New Aspects of Subfitness in Frames and Spaces

This paper contains some new facts about subfitness and weak subfitness. In the case of spaces, subfitness is compared with the axiom of symmetry, and certain seeming discrepancies are explained. Further, Isbell’s spatiality theorem in fact concerns a stronger form of spatiality (T ₁-spatiality) which is compared with the T _D -spatiality. Then, a frame is shown to be subfit iff it contains no non-trivial replete sublocale, and the relation of repleteness and subfitness is also discussed in spaces. Another necessary and sufficient condition for subfitness presented is the validity of the meet formula for the Heyting operation, which was so far known only under much stronger conditions.     

Toward a Rational Design of Highly Folded Peptide Cation Conformations. 3D Gas-Phase Ion Structures and Ion Mobility Characterization

Heptapeptide ions containing combinations of polar Lys, Arg, and Asp residues with non-polar Leu, Pro, Ala, and Gly residues were designed to study polar effects on gas-phase ion conformations. Doubly and triply charged ions were studied by ion mobility mass spectrometry and electron structure theory using correlated ab initio and density functional theory methods and found to exhibit tightly folded 3D structures in the gas phase. Manipulation of the basic residue positions in LKGPADR, LRGPADK, KLGPADR, and RLGPADK resulted in only minor changes in the ion collision cross sections in helium. Replacement of the Pro residue with Leu resulted in only marginally larger collision cross sections for the doubly and triply charged ions. Disruption of zwitterionic interactions in doubly charged ions was performed by converting the C-terminal and Asp carboxyl groups to methyl esters. This resulted in very minor changes in the collision cross sections of doubly charged ions and even slightly diminished collision cross sections in most triply charged ions. The experimental collision cross sections were related to those calculated for structures of lowest free energy ion conformers that were obtained by extensive search of the conformational space and fully optimized by density functional theory calculations. The predominant factors that affected ion structures and collision cross sections were due to attractive hydrogen bonding interactions and internal solvation of the charged groups that overcompensated their Coulomb repulsion. Structure features typically assigned to the Pro residue and zwitterionic COO-charged group interactions were only secondary in affecting the structures and collision cross sections of these gas-phase peptide ions.

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The Dedekind MacNeille site completion of a meet semilattice

The cuts of the classical Dedekind-MacNeille completion DM(S) of a meet semilattice S give rise to a natural cut coverage in the down-set frame \({\mathcal{D}S}\): down-set D covers element s if s lies below all upper bounds of D. This, in turn, leads to what we call the Dedekind-MacNeille frame extension DMF(S). The meet semilattices S for which DM(S) = DMF(S), which we refer to as proHeyting semilattices, can be specified by a simple formula, and we provide a number of equivalent characterizations. A sample result is that DM(S) = DMF(S) iff DM(S) is a Heyting algebra iff DM(S) coincides with the Bruns-Lakser injective envelope.     

Colored graphs without colorful cycles

A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a colored graph lacks colorful cycles iff it is Gallai, i.e., lacks colorful triangles. We then show that, under the operation mon ≡ m + n − 2, the omitted lengths of colorful cycles in a colored graph form a monoid isomorphic to a submonoid of the natural numbers which contains all integers past some point. We prove that several but not all such monoids are realized. We then characterize exact Gallai graphs, i.e., graphs in which every triangle has edges of exactly two colors. We show that these are precisely the graphs which can be iteratively built up from three simple colored graphs, having 2, 4, and 5 vertices, respectively. We then characterize in two different ways the monochromes, i.e., the connected components of maximal monochromatic subgraphs, of exact Gallai graphs. The first characterization is in terms of their reduced form, a notion which hinges on the important idea of a full homomorphism. The second characterization is by means of a homomorphism duality. The first author would like to express his thanks for support by project LN 00A056 of the Ministry of Education of the Czech Republic. The second author would like to express his thanks for support by project LN 00A056 of the Ministry of Education of the Czech Republic, by the NSERC of Canada and by the Gudder Trust of the University of Denver.     

Characterisation of methacrylate monoliths for bacteriophage purification

Binding of three different bacteriophages (phages), namely T7, lambda and M13 on methacrylate monoliths was investigated. Phage M13 exhibited the highest dynamic binding capacity of 4.5×10(13) pfu/mL while T7 and lambda showed capacity of 1×10(13) pfu/mL, all corresponding to values of around 1mg/mL. Interestingly, capacity for lambda phage was increased 5-fold by increasing NaCl concentration in a loaded sample from 0 to 0.2M while there was a constant capacity decrease for T7 and M13 phages. Under optimal conditions, recovery for all three phages approached 100%. Measurement of a pressure drop increase during loading enabled estimation of adsorbed phage layer thickness. At a maximal capacity it was calculated to be around 50 nm for T7 phage and 60 nm for lambda phage matching closely capside size thus indicating monolayer adsorption while 80 nm layer thickness was estimated for M13 phage showing its orientation along the pore.     

A stereospecific pathway for the introduction of deuterium on the brassinosteroid skeleton by reductive dechlorination of chlorocarbonates

A new and efficient procedure for the preparation of brassinosteroids labeled with hydrogen isotopes was developed. A four-step reaction sequence started with the selective oxidation of a 2,3-diol group to an α-hydroxy ketone, which was converted stereospecifically into a chlorocarbonate by reaction with triphosgene. A subsequent Pd-catalyzed reductive dechlorination with deuterium gas yielded deuterium-labeled brassinosteroid 2,3-carbonates. The reaction sequence was completed by base-catalyzed hydrolysis of the cyclic carbonate.     

Monomeric organoantimony(III) sulphide and selenide with terminal Sb-E bond (E = S, Se). Synthesis, structure and theoretical consideration

NCN chelated monomeric chalcogenides, LSbE (E = S (1), Se (2), L = 2,6-bis[N-(2',6'-dimethylphenyl)ketimino]phenyl), were synthesized and characterized with the help of elemental analysis, NMR spectroscopy and single-crystal X-ray diffraction analyses. The terminal Sb-E (E = S, Se) bonds in 1 and 2 were subjected to theoretical investigation and the results are compared with the hypothetical molecules, PhSb=E (E = S, Se, Te), and earlier reported analogues.     

Reproducible discrimination between gram-positive and gram-negative bacteria using surface enhanced Raman spectroscopy with infrared excitation

The on time diagnostics of bacterial diseases is one of the essential steps in the foregoing treatment of such pathogens. Here we sought to present an easy to use and robust method for the discrimination between Gram-positive (Enterococcus faecalis and Streptococcus pyogenes) and Gram-negative (Acinetobacter baumannii and Klebsiella pneumoniae) bacterial genera based on surface enhanced Raman scattering (SERS) spectroscopy. The robustness of our approach lies in the novel method for the production of the SER substrate based on silver nanoparticles and their subsequent re-crystallization in solutions containing high concentrations of chloride ions. The method presented here could be an interesting alternative both to commonly used histochemical approaches and commercial SERS substrates.