Markoff-Rosenberger triples in geometric progression

Solutions of the Markoff-Rosenberger equation ax^2+by^2+cz^2 = dxyz such that their coordinates belong to the ring of integers of a number field and form a geometric progression are studied.Comment: To appear in Acta Mathematica Hungaric

An algorithm for determining torsion growth of elliptic curves

We present a fast algorithm that takes as input an elliptic curve defined over $\mathbb Q$ and an integer $d$ and returns all the number fields $K$ of degree $d'$ dividing $d$ such that $E(K)_{tors}$ contains $E(F)_{tors}$ as a proper subgroup, for all $F \varsubsetneq K$. We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all $d \leq 23$ and collected various interesting data. In particular, we find a degree 6 sporadic point on $X_1(4,12)$, which is so far the lowest known degree a sporadic point on $X_1(m,n)$, for $m\geq 2$.Comment: 15 pages, Added Supplementary materia

Very long-range attractive and repulsive forces in Model Colloidal Dispersions

Experiments with polymer latex solutions show the coexistence of order-disorder structures of macroions. Because of the large macroions' sizes, this order-disorder phase coexistence imply the existence of very long-range attractive and repulsive forces, which can not be explained in terms of conventional direct interaction potentials, which are short-range. Here we apply an integral equations theory to a simple model for colloidal dispersions, at finite concentrations, calculate the particles distribution functions and the involved effective forces. We find very long-range attractive and repulsive forces among the like-charged macroions. The distribution functions are in qualitative agreement with experimental results. The origin of these forces are discussed in terms of an energy-entropy balance.Comment: 16 pages, seven figures. ECIS-201

Markoff-Rosenberger triples in arithmetic progression

We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and the classic Markoff equation x^2+y^2+z^2 = 3xyz over an arbitrary number field.Comment: To appear in Journal of Symbolic Computatio

Flujos de capital privado y calificaciones soberanas a mercados emergentes

La desaceleración coyuntural de la economía mundial iniciada en la segunda mitad del año 2000 –impulsada por los aumentos de las tasas de interés internacionales y de los precios del petróleo- se profundizó en el transcurso del presente año, debido, a la pérdida de dinamismo de la economía de los Estados Unidos. Así, los pronósticos apuntaban hacia una desaceleración de la economía global más pronunciada que la anticipada inicialmente. Los atentados terroristas del 11 de septiembre confirmaron esta percepción y propiciaron una mayor aversión al riesgo en los mercados financieros internacionales; aspecto que redundará, inevitablemente, en un menor acceso de las economías emergentes a los mercados voluntarios de capital. Al respecto, las proyecciones del flujo neto de capital privado hacia los países en desarrollo para 2001 y 2002 se ubican muy por debajo de los volúmenes observados durante la mayor parte de la década de los noventa

Analyzing the Mass-Rearing System of the California Red Scale Parasitoid Aphytis melinus (Hymenoptera: Aphelinidae)

Results from studies to improve mass rearing production of the parasitoid Aphytis melinus De Bach (Hymenoptera: Aphelinidae) are presented. Parasitoid production was carried out following standard commercial procedures using an alternative host, Aspidiotus nerii Bouché (Hemiptera: Diaspididae), infesting Cucurbita moschata (Duchesne) (Cucurbitaceae), butternut squash. We found that the initial number of A. melinus adults introduced into rearing cages to start production and the scale/parasitoid ratio in those cages profoundly influenced future parasitoid production. We also observed that scale parasitism was positively correlated with the production of parasitoid adults, but this relationship was negatively correlated if > 2.6 parasitoids per d, per cm2, were used in the cages to start parasitism. Supplemental honey (provided on the squash surface) had no clear impact on parasitoid production or survival, but improved host parasitism. Approximately 47% of the host scale population on squash was parasitized, with another 43.1% of the population recorded as dead. We found that ≤ 10 host scales per cm2 on squash was an adequate density for mass production purposes

A note on the Gauge Symmetries of Unimodular Gravity

The symmetries of Unimodular Gravity are clarified somewhat.Comment: 4 pages, v2: acknowledgments correcte