First stability eigenvalue characterization of Clifford hypersurfaces

The stability operator of a compact oriented minimal hypersurface is given by , where is the norm of the second fundamental form. Let be the first eigenvalue of and define . In 1968 Simons proved that for any non-equatorial minimal hypersurface . In this paper we will show that only for Clifford hypersurfaces. For minimal surfaces in , let denote the area of and let denote the genus of . We will prove that . Moreover, if is embedded, then we will prove that . If in addition to the embeddeness condition we have that , then we will prove that .

     

Automated flow-based anion-exchange method for high-throughput isolation and real-time monitoring of RuBisCO in plant extracts

In this work, a miniaturized, completely enclosed multisyringe-flow system is proposed for high-throughput purification of RuBisCO from Triticum aestivum extracts. The automated method capitalizes on the uptake of the target protein at 4 °C onto Q-Sepharose Fast Flow strong anion-exchanger packed in a cylindrical microcolumn (105 × 4 mm) followed by a stepwise ionic-strength gradient elution (0-0.8 mol/L NaCl) to eliminate concomitant extract components and retrieve highly purified RuBisCO. The manifold is furnished downstream with a flow-through diode-array UV/vis spectrophotometer for real-time monitoring of the column effluent at the protein-specific wavelength of 280 nm to detect the elution of RuBisCO. Quantitation of RuBisCO and total soluble proteins in the eluate fractions were undertaken using polyacrylamide gel electrophoresis (PAGE) and the spectrophotometric Bradford assay, respectively. A comprehensive investigation of the effect of distinct concentration gradients on the isolation of RuBisCO and experimental conditions (namely, type of resin, column dimensions and mobile-phase flow rate) upon column capacity and analyte breakthrough was effected. The assembled set-up was aimed to critically ascertain the efficiency of preliminary batchwise pre-treatments of crude plant extracts (viz., polyethylenglycol (PEG) precipitation, ammonium sulphate precipitation and sucrose gradient centrifugation) in terms of RuBisCO purification and absolute recovery prior to automated anion-exchange column separation. Under the optimum physical and chemical conditions, the flow-through column system is able to admit crude plant extracts and gives rise to RuBisCO purification yields better than 75%, which might be increased up to 96 ± 9% with a prior PEG fractionation followed by sucrose gradient step.     

Metrics on products of surfaces with non-positive sectional curvature

Let (S _i, g_i),i=1, 2 be two compact riemannian surfaces isometrically embedded in euclidean spaces. In this paper we show that ifM=S ₁×S₂,then for any functionF: M→R, the graph ofF, i.e. the manifold {(x, F(x)): x∈M}, does not have positive sectional curvature.     

Cembranoids from Eunicea sp. enhance insulin-producing cells proliferation

Nine new cembranoids 1–9 containing an α–methylene–γ–butyrolactone together with the known diterpenes 10–15 have been isolated from a crude extract of Eunicea sp. and their structures were established by spectroscopic methods. The proliferative effect of six of these compounds on insulin-producing cells (beta–cells) was evaluated.     

New examples of maximal space like surfaces in the anti-de Sitter space

Let be the three-dimensional anti-de Sitter space. In this paper we will construct new examples of complete maximal space like surfaces in . Moreover, we will prove that any complete maximal space like surface in with principal curvatures ±κ bounded away from zero must be isometric to the hyperbolic cylinder. Since the new examples that we have constructed have exactly two principal curvatures everywhere, we conclude that the condition on the principal curvatures on the previous result, i.e. the condition |κ(m)|>c>0, cannot be replaced by the condition |κ(m)|>0.     

A Characterization of Quadric Constant Scalar Curvature Hypersurfaces of Spheres

Let M?S ⁴ be a complete orientable hypersurface with constant scalar curvature. For any v∈R ⁵, let us define the two real functions \(l_{v}, f_{v}:M\to{\bf R}\) on M by l _v (x)=〈x,v〉 and f _v (x)=〈ν(x),v〉 with ν:M→S ⁴ a Gauss map of M. In this paper, we show that if we have that l _v =λf _v for some nonzero vector v∈R ⁵ and some real number λ, then M is either totally umbilical (a Euclidean sphere) or M is a Cartesian product of Euclidean spheres. We will also show with an example that the completeness condition is needed in this theorem.     

