A note on simple eigenvalues of matrix polynomials in queueing models with Erlang distributions

In this note, we study anE _k /E _m /1 queueing model where interarrival and service times are Erlang distributions with parametersk andm respectively. We prove that the roots of the characteristic polynomial associated with Erlang distributions are simple if the arrival and service rates are real. Based on this result, a general solution space of vectors for stationary probabilities is easily constructed.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals I. A New Look on the Covalent Bond in H2?

The character of the molecular orbitals can be better accounted for in terms of molecular adapted atomic orbitals and the Fock matrix expanded in these atomic orbital sets. A clean‐cut and unique criterion for the diradicals and the covalent bonds can be given for the molecular orbitals in both restricted and unrestricted Hartree‐Fock wavefunctions. Instead of the picture that overlap charge migrates into the bonding region, the new analysis displays another picture that the charge densities for the electrons with α and β spins give rise to two opposite spin density shifts. If the α one shifts from atom A toward atom B then it is vice versa for the β one. The spin density shifts proceed until the bonding molecular orbitals form.     

Tunneling conductance on surface of topological insulator ferromagnet/insulator/(s- or d-wave) superconductor junction: Effect of magnetically-induced relativistic mass

We investigate the tunneling conductance on the surface of topological insulator ferromagnet (F)/insulator (I)/superconductor (S) junction where superconducting type is either s- or d-wave paring. Topological insulators (TI) are insulating in bulk but conducting on the surface with the Dirac-fermion-like carriers. In contrast to the Dirac fermions in graphene, relativistic mass of the Dirac fermions in TI can be easily caused by applying magnetic field perpendicular to its surface. In this work, we emphatically focus on the effect of the magnetically-induced relativistic mass on the tunneling conductance of a TI-based F/I/S junction. We find that, due to the effect of spinless fermions as carriers in TI, the behavior of the tunneling conductance in a TI-based NIS junction resembles that in a nonmagnetic graphene-based NIS junction. In case of the d-wave paring F/I/S junction, increasing magnetically-induced relativistic mass changes the zero bias conductance dip (peak) to a zero bias conductance peak (dip). This behavior cannot be observed in a graphene-based F/I/S junction.     

Copolymerization of carbon dioxide with cyclohexene oxide catalyzed by bimetallic dysprosium complexes containing hydrazine‐functionalized Schiff‐base derivatives

A series of dinuclear Dy^III acetate complexes containing three different hydrazine‐functionalized Schiff‐base ligands ( hmb , hmi, and hb ) have been synthesized by one‐pot reaction with Dy(OAc)₃·4H₂O as the metal precursor. [Dy₂( hmb )₂(OAc)₄]·MeCN ( 1 ·MeCN) and [Dy₂( hmi )₂(OAc)₂(MeOH)₂]·H₂O ( 2 ·H₂O) with keto and enol forms of the corresponding ligands, respectively, were shown the similar core structures but different ratio of Dy^III to OAc^–. Moreover, the different coordination environments of complex [Dy₂( hb )₂(μ‐OAc)₂(OAc)₂(H₂O)₂]·DMF·H₂O ( 3 ·DMF·H₂O) also offered an opportunity to understand the relationship between structural model and catalytic properties. Bimetallic dysprosium complexes 1 – 3 were demonstrated to be active catalysts for copolymerization of carbon dioxide (CO₂) and cyclohexene oxide (CHO) without cocatalysts. To the best of our knowledge, well‐defined catalyst 2 appears to be the first example of an air‐stable bimetallic dysprosium complex that is effective for CO₂/CHO copolymerization and the formation of the perfectly alternating poly(cyclohexenecarbonate) with a high molecular weight. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 321–328     

Josephson Effect in Graphene： Comparison of Real and Pseudo Vector Potential Barriers

The Josephson currents through real vector potential （RVP） and pseudo vector potential （PVP） barriers in graphene are investigated. In graphene, the pseudo vector potential may be caused by a local strain. The comparison of supercurrents induced by the two type-barriers is focused. As a result, we find that not only will the RVP induce a transition Josephson current from the 0→π state but also causes the difference in the phases of the order parameters of the two superconducting graphene layers to shift from φ→2φ. The critical current is PVP-independent around the neutrality point while it strongly depends on the RVP. The vector potential dependence of critical current is found to be perfectly linear for both PVP and RVP barriers.     

