Numerical implementation of coherence for the example of the “Swiss Cross”

Summary We consider the two-dimensional Helmholtz equation u+u=0 inD with the boundary conditionsu=0 on D. D is the Swiss Cross — a region consisting of five unit squares. A method based on the concept of Coherence is utilized to determine an approximation for the first eigenvalue= ₁ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for ₁, and to test some conjectures on its relations with torsional rigidity.Dedicated to the memory of Professor Lathar Collatz     

On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Countable Fréchetα 1-spaces may be first countable

It is shown to be consistent that countable, Fréchet, ₁-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of length ₂.The research of both authors is partially supported by NSERC     

Fractionation and purification of antioxidant peptides from Chinese sturgeon (Acipenser sinensis) protein hydrolysates prepared using papain and alcalase 2.4L

Protein hydrolysates have the potential to be natural and safer sources of bioactive peptides. In this study, two proteases were used to hydrolyze Chinese sturgeon (Acipenser sinensis) protein, and the hydrolysates were then purified to yield antioxidant peptides. The degree of hydrolysis of 23.56 % and 18.14 % was obtained using papain and alcalase 2.4L, respectivly, and hydrolysates had 96.80 % and 87.24 % total amino acid content, respectivly. The papain hydrolysate (PH) and alcalase 2.4L hydrolysate (AH) showed good antioxidant activity against DPPH^? (IC₅₀ of 3.64 and 3.15 mg/mL) and ABTS^?+ (IC₅₀ of 1.92 and 1.58 mg/mL), respectively. The low-molecular-weight (<1000 Da) fraction of both hydrolysates demonstrated the highest antiradical activity (IC₅₀ of 2.59 and 2.31 mg/mL, DPPH) and (IC₅₀ of 1.54 and 1.36 mg/mL, ABTS), respectively. Nine peptides were separated from both hydrolysates using reverse phase high performance liquid chromatography (RP-HPLC). The IC₅₀ for ABTS^?+ scavenging activity of peptide P5 with valine, glycine and asparagine (MW of 282.13 Da) from PH, and peptide P3 with histidine, glycine and alanine (MW of 302.74 Da) from AH was 0.89 and 0.72 mg/mL, respectively. The fractions and purified peptides obtained from Chinese sturgeon hydrolysates could be utilized as natural antioxidant substitutes in pharmaceuticals and food products.     

Ultra-violet excited laser emission in Na2

Laser emission at different wavelengths in the range of 903–914 nm and around 2.5 m has been observed upon excitation of Na₂ by uv radiation from an excimer laser at 351 nm and an excimer pumped dye laser in this wavelength range. The emission is attributed to a cascade emission followed by . In addition, coupled with the laser emission around 910 nm, broad-band fluorescence peaking around 855.5 nm is observed which, eventually, may be the first observation of the bound-free transition in Na₂.     

Energetic Bio-Activation of Some Organic Molecules and Their Antioxidant Activity in the Pulp of the Moroccan Argan Tree «Argania spinosa L.»

Argania spinosa L. Skeels is an emblematic tree in Morocco, known worldwide for its medicinal and nutritional value. Its fruits contain kernels used to prepare an edible oil, the leaves are used to feed livestock, and its wood is used as fuel. If the oil acquires high importance, the other components of the fruit of the argan are undervalued. Our objective is to invest the waste of the argan industry. Particularly, our study aimed to assess the effect of thermal activation of argan pulp on its therapeutic value, its phenolic profile and its functional and physicochemical properties. After heat treatment, the HPLC analysis for the average total phenolic content varied from 2% to 37%, depending on temperature. The antioxidant activity was increased with heat treatment. Higher values of antioxidant activity, polyphenol and pigment content were recorded at 70 °C. Functional properties analysis indicated that water solubility index and water absorption capacity were significantly affected by heat stress. Physicochemical analysis showed that moisture content, titratable acidity and soluble solids were affected.     

Cornelian Cherry (Cornus mas L.) Extracts Exert Cytotoxicity in Two Selected Melanoma Cell Lines—A Factorial Analysis of Time-Dependent Alterations in Values Obtained with SRB and MTT Assays

Despite the fact that phytochemicals of Cornaceae species have long been discussed as possible auxiliary agents in contemporary treatment, the insights on their properties remain relatively scarce. This study focuses on Cornus mas L. (Cornelian cherry), the extracts of which are reported to exert a pleiotropic effect shown in both in vivo and in vitro studies. This study aimed to explore the cytotoxic effect of extracts from fruits of red (Cornus mas L. ‘Podolski’) and yellow (Cornus mas L. ‘Yantarnyi’ and ‘Flava’) Cornelian cherries on two melanoma cell lines (A375 and MeWo). The extracts were characterized in the context of the concentration of bioactive compounds of antioxidative properties. Cytotoxicity was investigated with the use of the following two assays: SRB and MTT. An additional, alternative protocol for the SRB assay was used in this study so as to account for possible bias. Cytotoxicity was assessed as a difference in the whole time series of cell viability, instead of analyzing differences in raw values (often found in the literature). Both extracts from Cornus mas L. induced cytotoxicity in both A375 and MeWo cell lines, although the response of these cells was different. Moreover, based on this study, there is no evidence for claiming a different magnitude of cytotoxicity between these two extracts.     

Umbelliferose Isolated from Cuminum cyminum L. Seeds Inhibits Antigen-Induced Degranulation in Rat Basophilic Leukemia RBL-2H3 Cells

Cuminum cyminum L. (cumin) is an annual plant of the Umbelliferae family native to Egypt. We previously showed that the aqueous extract of cumin seeds suppresses degranulation by downregulating the activation of antigen-induced intracellular signaling molecules in rat basophilic leukemia RBL-2H3 cells. However, the active substances in the extract have not yet been identified. Accordingly, herein, we aimed to ascertain the water-soluble substances present in cumin seeds that inhibit degranulation, which led to the identification of umbelliferose, a characteristic trisaccharide present in plants of the Umbelliferae family. Our study is the first to reveal the degranulation-suppressing activity of umbelliferose, and quantification studies suggest that cumin seed powder contains 1.6% umbelliferose. Raffinose, an isomer of umbelliferose, was also found to significantly suppress antigen-induced degranulation, but less so than umbelliferose. Both umbelliferose and raffinose contain sucrose subunits in their structures, with galactose moieties bound at different sites. These differences in structure suggest that the binding of galactose to the sucrose subunit at the α1-2 bond contributes to its strong degranulation-inhibiting properties.