A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Sistema de control remot d'una màquina de rajos X via web

El projecte desenvolupat té com a objectiu la millora en la gestió de la configuració de les màquines de rajos X de l'empresa Varpe. La principal funció d’aquestes màquines és la inspecció d'envasos de productes alimentaris, amb l'objectiu de detectar anomalies produïdes durant l'envasat. En l'actualitat la resolució d'incidències d'aquestes màquines requereix el desplaçament físic d'operaris a les localitzacions on estan situades les màquines. El projecte proporciona una nova forma de treball a partir de l'ús de bases de dades distribuïdes en les màquines de rajos X i que són gestionades per un servidor central. Entre d'altres, la principal avantatge d'aquesta gestió és que la reconfiguració i resolució d'indecències es pot realitzar fàcilment a través d'una aplicació web.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

X-ray diffraction, thermal analysis, and Raman scattering study of K2BeF4 and comparation to other member of the (beta)-K2SO4 family with ferroelectric -paraelectric transition

Thermal analysis, powder diffraction, and Raman scattering as a function of the temperature were carried out on K2BeF4. Moreover, the crystal structure was determined at 293 K from powder diffraction. The compound shows a transition from Pna21 to Pnam space group at 921 K with a transition enthalpy of 5 kJ/mol. The transition is assumed to be first order because the compound shows metastability. Structurally and spectroscopically the transition is similar to those observed in (NH4)2SO4, which suggests that the low-temperature phase is ferroelectric. In order to confirm it, the spontaneous polarization has been computed using an ionic model.

X-ray photoelectron spectroscopy analysis of ion¿beam¿induced oxidation of GaAs and AlGaAs

The oxidation of GaAs and AlGaAs targets subjected to O2+ bombardment has been analyzed, using in situ x¿ray photoelectron spectroscopy, as a function of time until steady state is reached. The oxides formed by the O2+ bombardment have been characterized in terms of composition and binding energy. A strong energy and angular dependence for the oxidation of As relative to Ga is found. Low energies as well as near normal angles of incidence favor the oxidation of As. The difference between Ga and As can be explained in terms of the formation enthalpy for the oxide and the excess supply of oxygen. In an AlGaAs target the Al is very quickly completely oxidized irrespective of the experimental conditions. The steady state composition of the altered layers show in all cases a preferential removal of As.

Evidence for oxygen-island formation on Al(111): Cluster-model theory and x-ray photoelectron spectroscopy

The O 1s x-ray photoelectron spectroscopy spectrum for Al(111)/O at 300 K shows two components whose behavior as a function of time and variation of detection angle are consistent with either (a) a surface species represented by the higher binding-energy (BE) component and a subsurface species represented by the lower BE component, or (b) small close-packed oxygen islands with the interior atoms represented by the lower BE component and the perimeter atoms by the higher BE component. We have modeled both situations using ab initio Hartree-Fock wave functions for clusters of Al and O atoms. For an O atom in a threefold site, it was found that a below-surface position gave a higher O 1s BE than an above-surface position, incompatible with interpretation (a). This change in the O 1s BE could arise because the bond for O to Al may have a more covalent character when the O is below the surface than when it is above the surface. We present evidence consistent with this view. An O adatom island with all the O atoms in threefold sites gives calculated O 1s BE's which are significantly higher for the perimeter O atoms. Further, the results for an isolated O island without the Al substrate present also give higher BE¿s for the perimeter atoms. Both these results are consistent with interpretation (b). Published scanning-tunneling-microscopy data supports the suggestion that the chemisorbed state consists of small, close-packed islands, whereas the presence of two vibrational modes in high-resolution electron-energy-loss spectroscopy data has been interpreted as representing surface and subsurface oxygen atoms. In light of the present results, we suggest that a vibrational interpretation in terms of interior and perimeter adatoms should be considered.

X-ray diffraction, thermal analysis, and Raman scattering study of K2BeF4 and comparation to other member of the (beta)-K2SO4 family with ferroelectric -paraelectric transition

Thermal analysis, powder diffraction, and Raman scattering as a function of the temperature were carried out on K2BeF4. Moreover, the crystal structure was determined at 293 K from powder diffraction. The compound shows a transition from Pna21 to Pnam space group at 921 K with a transition enthalpy of 5 kJ/mol. The transition is assumed to be first order because the compound shows metastability. Structurally and spectroscopically the transition is similar to those observed in (NH4)2SO4, which suggests that the low-temperature phase is ferroelectric. In order to confirm it, the spontaneous polarization has been computed using an ionic model.

