The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Análise citológica e cariométrica da ação da colchina sôbre a espermatogênese dos hemípteros

The action of colchicine upon the spermatogenesis of Triatoma infestans, (Hemipt. Heteroptera), has been studied and the different categories of giant spermatids that appear during the treatment have been compared with the nuclear volumes of the whole series of normal spermatogenetic stages. The following facts have been ascertained: 1) 4 hours after the treatment the gonial mitotic metaphases, and the 1st. and 2nd. metaphases of meiosis are stopped. The prophasic stages of meiosis and diakynesis appear to be normal. After 9 days of treatment, all the tetrads are broken in the meiotic metaphases and the cells appear with 44 and 22 chromosomes respectively, scattered in the cytoplasm. 2) At 9 days, practically all spermatogenetic stages have disappeared except for a few cysts of spermatogonia, and practically the whole testicle is full of cysts of spermatozoa and spermatid, with some large zones of necrosis with pycnotic nuclei. The spermatids appear to be of different sizes and the statistical analysis of the nuclear volumes gives a polymodal hystogram with 4 modes, whose volumes are in the ratio of 1:2:4:8. Ripe spermatozoa seem to have a certain volume variability, that has not been possible to analyse quantitatively. All these facts confirm what DOOLEY found in the colchicinized Orthoptera testicle. 3) The caryometric analysis conducted statistically on the normal stages of the spermatogenesis (resting spermatogonia, gonial prophases, leptotene, "confused stage", diakynesis, and spermatid) revealed the following facts: a) Considering the volume of the resting, spermatogonia as 1, their mitotic prophases have a volume of 2. Some rare prophases appear to have a volume of 4 and probably belong to tetraployd spermatogonia normally present in the testicle of Hemiptera. b) The first spermatocyte at the beginning of the auxocitary growth (leptotene) has a volume of 2, which is equal to that of them gonial prophase. It grows further during the "confused stage" and reduplicates, reaching thus the volume of 4. Diakynesis has a rather variable nuclear volume and it is higher than volume 4. This is probably of physico-chemical nature and not a growth increase. c) The spermatid at the beginning of the spermiogenetic process has a volume of 1 which is very constant and homogeneous. 4) These results can be summarized concluding that the meiotic process begins from a spermatogonium at the end of his mitotic interphasic growth (vol. 2) and instead of entering into the mitotic prophase transforms itself into the leptotene spermatocyte. During the diplotene ("confused stage") the volume of the nucleus doubles once more and reaches volume 4. In consequence of the two successive meiotic divisions the spermatid, although having an haploid number of chromosomes, has a nuclear volume of 1, just like the diploid spermatogonium. The interpretation of this strange result probably comes from the existence of the "tertiary split" in the chromosomes of the haploid set, that has been illustrated in the Hemiptera by HUGUES SCHRADER and in Orthoptera by MICKEY and co-workers. The tertiary split indicates that the chromosomes of the haploid set are constituted from almost two chromonemata, and this double constitution corresponds to the double cycle of reduplication that takes place during the spermatogenesis starting from the resting gonia. In Triatoma infestans the tertiary split appears in the chromosomes in the 1st. and 2nd. metaphases and in the diakynesis. In the blocked metaphases at the 9th. day of colchicinization some of the 44 elements scattered in the cytoplasm, show, when properly oriented, the split very clearly. Some new and strange facts revealed by SCHRADER and LEUCHTEMBERGER in Arvelius suggest the possibility of other interpretations of the rhythmic growth in special cases. There appears the necessity of more knowledge about the multiple or simple constitution of the chromosomes in somatic and spermatogonial mitosis.

La Participació del psicomotricista en el joc de l'infant

This study presents a research about the participation of psicomotricist in the play with children to find out what kind of conditions improve the development of their capacitys of relathionship. The research has four parts: 1) A teoretical revision about the terms of game, social participation and relathionship; 2) A case study based on different interviews with experts, psicomotricists and the observed psicomotricist and 4 deep observations 3) The categories of analysis from the triangulation of teoretical and case study sources of information; 4) Discussion and conclusions about general actuations of the psicomotricist, about specifical actuations with the children and about psicomotricist’s believes.

Petrol consumption and redistributive effects of its taxation in Spain

The objective of this paper is to estimate a petrol consumption function for Spain and to evaluate the redistributive effects of petrol taxation. We use micro data from the Spanish Household Budget Survey of 1990/91 and model petrol consumption taking into account the effect that income changes may have on car ownership levels, as well as the differences that exist between expenditure and consumption. Our results show the importance that household structure, place of residence and income have on petrol consumption. We are able to compute income elasticities of petrol expenditure, both conditional and unconditional on the level of car ownership. Non-conditional elasticities, while always very close to unit values, are lower for higher income households and for those living in rural areas or small cities. When car ownership levels are taken into account, conditional elasticities are obtained that are around one half the value of the non- conditional ones, being fairly stable across income categories and city sizes. As regards the redistributive effects of petrol taxation, we observe that for the lowest income deciles the share of petrol expenditure increases with income, and thus the tax can be regarded as progressive. However, after a certain income level the tax proves to be regressive.

