J2 effect and elliptic inclined periodic orbits in the collision three-body problem

The existence of a new class of inclined periodic orbits of the collision restricted three-body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Atomic Ordering and Martensitic Transitions in Cu-Zn-Al Shape Memory Alloys

We present results from both, calorimetric and dilatometric studies of the isothermal ordering process taking place in a Cu-Zn-Al shape memory alloy after quenches from Tq temperatures ranging from 350 K to 1200 K. The dissipated energy and the length variations of the system are obtained during the process. The change of these quantities in the whole process have been compared with the difference [MATH] between Ms, measured after the relaxation and Ms measured just after the quench. We obtain that these three quantities present, as a function of Tq, the same qualitative behaviour. These changes are then associated with changes of the L21 ordering after the quench in the system. The relaxational process does not follow a single exponential decay. Instead, a continuous slowing down is observed. A relaxation time [MATH] has been defined to characterize the relaxation rate. We show that [MATH] depends on both the annealing and the quenching (Tq [MATH] 800 K) temperatures through an Arrhenius law.

Dissemination of periodic mammography and patterns of use, by birth cohort, in Catalonia (Spain)

Background: In Catalonia (Spain) breast cancer mortality has declined since the beginning of the 1990s. The dissemination of early detection by mammography and the introduction of adjuvant treatments are among the possible causes of this decrease, and both were almost coincident in time. Thus, understanding how these procedures were incorporated into use in the general population and in women diagnosed with breast cancer is very important for assessing their contribution to the reduction in breast cancer mortality. In this work we have modeled the dissemination of periodic mammography and described repeat mammography behavior in Catalonia from 1975 to 2006. Methods: Cross-sectional data from three Catalan Health Surveys for the calendar years 1994, 2002 and 2006 was used. The dissemination of mammography by birth cohort was modeled using a mixed effects model and repeat mammography behavior was described by age and survey year. Results: For women born from 1938 to 1952, mammography clearly had a period effect, meaning that they started to have periodic mammograms at the same calendar years but at different ages. The age at which approximately 50% of the women were receiving periodic mammograms went from 57.8 years of age for women born in 1938–1942 to 37.3 years of age for women born in 1963–1967. Women in all age groups experienced an increase in periodic mammography use over time, although women in the 50–69 age group have experienced the highest increase. Currently, the target population of the Catalan Breast Cancer Screening Program, 50–69 years of age, is the group that self-reports the highest utilization of periodic mammograms, followed by the 40–49 age group. A higher proportion of women of all age groups have annual mammograms rather than biennial or irregular ones. Conclusion: Mammography in Catalonia became more widely implemented during the 1990s. We estimated when cohorts initiated periodic mammograms and how frequently women are receiving them. These two pieces of information will be entered into a cost-effectiveness model of early detection in Catalonia.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Glassy magnetic phase driven by short range charge and magnetic ordering in nanocrystalline La1/3Sr2/3FeO3-δ: Magnetization, Mössbauer, and polarized neutron studies

The charge ordered La1/3Sr2/3FeO3−δ (LSFO) in bulk and nanocrystalline forms are investigated using ac and dc magnetization, M¨ossbauer, and polarized neutron studies. A complex scenario of short-range charge and magnetic ordering is realized from the polarized neutron studies in nanocrystalline specimen. This short-range ordering does not involve any change in spin state and modification in the charge disproportion between Fe3+ and Fe5+ compared to bulk counterpart as evident in the M¨ossbauer results. The refinement of magnetic diffraction peaks provides magnetic moments of Fe3+ and Fe5+ are about 3.15 μB and 1.57 μB for bulk, and 2.7 μB and 0.53 μB for nanocrystalline specimen, respectively. The destabilization of charge ordering leads to magnetic phase separation, giving rise to the robust exchange bias (EB) effect. Strikingly, EB field at 5 K attains a value as high as 4.4 kOe for average size ∼70 nm, which is zero for the bulk counterpart. A strong frequency dependence of ac susceptibility reveals cluster-glass-like transition around ∼65 K, below which EB appears. Overall results propose that finite-size effect directs the complex glassy magnetic behavior driven by unconventional short-range charge and magnetic ordering, and magnetic phase separation appears in nanocrystalline LSFO.

Tailored Jeffamine molecular tools for ordering mesoporous Silica

Herein, we report the formation of organized mesoporous silica materials prepared from a novel nonionic gemini surfactant, myristoyl-end capped Jeffamine, synthesized from a polyoxyalkyleneamine (ED900). The behavior of the modified Jeffamine in water was first investigated. A direct micellar phase (L1) and a hexagonal (H1) liquid crystal were found. The structure of the micelles was investigated from the SAXS and the analysis by Generalized Indirect Fourier Transformation (GIFT), which show that the particles are globular of coreshell type. The myristoyl chains, located at the ends of the amphiphile molecule are assembled to form the core of the micelles and, as a consequence, the molecules are folded over on themselves. Mesoporous materials were then synthesized from the self-assembly mechanism. The recovered materials were characterized by SAXS measurements, nitrogen adsorptiondesorption analysis, transmission and scanning electron microscopy. The results clearly evidence that by modifying the synthesis parameters, such as the surfactant/silica precursor molar ratio and the hydrothermal conditions, one can control the size and the nanostructuring of the resulting material. It was observed that, the lower the temperature of the hydrothermal treatment, the better the mesopore ordering.

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Preparació d'òxids mesoporosos mitjançant nanocasting

S’ha sintetitzat pel mètode de nanocasting pols nanomètrica d’In2O3, NiO i Co3O4 utilitzant diferents mesoestructures de sílice (SBA-16, SBA-15 i KIT-6) com a motlle rígid. Les rèpliques obtingudes s’han caracteritzat amb les tècniques de difracció de raigs X, microscòpia electrònica de rastreig, microscòpia electrònica de transmissió d’alta resolució i BET. L’òxid d’indi, l’òxid de níquel i l’òxid de cobalt obtinguts a partir de la sílice SBA-15 i KIT-6 conserven perfectament l’estructura mesopòrica del motlle, amb valors del diàmetre de porus al voltant dels 7-8 nm. Les rèpliques del motlle SBA-15 estan formades per nanofilaments llargs, mentre que les rèpliques de KIT-6 presenten una estructura hexagonal. A partir del motlle de tipus gàbia (SBA-16), si bé el Co3O4 obtingut és mesopòric, en els altres dos casos (In2O3 i NiO) no s’ha observat ordenament. Per a les rèpliques In2O3 KIT-6 i NiO SBA-15, la caracterització mitjançant BET ha permès corroborar el caràcter mesoestructurat de les mostres.