Piecewise Convex Curves and their Integral Representation

2000 Mathematics Subject Classification: 52A10.A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the Riemann-Stieltjes integral with respect to an increasing, nonnegative and continuous from the right function s+. Further it is shown that the obtained representation relates to the support function of the set FG. Concerning the reverse question, namely what can be said for the curves that admit such representation, it is shown that they are exactly the curves that can be decomposed into finitely many convex arcs. This result suggests the name piecewise convex curves. In particular, the class of piecewise convex curves contains the convex curves being boundary sets of convex figures, therefore the results from the paper can be used as a tool for studying convex curves

Alkaloids from Mongolian species of Peganum multisectum (Maxim) Bobrov

Alkaloids of the aerial parts of P. multisectum (Maxim) Bobrov (Zygophyllaceae) growing in Mongolia have been studied by capillary Gas Chromatography-Mass Spectrometry (GC-MS) and Column Chromatography (CC). Four compounds comprising of 2-methylquinoline (1), 9-amino-2, 3,5,6,7,8-hexahydro-1H-cyclopenta [b] quinoline (2), vasicinone (3) and harmine (4) have been determined by GC-MS, while harmine (4), peganine (5), deoxypeganine (6), deoxyvasicinone (7) and harmane (8) were isolated as pure compounds by the CC. The structures of the five alkaloids 4, 5, 6, 7 and 8 were elucidated by the MS and 1H and 13C NMR analysis. The alkaloids 1, 2 and 8 were identified for the first time from this species.Mongolian Journal of Chemistry 16 (42), 2015, 48-5

Fatty acids and their esters from Cicuta virosa L.

n-Hexane and chloroform fractions of aerial parts and roots of Cicuta virosa L. were investigated by GC-MS. As a result of the study 25 fatty acids and their esters have been identified. Two unsaturated esters such as linoleic acid ethyl ester (IX, 16.66%), and n- hexadecanoic acid ethyl ester (VII, 10.12%), the fatty acid n-hexadecanioc acid (VI, 8.10%) made up the bulk of the aerial parts. Four unsaturated esters such as linoleic acid ethyl ester (IX, 10.15%), dibutylphthalate (XII, 9.55%), n-hexadecanoic acid ethyl ester (VII, 8.19%) and 9, 12, 15 - octadecatrienoic acid ethyl ester (X, 5.9%), two fatty acids as n-hexadecanoic acid (VI, 8,15%) and 9,12-octadecadienoic acid (VIII, 4,5%) predominated in the roots of Cicuta virosa L. These known fatty acids and their esters were found for the first time in this plant species. DOI: http://dx.doi.org/10.5564/mjc.v14i0.203 Mongolian Journal of Chemistry 14 (40), 2013, p71-7

Characteristics of pectic polysaccharides from leek obtained through consecutive extraction with various reaction agents

Five polysaccharide fractions of commensurable by yield, but different in composition were obtained through consecutive extraction with water, solutions of ammonium oxalate, sodium carbonate, hydrochloric acid and sodium hydroxide from the alcohol-insoluble residue (AIR) of leek. In the polyuronide part of these fractions besides galacturonic acid was found also glucuronic acid. In the neutral sugar fraction, the prevailing sugar was galactose, followed by rhamnose. The water-extractable pectic polysaccharide was highly homogenous (93.3% of it had molecular mass of 1.3×10 6 kDa) and protein content of 8% (the highest compared to the other extracted polysaccharides). Extraction with diluted hydrochloric acid yielded polysaccharide with the highest neutral sugar content of 71.1% and a low uronic acids content. The water-and chelate-extractable fractions had a lower L-rhamnose content (2.7% and 2.9%, respectively) and the other polysaccharide fractions from leek were characterized by a high L-rhamnose content (from 14 to 28%). The pectic polysaccharides obtained from leek have shown good immunostimulating properties. The highest immunostimulating activity has been shown by the water-and chelate-extractable polysaccharides, which are also characterized by a high polyuronic acid content and polysaccharides with molecular mass over 10 6 Da

