The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Absorption d'hydrogène dans des aluminiures de titane exposés à des environnements humides ; conséquences sur les propriétés mécaniques

Il est maintenant bien établi que les propriétés mécaniques des alliages à base de titane et notamment des aluminiures de titane soumis à différents types de sollicitation (traction uniaxiale, fatigue, fatigue-corrosion, ...) sont sensibles à la présence d'humidité dans l'atmosphère dans laquelle est effectué l'essai. Cependant les mécanismes responsables de cette perte des propriétés mécaniques restent mal connus. Des profils de diffusion du deutérium ont été mesurés par analyse ionique (SIMS) dans des aluminiures de titane présentant différentes microstructures (α2, γ, ou α2+γ) et exposés à la température ambiante à des environnements deutérés (air humide ou solutions aqueuses). Les résultats mettent en évidence un mécanisme de dissociation de l'eau à la surface des aluminiures de titane exposés à ces environnements. Ce mécanisme conduit à une absorption d'hydrogène dans les alliages dont l'amplitude dépend du pH de la solution aqueuse, de la microstructure de l'alliage et de sa déformation plastique en présence de l'environnement. Le film d'oxyde naturel formé à l'air à la surface du matériau limite à la fois la dissociation de l'eau et la diffusion de l'hydrogène dans l'alliage. Les propriétés mécaniques d'un alliage α2+γ brut de coulée sollicité en traction uniaxiale dépendent à la fois de l'orientation des lamelles α2 et γ par rapport à l'axe de traction et de la nature de l'environnement au contact de l'éprouvette au cours de l'essai. Une perte de ductilité est observée lors de sollicitations en présence de solutions aqueuses. L'effet prédominant de l'environnement semble être de favoriser l'amorçage de fissures à la surface du matériau en relation avec l'absorption d'hydrogène

The what and how components of cognitive control

In daily life, people show remarkable flexibility in adapting to novel circumstances. Although there is general agreement on which brain areas are involved in cognitive flexibility, little is known about the precise representational content of these cognitive control areas in different sub-processes involved in cognitive control. In the present study, we used an adaptation approach to differentiate the brain areas selectively representing the what and the how components of cognitive control in task preparation. When selectively repeating the task goal (the what component) without repeating the stimulus-response (S-R) mapping (the how component), task goal preferential adaptation was found in the left lateral prefrontal cortex, the medial prefrontal cortex and the left posterior parietal cortex. Within these areas, task goal specific adaptation was found in the left inferior frontal gyrus, the posterior part of the left inferior parietal lobule and the precuneus. Selectively repeating the S-R mapping, by contrast, resulted in S-R mapping preferential adaptation in the bilateral pre-central gyrus extending bilaterally to the intra-parietal lobule, indicating representation of the how component in these areas. Adaptation general to both task goal and S-R mapping was only found in Broca's area extending to the inferior frontal junction, suggesting that the what and the how components of cognitive control are similarly represented in this part of the brain

Goal-directed imitation in patients with Ideomotor Apraxia

Contains fulltext : 54642.pdf (publisher's version ) (Closed access)The present study compared imitation performance in patients with ideomotor apraxia (IMA), eight right hemispheric-damaged patients, and eight control participants without neurological damage in three experiments. Experiment 1 confirmed in the Goldenberg test that IMA patients were particularly impaired in hand gestures and combined finger and hand gestures, but not in the imitation of finger gestures, compared to the other two groups. Experiment 2, however, demonstrated that finger selection is not per se preserved in imitative behaviour in patients with IMA. Experiment 3 confirmed this finding in an experiment under visual control. Together, the results add evidence to the idea that imitation should be viewed from a goal-directed rather than a body-mapping perspective, and that highest priority is given to more distal aspects of imitation as reaching for the correct object, rather than the means used to achieve the goal of a modelled action

Molecular dynamics simulations on a parallel computer plastic crystals and related systems