Rotational Surfaces in $$S^{3}$$ with Constant Mean Curvature

There is a two-parametric family of rotational symmetric CMC surfaces; more precisely, for every real number H and every \(C\ge 2(H+\sqrt{1+H^2})\) there is a rotational symmetry surface \(\Sigma _{H,C}\) with mean curvature H. Perdomo (Asian J Math 14:73–108, 2010) showed that for every H between \(\cot \left( \frac{\pi }{m}\right) \) and \(\frac{m^2-2}{2\sqrt{m^2-1}}\) there exists an embedded rotational symmetric example with non-constant principal curvatures that is invariant under the cyclic group \(Z_m\). Recently Andrews and Li (J Differ Geom 99:169–189, 2015) showed that these embedded CMC tori are the only embedded genus 1 surfaces with CMC on the sphere. In this paper we complete the study of this family of CMC surfaces and we show that for every integer \(m>2\), there is a properly immersed example in this family that contains a great circle and is invariant under the cyclic group \(Z_m\). We will say that these examples contain the axis of symmetry. We also show that every non-isoparametric surface \(\Sigma _{H,C}\) is either properly immersed and invariant under the cyclic group \(Z_m\) for some integer \(m>1\) or it is dense in the region bounded by two isoparametric tori if the surface \(\Sigma _{H,C}\) does not contain the axis of symmetry or it is dense in the region bounded by a totally umbilical surface if the surface \(\Sigma _{H,C}\) contains the axis of symmetry.     

Effect of the Addition of Alginate and/or Tetracycline on Brushite Cement Properties

Calcium phosphate cements have the advantage that they can be prepared as a paste that sets in a few minutes and can be easily adapted to the shape of the bone defect, which facilitates its clinical application. In this research, six formulations of brushite (dicalcium phosphate dihydrated) cement were obtained and the effect of the addition of sodium alginate was analyzed, such as its capacity as a tetracycline release system. The samples that contain sodium alginate set in 4 or 5 min and showed a high percentage of injectability (93%). The cements exhibit compression resistance values between 1.6 and 2.6 MPa. The drug was released in a range between 12.6 and 13.2% after 7 days. The antimicrobial activity of all the cements containing antibiotics was proven. All samples reached values of cell viability above 70 percent. We also observed that the addition of the sodium alginate and tetracycline improved the cell viability.     

CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds

In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h ? [-1,-\frac2?{n-1}n)h\in[-1,-\frac{2\sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of S₁^n-1×\mathbbRS_1^{n-1}\times \mathbb{R} in the (n + 1)-dimensional de Sitter space S₁ⁿ⁺¹\hbox{\bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.     

Adsorption of endotoxins on Ca2+ iminodiacetic acid by metal ion affinity chromatography

Endotoxins (also known as lipopolysaccharides (LPS)) are undesirable by products of recombinant proteins, purified from Escherichia coli. LPS can be considered stable under a wide range of temperature and pH, making their removal one of the most difficult tasks in downstream processes during protein purification. The inherent toxicity of LPS makes their removal an important step for the application of these proteins in several biological assays and for a safe parenteral administration. Immobilized metal affinity chromatography (IMAC) enables the affinity interactions between the metal ions (immobilized on the support through the chelating compound) and the target molecules, thus enabling high efficiency separation of the target molecules from other components present in a mixture. Affinity chromatography is applied with Ca2+ iminodiacetic acid (IDA) to remove most of the LPS contaminants from the end product (more than 90%). In this study, the adsorption of LPS on an IDA-Ca2+was investigated. The adsorption Freundlich isotherm of LPS-IDA-Ca2+provides a theoretical basis for LPS removal. It was found that LPS is bound mainly by interactions between the phosphate group in LPS and Ca2+ligands on the beads. The factors such as pH (4.0 or 5.5) and ionic strength (1.0 mol/L) are essential to obtain effective removal of LPS for contaminant levels between endotoxin’ concentration values less than 100 EU/mL and 100000 EU/mL. This new protocol represents a substantial advantage in time, effort, and production costs.