Hydrophobically Modified Sulfobetaine Copolymers with Tunable Aqueous UCST through Postpolymerization Modification of Poly(pentafluorophenyl acrylate)

Polysulfobetaines, polymers carrying highly polar zwitterionic side chains, present a promising research field by virtue of their antifouling properties, hemocompatibility, and stimulus-responsive behavior. However, limited synthetic approaches exist to produce sulfobetaine copolymers comprising hydrophobic components. Postpolymerization modification of an activated ester precursor, poly(pentafluorophenyl acrylate), employing a zwitterionic amine, 3-((3-aminopropyl)dimethylammonio)propane-1-sulfonate, ADPS, is presented as a novel, one-step synthetic concept toward sulfobetaine (co)polymers. Modifications were performed in homogeneous solution using propylene carbonate as solvent with mixtures of ADPS and pentylamine, benzylamine, and dodecylamine producing a series of well-defined statistical acrylamido sulfobetaine copolymers containing hydrophobic pentyl, benzyl, or dodecylacrylamide comonomers with well-controllable molar composition as evidenced by NMR and FT-IR spectroscopy and size exclusion chromatography.This synthetic strategy was exploited to investigate, for the first time, the influence of hydrophobic modification on the upper critical solution temperature (UCST) of sulfobetaine copolymers in aqueous solution. Surprisingly, incorporation of pentyl groups was found to increase solubility over a wide composition range, whereas benzyl groups decreased solubility—an effect attributed to different entropic and enthalpic contributions of both functional groups. While UCST transitions of polysulfobetaines are typically limited to higher molar mass samples, incorporation of 0–65 mol % of benzyl groups into copolymers with molar masses of 25.5–34.5 kg/mol enabled sharp, reversible transitions from 6 to 82 °C in solutions containing up to 76 mM NaCl, as observed by optical transmittance and dynamic light scattering. Both synthesis and systematic UCST increase of sulfobetaine copolymers presented here are expected to expand the scope and applicability of these smart materials

Checkpoint-Dependent and -Independent Roles of Swi3 in Replication Fork Recovery and Sister Chromatid Cohesion in Fission Yeast

Multiple genome maintenance processes are coordinated at the replication fork to preserve genomic integrity. How eukaryotic cells accomplish such a coordination is unknown. Swi1 and Swi3 form the replication fork protection complex and are involved in various processes including stabilization of replication forks, activation of the Cds1 checkpoint kinase and establishment of sister chromatid cohesion in fission yeast. However, the mechanisms by which the Swi1–Swi3 complex achieves and coordinates these tasks are not well understood. Here, we describe the identification of separation-of-function mutants of Swi3, aimed at dissecting the molecular pathways that require Swi1–Swi3. Unlike swi3 deletion mutants, the separation-of-function mutants were not sensitive to agents that stall replication forks. However, they were highly sensitive to camptothecin that induces replication fork breakage. In addition, these mutants were defective in replication fork regeneration and sister chromatid cohesion. Interestingly, unlike swi3-deleted cell, the separation-of-functions mutants were proficient in the activation of the replication checkpoint, but their fork regeneration defects were more severe than those of checkpoint mutants including cds1Δ, chk1Δ and rad3Δ. These results suggest that, while Swi3 mediates full activation of the replication checkpoint in response to stalled replication forks, Swi3 activates a checkpoint-independent pathway to facilitate recovery of collapsed replication forks and the establishment of sister chromatid cohesion. Thus, our separation-of-function alleles provide new insight into understanding the multiple roles of Swi1-Swi3 in fork protection during DNA replication, and into understanding how replication forks are maintained in response to different genotoxic agents

