Exploring the Relationship Between Max-Cut and Stable Set Relaxations

The max-cut and stable set problems are two fundamental -hard problems in combinatorial optimization. It has been known for a long time that any instance of the stable set problem can be easily transformed into a max-cut instance. Moreover, Laurent, Poljak, Rendl and others have shown that any convex set containing the cut polytope yields, via a suitable projection, a convex set containing the stable set polytope. We review this work, and then extend it in the following ways. We show that the rounded version of certain `positive semidefinite' inequalities for the cut polytope imply, via the same projection, a surprisingly large variety of strong valid inequalities for the stable set polytope. These include the clique, odd hole, odd antihole, web and antiweb inequalities, and various inequalities obtained from these via sequential lifting. We also examine a less general class of inequalities for the cut polytope, which we call odd clique inequalities, and show that they are, in general, much less useful for generating valid inequalities for the stable set polytope. As well as being of theoretical interest, these results have algorithmic implications. In particular, we obtain as a by-product a polynomial-time separation algorithm for a class of inequalities which includes all web inequalities.     

Synthesis,Antibacterial, and Antifungal Activities of Imidazo[2,1-c][1,2,4]triazoles and 1,2,4-Triazolo[4,3-a]pyrimidinones

A straightforward method has been developed for the synthesis of 1-phenyl-imidazo [2,1-c][1,2,4]triazole derivatives 5a–j and 1-phenyl-[1,2,4]triazolo[4,3-a]pyrimidinones derivatives 6a–g starting from 5-amino-1-phenyl[1,2,4]triazole and p-toluenesulfonic acid (PTSA). This methodology affords a number of 1-phenyl-imidazo [2,1-c][1,2,4]triazoles 5a–j and 1-phenyl-[1,2,4]triazolo[4,3-a]pyrimidinones 6a–g in reasonable yields and short reaction times. The structures of all new compounds were elucidated using infrared, ¹H and ¹³C NMR, and high-resolution mass spectrometry. Some of the newly synthesized compounds were screened for their antimicrobial activity.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications ^® for the following free supplemental resource(s): Full experimental and spectral details.]     

Risk sensitive impulse control of non-Markovian processes

We consider the problem of an optimal stochastic impulse control of non-Markovian Processes when the expression of the cost functional integrates sensitiveness with respect to the risk. For this class, we try to establish the existence of an optimal strategy. We prove that our impulse control problem could be reduced to an iterative sequence of optimal stopping ones. Basically, the problem is solved using techniques involving the Snell envelope notion.     

Antibacterial and antioxidant properties of mixed linkage beta-oligosaccharides from extracted β-glucan hydrolysed by Penicillium occitanis EGL lichenase

The aim of this study was first to ascertain the chemical composition and the physicochemical properties of cereal extracted β-glucan from barley flour. Secondly, to assess the antioxidant properties and the antibacterial properties of extracted β-glucan hydrolysates. The proximate composition, FT-IR and scanning electron microscopy of extracted β-Glucan were studied. Hydrolysates from extracted β-glucan, obtained by lichenase EG_L from Penicillium occitanis, were a mixed linkage beta-oligosaccharides (MLBO) of trisaccharides and tetrasaccharides. MLBO showed a DPPH radical scavenger with IC50 about 1.8 ± 0.01 mg/mL whereas the IC50 of extracted β-glucan was about 5 ± 0.01 mg/mL. MLBO showed a high antioxidative capacity (175 μmol/mL α-tocopherol equivalents) at 5 mg/mL. The antimicrobial activity was confirmed against all tested bacteria especially at 20 mg/mL of MLBO while no inhibition was observed for all the strains used after the addition of either EG_L or extracted β-glucan.     

Production of Mixed-Linkage Beta-Oligosaccharides from Lichenan Using Immobilized Bacillus licheniformis UEB CF Lichenase

Lichenase from Bacillus licheniformis UEB CF was immobilized on Amberlite IR120 H. The immobilization yield and lichenase activity were 87 and 92.81?% of initial activity, respectively. The immobilized enzyme exhibited a shift in the optimal pH from 5.0 to 3.0, but the activity optimal temperature was not affected. The immobilized enzyme showed a residual activity of 50?% after five uses. It also exhibited high storage stability and retained 50?% of its initial activity after 120?days at 4?°C. The main hydrolysis products yielded from lichenan were trisaccharide and tetrasaccharide. The resulting mixed-linkage beta-oligosaccharides could be used as a special nutriment for lactic bacteria.     

