Even factors with a bounded number of components in iterated line graphs

We consider even factors with a bounded number of components in the n-times iterated line graphs L ⁿ (G). We present a characterization of a simple graph G such that L ⁿ (G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L ⁿ (G) and also show that the minimum number of components of even factors in L ⁿ (G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.     

Difference operators for partitions under the Littlewood decomposition

Let n be a positive integer. Let \(\delta _3(n)\) denote the difference between the number of (positive) divisors of n congruent to 1 modulo 3 and the number of those congruent to 2 modulo 3. In 2004, Farkas proved that the arithmetic convolution sum

$$\begin{aligned} D_3(n):=\sum _{j=1}^{n-1}\delta _3(j)\delta _3(n-j) \end{aligned}$$

satisfies the relation

$$\begin{aligned} 3D_3(n)+\delta _3(n)={\sum _{\mathop {_{d \mid n}}\limits _{3 \not \mid d}}}d. \end{aligned}$$

In this paper, we use a result about binary quadratic forms to prove a general arithmetic convolution identity which contains Farkas’ formula and two other similar known formulas as special cases. From our identity, we deduce a number of analogous new convolution formulas.

     

Transformation of a close-packed Au nanoparticle/polymer monolayer into a large area array of oriented Au nanowires via E-beam promoted uniaxial deformation and room temperature sintering

Transformation of 2D Au nanoparticle (NP) arrays into large scale, ordered, and oriented nanorod/nanowire arrays supported on a transferrable polymer film has been accomplished. E-beam irradiation followed by room temperature aging of a suspended Au NP/polymethylmethacrylate (PMMA) polymer close packed monolayer results in one-dimensional nanoparticle aggregation, reorientation, and sintering into a high density array of oriented Au nanowires with coherent single-crystal-like interfaces. Molecular dynamics simulations of alkane-thiol capped Au NPs, interacting through the Vincent potential and undergoing 2D Poisson compression, account semiquantitatively for the qualitative features of the transformation. This fabrication approach should be extendable to directing 1D aggregation of highly anisotropic nanostructures in arbitrary NP systems.     

Lowest energy electronic transition in aqueous Cl(-) salts: Cl(-) → (H2O)6 charge transfer transition

We use UV resonance Raman spectroscopy to probe the lowest energy allowed electronic transitions of aqueous solutions containing Cl(-) salts. We show that the waters hydrating the Cl(-) are involved in charge transfer transitions that transfer electron density from Cl(-) to the water molecules. These charge transfer transitions cause significant change in the H-O-H bond angle in the excited state, which results in a strong enhancement of the preresonance Raman intensity of the water bending modes. Our work gives the first insight into the lowest allowed electronic transition of hydrated Cl(-).     

A facile process for the asymmetric synthesis of β-trifluoromethylated β-amino ketones via addition of ketone enolates to sulfinylimine

An efficient method for the asymmetric synthesis of β-trifluoromethylated β-amino ketones via addition of ketone-derivative enolates to trifluoromethylated sulfinylimine has been developed, with good chemical yields and excellent diastereoselectivities. This practical method was also proved to be suitable for large-scale preparation.     

Lanthanide radii controlled one-dimensional polymer and dinuclear complexes and their fluorescent properties

A bi-phosphonate ligand tetraethyl-(2,3,5,6-tetramethyl-1,4-phenylene) bis(methylene)diphosphonate has been designed and synthesized. The bi-phosphonate as a bridging ligand reacts with lanthanide nitrates forming four different types of 1D coordination complexes: ribbon polymer (type I), semi-ribbon polymer (type II), zigzag polymer (type III), and dinuclear-triligand short chain (type IV), which changed according to the decrease of the radius of the lanthanide. They have been characterized by IR spectroscopy, elemental analysis, and X-ray diffraction spectroscopy. The photophysical properties of Sm(3+), Eu(3+), Tb(3+) and Dy(3+) complexes at room temperature were also investigated. They exhibit strong fluorescence by excitation of the Ln(3+) ion absorption bands and the quantum yield values of Eu(3+) and Tb(3+) complexes are no less than 20%.     

Knowledge-based scoring functions in drug design: 3. A two-dimensional knowledge-based hydrogen-bonding potential for the prediction of protein-ligand interactions

Hydrogen bonding is a key contributor to the molecular recognition between ligands and their host molecules in biological systems. Here we develop a novel orientation-dependent hydrogen bonding potential based on the geometric characteristics of hydrogen bonds observed in 44,585 protein-ligand complexes. We find a close correspondence between the empirical knowledge and the energy landscape inferred from the distribution of HBs. A scoring function based on the resultant hydrogen-bonding potentials discriminates native protein-ligand structures from incorrectly docked decoys with remarkable predictive power.     

An asymptotics look at the generalized inference

This paper provides an asymptotics look at the generalized inference through showing connections between the generalized inference and two widely used asymptotic methods, the bootstrap and plug-in method. A generalized bootstrap method and a generalized plug-in method are introduced. The generalized bootstrap method can not only be used to prove asymptotic frequentist properties of existing generalized confidence regions through viewing fiducial generalized pivotal quantities as generalized bootstrap variables, but also yield new confidence regions for the situations where the generalized inference is unavailable. Some examples are presented to illustrate the method. In addition, the generalized F-test (Weerahandi, 1995 [26]) can be derived by the generalized plug-in method, then its asymptotic validity is obtained.     

Regioselective synthesis of 5-trifluoromethyl-1,2,3-triazole nucleoside analogues via TBS-directed 1,3-dipolar cycloaddition reaction

Herein described was a straightforward method for the highly regioselective synthesis of 5-trifluoromethyl-1,2,3-triazole nucleoside analogues, which featured the utilization of tert-butyldimethylsilyl (TBDMS) group as the directing group in the 1,3-dipolar cycloaddition reactions. 4-tert-Butyldimethylsilyl-5-trifluoromethyl-1,2,3-triazole nucleoside analogues were generated as the only cycloaddition products in moderate yields (15-79%) via the treatment of glycosyl azides with 3,3,3-trifluoro-1-tert-butyldimethylsilylpropyne 1 in toluene at 85 °C. Removal of TBS groups in these triazole cycloadducts with tetrabutylammonium fluoride (TBAF) smoothly afforded the various 5-trifluoromethyl-1,5-disubstituted 1,2,3-triazole nucleoside analogues in good yields (40-88%).