Enumeration of kk-Fibonacci Paths using Infinite Weighted Automata

In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of $F_{k,l}$ colors, where $F_{k,l}$ is the $l$th $k$-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.Comment: arXiv admin note: substantial text overlap with arXiv:1310.244

Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process

We rederive the equations of motion for relativistic strings, that is, one-dimensional elastic bodies whose internal energy depends only on their stretching, and use them to study circular string loops rotating in the equatorial plane of flat and black hole spacetimes. We start by obtaining the conditions for equilibrium, and find that: (i) if the string's longitudinal speed of sound does not exceed the speed of light then its radius when rotating in Minkowski's spacetime is always larger than its radius when at rest; (ii) in Minkowski's spacetime, equilibria are linearly stable for rotation speeds below a certain threshold, higher than the string's longitudinal speed of sound, and linearly unstable for some rotation speeds above it; (iii) equilibria are always linearly unstable in Schwarzschild's spacetime. Moreover, we study interactions of a rotating string loop with a Kerr black hole, namely in the context of the weak cosmic censorship conjecture and the Penrose process. We find that: (i) elastic string loops that satisfy the null energy condition cannot overspin extremal black holes; (ii) elastic string loops that satisfy the dominant energy condition cannot increase the maximum efficiency of the usual particle Penrose process; (iii) if the dominant energy condition (but not the weak energy condition) is violated then the efficiency can be increased. This last result hints at the interesting possibility that the dominant energy condition may underlie the well known upper bounds for the efficiencies of energy extraction processes (including, for example, superradiance).Comment: 32 pages, 6 figures; v2: minor improvements; v3: small changes, matches final published version; v4: typos in the references fixe

Ethnic identity and dietary habits among Hispanic immigrants in Spain

Immigration has become a new phenomenon in Spanish society during the last years. In 2007, immigrants represented around 10% of total population, with 35% coming from Latin-American countries. When immigrants arrive, they bring their own values and cultural symbols, which, essentially, are different from those of the indigenous population. As time goes through, two alternative processes are observed: 1) a gradual switch towards the Host Society values; or 2) a maintenance of their ethnical identity. Focussing in the Latin-American immigrants in Barcelona, the objective of this paper is twofold: 1) to measure their degree of ethnical identity; and 2) to analyse the relationship between food habits and their ethnical identity. Food habits refer here to the consumption of traditional meals from their country of origin. Face-to-face interviews with a representative sample of Latin American immigrants in the Metropolitan area of Barcelona are undertaken. First, socioeconomics characteristics of the sample are described. Second, the MEIM scale is used to measure their ethnical identity, which combines aspects from the social identity and personal development theories. Finally, a Multinomial Logit Model is estimated to identify the relationship between food habits and ethnical identity. Results indicate that the higher the level of ethnic identity and feeling of belonging, the greater the persistence of dietary habits from the country of origin.Ethnic identity, Food habits, Latin American immigrants, Spain., Agricultural and Food Policy,