Electrochemical DNA biosensor for polycyclic aromatic hydrocarbon detection

Four DNA electrochemical biosensors using four types of DNA (calf thymus ssDNA, calf thymus dsDNA, salmon testis ssDNA and salmon testis dsDNA) were constructed using graphite screen printed electrodes. These biosensors were exploited as analytical tool to detect polycyclic aromatic hydrocarbons-DNA interactions using benzo(a)anthracene and phenantrene as model analytes, the guanine oxidation peak variation being the signal revealing the interaction between PAHs and immobilized DNA. The salmon testis ssDNA biosensor resulted as the most promising device and was further evaluated for benzo(a)anthracene, fluorene, indeno(1,2,3-cd)pyrene, anthracene, and phenanthrene in 5–40 ng mL^?1 solutions, and for benzo(a)pyrene (5–50 ng mL^?1). A concentration dependent variation of the DNA guanine oxidation peak was observed for all compounds. The effect of benzo(a)pyrene ultraviolet (UV) activation on the benzo(a)pyrene (BaP)-DNA interaction was evaluated at concentration levels of 20 and 50 ng mL^?1, and a 3.5- and 2.7-fold increases of the guanine oxidation peak was measured respectively. The salmon testis ssDNA biosensor was examined with PAHs contaminated samples of Mytilus galloprovincialis. Upon UV irradiation of three sample extracts exceeding the BaP maximum level, a positive variation of the DNA guanine oxidation was obtained. An average 2.4-fold increase of the guanine oxidation peak was detected demonstrating that the sensor can be used to detect toxic degradation products of PAHs.     

Synthesis and crystal structure of N-benzylmethy- lammonium pentachlorothallate (III), [C6H5CH2NH2CH3]2TlCl5

N-Benzylmethylammonium pentachlorothallate (III) salt crystallizes in the monoclinic system P2₁/c with the following unit cell dimensions: a = 10.9540 (8), b = 12.559(1), c = 18.099(2)Å, = 112.1(3)° and Z = 4. The examination of the structure shows an alternate stacking of inorganic layers of pentachlorothallate (III) anions and organic layers of [C₆H₅CH₂NH₂CH₃]⁺ cations parallel to the c axis. The cohesion forces of the packing of N-benzylmethylammonium units in the layer and between two adjacent layers are provided by hydrogen bonds (N—HsCl) and van der Waals contacts.     

Phytochemical Investigation of New Algerian Lichen Species: Physcia Mediterranea Nimis

The present study provides new data concerning the chemical characterisation of Physcia mediterranea Nimis, a rare Mediterranean species belonging to the family Physciaceae. The phytochemical screening was carried out using GC-MS, HPLC-ESI-MS-MS, and NMR techniques. Hot extraction of n-hexane was carried out, followed by separation of the part insoluble in methanol: wax (WA-hex), from the part soluble in methanol (ME-hex). GC-MS analysis of the ME-hex part revealed the presence of methylbenzoic acids such as sparassol and atraric acid and a diterpene with a kaurene skeleton which has never been detected before in lichen species. Out of all the compounds identified by HPLC-ESI-MS-MS, sixteen compounds are common between WA-hex and ME-hex. Most are aliphatic fatty acids, phenolic compounds and depsides. The wax part is characterised by the presence of atranorin, a depside of high biological value. Proton 1H and carbon 13C NMR have confirmed its identification. Atranol, chloroatranol (depsides compound), Ffukinanolide (sesquiterpene lactones), leprolomin (diphenyl ether), muronic acid (triterpenes), and ursolic acid (triterpenes) have also been identified in ME-hex. The results suggested that Physcia mediterranea Nimis is a valuable source of bioactive compounds that could be useful for several applications as functional foods, cosmetics, and pharmaceuticals.     

Heterogeneous Catalysis in Acetylation of Alcohols and Phenols Promoted by Zirconium Sulfophenyl Phosphonate

Layered zirconium sulfophenyl phosphonate was found to be an efficient heterogeneous catalyst for the acetylation of alcohols and phenols.     

Nuclear magnetic resonance J coupling constant polarizabilities of hydrogen peroxide: A basis set and correlation study

In this article, we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constant with respect to an external electric field and play an important role for both chiral discrimination and solvation effects on NMR coupling constants. In this study, we illustrate the effects of one‐electron basis sets and electron correlation both at the level of density functional theory as well as second‐order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to perform calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We find a systematic but rather slow convergence with the one‐electron basis set and that augmentation functions are required. We observe also large and nonsystematic correlation effects with significant differences between the density functional and wave function theory methods. © 2012 Wiley Periodicals, Inc.