On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

La crisi sub-prime i el crack de 1929: Comparació d'episodis d'eufòria financera

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 present investigació té per objecte d’estudi la relació, atès el període de turbulències econòmiques que travessa el món globalitzat, entre els episodis d’eufòria financera i les crisi financeres i econòmiques, i la periodicitat amb les que aquestes es produeixen. Aquesta pretén confrontar-se des d’una aproximació històric-econòmica, mitjançant l’anàlisi i la comparació de dos successos -el crack borsari de 1929 i la crisi sub-prime- per tal de demostrar la existència de comuns denominadors, i, a la llum dels resultats, apreciar les conclusions que aporta la Història. Serà, doncs, aquesta periodicitat i les seves implicacions la qual s'ambicionarà contrastar amb la realitat mitjançant l'aplicació i l'anàlisi pràctica de dos episodis rellevants i paradigmàtics, amb el recolzament i l'autoritat del model comparatiu establerts per l'economista John Kenneth Galbraith al seu llibre ''Breve historia de la euforia financiera''.

On [summation of 1 raised to the power 1] equivalence relations over the natural numbers

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

Prime Property Institutions for a Subprime Era: Exploring Innovative Models of Residential Development and Finance

This paper breaks new ground toward contractual and institutional innovation in models of homeownership, equity building, and mortgage enforcement. Inspired by recent developments in the affordable housing sector and in other types of public financing schemes, this paper suggests extending institutional and financial strategies such as timeand place-based division of property rights, conditional subsidies, and credit mediation to alleviate the systemic risks of mortgage foreclosure. Alongside a for-profit shared equity scheme that would be led by local governments, we also outline a private market shared equity model, one of bootstrapping home buying with purchase options.

Prime property institutions for a subprime era: Toward innovative models of homeownership

This Article breaks new ground toward contractual and institutional innovation in models of homeownership, equity building, and mortgage enforcement. Inspired by recent developments in the affordable housing sector and other types of public financing schemes, we suggest extending institutional and financial strategies such as time- and place-based division of property rights, conditional subsidies, and credit mediation to alleviate the systemic risks of mortgage foreclosure. Two new solutions offer a broad theoretical basis for such developments in the economic and legal institution of homeownership: a for-profit shared equity scheme led by local governments alongside a private market shared equity model, one of "bootstrapping home buying with purchase options".

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

The size and distribution of donations: Effects of numbers of potential recipients

Whereas much literature exists on choice overload, little is known about effects of numbers of alternatives in donation decisions. How do these affect both the size and distribution of donations? We hypothesize that donations are affected by the reputation of recipients and increase with their number, albeit at a decreasing rate. Allocations to recipients reflect different concepts of fairness equity and equality. Both may be employed but, since they differ in cognitive and emotional costs, numbers of recipients are important. Using a cognitive (emotional) argument, distributions become more uniform (skewed) as numbers increase. In a survey, respondents indicated how they would donate lottery winnings of 50 Euros. Results indicated that more was donated to NGO s that respondents knew better. Second, total donations increased with the number of recipients albeit at a decreasing rate. Third, distributions of donations became more skewed as numbers increased. We comment on theoretical and practical implications.

Bounds for the Betti numbers of generalized Cohen-Macaulay ideals

Upper bounds for the Betti numbers of generalized Cohen-Macaulay ideals are given. In particular, for the case of non-degenerate, reduced and ir- reducible projective curves we get an upper bound which only depends on their degree.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

Euphorbia L. subsect. Esula (Boiss. in DC.) Pax in the Iberian Peninsula. Leaf surface, chromosome numbers and taxonomic treatment

Presentem l'estudi taxonòmic dels représentants d'Euphorbia subsect. Esula a la Península Ibèrica. Prèviament, s'inclou un primer capítol dedicai a l'estudi de les epidermis foliars i un segon capítol sobre nombres cromosòmics...