Of the importance of a leaf: the ethnobotany of sarma in Turkey and the Balkans

BACKGROUND: Sarma - cooked leaves rolled around a filling made from rice and/or minced meat, possibly vegetables and seasoning plants - represents one of the most widespread feasting dishes of the Middle Eastern and South-Eastern European cuisines. Although cabbage and grape vine sarma is well-known worldwide, the use of alternative plant leaves remains largely unexplored. The aim of this research was to document all of the botanical taxa whose leaves are used for preparing sarma in the folk cuisines of Turkey and the Balkans. Methods: Field studies were conducted during broader ethnobotanical surveys, as well as during ad-hoc investigations between the years 2011 and 2014 that included diverse rural communities in Croatia, Bosnia and Herzegovina, Serbia, Kosovo, Albania, Macedonia, Bulgaria, Romania, and Turkey. Primary ethnobotanical and folkloric literatures in each country were also considered. Results: Eighty-seven botanical taxa, mainly wild, belonging to 50 genera and 27 families, were found to represent the bio-cultural heritage of sarma in Turkey and the Balkans. The greatest plant biodiversity in sarma was found in Turkey and, to less extent, in Bulgaria and Romania. The most commonly used leaves for preparing sarma were those of cabbage (both fresh and lacto-fermented), grape vine, beet, dock, sorrel, horseradish, lime tree, bean, and spinach. In a few cases, the leaves of endemic species (Centaurea haradjianii, Rumex gracilescens, and R. olympicus in Turkey) were recorded. Other uncommon sarma preparations were based on lightly toxic taxa, such as potato leaves in NE Albania, leaves of Arum, Convolvulus, and Smilax species in Turkey, of Phytolacca americana in Macedonia, and of Tussilago farfara in diverse countries. Moreover, the use of leaves of the introduced species Reynoutria japonica in Romania, Colocasia esculenta in Turkey, and Phytolacca americana in Macedonia shows the dynamic nature of folk cuisines. Conclusion: The rich ethnobotanical diversity of sarma confirms the urgent need to record folk culinary plant knowledge. The results presented here can be implemented into initiatives aimed at re-evaluating folk cuisines and niche food markets based on local neglected ingredients, and possibly also to foster trajectories of the avant-garde cuisines inspired by ethnobotanical knowledge

SNP-SNP interactions in breast cancer susceptibility

BACKGROUND: Breast cancer predisposition genes identified to date (e.g., BRCA1 and BRCA2) are responsible for less than 5% of all breast cancer cases. Many studies have shown that the cancer risks associated with individual commonly occurring single nucleotide polymorphisms (SNPs) are incremental. However, polygenic models suggest that multiple commonly occurring low to modestly penetrant SNPs of cancer related genes might have a greater effect on a disease when considered in combination. METHODS: In an attempt to identify the breast cancer risk conferred by SNP interactions, we have studied 19 SNPs from genes involved in major cancer related pathways. All SNPs were genotyped by TaqMan 5'nuclease assay. The association between the case-control status and each individual SNP, measured by the odds ratio and its corresponding 95% confidence interval, was estimated using unconditional logistic regression models. At the second stage, two-way interactions were investigated using multivariate logistic models. The robustness of the interactions, which were observed among SNPs with stronger functional evidence, was assessed using a bootstrap approach, and correction for multiple testing based on the false discovery rate (FDR) principle. RESULTS: None of these SNPs contributed to breast cancer risk individually. However, we have demonstrated evidence for gene-gene (SNP-SNP) interaction among these SNPs, which were associated with increased breast cancer risk. Our study suggests cross talk between the SNPs of the DNA repair and immune system (XPD-[Lys751Gln] and IL10-[G(-1082)A]), cell cycle and estrogen metabolism (CCND1-[Pro241Pro] and COMT-[Met108/158Val]), cell cycle and DNA repair (BARD1-[Pro24Ser] and XPD-[Lys751Gln]), and within carcinogen metabolism (GSTP1-[Ile105Val] and COMT-[Met108/158Val]) pathways. CONCLUSION: The importance of these pathways and their communication in breast cancer predisposition has been emphasized previously, but their biological interactions through SNPs have not been described. The strategy used here has the potential to identify complex biological links among breast cancer genes and processes. This will provide novel biological information, which will ultimately improve breast cancer risk management