An extremal problem of Erdős in interpolation theory

AbstractOne of the intriguing problems of interpolation theory posed by Erdős in 1961 is the problem of finding a set of interpolation nodes in [−1, 1] minimizing the integral In of the sum of squares of the Lagrange fundamental polynomials. The guess of Erdős that the optimal set corresponds to the set F of the Fekete nodes (coinciding with the extrema of the Legendre polynomials) was disproved by Szabados in 1966.Another aspect of this problem is to find a sharp estimate for the minimal value I★n of the integral. It was conjectured by Erdős, Szabados, Varma and Vertesi in 1994 that asymptotically I★n − In(F) = o(1n).In the present paper, we use a numerical approach in order to find the solution of this problem. By applying an appropriate optimization technique, we found the minimal values of the integral with high precision for n from 3 up to 100. On the basis of these results and by using Richardson's extrapolation method, we found the first two terms in the asymptotic expansion of I∗n, and thus, disproved the above-mentioned conjecture. Moreover, by using some heuristic arguments, we give an analytic description of nodes which are, for all practical purposes, as useful as the optimal nodes

The Afterlife of Jennifer Laude: Trans Necropolitics and Trans Utopias

Jennifer Laude is a filipino trans woman who was murdered by a visiting member of the United States army in 2014. Her murder led to several protests in the Philippines and in the United States led by both queer and anti-imperialist movements that urged for the rejection of the \u27Visiting Forces Agreement\u27 in the Philippines. This essay explores how Laude\u27s murder is located in a climate of \u27trans necropolitics\u27 that allocates death and disposability to unruly trans and brown bodies who fail to comply with cis-normative gender ideals. This essay understands her murder (and her afterlife) beyond her individual body, looking at the disciplinary effects it has on other trans bodies who are collectively subjected to a \u27slow death\u27 in a necropolitical regime. Likewise, this essay also explores how the protests that followed Laude\u27s death have transformed the meaning of her transness, rendering her a body worth grieving. This transforms the possibilities for trans bodies in life, giving Laude\u27s afterlife a utopian force in envisioning emergent trans and anti-imperial futurities

Pretransitional phenomena in dilute crystals with first-order phase transition

Pretransitional phenomena at first-order phase transition in crystals diluted by 'neutral' impurities (analogue of nonmagnetic atoms in dilute magnets) are considered. It is shown that field dependence of order parameter becomes nonanalytical in the stability region of the ordered phase, while smeared jumps of thermodynamic parameters and anomalous (non-exponential) relaxation appear near transition temperature of pure crystal.Comment: 4 page

SEM and AFM characterization of surface of two RMGICs for degradation before and after modification with bioactive glass ceramic

“This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Adhesion Science and Technology on 09/12/2015, available online: http://www.tandfonline.com/10.1080/01694243.2015.1115603."Objectives: The aim of this study was to evaluate the effect of bioactive glass–ceramic particles (Biosilicate®) addition on surface nanoroughness and topography of Resin-modified glass ionomer cements (RMGICs).Methods: Experimental materials were made by incorporating 2 wt% of Biosilicate® into Fuji II LC® (FL) and Vitremer® (VT) powders. Disks of RMGICs (with and without Biosilicate®) measuring 0.5 cm (diameter) × 0.5 mm (thickness) were fabricated and polished. Samples were stored at 37 °C in dry or immersed in distilled water for 30 days. Digital images (20 × 20 μm) from the surfaces were obtained by means of an atomic force microscopy. Three images were acquired for each sample, and four nanoroughness measurements were performed in each image. Nanoroughness (Ra, nm) was assessed by Nanoscope Software V7. Data were analyzed with ANOVA and Student–Newman–Keuls multiple comparisons (p < 0.05). SEM images were obtained for surface topography analysis.Results: FL was significantly rougher than VT (p < 0.05) in wet and dry conditions. The addition of Biosilicate® increased the surface roughness in VT and decreased in FL, regardless of the storage media (p ≤ 0.05). No differences existed between materials and storage conditions after Biosilicate® addition. Significance: The Biosilicate® particles addition produced changes on the surface nanoroughness of the RMGICs. These changes depended on the particles size of the original cements in dry conditions. In water storage, dissolution of the Biosilicate® particles, a silica-rich gel formation, and a hydroxyl carbonate apatite precipitation on the surface of the materials changed the nanoroughness surface. FL was the roughest in both conditions.Significance: The Biosilicate® particles addition produced changes on the surface nanoroughness of the RMGICs. These changes depended on the particles size of the original cements in dry conditions. In water storage, dissolution of the Biosilicate® particles, a silica-rich gel formation, and a hydroxyl carbonate apatite precipitation on the surface of the materials changed the nanoroughness surface. FL was the roughest in both conditions.MINECO/FEDERMAT2014-52036-P

