Shift graphs on precompact families of finite sets of natural numbers

We study graphs defined on families of finite sets of natural numbers and their chromatic properties. Of particular interest are graphs for which the edge relation is given by the shift. We show that when considering shift graphs with infinite chromatic number, one can center attention on graphs defined on precompact thin families. We define a quasi-order relation on the collection of uniform families defined in terms of homomorphisms between their corresponding shift graphs, and show that there are descending ${\omega }_1$-sequences. Specker graphs are also considered and their relation with shift graphs is established. We characterize the family of Specker graphs which contain a homomorphic image of a shift graph.     

Discrete numerical investigation of the ratcheting phenomenon in granular materials

Several relevant geotechnical works, such as railway and road embankments, offshore foundations and vibrating machine foundations, are affected by the progressive accumulation of irreversible settlements. These latter represent the macroscopic evidence of the progressive rearrangement of particles under cycling loading, which is commonly referred to, in the literature, as ratcheting. This phenomenon is well known, but it is quite difficult to describe it by means of an appropriate constitutive model. As a consequence, the evaluation of durability of the aforementioned structures remains an open problem. In this article, the phenomenon will be approached by employing a Distinct Element model capable of describing the evolution of the microstructure induced by cyclic mechanical perturbations. Several analyses are performed in order to stress the influence of both the stress level and loading history on the mechanical response of a numerical model of a sand specimen. The numerical analyses are intended to provide an experimental background for conceiving a simplified macro approach based on generalised plasticity theory. In particular by means of probe test the plastic potential and the hardening parameters will be defined as a function of the current stress state and loading history.     

Search for hyperdeformed structures populated in the <Superscript>37</Superscript>Cl+<Superscript>120</Superscript>Sn reaction by using EUROBALL III

The ridge structure with ΔE_γ=±30 keV, observed in the past in coincidence with protons emitted in the reaction 187 MeV ³⁷Cl +¹²⁰Sn and attributed to an hyperdeformed nuclear shape in ¹⁵²Dy, has been studied in a new experiment performed with the EUROBALL III array. The ridge is now observed in coincidence with transitions in the yrast superdeformed band of ¹⁵²Dy but no discrete rotational bands have been identified. Received: 7 February 2000     

The Active Gravitational Mass of a Heat Conducting Sphere Out of Hydrostatic Equilibrium

We obtain an expression for the activegravitational mass of a relativistic heat conductingfluid, just after its departure from hydrostaticequilibrium, on a time scale of the order of relaxationtime. It is shown that an increase of acharacteristic parameter leads to larger (smaller)values of active gravitational mass of collapsing(expanding) spheres, enhancing thereby the instabilityof the system.     

The width of the giant dipole resonance built on excited states of Cu compound nuclei

Continuumγ- ray spectra from the decay of⁵⁹Cu formed at an excitation energy of 100 MeV and angular momenta up to 43? by means of the reaction 190 MeV³²S +²⁷Al have been measured and analyzed. The parameters of the Giant Dipole Resonance (GDR) have been extracted using the statistical model. The derived GDR width confirms the sizeable broadening of this resonance in⁵⁹Cu already reported in our earlier investigation at 77 MeV excitation energy (J_crit=38?). Estimates of the GDR width have been performed in the adiabatic approximation. Predicted values account qualitatively for the experimental data of⁵⁹Cu as well as of the heavier isotope⁶³Cu, in which the broadening was not seen up to 77MeV excitation (J_crit=35?). The present analysis demonstrates the strong sensitivity of the GDR to spin effects in this mass region.     

The population of super- and hyper-deformed structures as a probe for fusion dynamics

Experimental data collected so far demonstrate that the population of superdeformed (SD) structures in nuclei with mass A～150 is influenced by the asymmetry in the entrance channel of the reaction. Furthermore, evidences for the population of hyperdeformed (HD) structures in the same mass region have been obtained only when charged particles are emitted in the evaporation chain. Dynamical model calculations show that in the reactions used to populate SD bands the equilibration times of the compound nuclei are not very sensitive on the mass asymmetry of the entrance channel. A qualitative understanding of both phenomena (SD and HD) is obtained assuming a link between the population of evaporation residues at very high spin and the dynamical hindrance of fission. Recent experimental results obtained in this field at the GASP spectrometer are presented for the case of the¹⁵²Dy nucleus populated in the³⁷Cl+¹²⁰Sn reaction. Proton and alpha particle spectra in coincidence with SD structures have been obtained. A sizeable difference is evidenced between alpha particle spectra in coincidence with SD and normally deformed structures.     

Parameterized partition relations on the real numbers

We consider several kinds of partition relations on the set of real numbers and its powers, as well as their parameterizations with the set of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every well ordered partition of there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of there is and a sequence of perfect sets such that the product lies in one piece of the partition, where is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. This work was supported by the research projects MTM 2005-01025 of the Spanish Ministry of Science and Education and 2005SGR-00738 of the Generalitat de Catalunya. A substantial part of the work was carried out while the second-named author was ICREA Visiting Professor at the Centre de Recerca Matemàtica in Bellaterra (Barcelona), and also during the first-named author’s stays at the Instituto Venezolano de Investigaciones Científicas and the California Institute of Technology. The authors gratefully acknowledge the support provided by these institutions.     

Quality of Service Measurements over an Optical GMPLS Wide Area Access Network

The introduction of intelligence for management and control of optical networks based on internet protocol and the quality of service (QoS) are key issues for the evolution of the next generation network. In this paper the authors report experimental results on QoS measurements related to different real time multimedia services in an optical network based on a ring configuration obtained by means of the fibers contained in an installed cable between Rome and Pomezia, core routers with optical Gigabit Ethernet interfaces and configured with differentiated service over multi-protocol label switching architecture.     

Letter: Measuring the Strength of Dissipative Inflation

We comment on recently proposed dissipative inflationary models. It is shown that the strength of the inflationary expansion is related to a specific combination of thermodynamic variables which is known to measure the instability of self-gravitating dissipative systems.     

Development of a Molecularly Imprinted Poly(Acrylic Acid)‐MWCNT Nanocomposite Electrochemical Sensor for Tramadol Determination in Pharmaceutical Samples

A new voltammetric sensor based on molecularly imprinted poly(acrylic acid)‐MWCNT nanocomposite (MIP‐MWCNT) drop‐coated onto glassy carbon electrode (GCE) was developed and applied to tramadol (TR) determination in pharmaceutical samples. The voltammetric sensor prepared by suspension of MIP‐MWCNT at 1 : 1 (w/w) ratio show an improved performance compared to unmodified GCE. The electrochemical method is based on preconcentration of tramadol onto MIP‐MWCNT modified GCE surface at ?1.5 V vs Ag/AgCl for 180 s in 0.1 Britton‐Robinson buffer (pH 8.0) at stirred solution. Upon preconcentration, the differential anodic voltammogram was recorded under the optimized condition giving rise to an analytical curve varying from 9.0 up to 30.0 μmol L^?1 (R²=0.997) and limits of detection and quantification of 1.4 and 4.8 μmol L^?1, respectively. The method precision was assessed in terms of intraday (n=6) and interday (two consecutive days) precision, giving relative standard deviations (RSD%) values between 2.8 to 7.4 %. Excipients usually found in pharmaceutical pills (magnesium stearate, microcrystalline cellulose, starch, and silica) and paracetamol were evaluated as potential interferents, however no interference was evidenced in TR determination. The method applicability was evaluated by TR analysis in pharmaceutical samples. Moreover, the method accuracy was attested by comparison of addition and recovery assays with a reference technique (high‐performance liquid chromatography).