Quadratic differential equations in -graded algebras

Quadratic differential equations whose associated algebra has an automorphism of order two are studied. Under hypotheses that naturally generalize the cases where the even or odd part of the algebra is one dimensional, the following are examined: structure theory of the associated algebra (ideal structure, simplicity, solvability, and nilpotence), derivations and first integrals, trajectories given by derivations, and Floquet decompositions.

     

XPS and NEXAFS studies of aliphatic and aromatic amine species on functionalized surfaces

The chemical constitution of functionalized supports is an important parameter that determines their performance in a broad range of applications, e.g. for immobilization of biomolecules. Supports with amino functionalized surfaces are also often used for DNA microarray experiments. However, spectral data which have been reported for surfaces with amino functionalities suffer from some inconsistencies. In this article a detailed XPS (X-ray photoelectron spectroscopy) and NEXAFS (Near edge X-ray absorption fine structure) database for amino functionalized surfaces is presented. Amino-terminated surfaces prepared from aliphatic and aromatic aminosilanes or aminothiols and a field sample are considered. Effects of aging in air and damage by radiation are addressed as well.     

Bonding in some covalent derivatives of the 1,2,3,4-thiatriazole-5-thiolate anion. A topological study

The study of pseudohalides has found a deep interest to nonmetal chemists for many years. Due to the similarities between the halides and the pseudohalides, the pseudohalide family of compounds is of fundamental chemical interest. The pseudohalide concept was introduced in 1925 and since its introduction, the pseudohalide principle has been used extensively in nonmetal chemistry to predict the structure and stability of many molecular species.

The so-called ‘azidodithiocarbonate’ anion, more properly referred to as the 1,2,3,4-thiatriazole-5-thiolate anion, CS2N3-, is of particular interest. In a short communication we have recently reported the topological study of some CS2N3-containing species reported by Crawford et al. Previous reports on these compounds showed that in covalent derivatives, not only does the ring remain intact but also the site of attachment of the R group is most likely at the exocyclic sulfur atom in contrast to the previously suggested N-R connectivity. Therefore, the structure and bonding of derivatives of the CS2N3- moiety is clearly an important question.

With that in our mind, we undertook a topological analysis, based on the AIM theory, to gain more insight into the bonding in covalent derivatives of CS2N3- moiety, trying to find an explanation to the origin of the NH and S-H connectivities. The question is: which is the reason that makes all the covalent derivatives prefer the S-R connectivity while the hydracid has an N-H one?     

Synthesis of an aryl 2-deoxy-β-glycosyl tetrasaccharide to probe retaining endo-glycosidase mechanism

The synthesis of the 1,3–1,4-β-glucanase substrate analogue 4-nitrophenyl O-β-d-glucopyranosyl-(1→4)-O-β-d-glucopyranosyl-(1→4)-O-β-d-glucopyranosyl-(1→3)-2-desoxi-β-d-glucopyranoside 2 is reported. Starting from the main tetrasaccharide obtained by enzymatic depolymerization of barley β-glucan, the synthetic scheme involves preparation of the corresponding 3-O-substituted glycal which was converted into a 2-deoxy-α-glycosyl iodide as a glycosyl donor. The key glycosylation step was successfully achieved by nucleophilic substitution of the iodide donor with 4-nitrophenolate with high β-selectivity.     

Double photoexcitation of helium in a strong dc electric field

We report the first experimental measurements of the effect of an applied field on the photoexcitation and autoionization of doubly excited states of helium. Ground-state photoionization spectra have been measured in the region below the He+(N=2) threshold with static electric fields of up to 84.4 kV/cm across the interaction region. The results are compared to the theoretical calculations of Chung et al. [J. Phys. B 34, 165 (2001)]], which are the only calculations available in this regime. Transitions to several states in the N=2, n=6 manifold are assigned, and a wealth of new structure is observed. Our data show that many more series are mixed in by the field than those predicted by theory.     

On regular self-complementary graphs

A regular self-complementary graph is presented which has no complementing permutation consisting solely of cycles of length four. This answers one of Kotzig's questions.     

Low-temperature synthetic method for size-controlled CdSe nanocrystals: utilization of boron selenide

By employing B(2)Se(3) as a selenium source, we demonstrate that at reaction temperatures as low as 60 [degree]C, relatively monodisperse, fluorescent CdSe nanocrystals can be conveniently prepared in various sizes selected from 2 to 13 nm.     

An exact algorithm for side-chain placement in protein design

Computational protein design aims at constructing novel or improved functions on the structure of a given protein backbone and has important applications in the pharmaceutical and biotechnical industry. The underlying combinatorial side-chain placement (SCP) problem consists of choosing a SCP for each residue position such that the resulting overall energy is minimum. The choice of the side-chain then also determines the amino acid for this position. Many algorithms for this NP{\mathcal{NP}}-hard problem have been proposed in the context of homology modeling, which, however, reach their limits when faced with large protein design instances. In this paper, we propose a new exact method for the SCP problem that works well even for large instance sizes as they appear in protein design. Our main contribution is a dedicated branch-and-bound algorithm that combines tight upper and lower bounds resulting from a novel Lagrangian relaxation approach for SCP. Our experimental results show that our method outperforms alternative state-of-the-art exact approaches and makes it possible to optimally solve large protein design instances routinely.