Even factor of bridgeless graphs containing two specified edges

An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let G be a bridgeless simple graph with minimum degree at least 3. Jackson and Yoshimoto (2007) showed that G has an even factor containing two arbitrary prescribed edges. They also proved that G has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges e₁ and e₂ of G, there is an even factor containing e₁ and e₂ in which each component containing neither e₁ nor e₂ has order at least four. In this paper we improve this result and prove that G has an even factor containing e₁ and e₂ such that each component has order at least four.     

Synthesis of Novel 1‐(Benzo[d]thiazol‐2‐yl)‐1H‐pyrrol‐2(5H)‐ones

The titled products comprising of two mutually merged bioactive nucleuses, 2‐aminobenzo[d]thiazole and 2,5‐dihydropyrrole rings, were obtained from the reaction between dialkyl acetylenedicarboxylates and alkyl 2‐(benzo[d]thiazol‐2‐yl)amino‐2‐oxoacetates in the presence of triphenylphosphine at RT.     

Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory

The vibration of elastic thin nanoplates traversed by a moving nanoparticle involving Coulomb friction is investigated using the nonlocal continuum theory of Eringen. The eigen function technique and the Laplace transform method are employed to solve the governing equations of the nanoplate. The explicit expressions of the in-plane and transverse displacements are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight line. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. The effects of small-scale parameters and velocity of the moving nanoparticle on the dynamic response as well as the dynamic amplitude factors (DAFs) of the in-plane and transverse displacements are then explored in some detail. The results indicate that the magnitude of DAF of the transverse displacement of the nanoplate (i.e., DAF_w) increases with the first small-scale effect parameter, irrespective of the values of the second small-scale effect parameter and the velocity of the moving nanoparticle. As the first small-scale effect parameter grows, the maximum values of DAF_w as a function of the moving nanoparticle velocity increase and generally occur in the lower levels of the moving nanoparticle velocity.     

Investigating the interactions of the first 17 amino acid residues of Huntingtin with lipid vesicles using mass spectrometry and molecular dynamics

The first 17 amino acid residues of Huntingtin protein (Nt17 of htt) are thought to play an important role in the protein's function; Nt17 is one of two membrane binding domains in htt. In this study the binding ability of Nt17 peptide with vesicles comprised of two subclasses of phospholipids is studied using electrospray ionization ‐ mass spectrometry (ESI‐MS) and molecular dynamics (MD) simulations. Overall, the peptide is shown to have a greater propensity to interact with vesicles of phosphatidylcholine (PC) rather than phosphatidylethanolamine (PE) lipids. Mass spectra show an increase in lipid‐bound peptide adducts where the ordering of the number of such specie is 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC) > 1‐palmitoyl‐2‐oleoyl‐glycero‐3‐phosphocholine (POPC) > 1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3 phosphoethanolamine (POPE). MD simulations suggest that the compactness of the bilayer plays a role in governing peptide interactions. The peptide shows greater disruption of the DOPC bilayer order at the surface and interacts with the hydrophobic tails of lipid molecules via hydrophobic residues. Conversely, the POPE vesicle remains ordered and lipids display transient interactions with the peptide through the formation of hydrogen bonds with hydrophilic residues. The POPC system displays intermediate behavior with regard to the degree of peptide‐membrane interaction. Finally, the simulations suggest a helix stabilizing effect resulting from the interactions between hydrophobic residues and the lipid tails of the DOPC bilayer.     

Structural paradigms in macropolyhedral boranes

Macropolyhedral borane clusters are concave polyhedra constituting fused convex simple polyhedra. They are formally obtained by condensation of simple polyhedral boranes under elimination of between one and four BH(3) or isoelectronic units. The number of eliminated vertexes from simple polyhedra equals the number of shared vertexes in macropolyhedral boranes. For each of the eight classes with general formulae ranging from B(n)H(n-4) to B(n)H(n+10), more than one structure type is possible, differing in the number of shared vertexes and in the types of the two combined cluster fragments. However, only one type of "potential structures" is represented by experimentally known examples and is found to be favored by theoretical calculations. A sophisticated system exists among the favored macropolyhedral borane structures. For each class of macropolyhedral boranes, the number of skeletal electron pairs is directly related to the general formula, the number of shared vertexes and the type of fused cluster fragments. In order to predict the distribution of vertexes among the fused fragments, we propose the concept of preferred fragments. Preferred fragments are those usually present in the thermodynamically most stable structure of a given class of macropolyhedral boranes and are also frequently observed in the experimentally known structures. This allows us to completely predict the cluster framework of the thermodynamically most stable macropolyhedral borane isomers.