Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Equacions diferencials i models

En tot cas, jo voldria que aquesta conferència fos això que he dit: una breu lliçó sobre la importància de les equacions diferencials. Parlaré d'elles des de el punt de vista del models, és a dir, dels fenòmens que modelitzeu. I intentaré explicar que malgrat el seu origen antic, totes elles segueixen presentant avui en dia problemes nous i interessants, tant des de el punt de vista teòric com pràctic.

Gestió d'un projecte per optimitzar recursos informàtics

Estudi per verificar la hipòtesis plantejada inicial sobre que moltes empreses implementen nous sistemes integrals i segueixen efectuant tasques rutinàries sense aprofitar aquests nous sistemes, fent duplicitat de tasques i malgastant recursos informàtics.

La Corona immarcescible : pintures de l'antiguitat tardana de la necròpolis alta d'Oxirinc (Mínia, Egipte)

La primera publicació de l’Institut enceta la Sèrie Documenta, que respon a la voluntat de promoure i editar estudis que donin a conèixer i emmarquin científicament nous elements de la cultura material de l’antiguitat clàssica.Aquest llibre estudia un conjunt de pintura mural dels segles V o VI que decorava les parets d’una casa funerària, convertida després en oratori, i que fou descoberta a la necròpolis alta de l’antiga ciutat d’Oxirinc (Mínia, Egipte). El cicle pictòric presenta una sobrietat simbolista que evoluciona després en una iconografia rica en figures i colors.Tot això, completat per la gens menyspreable qualitat artística de les representacions pictòriques, fa d’aquest conjunt una peça arqueològica molt singular.L’estudi inclou un primer capítol a càrrec del Dr. Josep Padró, de la Universitat de Barcelona, Maite Mascort i Hassan Ibrahim Amer, on es sintetitzen els treballs arqueològics i històrics realitzats, des de l’any 1992, a l’antiga Oxirin. Tot seguit, la Dra. Eva Subías, investigadora de la Universitat Rovira i Virgili i col·laboradora de l’Institut des del primer moment, ens ofereix l’estudi històricoartístic del cicle mural. Finalment, Concepció Piedrafita ens dóna la lectura i traducció dels textos grecs presents en les pintures.L’obra inclou una presentació a càrrec de Josep Guitart, director de l’Institut Català d’Arqueologia Clàssica i una traducció dels textos al francès.

¿Se puede hablar de una metrología ilercavona? Sobre la posible existencia de una unidad de medida lineal en la Ilercavonia

A partir del análisis metrológico realizado en 4 asentamientos ibéricos del tramo final del Ebro, en la región ilercavona planteamos la utilización de una unidad de medida basada en un pie de 0,32 m. Su primera aplicación probable se identifica en la torre bipartita del Castellot de la Roca Roja de Benifallet (final del siglo v a.C.), pero será entre los siglos iii y ii a.C. cuando tendrá una mayor adaptación, como se puede apreciar en su uso en la trama urbana de El Castellet de Banyoles de Tivissa, el sistema defensivo de Sant Miquel de Vinebre y probablemente en el edificio singular del Perengil de Vinaròs. Su mayor difusión durante el siglo iii a.C. se relaciona con el momento de concentración de poblamiento en el territorio ilercavón en grandes núcleos, como El Castellet de Banyoles, dentro de un fenómeno de jerarquización del territorio que muestra un sistema económico centralizado de tipo protoestatal.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

Actuación ante los delitos contra la propiedad intelectual e industrial desde el punto de vista jurídico [presentació associada a la ponència]

Sus formas de manifestación, comisión y desarrollo directamente relacionadas con el propio desarrollo de la tecnología; Son una fuente lucrativa para los grupos delictivos organizados y un medio fácil y de poco coste para la obtención de importantes beneficios y con menor riesgo de castigo; Especial idiosincrasia de las localidades de esta comunidad autónoma, favorece su proliferación; Genera un fenómeno sociológico singular : empatía o solidaridad que determina un menor reproche social; -Escasa conciencia popular del carácter delictivo de algunas de estas conductas; -Figura delictiva que entraña organización compleja siendo el Top manta nada más que la “punta del iceberg”. Necesidad de una visión jurídica global para analizar este tipo de delitos y abordarlos adecuadamente.

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

Exact results for Wilson loops in arbitrary representations

We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of TeX = 4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.

Robust power allocation algorithms for MIMO OFDM systems with imperfect CSI

This paper presents a Bayesian approach to the design of transmit prefiltering matrices in closed-loop schemes robust to channel estimation errors. The algorithms are derived for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. Two different optimizationcriteria are analyzed: the minimization of the mean square error and the minimization of the bit error rate. In both cases, the transmitter design is based on the singular value decomposition (SVD) of the conditional mean of the channel response, given the channel estimate. The performance of the proposed algorithms is analyzed,and their relationship with existing algorithms is indicated. As withother previously proposed solutions, the minimum bit error rate algorithmconverges to the open-loop transmission scheme for very poor CSI estimates.