Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations

Cataloged from PDF version of article.Using the formulation of the immersion of a two-dimensional surface into the three-dimensional Euclidean space proposed recently, a mapping from each symmetry of integrable equations to surfaces in ℝ3 can be established. We show that among these surfaces the sphere plays a unique role. Indeed, under the rigid SU(2) rotations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine-Gordon equation are homeomorphic to a sphere. We also find some new Weingarten surfaces arising from the deformations of the modified Kurteweg-de Vries and of the nonlinear Schrödinger equations. Surfaces can also be associated with the motion of curves. We study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity. © 2000 American Institute of Physics

Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Antibacterial, antioxidant and anti-proliferative properties and zinc content of five south Portugal herbs

Context: Crataegus monogyna L. (Rosaceae) (CM), Equisetum telmateia L. (Equisataceae) (ET), Geranium purpureum Vil. (Geraniaceae) (GP), Mentha suaveolens Ehrh. (Lamiaceae) (MS), and Lavandula stoechas L. spp. luisieri (Lamiaceae) (LS) are all medicinal. Objective: To evaluate the antioxidant, antiproliferative and antimicrobial activities of plant extracts and quantify individual phenolics and zinc. Material and methods: Aerial part extracts were prepared with water (W), ethanol (E) and an 80% mixture (80EW). Antioxidant activity was measured with TAA, FRAP and RP methods. Phenolics were quantified with a HPLC. Zinc was quantified using voltammetry. Antibacterial activity (after 48 h) was tested using Enterococcus faecalis, Bacillus cereus, Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa and Listeria monocytogenes. Antiproliferative activity (after 24 h) was tested using HEP G2 cells and fibroblasts. Results: Solvents influenced results; the best were E and 80EW. GP had the highest antioxidant activity (TAA and FRAP of 536.90mg AAE/g dw and 783.48mg TE/g dw, respectively). CM had the highest zinc concentration (37.21 mg/kg) and phenolic variety, with neochlorogenic acid as the most abundant (92.91 mg/100 g dw). LS was rich in rosmarinic acid (301.71 mg/100 g dw). GP and LS inhibited the most microorganisms: B. cereus, E. coli and S. aureus. GP also inhibited E. faecalis. CM had the lowest MIC: 5830 mu g/mL. The antibacterial activity is explained by the phenolics present. LS and CM showed the most significant anti-proliferative activity, which is explained by their zinc content. Conclusion: The most promising plants for further studies are CM, LS and GP.FCT, Fundacao para a Ciencia e a Tecnologia of Portugal [SFRH/BSA/139/2014

Relationship between Neural Alteration and Perineural Invasion in Pancreatic Cancer Patients with Hyperglycemia

Background: Patients with higher levels of fasting serum glucose have higher death rates from pancreatic cancer compared to patients with lower levels of fasting serum glucose. However, the reasons have not been studied. The goal of the current study was to examine the neural alterations in pancreatic cancer patients with hyperglycemia and to identify the relationship between the neural alterations and perineural invasion. Methodology/Principal Findings: The clinical and pathological features of 61 formalin-fixed pancreatic cancer specimens and 10 normal pancreases as controls were analyzed. Furthermore, the expression of Protein Gene Product 9.5 (PGP9.5), Myelin P0 protein (MPP), NGF, TrkA, and p75 were examined by immunohistochemistry. The median number of nerves, the median area of neural tissue, and the median nerve diameter per 10 mm 2 were larger in the hyperglycemia group than those in the euglycemia group (p = 0.007, p = 0.009, and p = 0.004, respectively). The integrated optical density (IOD) of MPP staining was lower in the hyperglycemia group than those in the euglycemia group (p = 0.019), while the expression levels of NGF and p75 were higher in the hyperglycemia group than those in the euglycemia group (p = 0.002, and p = 0.026, respectively). The nerve bundle invasion of pancreatic cancer was more frequent in the hyperglycemia group than in the euglycemia group (p = 0.000). Conclusions/Significance: Nerve damage and regeneration occur simultaneously in the tumor microenvironment o

Effect of Air Injection on Nucleation Rates: An Approach from Induction Time Statistics

