Signed degree sets in signed graphs

The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph.     

Additive functions

1<q<2 L:= _n=1 1/q ⁿ=1/q–1. [0,1] _n()=1, A _n:= _i=1 ^n–1 _i(x)/q^i+1/n x _n(x)=0, _n>. , = _{n=1 n}(x)/qⁿ. F: [0,L]R , F(x)= _{n=1 n}(x)a_n, _n=1 ¦a _n¦<. [0,L]. q(1,2), . , q(1, 2), . .     

An alternative method for pucker determination in carbohydrates from residual dipolar couplings: a solution NMR study of the fructofuranosyl ring of sucrose

A simple solution NMR method is presented for pucker determination of five-membered rings using only residual dipolar couplings obtained in a single liquid crystalline medium, DMPC/DHPC bicelles (DMPC = dimyristoylphosphatidylcholine; DHPC = dihexanoylphosphatidylcholine). The method was applied to determine the pucker of the fructofuranosyl ring of sucrose. The results indicate a fructofuranosyl pucker phase in the 20 degrees - 70 degrees range. The pucker phases are in agreement with those from previous NMR and optical spectroscopic studies and, importantly, do not rely on empirically parametrized Karplus curves. Furthermore, the analysis implies more than one stable pucker phase and rapid ring interconversion in this range. The present results suggest that using residual dipolar couplings alone can reveal multiple conformations present in solution. Hence, when a sufficient number of residual dipolar coupling constants is measured, the outcome is a robust, reliable, and independent route for determining carbohydrate and nucleic acid structure by NMR spectroscopy.     

Discriminating the helical forms of peptides by NMR and molecular dynamics simulation

The HNCO NMR pulse sequence was applied to three selectively labeled (15)N and (13)C isotopic homologues of the peptide Ac-WAAAH(AAARA)(3)A-NH(2) to probe directly for hydrogen bonds between residues 8 and 11 (characteristic of a 3(10)-helix), 8 and 12 (alpha-helix), and 8 and 13 (pi-helix). The experiments demonstrate conclusively, and in agreement with circular dichroism studies, that the center of the peptide is alpha-helical; there is no discernible 3(10)- or pi-helix at these specific positions. Molecular dynamics simulations of the preceding peptide and Ac-(AAAAK)(3)A-NH(2) in water using the potential energy parameter set CHARMM22/CMAP correctly yield an alpha-helix, in contrast to simulations with the set CHARMM22, which result in a pi-helix.     

Some regularity properties of algorithms and additive functions with respect to them

Summary The paper deals with the behaviour of the so-called algorithms with respect to interval filling sequences A connection is established between the uniquely representable points and the continuity points of the algorithms; also strong continuity properties on monotonic algorithms are proved. Finally the results are applied to additive functions. The theorems extend some former results by the authors, by I. Kátai and by A. Járai.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

The use of acridine orange base (AOB) as molecular probe to characterize nonaqueous AOT reverse micelles

The behavior of acridine orange base (AOB) in nonaqueous reverse micelles composed of n-heptane/AOT/polar solvent has been performed. Ethylene glycol (EG), propylene glycol (PG), glycerol (GY), formamide (FA), dimethylformamide (DMF), and dimethylacetamide (DMA) were employed as water substitutes. The studies were performed by static and time-resolved emission spectroscopy. Thus, the distribution of AOB between the two pseudophases of the aggregates was quantified by measuring the partition constants from emission spectra at different surfactant concentration. Similar values to those obtained by means of absorption spectroscopy were obtained. This match is indicating that AOB is not experiencing partition during the lifetime of the excited state. Partitioning to the micelles is strongly favored in micelles containing hydrogen-bond donor (HBD) solvents rather than non-HBD solvents. Variations of fluorescence lifetimes with AOT concentration confirm these results. By the solvatochromic behavior of AOB in the different systems it is shown that the microenvironment at the interface is distinct from that of the bulk polar solvent, indicating that the probe senses no "free" solvent. The steady state anisotropy (r) was measured for EG/AOT/n-heptane and DMF/AOT/n-heptane systems as representatives for HBD and non-HBD polar solvents, respectively. The value of r is higher in the micelles containing EG than that obtained with DMF, and increases with AOT concentration. This is explained as due to highly structured polar solvents in the inner core. EG is interacting with the polar heads of AOT through hydrogen-bond interaction, while DMF can only interact with the Na+ counterions. This is confirmed by the time-resolved emission spectra (TRES) of the probe in the micellar systems, in comparison with the bulk solvents.     

Stereospecific Synthesis of Steroidal 20,16-γ-Carbolactones

Two strategies have been explored for the synthesis of steroidal 20,16-γ-carbolactones from the corresponding 17-ketoandrostane. A highly efficient, stereospecific protocol has been developed for the β-oriented cis-γ-lactone, based on a Michael addition of cyanide to a conjugated ketone. A different approach, involving prior attachment of a 3-carbon side chain on C-17 of a 17-oxo-16β-acetoxy-androstane led to the epimeric, α-oriented lactone.     

Direct assignment of the absolute configuration of a distinct class of deoxyribonucleoside cyclic N-acylphosphoramidites at phosphorus by M-GOESY nuclear magnetic resonance spectroscopy

The determination of the absolute configuration of deoxyribonucleoside cyclic N-acylphosphoramidites at phosphorus toward the synthesis of P-stereodifined phosphorothioated oligodeoxyribonucleotides is easily accomplished with computer-assisted molecular modeling and M-GOESY NMR spectroscopy. Specifically, computer-modeling diasteromeric phosphoramidite 3 has identifed a proximal (2.55 A) through-space interaction between benzylic H-5 and sugar H-2' ', which can predictably be detected by M-GOESY NMR in SP-3 but not in RP-3 because of being too distant (5.85 A). Consistent with computer-assisted modeling predictions, M-GOESY NMR spectra of SP-3 and RP-3 revealed NOE signals generated from nuclei near the selectively excited H-2' ' that are common to both SP-3 and RP-3, namely those of H-2', H-4', H-3', and H-1'. In addition, a diagnostic NOE signal at 5.5 ppm (benzylic H-5) is, as predicted, only detected in SP-3 and thus provides an unequivocal assessment of the configuration of the diastereomer at phosphorus. M-GOESY NMR data also confirm that the condensation of deoxyribonucleoside cyclic N-acylphosphoramidites with base-activated nucleosidic or nucleotidic 5'-hydroxyls proceeds via a single nucleophilic event.