Two-dimensional Newton's problem of minimal resistance

Newton's problem of minimal resistance is one of the first problems of optimal control: it was proposed, and its solution given, by Isaac Newton in his masterful Principia Mathematica, in 1686. The problem consists of determining, in dimension three, the shape of an axis-symmetric body, with assigned radius and height, which offers minimum resistance when it is moving in a resistant medium. The problem has a very rich history and is well documented in the literature. Of course, at a first glance, one suspects that the two dimensional case should be well known. Nevertheless, we have looked into numerous references and asked at least as many experts on the problem, and we have not been able to identify a single source. Solution was always plausible to everyone who thought about the problem, and writing it down was always thought not to be worthwhile. Here we show that this is not the case: the two-dimensional problem is richer than the classical one, being, in some sense, more interesting. Novelties include: (i) while in the classical three-dimensional problem only the restricted case makes sense (without restriction on the monotonicity of admissible functions the problem does not admit a local minimum), we prove that in dimension two the unrestricted problem is also well-posed when the ratio of height versus radius of base is greater than a given quantity; (ii) while in three dimensions the (restricted) problem has a unique solution, we show that in the restricted two-dimensional problem the minimizer is not always unique - when the height of the body is less or equal than its base radius, there exists infinitely many minimizing functions

Results of the MRI substudy of the intravenous magnesium efficacy in stroke trial

<p><b>Background and Purpose:</b>Although magnesium is neuroprotective in animal stroke models, no clinical benefit was confirmed in the Intravenous Magnesium Efficacy in Stroke (IMAGES) trial of acute stroke patients. The Magnetic Resonance in IMAGES (MR IMAGES) substudy investigated the effects of magnesium on the imaging surrogate outcome of infarct growth.</p> <p><b>Methods:</b> IMAGES trial patients in participating centers were randomized to receive either intravenous magnesium or placebo within 12 hours of stroke onset. Infarct growth was defined as volume difference between baseline diffusion-weighted imaging and day 90 fluid-attenuated inversion recovery image lesions. Patients who died were imputed the largest infarct growth observed.</p> <p><b>Results:</b> Among the 90 patients included in the primary analysis, there was no difference in infarct growth (median absolute growth, P=0.639; median percentage growth, P=0.616; proportion with any growth, P=0.212) between the 46 treated with magnesium and 44 with placebo. Infarct growth correlated with NIHSS score change from baseline to day 90. There was a trend showing baseline serum glucose correlated with infarct growth with magnesium treatment, but not in the placebo group. The mismatch frequency was reduced from 73% to 47% by increasing the mismatch threshold from >20% to >100% of core volume.</p> <p><b>Conclusions:</b> Infarct growth, confirmed here as a surrogate for clinical progression, was similar between magnesium and placebo treatment, paralleling the main IMAGES trial clinical outcomes. Glucose was a covariate for infarct growth with magnesium treatment. A more stringent mismatch threshold to define penumbra more appropriately would have excluded half of the patients in this 12-hour time window stroke study.</p&gt

Whose Algorithm Says So

Financial advisors seek to accurately measure individuals' risk preferences and provide sound personalized investment advice. Both advice tasks are increasingly offered through automated online technologies. Little is known, however, about what drives individuals' acceptance of such automated financial advice and, from a consumer point of view, which firms may be best positioned to provide such advice. We generate novel insights on these questions by conducting a real-world empirical study using an interactive automated online tool that employs an innovative computer algorithm to build pension investment profiles, the “Pension Builder,” and a large, representative sample. We focus on the role that two key firm characteristics have on consumer acceptance of pension investment advice generated by computer algorithms running on automated interactive online tools: profit orientation and role in the sales channel. We find that consumers' perceptions of trust and expertise of the firm providing the automated advice are important drivers of advice acceptance (besides a strong impact of the satisfaction with the consumer–online tool interaction), and that these constructs themselves are clearly influenced by the for-profit vs. not-for-profit orientation and the product provider vs. advisor only role in the sales channel of the firm pr