Density functional study of structural and electronic properties of maximum‐spin n+1Aun−1Ag clusters

The structures and relative stabilities of high‐spin ⁿ⁺¹Au_n?1Ag and ⁿAu_n?1Ag⁺ (n = 2–8) clusters have been studied with density functional calculation. We predicted the existence of a number of previously unknown isomers. Our results revealed that all structures of high‐spin neutral or cationic Au_n?1Ag clusters can be understood as a substitution of an Au atom by an Ag atom in the high‐spin neutral or cationic Au_n clusters. The properties of mixed gold–silver clusters are strongly sized and structural dependence. The high‐spin bimetallic clusters tend to be holding three‐dimensional geometry rather than planar form represented in their low‐spin situations. Silver atom prefers to occupy those peripheral positions until to n = 8 for high‐spin clusters, which is different from its position occupied by light atom in the low‐spin situations. Our theoretical calculations indicated that in various high‐spin Au_n?1Ag neutral and cationic species, ⁵Au₃Ag, ³AuAg and ⁵Au₄Ag⁺ hold high stability, which can be explained by valence bond theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Studies of two different types of intramolecular C–H···F–C interactions from polyfluorinated diiodometal(II) diimine complexes

The X‐ray crystal structures of the polyfluorinated complexes [5,5′‐bis(HCF₂CF₂CF₂CF₂CH₂OCH₂)‐2,2′‐bpy]MI₂ ( 55‐8F‐PtI ₂ and 55‐8F‐PdI ₂ where M = Pt and Pd, respectively) were obtained. These two structures are found to show not only two different types of intramolecular, six‐membered cyclic C–H···F–C interactions (F₂C–H···F–C and HC–H···F–C) as important structural features but also alternating fluorinated and non‐fluorinated layers. The F₂C–H···F–C interactions, which are close to the metal core, are much better structurally characterized in this type of complexes with fluorous ponytails at the 5,5′ positions than those previously reported at the 4,4′ positions. The molecular planes of (bpy)MI₂ are extended by self‐matching, using two C–H···I hydrogen bonds and one C–H···F–C blue‐shifting hydrogen bond. The F₂C–H···F–C hydrogen bonds interact at the supramolecular level such that one polyfluorinated ponytail of the title compounds is transoid without an intramolecular C–H···F–C interaction, while the other polyfluorinated ponytail is cisoid with an intramolecular C–H···F–C interaction. Why one ponytail is cisoidal while the other is transoidal will be explained. Furthermore, the second type of C–H···F–C interactions involving the methylene H atom has been identified for the first time. In addition, these two metal structures are studied by density functional theory (DFT).     

Facile Synthesis of Polyaniline‐Polypyrrole Nanofibers for Application in Chemical Deposition of Metal Nanoparticles

Polyaniline‐polypyrrole (PANI‐PPy) nanofibers with high aspect ratios have been synthesized by a one‐step, surfactant‐assisted chemical oxidative polymerization from mixtures of aniline (An) and pyrrole (Py) monomers. PANI‐PPy nanofibers synthesized with an excess of either PANI or PPy show similar spectral (UV‐vis and FT‐IR) characteristics as the individual homopolymers, whereas nanofibers from an equimolar mixture of An and Py display unique spectral characteristics. PANI‐PPy nanofibers undergo a spontaneous redox reaction with metal ions to produce metal nanoparticles with various morphologies and/or sizes. These findings may open new opportunities for synthesizing functional polymer nanofibers and metal nanoparticles with controllable sizes and/or morphologies.