Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

New Evidence on Allyn Young’s Style and Influence as a Teacher

This paper publishes the hitherto unpublished correspondence between Allyn Abbott Young’s biographer Charles Blitch and 17 of Young’s former students or associates. Together with related biographical and archival material, the paper shows the way in which this adds to our knowledge of Young’s considerable influence as a teacher upon some of the twentieth century’s greatest economists. The correspondents are as follows: James W Angell, Colin Clark, Arthur H Cole, Lauchlin Currie, Melvin G de Chazeau, Eleanor Lansing Dulles, Howard S Ellis, Frank W Fetter, Earl J Hamilton, Seymour S Harris, Richard S Howey, Nicholas Kaldor, Melvin M Knight

On Public Inefficiencies in a Mixed Duopoly

The aim of this paper is to investigate the welfare effect of a change in the public firms objective function in oligopoly when the government takes into account the distortionary effect of rising funds by taxation (shadow cost of public funds). We analyze the impact of a shift from welfare- to profit-maximizing behaviour of the public firm on the timing of competition by endogenizing the determination of simultaneous (Nash-Cournot) versus sequential (Stackelberg) games using the game with observable delay proposed by Hamilton and Slutsky (1990). Differently from previous work that assumed the timing of competition, we show that, absent efficiency gains, instructing the public firm to play as a private one never increases welfare. Moreover, even when large efficiency gains result from the shift in public firm's objective, an inefficient public firm that maximizes welfare may be preferred.

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.

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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

A computational and geometric approach to phase resetting curves and surfaces

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

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Genuine savings and future well-being in Germany, 1850-2000

Genuine Savings (GS), also known as ‘net adjusted savings’, is a composite indicator of the sustainability of economic development. Genuine Savings reflects year-on-year changes in the total wealth or capital of a country, including net investment in produced capita, investment in human capital, depletion of natural resources, and damage caused by pollution. A negative Genuine Savings rate suggests that the stock of national wealth is declining and that future utility must be less than current utility, indicating that economic development is non-sustainable (Hamilton and Clemens, 1999). We make use of data over a 150 year period to examine the relationship between Genuine Savings and a number of indicators of well-being over time, and compare the relative changes in human, produced, and components of natural capital over the period. Overall, we find that the magnitude of genuine savings is positively related to changes in future consumption, with some evidence of a cointegrating relationship. However, the relationships between genuine savings and infant mortality or average heights are less clear.

Estimació de les emissions de metà generades per fermentació entèrica a la ramaderia bovina a Catalunya, com a font de gasos d'efecte hivernacle (GEH)

L’emissió de GEH generats per processos relacionats amb l’activitat antropogènica ha provocat que la temperatura mitjana de la Terra augmenti, originant el que es coneix com escalfament global. Les possibles conseqüències negatives per al conjunt de la biosfera han portat a l’adopció d’acords internacionals que obliguen als diferents Estats a realitzar Inventaris Nacionals d’Emissions a l’Atmosfera. El CH4, que és exhalat o eructat com a resultat del procés de fermentació entèrica dels remugants, genera un impacte que ha de ser quantificat en els diferents inventaris. En aquest projecte s’ha realitzat l’estimació del CH4 generat per la fermentació entèrica dels bovins a Catalunya. Per aquest objectiu s’han utilitat les equacions explicitades a les directrius del Panel Intergovernamental sobre el Canvi Climàtic (IPCC), així com l’equació de Cambra, L. et al. (2008) per a la determinació del factor de conversió Ym. El resultat final rebaixa les quantitats inventariades tant per l’administració catalana com per l’espanyola.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

La programació al servei de la matemàtica

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. La programació al servei de la matemàtica és un programa informàtic fet amb Excel i Visual Basic. Resol equacions de primer grau, equacions de segon grau, sistemes d'equacions lineals de dues equacions i dues incògnites, sistemes d'equacions lineals compatibles determinats de tres equacions i tres incògnites i troba zeros de funcions amb el teorema de Bolzano. En cadascun dels casos, representa les solucions gràficament. Per a això, en el treball s'ha hagut de treballar, en matemàtiques, amb equacions, nombres complexos, la regla de Cramer per a la resolució de sistemes, i buscar la manera de programar un mètode iteratiu pel teorema de Bolzano. En la part gràfica, s'ha resolt com fer taules de valors amb dues i tres variables i treballar amb rectes i plans. Per la part informàtica, s'ha emprat un llenguatge nou per l'alumne i, sobretot, ha calgut saber decidir on posar una determinada instrucció, ja que el fet de variar-ne la posició una sola lí­nea ho pot canviar tot. A més d'això, s'han resolt altres problemes de programació i també s'ha realitzat el disseny de pantalles.

A rapid, reliable method of evaluating growth and viability of intraerythrocytic protozoan hemoparasites using fluorescence flow cytometry

Fluorescence flow cytometry was employed to assess the potential of a vital dye, hydroethiedine, for use in the detection and monitoring of the viability of hemoparasites in infected erythrocytes, using Babesia bovis as a model parasite. The studies demonstrated that hydroethidine is taken up by B. bovis and metabolically converted to the DNA binding fluorochrone, ethidium. Following uptake of the dye, erythrocytes contamine viable parasites were readily distinguished and quantitated. Timed studies with the parasiticidal drug, Ganaseg, showed that it is possible to use the fluorochrome assay to monitor the effects of the drug on the rate of replication and viability of B. bovis in culture. The assay provides a rapid method for evaluation of the in vitro effect of drugs on hemoparasites and for analysis of the effect of various components of the immune response, such as lymphokines, monocyte products, antibodies, and effector cells (T, NK, LAK, ADCC) on the growth and viability of intraerythrocytic parasites.