Remarks on hard Lefschetz conjectures on Chow groups

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

On Damage Spreading Transitions

We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able to show analitically that the evolution of the damage between two systems driven by the same noise has the same structure of a directed percolation problem. By means of a mean field approximation, we map the density phase transition into the damage phase transition, obtaining a reliable phase diagram. We extend this analysis to all symmetric cellular automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Galois sections for abelianized fundamental groups

Given a smooth projective curve $X$ of genus at least 2 over a number field $k$, Grothendieck's Section Conjecture predicts that the canonical projection from the \'etale fundamental group of $X$ onto the absolute Galois group of $k$ has a section if and only if the curve has a rational point. We show that there exist curves where the above map has a section over each completion of $k$ but not over $k$. In the appendix Victor Flynn gives explicit examples in genus 2. Our result is a consequence of a more general investigation of the existence of sections for the projection of the \'etale fundamental group `with abelianized geometric part' onto the Galois group. We give a criterion for the existence of sections in arbitrary dimension and over arbitrary perfect fields, and then study the case of curves over local and global fields more closely. We also point out the relation to the elementary obstruction of Colliot-Th\'el\`ene and Sansuc.Comment: This is the published version, except for a characteristic 0 assumption added in Section 5 which was unfortunately omitted there. Thanks to O. Wittenberg for noticing i

Noncommutative Geometry in the Framework of Differential Graded Categories

In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on noncommutative motives. We propose a motivic measure with values in a motivic ring. This enables us to introduce certain zeta functions of noncommutative spaces.Comment: 19 pages. Minor corrections and one reference added; to appear in the proceedings volume of AGAQ Istanbul, 200

Level of performance of independent nursing functions by staff nurses in selected hospitals in Cavite

This study used a non-experimental descriptive method of research. Using purposive sampling technique, the respondents consisted of staff nurses in selected hospitals in Cavite. The data gathering instrument was a questionnaire, which was adapted from an undergraduate thesis by De Villa, Salazar and Sevilla (2001) entitled “The performance status of community health nurses functions in selected municipalities in Cavite” and was modified accordingly. The statistical treatments utilized were frequency, percentage, f-test or ANOVA and t-test. The study concluded that, 1) Majority of the respondents were 24-27 years old, female, single, had more than one (1) year of experience, had handled more than 10 patients and had monthly income of P10,000 and below; 2) The overall mean level of performance of independent nursing functions by staff nurses was 4.35. This indicates that the nurses perform their independent nursing functions in a moderate extent; 3) The level of performance of independent nursing functions of staff nurses was not significantly related to age, gender, civil status, length of experience and monthly income; 4) The level of performance of independent nursing functions by staff nurses was significantly related to nurse to patient ratio; 5) There was a significant difference in the level of performance of independent nursing functions by staff nurses when grouped according to nurse to patient ratio