Four molecular dynamics projects concerning dynamic molecular disorder are discussed, all having in common the fact that they are being done on a computer which is an array of parallel processors. The computer architecture is ideal for these systems as the molecules do not undergo translational diffusion.The first system is SF6 both in the plastic phase and below, where two phase transitions have been identified. In the plastic phase orientational disorder is apparent, the molecules arranging themselves so as to minimise the effect of the frustration between the nearest neighbour attraction and the next-nearest neighbour repulsion. The phase transitions represent the compromises enforced by this frustration as the temperature is lowered. A time correlation analysis shows that it is unlikely that phonon-like modes can exist in the plastic phase.The second system is naphthalene very near to melting, where the predominant molecular reorientation is about the axis of greatest inertia. This is contrasted with experimental results which suggest that the reorientation about the axis of least inertia is associated with melting, the other reorientations not being catastrophic for the crystallinity of the system. Arguments are presented that the system does not have a plastic phase just below the melting point.The third system is butane, where the molecule itself has internal degrees of freedom which are incorporated in the model. A number of crystal phases have been discovered, most of which must be metastable. On warming the stable triclinic phase to a temperature above the plastic transition in the real system, the model system takes on an orthorhombic structure where the symmetry is a time average.The last system discussed is an invented two-dimensional system of molecules we call quaternane, as they have four atoms arranged in a chain. Each molecule has two internal degrees of freedom both of which carry a double-well potential. The system develops domain walls when warmed from a low-temperature crystal phase, and it is apparent that the structure within the walls shows smectic liquid-crystal-like behaviour. This model could well prove to be a starting point for liquid-crystal simulations at the atomic level

Equine protease inhibitor system as a marker for the diagnosis of chronic obstructive pulmonary disease (COPD)

The protease inhibitor system (PI) was investigated to ascertain if it can be used as a marker of chronic obstructive pulmonary disease (COPD) in thoroughbred horses. Serum samples were taken from healthy thoroughbreds (n = 13) and those diagnosed as having COPD (n = 24) or inflammatory airway disease (IAD, n = 38) as well as from 3,600 undiagnosed thoroughbred horses. PI allelic and genotypic frequencies were estimated using protein electrophoresis on starch and polyacrylamide gels. The four groups of horses showed high genotypic similarity and none of the observed alleles or genotypes of the equine PI system were found to be associated with COPD

Nitridergic platelet pathway activation by hementerin, a metalloprotease from the leech Haementeria depressa

Hementerin (HT) is an 80 kDa fibrino(geno)lytic metalloprotease, purified from saliva of the leech Haementeria depressa. in the present report, the effect of HT on several functional parameters of human platelets was assessed. HT inhibited platelet aggregation and ATP release induced by different agonists such as ADP, adrenaline, collagen, thrombin, and arachidonic acid. HT did neither modify the expression of platelet glycoproteins (Ib, IIbIIIa, IaIIa, IV) nor intraplatelet fibrinogen levels, whereas it markedly decreased CD62P and CD63 levels after the stimulation with thrombin. HT significantly increased thrombininduced platelet Ca2+ intracellular levels, cGMP content and nitric oxide synthase (NOS) activity. the effect of HT on platelet aggregation was reversed by two NOS inhibitors, N-omega-Nitro-L-arginine methyl ester and 2 N-G-Nitro-L-arginine. in summary, these results indicate that HT is an effective inhibitor of human platelet aggregation, presumably through activation of the platelets nitridergic pathway.Inst Butantan, Lab Bioquim & Biofis, BR-05503900 São Paulo, BrazilAcad Nacl Med Buenos Aires, IIHEMA, Buenos Aires, DF, ArgentinaUniv Buenos Aires, Fac Med, Dept Bioquim Humana, Buenos Aires, DF, ArgentinaUniversidade Federal de São Paulo, Dept Bioquim, São Paulo, BrazilUniversidade Federal de São Paulo, Dept Bioquim, São Paulo, BrazilWeb of Scienc

Hydrogen permeation in nanostructured bainitic steel

Hydrogen permeation of nanostructured bainitic steel, produced at two different transformation temperatures, i.e., 473.15 K (200 A degrees C) BS-200 and 623.15 K (350 A degrees C) BS-350, was determined using Devanathan-Stachurski hydrogen permeation cell and compared with that of mild steel. Nanostructured bainitic steel showed lower effective diffusivity of hydrogen as compared to the mild steel. The BS-200 steel, which exhibited higher volume fraction of bainitic ferrite phase, showed lower effective diffusivity than BS-350 steel. The finer microstructural constituents (bainitic ferrite laths and retained austenite films) and higher dislocation density in the bainitic ferrite phase of BS-200 steel can be attributed to its lower effective diffusivity as compared to BS-350 steel and mild steel