On the poisson output of queueing systems with dependent service times

In this paper a method is stated to conclude that the output of given queueing system is POISSON from the steady-state probabilities and from the behavior of the queueing system at jump epochs, i.e. at epochs when the system state can be changed. The corresponding statement for queueing systems described by Markov processes with denumber-able state space will be generalized to systems which can have arbitrary service time distributions if the steady-state probabilities are insensitive with respect to these distributions.     

Structures and Spectral Characteristics of Silylborane,Silylaluminum Hydride,Silylphosphine, and Silyl Mercaptan

The vibrational frequencies of several silanes H₃SiX (X=BH₂, AlH₂, PH₂ and SH) are determined. The infrared and Raman spectra are plotted. Several scale procedures were use to improve the theoretical spectra. The geometric parameters in the planar, staggered and eclipsed structures of these species are fully optimized and compared with ab initio calculations. Basis set effects on the calculated structures are discussed. A few thermodynamic parameters, net atomic charges, dipole moment and energy are also computed.     

A Curtin–Hammett pentamethylene chain symmetrization process in the Bergman cyclization of an 11‐membered ring enediyne

Pentamethylene chain conformational effects for the Bergman cyclization of the 11‐membered ring enediyne, (3Z)‐3‐cycloundecene‐1,5‐diyne, 2, are examined theoretically with unrestricted Becke, three‐parameter, Lee–Yang–Parr/6‐31 G(d,p) calculations. A C₁ symmetric enediyne conformation was found to be the global minimum, where its nonsymmetric pentamethylene chain prevented π‐orbital alignment of the acetylene groups for C–C σ bond product formation. The Bergman cyclization of 2 was found to be conformationally dependent. In a Curtin–Hammett type process, the C₁ symmetric 2 inverts to one of the C_S or C₂ symmetric conformers required for the Bergman cyclization, which produced a C_S or C₂ symmetric 1,4‐diradical intermediate. The activation energy for the cyclization is slightly higher to reach the C₂ symmetry diradical compared with the C_S symmetry diradical. Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis,spectral, DFT calculations and antibacterial studies of Fe(III) complexes of new fluorescent Schiff bases derived from imidazo[4',5':3,4]benzo[1,2‐c]isoxazole

New fluorescent heterocyclic ligands were synthesized by the reaction of 8‐(4‐chlorophenyl)‐3‐alkyl‐3H‐imidazo[4',5':3,4]benzo [1,2‐c]isoxazol‐5‐amine with p‐hydroxybenzaldehyde and p‐chlorobenzaldehyde in good yields. The coordination ability of the ligands with Fe³⁺ ion was examined in an aqueous metanolic solution. Schiff base ligands and their metal complexes were characterized by elemental analyses, IR, UV–vis, mass, and NMR spectra. The optical properties of the compounds were investigated and the results showed that the fluorescence of all compounds is intense and their obtained emission quantum yields are around 0.15 – 0.53. Optimized geometries and assignment of the IR bands and NMR chemical shifts of the new complexes were also computed by using density functional theory (DFT) methods. The DFT‐calculated vibrational wavenumbers and NMR chemical shifts are in good agreement with the experimental values, confirming suitability of the optimized geometries for Fe(III) complexes. Also, the 3D‐distribution map for HOMO and LUMO of the compounds were obtained. The new compounds showed potent antibacterial activity and their antibacterial activity (MIC) against Gram‐positive and Gram‐negative bacterial species were also determined. Results of antibacterial test revealed that coordination of ligands to Fe(III) leads to improvement in the antibacterial activity.     

Cyclic welding behavior of covalent adaptable network polymers

Surface welding effect of covalent adaptable network (CAN) polymers enables self‐healing, reprocessing and recycling of thermosets, but little is known about their welding behaviors during repeated welding‐peeling cycles. In this article, we study the cyclic welding effect of an epoxy based thermal‐sensitive CAN. Surface roughness is generated by rubbing the sample on sandpapers with different grid sizes. The welding‐peeling cycles are repeated on the same pair of samples for five times, with roughness amplitude and interfacial fracture energy measured in each cycle. It is shown that the roughness gradually decreases during the repeated welding cycles, especially when a long welding time or high welding pressure is applied. Even though lower roughness amplitude promotes the contact area, the interfacial fracture energy reduces due to the increased BER activation energy after long‐time heating. A multiscale constitutive model is adopted, where we incorporate an explicit expression of interfacial contact area as a function of root‐mean‐square roughness parameter. The model is able to capture the evolving interfacial fracture energy during repeated welding cycles by using the measured roughness parameter, network modulus and BER activation energy. The study provides theoretical basis for the design and applications of CANs involving cyclic welding‐peeling operations. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 402–413.     

Effective permittivity of liquid crystal nanodispersions and composites with different pore structure

The volume filling fraction dependence of the effective permittivity of the nematic liquid crystal 4-n-pentyl-4’-cyanobiphenyl embedded in different porous membranes and dispersed with aerosil nanoparticles was determined using broadband dielectric spectroscopy in the frequency range from 10⁶ to 10⁹ Hz. The experimental data were analyzed and compared with some existing theories based on the effective medium approximation and their modifications. The obtained effective permittivities as a function of the volume filling fraction lie between the lower limits of the Wiener and Hashin–Shtrikman bounds. The observed shift of the experimental points reflects the changes in the structure of the investigated composites.     

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆(picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃](C₃H₅N₂)₃ ⋅ 3H₂O series (Ln=Ce–Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.     

Pressure controllable phase transition in MoTe2 by the interlayer band occupancy

High pressure can effectively control the phase transition of MoTe₂ in experiment, but the mechanism is still unclear. In this work, we show by first-principles calculations that the phase transition is suppressed and $1T^{\prime }$ phase becomes more stable under high pressure, which originates from the pressure-induced change of the interlayer band occupancies near the Fermi energy. Specifically, the interlayer states of $1T^{\prime }$ phase tend to be fully occupied under high pressure, while they keep partially occupied for the $T_d$ phase. The increase of the band occupancies makes the $1T^{\prime }$ phase more favorable in energy and prevents the structure changing from $1T^{\prime }$ to $T_d$ phase. Moreover, we also analyze the superconductivity under high pressure based on BCS theory by calculating the density of states and phonon spectra. Our results may shed some light on understanding the relationship between the interlayer band occupancy and crystal stability of MoTe₂ under high pressures.     

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.