novo lipogenesis is increased in critically ill patients.

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.

Comparative cost-effectiveness analyses of cardiovascular magnetic resonance and coronary angiography combined with fractional flow reserve for the diagnosis of coronary artery disease.

BACKGROUND: According to recent guidelines, patients with coronary artery disease (CAD) should undergo revascularization if significant myocardial ischemia is present. Both, cardiovascular magnetic resonance (CMR) and fractional flow reserve (FFR) allow for a reliable ischemia assessment and in combination with anatomical information provided by invasive coronary angiography (CXA), such a work-up sets the basis for a decision to revascularize or not. The cost-effectiveness ratio of these two strategies is compared. METHODS: Strategy 1) CMR to assess ischemia followed by CXA in ischemia-positive patients (CMR + CXA), Strategy 2) CXA followed by FFR in angiographically positive stenoses (CXA + FFR). The costs, evaluated from the third party payer perspective in Switzerland, Germany, the United Kingdom (UK), and the United States (US), included public prices of the different outpatient procedures and costs induced by procedural complications and by diagnostic errors. The effectiveness criterion was the correct identification of hemodynamically significant coronary lesion(s) (= significant CAD) complemented by full anatomical information. Test performances were derived from the published literature. Cost-effectiveness ratios for both strategies were compared for hypothetical cohorts with different pretest likelihood of significant CAD. RESULTS: CMR + CXA and CXA + FFR were equally cost-effective at a pretest likelihood of CAD of 62% in Switzerland, 65% in Germany, 83% in the UK, and 82% in the US with costs of CHF 5'794, euro 1'517, £ 2'680, and $ 2'179 per patient correctly diagnosed. Below these thresholds, CMR + CXA showed lower costs per patient correctly diagnosed than CXA + FFR. CONCLUSIONS: The CMR + CXA strategy is more cost-effective than CXA + FFR below a CAD prevalence of 62%, 65%, 83%, and 82% for the Swiss, the German, the UK, and the US health care systems, respectively. These findings may help to optimize resource utilization in the diagnosis of CAD.

An algorithm for semi-infinite polynomial optimization

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

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.

Enriched basaltic andesites from mid-crustal fractional crystallization, recharge, and assimilation (Pilavo Volcano, Western Cordillera of Ecuador)

The origin of andesite is an important issue in petrology because andesite is the main eruptive product at convergent margins, corresponds to the average crustal composition and is often associated with major Cu-Au mineralization. In this study we present petrographic, mineralogical, geochemical and isotopic data for basaltic andesites of the latest Pleistocene Pilavo volcano, one of the most frontal volcanoes of the Ecuadorian Quaternary arc, situated upon thick (30-50 km) mafic crust composed of accreted Cretaceous oceanic plateau rocks and overlying mafic to intermediate Late Cretaceous-Late Tertiary magmatic arcs. The Pilavo rocks are basaltic andesites (54-57 center dot 5 wt % SiO(2)) with a tholeiitic affinity as opposed to the typical calc-alkaline high-silica andesites and dacites (SiO(2) 59-66 wt %) of other frontal arc volcanoes of Ecuador (e.g. Pichincha, Pululahua). They have much higher incompatible element contents (e.g. Sr 650-1350 ppm, Ba 650-1800 ppm, Zr 100-225 ppm, Th 5-25 ppm, La 15-65 ppm) and Th/La ratios (0 center dot 28-0 center dot 36) than Pichincha and Pululahua, and more primitive Sr ((87)Sr/(86)Sr similar to 0 center dot 7038-0 center dot 7039) and Nd (epsilon(Nd) similar to +5 center dot 5 to +6 center dot 1) isotopic signatures. Pilavo andesites have geochemical affinities with modern and recent high-MgO andesites (e.g. low-silica adakites, Setouchi sanukites) and, especially, with Archean sanukitoids, for both of which incompatible element enrichments are believed to result from interactions of slab melts with peridotitic mantle. Petrographic, mineral chemistry, bulk-rock geochemical and isotopic data indicate that the Pilavo magmatic rocks have evolved through three main stages: (1) generation of a basaltic magma in the mantle wedge region by flux melting induced by slab-derived fluids (aqueous, supercritical or melts); (2) high-pressure differentiation of the basaltic melt (at the mantle-crust boundary or at lower crustal levels) through sustained fractionation of olivine and clinopyroxene, leading to hydrous, high-alumina basaltic andesite melts with a tholeiitic affinity, enriched in incompatible elements and strongly impoverished in Ni and Cr; (3) establishment of one or more mid-crustal magma storage reservoirs in which the magmas evolved through dominant amphibole and clinopyroxene (but no plagioclase) fractionation accompanied by assimilation of the modified plutonic roots of the arc and recharge by incoming batches of more primitive magma from depth. The latter process has resulted in strongly increasing incompatible element concentrations in the Pilavo basaltic andesites, coupled with slightly increasing crustal isotopic signatures and a shift towards a more calc-alkaline affinity. Our data show that, although ultimately originating from the slab, incompatible element abundances in arc andesites with primitive isotopic signatures can be significantly enhanced by intra-crustal processes within a thick juvenile mafic crust, thus providing an additional process for the generation of enriched andesites.

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].

Hours worked - Productivity puzzle: identification in fractional integration settings

A recent finding of the structural VAR literature is that the response of hours worked to a technology shock depends on the assumption on the order of integration of the hours. In this work we relax this assumption, allowing for fractional integration and long memory in the process for hours and productivity. We find that the sign and magnitude of the estimated impulse responses of hours to a positive technology shock depend crucially on the assumptions applied to identify them. Responses estimated with short-run identification are positive and statistically significant in all datasets analyzed. Long-run identification results in negative often not statistically significant responses. We check validity of these assumptions with the Sims (1989) procedure, concluding that both types of assumptions are appropriate to recover the impulse responses of hours in a fractionally integrated VAR. However, the application of longrun identification results in a substantial increase of the sampling uncertainty. JEL Classification numbers: C22, E32. Keywords: technology shock, fractional integration, hours worked, structural VAR, identification