Variations In Desiccation Tolerance In Seeds Of Eugenia Pyriformis: Dispersal At Different Stages Of Maturation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Eugenia pyriformis Cambess., known locally as uvaieira, a species of fruit-bearing tree with both pharmacological and gastronomic potential, has seeds which are sensitive to desiccation. The aim of this study was to analyse whether the degree of tolerance to desiccation of uvaieira seeds depends on the stage of maturation of the seeds at shedding. This, in turn, depends on the environmental conditions in which the seeds develop, including the accumulation of degree-days and rainfall in the period. Seeds were collected from the ripe fruit of parent plants located in the states of São Paulo and Minas Gerais, Brazil, submitted to drying and analysed for water content and germination. A completely randomised design was used in a 20 × 3 factorial scheme (source of material x level of drying). The degree of desiccation tolerance differs between region and period of collection, even for the same parent plant when the seeds are collected in different years. The water and thermal conditions of the environment during seed development modify the maturation cycle, the physiological quality and the acquisition of desiccation tolerance. In uvaieira seeds, desiccation tolerance depends on the physiological maturity of the seeds at the time of dispersal, which is associated with the environmental conditions.471118126CAPES, Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES

Effect Of Post Type And Restorative Techniques On The Strain And Fracture Resistance Of Flared Incisor Roots