From disruption of the supersaturated solution to improved mass transfer in the crystallizing suspension, the introduction of a moving gas phase in a crystallizer could lead to improved rates of nucleation and crystal growth. In this work, saturated air has been injected to batch crystallizers to study the effects on formation of the first crystal and subsequent turbidity buildup. To account for the typically large sample-to-sample variation, nucleation rates were evaluated for a large number of replicates using probability distributions of induction times. The slope and the intercept of the distributions were studied independently, allowing the simultaneous determination of the mean induction time and a certain detection delay related to the rate of crystal growth after formation of the first nucleus. When saturated air was injected in aqueous glycine solutions, the average detection delay was reduced from 69 to 13 min, and the mean induction time decreased from 128 to 36 min. The effect on aqueous solutions of l-arginine was less apparent, with a detection delay reduction from 15 to 3 min, and no significant changes on the rate of primary nucleation. These results demonstrate the potential of this technique for reduction in nucleation induction time and improved mass deposition rates in crystallization operations

Aplinkos įtaka duoninių (Triticum aestivum L.) ir kietųjų (Triticum durum Desf.) kviečių albuminų kiekiui

Albumins or water soluble proteins (wsp) in wheat are important as nutrients containing high content of essential amino acids such as lysine, tryptophan, methionine, and also asparagine, glutamine, arginine, and proline in comparison to storage proteins-glutenins and gliadins. Fifteen bread wheat (Triticum aestivum L.) and 15 durum wheat (Triticum durum Desf.) genotypes were evaluated across six different environments for two years to determine the content of albumins in grains. The purpose of this research was to determine the variability of the albumins content of the tested bread wheat and durum wheat genotypes, effects of environment, genotype and their interaction (GEI) on the trait of interest, heritability in a broad sense, stability, and also to interpret GEI by climatic factors modelling. The statistical procedure included analysis of variance, sites regression and factorial regression. The mean content of albumins was 20.23 g kg-1 in bread wheat and 23.12 g kg-1 in durum wheat. Environment followed by GEI was the most important in determining albumins content. The heritability in a broad sense was low, i.e. 31.3% for bread wheat and only 2.4% for durum wheat. GEI for the albumins content was explained with the efficacy of 94.7% and 94.2% of sum of squares, for bread wheat and durum wheat, respectively, by the following models: mean temperature in May, winter moisture reserves, minimum temperature in April and March for bread wheat; and precipitation sum in April, sunshine hours sum in March, maximum temperature in May, and winter moisture reserves for durum wheat. The simultaneous selection for high albumins content and good stability proved to be possible for bread wheat genotypes, but less for durum wheat genotypes due to unsatisfactory stability

Mutation update and genotype-phenotype correlations of novel and previously described mutations in TPM2 and TPM3 causing congenital myopathies

Mutations affecting skeletal muscle isoforms of the tropomyosin genes may cause nemaline myopathy, cap myopathy, core-rod myopathy, congenital fiber-type disproportion, distal arthrogryposes, and Escobar syndrome. We correlate the clinical picture of these diseases with novel (19) and previously reported (31) mutations of the TPM2 and TPM3 genes. Included are altogether 93 families: 53 with TPM2 mutations and 40 with TPM3 mutations. Thirty distinct pathogenic variants of TPM2 and 20 of TPM3 have been published or listed in the Leiden Open Variant Database (http://www.dmd.nl/). Most are heterozygous changes associated with autosomal-dominant disease. Patients with TPM2 mutations tended to present with milder symptoms than those with TPM3 mutations, DA being present only in the TPM2 group. Previous studies have shown that five of the mutations in TPM2 and one in TPM3 cause increased Ca2+ sensitivity resulting in a hypercontractile molecular phenotype. Patients with hypercontractile phenotype more often had contractures of the limb joints (18/19) and jaw (6/19) than those with nonhypercontractile ones (2/22 and 1/22), whereas patients with the non-hypercontractile molecular phenotype more often (19/22) had axial contractures than the hypercontractile group (7/19). Our in silico predictions show that most mutations affect tropomyosin–actin association or tropomyosin head-to-tail binding