The hydrogen‐bonding network in deacetyl­cephalothin

The structural analysis of deacetyl­cephalothin [systematic name: (6R,7R)‐3‐hydroxy­methyl‐8‐oxo‐7‐(2‐thio­phen‐2‐yl­acetyl­amino)‐5‐thia‐1‐aza­bicyclo­[4.2.0]oct‐2‐ene‐2‐carboxylic acid], C₁₄H₁₄N₂O₅S₂, shows that the geometry of the central bicyclic moiety is close to the geometry exhibited by other biologically active cephalosporin antibiotics. The mol­ecules are arranged in a helical chain running parallel to the 2₁ axis via a strong O—H⋯O hydrogen bond. The main helices are zipped together via N—H⋯O inter­actions, forming infinite layers. The supramolecular architecture is stabilized by O—H⋯S and C—H⋯O hydrogen bonds.     

Independent determination of the complex refractive index and wave impedance by time-domain terahertz spectroscopy

We present a method for simultaneous determination of the refractive index and wave impedance - or equivalently of the dielectric permittivity and magnetic permeability - of bulk samples. Two independent complex spectroscopic quantities required for an unambiguous evaluation are experimentally obtained by temporal windowing of time domain waveforms measured in the transmission or reflection geometry. We discuss several approaches that can be used for the evaluation of the complex refractive index and wave impedance; three are quantitatively analyzed and compared. Successful evaluation of the dielectric and magnetic dispersion then crucially depends on the accuracy of the wave impedance measurements.     

On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains

We analyze the eigenstructure of count-data Markov chains. Our main focus is on so-called CLAR(1) models, which are characterized by having a linear conditional mean, and also on the case of a finite range, where the second largest eigenvalue determines the speed of convergence of the forecasting distributions. We derive a lower bound for the second largest eigenvalue, which often (but not always) even equals this eigenvalue. This becomes clear by deriving the complete set of eigenvalues for several specific cases of CLAR(1) models.     

An axiomatic duality framework for the theta body and related convex corners

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the corresponding antiblocking duality relations. Our framework describes several semidefinite and polyhedral relaxations of the stable set polytope of a graph as generalized theta bodies. As a by-product of our approach, we introduce the notion of “Schur Lifting” of cones which is dual to PSD Lifting (more commonly used in SDP relaxations of combinatorial optimization problems) in our axiomatic generalization. We also generalize the notion of complements of graphs to diagonally scaling-invariant polyhedral cones. Finally, we provide a weighted generalization of the copositive formulation of the fractional chromatic number by Dukanovic and Rendl from 2010.     

On 2-Connected Spanning Subgraphs with Bounded Degree in K 1,r -Free Graphs

For any integer r > 1, an r-trestle of a graph G is a 2-connected spanning subgraph F with maximum degree Δ(F) ≤ r. A graph G is called K _1,r -free if G has no K _1,r as an induced subgraph. Inspired by the work of Ryjáček and Tkáč, we show that every 2-connected K _1,r -free graph has an r-trestle. The paper concludes with a corollary of this result for the existence of k-walks.     

Chemical Composition and Biological Activity of Argentinian Propolis of Four Species of Stingless Bees

The chemical composition of propolis of four species of stingless bees (SLBs) from Argentina was determined, and its antibacterial and anticancer activity was evaluated on selected types of microbes and cancer cell lines. Volatile secretions of all propolis samples are formed by 174 C₂–C₁₅ organic compounds, mainly mono- and sesquiterpenes and their derivatives. The chromatograms of ether extracts showed 287 peaks, of which 210 were identified. The most representative groups in the extracts of various propolis samples were diterpenoids (mainly resin acids), triterpenoids and phenolic compounds: long-chain alkenyl phenols, resorcinols and salicylates. The composition of both volatile and extractive compounds turned out to be species-specific; however, in both cases, the pairwise similarity of the propolis of Scaptotrigona postica and Tetragonisca fiebrigi versus that of Tetragona clavipes and Melipona quadrifasciata quadrifasciata was observed, which indicated the similarity of the preferences of the respective species when choosing plant sources of resin. The composition of the studied extracts completely lacked flavonoids and phenolcarboxylic acids, which are usually associated with the biological activity and medicinal properties of propolis. However, tests on selected microbial species and cancer cell lines showed such activity. All propolis samples tested against Paenibacillus larvae, two species of Bacillus and E. coli showed biofilm inhibition unrelated to the inhibition of bacterial growth, leading to a decrease in their pathogenicity. Testing the anticancer activity of ether extracts using five types of cell cultures showed that all four types of propolis studied inhibit the growth of cancer cells in a dose- and time-dependent manner. Propolis harvested by T. clavipes demonstrated the highest cytotoxicity on all tested cell lines.     