Restoring flared endodontically treated teeth continues to be a challenge for clinicians. This study evaluated the effect of post types and restorative techniques on the strain, fracture resistance, and fracture mode of incisors with weakened roots. One hundred five endodontically treated bovine incisors roots (15 mm) were divided into 7 groups (n=15). The two control groups were (C) intact roots restored with Cpc (cast posts and core) or Gfp (glass fiber posts). The five experimental groups were (F) flared roots restored with GfpAp (Gfp associated with accessory glass fiber posts), GfpRc (anatomic Gfp, relined with composite resin), and GfpRcAp (anatomized Gfp with resin and accessory glass fiber posts). All teeth were restored with metal crowns. Mechanical fatigue was performed with 3x10 5/50 N. Specimens were loaded at 45°, and the strain values (μS) were obtained on root buccal and proximal surfaces. Following that, the fracture resistance (N) was measured. One-way ANOVA and Tukey's HSD tests (α=0.05) were applied, and failure mode was checked. No significant difference in strain values among the groups was found. Cpc presented lower fracture resistance and more catastrophic failures in flared roots. Gfp associated with composite resin or accessory glass fiber posts seems to be an effective method to improve the biomechanical behavior of flared roots.223230237Coelho, C.S., Biffi, J.C., Silva, G.R., Abrahão, A., Campos, R.E., Soares, C.J., Finite element analysis of weakened roots restored with composite resin and posts (2009) Dent Mater J, 28, pp. 671-678Teixeira, C.S., Silva-Sousa, Y.T., Sousa-Neto, M.D., Bond strength of fiber posts to weakened roots after resin restoration with different light-curing times (2009) J Endod, 35, pp. 1034-1039Zogheib, L.V., Pereira, J.R., do Valle, A.L., de Oliveira, J.A., Pegoraro, L.F., Fracture resistance of weakened roots restored with composite resin and glass fiber post (2008) Braz Dent J, 19, pp. 329-333Marchi, G.M., Mitsui, F.H., Cavalcanti, A.N., Effect of remaining dentine structure and thermal-mechanical aging on the fracture resistance of bovine roots with different post and core systems (2008) Int Endod J, 41, pp. 969-976da Silveira, T.C., Santos, F.M.C., Silva-Sousa, Y.T., de Sousa-Neto, M.D., Interfacial evaluation of experimentally weakened roots restored with adhesive materials and fibre posts: An SEM analysis (2008) J Dent, 36, pp. 672-682Moosavi, H., Maleknejad, F., Kimyai, S., Fracture resistance of endodontically-treated teeth restored using three root- reinforcement methods (2008) J Contemp Dent Pract, 9, pp. 30-37Bonfante, G., Kaizer, O.B., Pegoraro, L.F., do Valle, A.L., Fracture strength of teeth with flared root canals restored with glass fibre posts (2007) Int Dent J, 57, pp. 153-160Santos, A.F., Meira, J.B., Tanaka, C.B., Xavier, T.A., Ballester, R.Y., Lima, R.G., Can fiber posts increase root stresses and reduce fracture? (2010) J Dent Res, 89, pp. 587-591da Silva, N.R., Raposo, L.H., Versluis, A., Fernandes-Neto, A.J., Soares, C.J., The effect of post, core, crown type, and ferrule presence on the biomechanical behavior of endodontically treated bovine anterior teeth (2010) J Prosthet Dent, 104, pp. 306-317Silva, N.R., Castro, C.G., Santos-Filho, P.C., Silva, G.R., Campos, R.E., Soares, P.V., Influence of different post design and composition on stress distribution in maxillary central incisor: Finite element analysis (2009) Indian J Dent Res, 20, pp. 153-158Santos-Filho, P.C., Castro, C.G., Silva, G.R., Campos, R.E., Soares, C.J., Effects of post system and length on the strain and fracture resistance of root filled bovine teeth (2008) Int Endod J, 41, pp. 493-501Soares, C.J., Castro, C.G., Santos, F.P.C., Soares, P.V., Magalhaes, D., Martins, L.R., Two-dimensional FEA of dowels of different compositions and external surface configurations (2009) J Prosthodont, 18, pp. 36-42Macedo, V.C., de Faria, S.A.L., Martins, L.R., Effect of cement type, relining procedure, and length of cementation on pull-out bond strength of fiber posts (2010) J Endod, 36, pp. 1543-1546Leitune, V.C., Collares, F.M., Werner, S.S.M., Influence of chlorhexidine application at longitudinal push-out bond strength of fiber posts (2010) Oral Surg Oral Med Oral Pathol Oral Radiol Endod, 110, pp. 77-81Novais, V.R., Quagliatto, P.S., Bona, A.D., Correr-Sobrinho, L., Soares, C.J., Flexural modulus, flexural strength, and stiffness of fiber-reinforced posts (2009) Indian J Dent Res, 20, pp. 277-281Marchi, G.M., Paulillo, L.A., Pimenta, L.A., de Lima, F.A., Effect of different filling materials in combination with intraradicular posts on the resistance to fracture of weakened roots (2003) J Oral Rehabil, 30, pp. 623-629Soares, C.J., Pizi, E.C., Fonseca, R.B., Martins, L.R., Influence of root embedment material and periodontal ligament simulation on fracture resistance tests (2005) Braz Oral Res, 19, pp. 11-16Huysmans, M.C., Peters, M.C., van der Varst, P.G., Plasschaert, A.J., Failure behaviour of fatigue-tested post and cores (1993) Int Endod J, 26, pp. 294-300Soares, P.V., Santos-Filho, P.C., Gomide, H.A., Araujo, C.A., Martins, L.R., Soares, C.J., Influence of restorative technique on the biomechanical behavior of endodontically treated maxillary premolars. Part II: Strain measurement and stress distribution (2008) J Prosthet Dent, 99, pp. 114-122Kishen, A., Kumar, G.V., Chen, N.N., Stress-strain response in human dentine: Rethinking fracture predilection in post-core restored teeth (2004) Dent Traumatol, 20, pp. 90-10

Cell adhesion and proliferation onto chitosan-based membranes treated by plasma surface modification

Surface properties play a vita role in the functioning of a biomaterial. Cellular adherence and growth onto biomaterials can be enhanced in biomaterial modifications of their surface. In this work, the cell behaviour on chitosan membranes modified by argon and nitron-plasma treatments was investigated. Characterization of the membranes was performed using atomic force microscopy, contact angle measurements, and X-ray photoelectron spectroscopy. Cytotoxicity assessment and direct contact assay were carried out for untreated and treated chitosan membranes using L929 fibroblast-like cells. Cell morphology and cell viability were assessed to evaluate the cell attachment and proliferation. Changes in terms of roughness, surface chemistry, and hydrophilicity/hydrophobic balance of chitosan-modified membranes were observed. Regarding cell studies, the findings revealed that the extracts of all membranes do not induce cytotoxicity effects. Moreover, the in vitro assays evidenced an improvement of the L929 adhesion, and attachment when compared to untreated chitosan membranes. overall, the data obtained clearly demonstrated that plasma treatments constitute an effective way of improving the biocompatibility of chitosan membranes towards to their use in biomedical applications.S. M. Luna acknowledges the support of the Programme Alssan - The European Union Programme of High Level Scholarships for Latin America (scholarship No E04M041362CO) and Silva SS acknowledge the support of the Portuguese Foundation for Science and Technology, (SFRH/BPD/45307/2008). This work was also partially supported by the European Union-funded - STREP project HIPPOCRATES (NMP3-CT-2003-505758) and was carried out under the scope of European NoE EXPERTISSUES (NMP3-CT-2004-500283)