Response of the Thermal Conductivity as a Function of Water Content of a Burnt Mediterranean Loam Soil

The purpose of this research is to explore the variability on the soil thermal conductivity -λ- after a prescribe fire, and to assess the effects of the ashes on the heat transfer once it"s were incorporated into the soil matrix. Sampling plot was located in the Montgrí Massif (NE of Spain). A set of 42 soil samples between surface and 5 cm depth was collected before and after the fire. To characterize the soil chemical and physical variables were analyzed. To determine the vari-ability on the soil λ a dry-out curve per scenario (before and after fire) was determined. SoilRho® method based on ASTM D-5334-08 which was validated by LabFerrer was used. Soil thermal conductivity has shown changes in their values. Indeed, in all moisture scenarios the values of soil λ decreased after soil was burnt. The critical point in the rela-tionship ϴ (λ) for the soil after fire which always was stronger than soil before to be burnt. Soil with"white" ashes showed a high thermal conductivity. An X-Ray diffractometry analysis allowed to clarify and to verify these results. To sum up, we could say that thermal conductivity presents changes when the scenario changes, i.e. before and after to be burnt. On the other hand, the volume of ashes incorporated on the soil increased the differences between no burnt and burnt soil, showing even some improvements on the heat transfer when water content started to govern the process.

DWI and complex brain network analysis predicts vascular cognitive impairment in spontaneous hypertensive rats undergoing executive function tests

The identification of biomarkers of vascular cognitive impairment is urgent for its early diagnosis. The aim of this study was to detect and monitor changes in brain structure and connectivity, and to correlate them with the decline in executive function. We examined the feasibility of early diagnostic magnetic resonance imaging (MRI) to predict cognitive impairment before onset in an animal model of chronic hypertension: Spontaneously Hypertensive Rats. Cognitive performance was tested in an operant conditioning paradigm that evaluated learning, memory, and behavioral flexibility skills. Behavioral tests were coupled with longitudinal diffusion weighted imaging acquired with 126 diffusion gradient directions and 0.3 mm(3) isometric resolution at 10, 14, 18, 22, 26, and 40 weeks after birth. Diffusion weighted imaging was analyzed in two different ways, by regional characterization of diffusion tensor imaging (DTI) indices, and by assessing changes in structural brain network organization based on Q-Ball tractography. Already at the first evaluated times, DTI scalar maps revealed significant differences in many regions, suggesting loss of integrity in white and gray matter of spontaneously hypertensive rats when compared to normotensive control rats. In addition, graph theory analysis of the structural brain network demonstrated a significant decrease of hierarchical modularity, global and local efficacy, with predictive value as shown by regional three-fold cross validation study. Moreover, these decreases were significantly correlated with the behavioral performance deficits observed at subsequent time points, suggesting that the diffusion weighted imaging and connectivity studies can unravel neuroimaging alterations even overt signs of cognitive impairment become apparent.

Pancreatic Cancer Cell Glycosylation Regulates Cell Adhesion and Invasion through the Modulation of a2b1 Integrin and E-Cadherin Function

In our previous studies we have described that ST3Gal III transfected pancreatic adenocarcinoma Capan-1 and MDAPanc-28 cells show increased membrane expression levels of sialyl-Lewis x (SLex) along with a concomitant decrease in α2,6-sialic acid compared to control cells. Here we have addressed the role of this glycosylation pattern in the functional properties of two glycoproteins involved in the processes of cancer cell invasion and migration, α2β1 integrin, the main receptor for type 1 collagen, and E-cadherin, responsible for cell-cell contacts and whose deregulation determines cell invasive capabilities. Our results demonstrate that ST3Gal III transfectants showed reduced cell-cell aggregation and increased invasive capacities. ST3Gal III transfected Capan-1 cells exhibited higher SLex and lower α2,6-sialic acid content on the glycans of their α2β1 integrin molecules. As a consequence, higher phosphorylation of focal adhesion kinase tyrosine 397, which is recognized as one of the first steps of integrin-derived signaling pathways, was observed in these cells upon adhesion to type 1 collagen. This molecular mechanism underlies the increased migration through collagen of these cells. In addition, the pancreatic adenocarcinoma cell lines as well as human pancreatic tumor tissues showed colocalization of SLex and E-cadherin, which was higher in the ST3Gal III transfectants. In conclusion, changes in the sialylation pattern of α2β1 integrin and E-cadherin appear to influence the functional role of these two glycoproteins supporting the role of these glycans as an underlying mechanism regulating pancreatic cancer cell adhesion and invasion