Independent ferroelectric contributions and rare-earth-induced polarization reversal in multiferroic TbMn2O5

Three independent contributions to the magnetically induced spontaneous polarization of multiferroic TbMn2O5 are uniquely separated by optical second harmonic generation and an analysis in terms of Landau theory. Two of them are related to the magnetic Mn3+/4+ order and are independent of applied fields of up to 7 T. The third contribution is related to the long-range antiferromagnetic Tb3+ order. It shows a drastic decrease upon the application of a magnetic field and mediates the change of sign of the spontaneous electric polarization in TbMn2O5. The close relationship between the rare-earth long-range order and the non-linear optical properties points to isotropic Tb-Tb exchange and oxygen spin polarization as mechanism for this rare-earth induced ferroelectricity.Comment: 8 pages, 5 figure

A zinc-doped endodontic cement facilitates functional mineralization and stress dissipation at the dentin surface

The purpose of this study was to evaluate nanohardness and viscoelastic behavior of dentin surfaces treated with two canal sealer cements for dentin remineralization. Dentin surfaces were subjected to: i) 37% phosphoric acid (PA) or ii) 0.5 M ethylenediaminetetraacetic acid (EDTA) conditioning prior to the application of two experimental hydroxyapatite-based cements, containing sodium hydroxide (calcypatite) or zinc oxide (oxipatite), respectively. Samples were stored in simulated body fluid during 24 h or 21 d. The intertubular and peritubular dentin were evaluated using a nanoindenter to assess nanohardness (Hi). The load/displacement responses were used for the nano-dynamic mechanical analysis to estimate complex modulus (E*) and tan delta (?). The modulus mapping was obtained by imposing a quasistatic force setpoint to which a sinusoidal force was superimposed. AFM imaging and FESEM analysis were performed. After 21 d of storage, dentin surfaces treated with EDTA+calcypatite, PA+calcypatite and EDTA+oxipatite showed viscoelastic discrepancies between peritubular and intertubular dentin, meaning a risk for cracking and breakdown of the surface. At both 24 h and 21 d, tan ? values at intertubular dentin treated with the four treatments performed similar. At 21 d time point, intertubular dentin treated with PA+oxipatite achieved the highest complex modulus and nanohardness, i.e., highest resistance to deformation and functional mineralization, among groups. Intertubular and peritubular dentin treated with PA+oxipatite showed similar values of tan ? after 21 d of storage. This produced a favorable dissipation of energy with minimal energy concentration, preserving the structural integrity at the dentin surface

Hydroxyapatite-based cements induce different apatite formation in radicular dentin

Objectives. To investigate crystallinity and ultrastructure of the formed hydroxyapatite at radicular cervical and apical dentin after being treated with three different canal sealers. Methods. Cervical and apical root dentin surfaces were treated with two experimental hydroxyapatite-based sealers, containing sodium hydroxide (calcypatite) or zinc oxide (oxipatite) and an epoxy resin-based canal sealer (AH Plus); gutta-percha without sealer was included as control. Dentin surfaces were studied by X-ray diffraction and transmission electron microscopy through selected area diffraction and bright-field imaging after 24 h and 12 m of storage. Results. Root cervical dentin treated with calcypatite and oxipatite produced poor crystallinity of new minerals, wide amorphous phase and non-stoichiometry. Reflections at the 002 plane and the corresponding diffraction rings attained lower values in the Scherrer equation and the Scherrer-Wilson equation in samples treated with both HAp-based sealers than in specimens without sealer or with AH Plus. At root cervical dentin treated with calcypatite, shorter and wider crystallite size formations and lower crystals grain size were found, if compared to those encountered at oxipatite treated dentin. Oxipatite attained improved crystallographic atomic order and less structural variation in both distances and angles. Apical dentin treated with oxipatite attained preferred grain orientation with polycrystalline lattices. Significance. The immature crystallites formed in dentin treated with calcypatite and oxipatite will account for high hydroxyapatite solubility and remineralizing activity. New polycrystalline formations encountered in apical dentin treated with oxipatite may also produce high mechanical performance.This work was supported by the Ministry of Economy and Competitiveness (MINECO) and European Regional Development Fund (FEDER) Project MAT2017-85999-P

Ground state representations of loop algebras

Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.Comment: 22 pages, no figur

Ensuring Economic Viability and Sustainability of Coffee Production

Coffee, the world’s favorite beverage, provides livelihoods for at least 60 million people across dozens of countries. Yet this beloved drink is experiencing a sustainability crisis. A sustained decline in world coffee prices has squeezed coffee producers, and thrown a tremendous number of producers below the global extreme poverty line. This report presents our research into sustainability within the coffee sector, including the results of our analytical and empirical modeling, and provides several recommendations