Minimal truncations of supersingular p-divisible groups

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Lower bounds for the number of limit cycles of trigonometric Abel equations

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Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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Periodic orbits in complex Abel equation

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The bogomolov conjecture for totally degenerate Abelian varieties

We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place.

Tropical varieties for non-archimedean analytic spaces

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A Multisectorial model of prices: the SAM approach

Social Accounting Matrices (SAM) are normally used to analyse the income generation process. They are also useful, however, for analysing the cost transmission and price formation mechanisms. For price contributions, Roland-Holst and Sancho (1995) used the SAM structure to analyse the price and cost linkages through a representation of the interdependence between activities, households and factors. This paper is a further analysis of the cost transmission mechanisms, in which I add the capital account to the endogenous components of the Roland-Holst and Sancho approach. By doing this I reflect the responses of prices to the exogenous shocks in savings and investment. I also present an additive decomposition of the global price effects into categories of interdependence that isolates the impact on price levels of shocks in the capital account. I use a 1994 Social Accounting Matrix to make an empirical application of the Catalan economy. Keywords: social accounting matrix, cost linkages, price transmission, capital account. JEL Classification: C63, C69, D59.

Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

La tabla del tres: I- Las categorías peirceanas

La evolución del pensamiento peirceano parece experimentar una sucesión de giros y rupturas internas, entre ellos la aparición de la fenomenología en el cambio de siglo, junto con la emergencia de Hegel en lugar de Kant como fuente de inspiración. Sin embargo, si nos tomamos en serio el resultado tanto de sus investigaciones kantianas como de las hegelianas, es decir, las categorías, podemos reconocer una continuidad general dentro del pensamiento de Peirce. En lugar de una confusión de tendencias “empíricas” y “metafísicas,” descubrimos una sistemática transformación empírica de la metafísica. -- L’evolució del pensament peirceà sembla experimentar una successió de girs i ruptures internes, entre ells l’aparició de la fenomenologia amb el canvi de segle, juntament amb l’emergència de Hegel en lloc de Kant com a font d’inspiració. Però si ens prenem seriosament el resultat tant de les seves investigacions kantianes com de les hegelianes, això és, les categories, podem reconèixer una continuïtat general dins del pensament de Peirce. Enlloc d’una confusió de tendències “empíriques” i “metafísiques,” descobrim una sistemàtica transformació empírica de la metafísica

Indicadors de pressió ambiental a les platges de Menorca: prova pilot (IPAPM'pp)

L’augment del turisme experimentat des de principis dels anys 70 a l’illa de Menorca (Illes Balears, Espanya) ha provocat un impacte sobre les seves platges, el seu principal atractiu turístic. Molts d’aquests impactes s’incrementen durant la temporada alta, compresa entre els mesos de maig a octubre. L’objectiu principal d’aquest projecte és l’elaboració d’un sistema d’indicadors de pressió ambiental útils per a l’anàlisi de les platges. La zona objecte d’estudi de la prova-pilot, correspon a les platges del sud-oest de Menorca, aquestes cales són les que actualment es troben sotmeses a una major pressió. Es tracta de catorze platges tipificades en tres categories (A, B, C) segons les característiques del tipus d’espai on es troben situades. Són les platges de: Cala Degollador, Cala Blanca, Cala’n Bosch, Son Xoriguer, Son Saura-Es Banyul, Son Saura-Bellavista, Es Talaier, Cala Turqueta, Cala Macarelleta, Cala Macarella, Cala Galdana, Cala Mitjana, Cala Trebalúger i Cala Escorxada. Partint d’un treball bibliogràfic, s’ha realitzat una selecció de mig centenar d’indicadors potencials dels quals catorze han format part dels IPAPM’pp, mitjançant l’elaboració d’una anàlisi multicriteri. Per a cada un dels IPAPM’pp s’ha desenvolupat una metodologia amb les corresponents fitxes individuals descriptives per al seu seguiment temporal. En aquest primer estudi, l’indicador que presenta un nombre de valors no acceptables en una major proporció de platges, és l’indicador 3. Índex de valoració de les mesures de conservació del sistema natural, seguit de l’indicador 6. Superfície subsistema sorra per usuari. El 2006, les platges de tipologia A, presenten un major percentatge positiu de les variables dels indicadors. Les platges de tipologia B i C presenten un percentatge menor d’acceptabilitat dels valors dels indicadors.