Soluble Extracellular Polymeric Substances Produced by Parachlorella kessleri and Chlorella vulgaris: Biochemical Characterization and Assessment of Their Cadmium and Lead Sorption Abilities

In the present study, the potential of lead and cadmium removal by the extracellular polymeric substances (EPS) produced from Parachlorella kessleri and Chlorella vulgaris were investigated. Carbohydrates were the dominant components of EPS from both analyzed species. The contents of reducing sugars, uronic acids, and amino acids were higher in EPS synthesized by C. vulgaris than in EPS from P. kessleri. The analysis of the monosaccharide composition showed the presence of rhamnose, mannose and galactose in the EPS obtained from both species. The ICP-OES (inductively coupled plasma optical emission spectrometry) analyses demonstrated that C. vulgaris EPS showed higher sorption capacity in comparison to P. kessleri EPS. The sorption capacity of C. vulgaris EPS increased with the increase in the amount of metal ions. P. kessleri EPS had a maximum sorption capacity in the presence of 100 mg/L of metal ions. The FTIR analysis demonstrated that the carboxyl, hydroxyl, and carbonyl groups of EPS play a key role in the interactions with metal ions. The present study showed C. vulgaris EPS can be used as a biosorbent in bioremediation processes due to its biochemical composition, the presence of significant amounts of negatively charged uronic acids, and higher sorption capacity.     

Glycosylation of organic phosphorus thio- and selenoacids—II: The reaction of organic phosphorus thioselenoacids with glycosyl bromides under kinetically and thermodynamically controlled conditions

Ambident anions derived from phosphorus thioselcnoacids were glycosylated with 2,3,4,6 - tetra - O - acetyl - α - d - glucopyranosyl bromide, 2,3,4,6 - tetra - O - acetyl - α - d - galactopyranosyl bromide and 2,3,4 - tri- O - acetyl - α - d - xylopyranosyl bromide. The products were β-Se-glucosyl- and β-S-glucosylthioselenoates. The Se/S ratio of the glycosylated phosphorothioselenoates depends on the reaction conditions. At higher temperatures an equilibrium was observed. As a result of this equilibrium the Se/S ratio of the linkages formed in the glycosylated products was different from that observed under kinetic control. The structures of the glycosylated phosphorothioselenoates were confirmed by spectroscopy, independent synthesis and selective oxidation.     

The stable set problem and the lift-and-project ranks of graphs

We study the lift-and-project procedures for solving combinatorial optimization problems, as described by Lovász and Schrijver, in the context of the stable set problem on graphs. We investigate how the procedures' performances change as we apply fundamental graph operations. We show that the odd subdivision of an edge and the subdivision of a star operations (as well as their common generalization, the stretching of a vertex operation) cannot decrease the N₀-, N-, or N₊-rank of the graph. We also provide graph classes (which contain the complete graphs) where these operations do not increase the N₀- or the N-rank. Hence we obtain the ranks for these graphs, and we also present some graph-minor like characterizations for them. Despite these properties we give examples showing that in general most of these operations can increase these ranks. Finally, we provide improved bounds for N₊-ranks of graphs in terms of the number of nodes in the graph and prove that the subdivision of an edge or cloning a vertex can increase the N₊-rank of a graph.Research of these authors was supported in part by a PREA from Ontario, Canada and research grants from NSERC.Mathematics Subject Classification (2000): 0C10, 90C22, 90C27, 47D20