Hamilton 2004 Annual County Profile, 2004

County Profile

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

In principio erat liber : l'organisation du premier livre de motets de Tomás Luis de Victoria (Venise, 1572)

L'organisation du premier livre de motets de Tomás Luis de Victoria, publié à Venise en 1572 chez les Fils d'Antonio Gardano (RISM V 1421), repose sur une stratification d'éléments divers mais complémentaires. Les pièces sont organisées en quatre groupes : quatorze à 4 voix, neuf à 5 voix, neuf à 6 voix et une à 8 voix. Elles forment des paires modales. Les derniers motets des groupes reposent sur des écritures individualisées (ad aequales, canon à l'unisson, Tenormotette, motet à double choeur). De plus, un jeu avec le nombre de parties, une et deux essentiellement, intervient entre les groupes et à l'intérieur. Les textes émanent de plusieurs rites (avilais, prétridentin et tridentin) et sources. Lorsque c'est nécessaire, le compositeur les remanie pour qu'ils s'adaptent à l'organisation du recueil. Au bout du compte, le livre veut être un objet ayant un certain poids et qui dit quelque chose de plus qu'une simple addition de pièces. C'est précisément ce dont a besoin le jeune compositeur pour prendre une place sur le marché du motet avec ce qui constitue son premier « opus ». Dans la dédicace qu'il signe lui-même, Victoria inscrit son édition dans la mouvance de la musica reservata puisqu'il la destine d'abord aux connaisseurs. Or, c'est précisément cette organisation complexe qui permet au musicien d'inscrire son recueil dans une lignée de publications savantes, initiées semble-t-il par le livre de motets à 5 voix d'Adrian Willaert, qui date de 1539.

A quantitative test of Hamilton's rule for the evolution of altruism.

The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.

Audit report on the Hamilton County Solid Waste Commission for the year ended June 30, 2011

Audit report on the Hamilton County Solid Waste Commission for the year ended June 30, 2011

Report on the Hamilton County Sheriff’s Office for the period July 1, 2008 through June 30, 2012

Report on the Hamilton County Sheriff’s Office for the period July 1, 2008 through June 30, 2012

Who wrote the Second Ave maris stella of Tomás Luis de Victoria?

Contrary to what Felipe Pedrell indicates, the second Ave maris stella in his Victoria's collected works (vol. V, 1908, pp. 100-3, n° 33) doesn't appear in the collection published in 1600 in Madrid by the composer, nor in any other of the musician's books. In the 1600 edition, Victoria reissues the two first verses (plainchant followed by polyphony) of the Ave maris stella published in 1576 and then again in 1581. The earliest source of the problematic Ave maris stella is Munich, Bayerische Staatsbibliothek, Musik-Abteilung, 2 Mus. pr. 23 handschriftlicher Beiband, dating from the third quarter oft he seventeenth century. This source is a manuscrit that runs as an appendix to the 1581 edition of Victoria's hymns. No attributions are given in the manuscript. The first attributions of the piece to Victoria arise in the nineteenth century, in manuscripts copied by Johann Michael Hauber, Johann Caspar Aiblinger, August Baumgartner and Carl Proske, and preserved in Munich and Regensburg. Proske pubished the piece in his Musica divina in 1859 (Annus primus, vol. III, pp. 419-24). The most probable hypothesis ist that Pedrell had knowledge of the second Ave maris stella, under the spanish composer's name, via Proske's Musica divina. In all likelihood the piece is not by Victoria, not least because the composer has never written odd polyphonic verses of hymns. In his Studies in the Music of Tomás Luis de Victoria (2001), Eugene Casjen Cramer relies on the supposed authenticity of the work to ascribe the others pieces of Munich, Bayerische Staatsbibliothek, Musik-Abteilung, 2 Mus. pr. 23 handschriftlicher Beiband to the composer. These attributions should therefore be refuted.

Cracking and Seating to Retard Reflective Cracking - Hamilton County, HR-277, 1993

The crack and seat (C & S) method of rehabilitating concrete pavements has been proposed to reduce the incidence of reflective cracking in asphalt overlays. These cracked pieces help reduce the thermal effects on lateral joint movement while the seating of slab pieces reduces vertical movement. This 1986 project demonstrated that a 0.6 m x 0.9 m (2 ft x 3 ft) cracking pattern was optimal to retard reflective cracking in an asphalt overlay. The best performance among three C & S test sections was section 4 with a 0.6 m x 0.9 m (2 ft x 3 ft) cracking pattern and 7.6 cm (3 in) overlay. Structural ratings determined from the Road Rater™ indicated little difference between each C & S section with varying AC thicknesses and crack spacings. Although reflection cracking is reduced in the early years after construction, the effectiveness of the C & S method diminishes over time.

Hamilton County, Township 86 North Range 26 West

Des Moines River Plat Maps.