Deformations of the hemisphere that increase scalar curvature

Consider a compact Riemannian manifold M of dimension n whose boundary ?M is totally geodesic and is isometric to the standard sphere S ^n?1. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n?1), then M is isometric to the hemisphere $S_{+}^{n}$ equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo??s Conjecture in dimension n??3.     

Alternatives to a Semi-Parametric Estimator of Parameters of Rare Events—The Jackknife Methodology*

In this paper, and in a context of regularly varying tails, we propose different alternatives to a well-known estimator of the tail index—the Hill estimator (Hill, 1975). These alternatives have essentially in mind a reduction in bias, preferably without increasing Mean Square Error, by the use of suitable Generalized Jackknife methodologies (Gray and Schucany, 1972). The first estimate obtained through this methodolgy is the one introduced by Peng (1998), under a different context. Other Generalized Jackknife estimators are linear combinations of Hill estimators at different levels. This methodology of affine combinations of Hill estimators at different levels may be easily generalized to other semi-parametric estimators of the tail index, like Pickands' estimator (Pickands, 1975) or the Moment's estimator (Dekkers et al., 1989), and consequently to a general real tail index, seeming to be a promising field of research.     

Spectrophotometric study of the equilibria in aqueous copper(II) azide solutions

The reaction between copper (II) and azide has been studied spectrophotometrically at four wavelengths, at 25 degrees , and ionic strength 4.00M (sodium perchlorate). The formation constants beta(2) and beta(3) found are 2.90 +/- 0.08 x 10(4) and 3.02 +/- 0.07 x 10(6) respectively. The results obtained from potentiometric measurements with a solid-state electrode disagree with those calculated from the spectrophotometric data. Causes of the discrepancy are discussed.     

A new cytokinin from the fruits of zantedeschiaaethiopica

A new purine derivative with cytokinin activity was isolated from the cuckoo-pint fruits ($\text{Zantedeschia}$$\text{aethiopica}$) and identified as 6-(o-hydroxybenzylamino)-2-methylthio-9-β-D-glucofuranosylpurine $\text{1}$.     

A strong form of almost differentiability

We present a uniformization of Reeken’s macroscopic differentiability (see [5]), discuss its relations to uniform differentiability (see [6]) and classical continuous differentiability, prove the corresponding chain rule, Taylor’s theorem, mean value theorem, and inverse mapping theorem. An attempt to compare it with the observability (see [1, 4]) is made too.     

Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS₅ braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact five-dimensional warped solutions which are associated with conformal bulk fields of weight –4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.     

Influence of the atomic structure on the Raman spectra of graphite edges

A study of step edges in graphite with different atomic structures combining Raman spectroscopy and scanning probe microscopy is presented. The orientation of the carbon hexagons with respect to the edge axis, in the so-called armchair or zigzag arrangements, is distinguished spectroscopically by the intensity of a disorder-induced Raman peak. This effect is explained by applying the double resonance theory to a semi-infinite graphite crystal and by considering the one-dimensional character of the defect.     

Unmanned platform for long-range remote analysis of volatile compounds in air samples

This paper describes a long-range remotely controlled CE system built on an all-terrain vehicle. A four-stroke engine and a set of 12-V batteries were used to provide power to a series of subsystems that include drivers, communication, computers, and a capillary electrophoresis module. This dedicated instrument allows air sampling using a polypropylene porous tube, coupled to a flow system that transports the sample to the inlet of a fused-silica capillary. A hybrid approach was used for the construction of the analytical subsystem combining a conventional fused-silica capillary (used for separation) and a laser machined microfluidic block, made of PMMA. A solid-state cooling approach was also integrated in the CE module to enable controlling the temperature and therefore increasing the useful range of the robot. Although ultimately intended for detection of chemical warfare agents, the proposed system was used to analyze a series of volatile organic acids. As such, the system allowed the separation and detection of formic, acetic, and propionic acids with signal-to-noise ratios of 414, 150, and 115, respectively, after sampling by only 30 s and performing an electrokinetic injection during 2.0 s at 1.0 kV.     

Molecular Modeling Approaches Can Reveal the Molecular Interactions Established between a Biofilm and the Bioactive Compounds of the Essential Oil of Piper divaricatum

Molecular modeling approaches are used in a versatile way to investigate the properties of diverse organic and inorganic structures such as proteins, biomolecules, nanomaterials, functionalized nanoparticles, and membranes. However, more detailed studies are needed to understand the molecular nature of interactions established in gelatin biofilms impregnated with bioactive compounds. Because of this, we used computational methods to evaluate how the major compounds of Piper divaricatum essential oil can interact with the gelatin biofilm structure. For this, we used as inspiration the paper published, where various properties of the essential oil impregnated gelatin biofilm P. divaricatum are reported. After our computer simulations, we related our molecular observations to biofilm’s structural and mechanical properties. Our results suggest that the major compounds of the essential oil were able to interrupt intermolecular interactions between the chains of the biofilm matrix. However, the compounds also established interactions with the amino acid residues of these chains. Our molecular analyses also explain changes in the structural and mechanical properties of the essential oil-impregnated biofilm. These results can support the planning of functional packaging impregnated with bioactive compounds that can protect food against microorganisms harmful to human health.