Co-crystal of suberic acid and 1,2-bis(4-pyridyl)ethane: A new case of packing polymorphism

The polymorphic behaviour of a co-crystal composed of neutral suberic acid and 1, 2-bis(4-pyridyl)ethane is reported. A multidisciplinary approach has been employed, using thermal analysis methods (differential scanning calorimetry and polarized light thermomicroscopy), spectroscopic methods (infrared spectroscopy) and X-ray single crystal and powder diffraction. Two new polymorphs, I and III; have been identified, and for one of them the crystal structure has been elucidated and compared to that of a known polymorph, form II, showing that the assembling of the molecules in chains via H-bonds is a common feature of both polymorphs. Polymorph II, obtained by crystallization from an aqueous or ethanol solution or by grinding, undergoes a solid-solid transition to polymorph I, which melts at 180.5 °C. Upon cooling from the melt, polymorph I is obtained, and a solid-solid transformation also occurs, to polymorph III''. Polymorph III was obtained serendipitously in an attempt to prepare a Nd(III) complex. The relative stability of the three polymorphic forms was established

Aging increases susceptibility to high fat diet-induced metabolic syndrome in C57BL/6 mice: Improvement in glycemic and lipid profile after antioxidant therapy

Nonalcoholic fatty liver disease (NAFLD) has been considered a novel component of the metabolic syndrome (MetS), with the oxidative stress participating in its progression. This study aimed to evaluate the metabolic profile in young and old mice with MetS, and the effects of apocynin and tempol on glycemic and lipid parameters. Young and old C57BL/6 mice with high fat diet- (HFD-) induced MetS received apocynin and tempol 50 mg·kg(-1)/day in their drinking water for 10 weeks. After HFD, the young group showed elevated fasting glucose, worsened lipid profile in plasma, steatosis, and hepatic lipid peroxidation. Nevertheless, the old group presented significant increase in fasting insulin levels, insulin resistance, plasma and hepatic lipid peroxidation, and pronounced steatosis. The hepatic superoxide dismutase and catalase activity did not differ between the groups. Tempol and apocynin seemed to prevent hepatic lipid deposition in both groups. Furthermore, apocynin improved glucose tolerance and insulin sensitivity in old mice. In summary, old mice are more susceptible to HFD-induced metabolic changes than their young counterparts. Also, the antioxidant therapy improved insulin sensitivity and glucose tolerance, and in addition, apocynin seemed to prevent the HFD-induced hepatic fat deposition, suggesting an important role of oxidative stress in the induction of NAFLD

Brane-world Quantum Gravity

The Arnowitt-Deser-Misner canonical formulation of general relativity is extended to the covariant brane-world theory in arbitrary dimensions. The exclusive probing of the extra dimensions makes a substantial difference, allowing for the construction of a non-constrained canonical theory. The quantum states of the brane-world geometry are defined by the Tomonaga-Schwinger equation, whose integrability conditions are determined by the classical perturbations of submanifolds contained in the Nash's differentiable embedding theorem. In principle, quantum brane-world theory can be tested by current experiments in astrophysics and by near future laboratory experiments at Tev energy. The implications to the black-hole information loss problem, to the accelerating cosmology, and to a quantum mathematical theory of four-sub manifolds are briefly commented.Comment: 14 pages, no figures, JHEP format, to appear in JHEP April 200

Empathy in preschool Portuguese children: validation of the empathy questionnaire (EmQue)

Developmental pathways of social-emotional and cognitive functioning - ou