Almost sure comparison of birth and death processes with application to M/M/s queueing systems

Given conditions, which concern the infinitesimal parameters of two birth and death processes, the processes are constructed on the same probability space such that one process is almost surely larger than the other. Application is made to M/M/s queueing systems. Stochastic comparisons of queue length and virtual waiting time in two M/M/s systems are obtained.     

Catalytic activity of CeO2 and Pr2O3 for the liquid-phase benzylation of o-xylene to 3,4 – dimethyldiphenylmethane

The liquid phase benzylation of o-xylene with benzyl chloride over rare earth oxide catalysts like CeO₂ and Pr₂O₃ was studied in a batch reactor at atmospheric pressure and 363 K. Surface area, pore volume, DTA, acid strength distribution on the catalyst surface and optimum temperature of the catalyst are reported.     

Solutions of SPDE’s Associated with a Stochastic Flow

Potential Analysis - We consider the following stochastic partial differential equation, $$\begin{array}{@{}rcl@{}} &&dY_{t} = L^{\ast} Y_{t} dt + A^{\ast} Y_{t} \cdot dB_{t}\\...     

Characterisation of nickel silicide thin films by spectroscopy and microscopy techniques

This article discusses the formation and detailed materials characterisation of nickel silicide thin films. Nickel silicide thin films have been formed by thermally reacting electron beam evaporated thin films of nickel with silicon. The nickel silicide thin films have been analysed using Auger electron spectroscopy (AES) depth profiles, secondary ion mass spectrometry (SIMS), and Rutherford backscattering spectroscopy (RBS). The AES depth profile shows a uniform NiSi film, with a composition of 49-50% nickel and 51-50% silicon. No oxygen contamination either on the surface or at the silicide-silicon interface was observed. The SIMS depth profile confirms the existence of a uniform film, with no traces of oxygen contamination. RBS results indicate a nickel silicide layer of 114 nm, with the simulated spectra in close agreement with the experimental data. Atomic force microscopy and transmission electron microscopy have been used to study the morphology of the nickel silicide thin films. The average grain size and average surface roughness of these films was found to be 30-50 and 0.67 nm, respectively. The film surface has also been studied using Kikuchi patterns obtained by electron backscatter detection.     

Lowest electronic states of neutral and ionic LiN

We have investigated the potential energy curves (PECs) of the LiN heteronuclear diatomic molecule, including its ionic species LiN⁺ and LiN⁻, using explicitly correlated multi-reference configuration interaction (MRCI-F12) calculations in conjunction with the correlation consistent quintuple-𝜁 basis set. The effect of core–valence correlation, scalar relativistic effects, and the size of the basis sets has been investigated. A comprehensive set of spectroscopic constants determined based on the above-mentioned calculations are also reported for the lowest electronic states and all systems, including dissociation energies, harmonic and anharmonic vibrational frequencies, and rotational constants. Additional parameters, such as the dipole moments, equilibrium spin-orbit constants, excitation energies, and rovibrational energy levels, are also documented. We found that the three triplet states of LiN, namely, X ³∑⁻, A ³Π, and 2 ³∑⁻, exhibit substantial potential wells in the PEC diagrams, while the quintet states are repulsive in nature. The ground state of the anion also shows a deep potential well in the vicinity of its equilibrium geometry. In contrast, the ground and excited states of the cation are very loosely bound. Charge transfer properties of each of these states are also analyzed to obtain an in-depth understanding of the interatomic interactions. We found that the core–valence correlation has a substantial effect on the calculated spectroscopic constants.     

Conditions for the existence of decision horizons for discounted problems in a stochastic environment: A note

In this note, we extend the sufficiency conditions obtained by Bean and Smith for the existence of decision and forecast horizons in discounted deterministic problems to a stochastic environment. Also developed are some examples for illustration of the results and the need for the development of necessary and sufficient conditions for undiscounted problems.     

Temperature‐induced self‐assembly and metal‐ion stabilization of histidine functional block copolymers

Histidine functional block copolymers are thermally self‐assembled into polymer micelles with poly‐N‐isopropylacrylamide in the core and the histidine functionality in the corona. The thermally induced self‐assemblies are reversible until treated with Cu²⁺ ions at 50 °C. Upon treatment with 0.5 equivalents of Cu²⁺ relative to the histidine moieties, metal‐ion coordination locks the self‐assemblies. The self‐assembly behavior of histidine functional block copolymers is explored at different values of pH using DLS and ¹H NMR. Metal‐ion coordination locking of the histidine functional micelles is also explored at different pH values, with stable micelles forming at pH 9, observed by DLS and imaged by atomic force microscopy. The thermal self‐assembly of glycine functional block copolymers at pH 5, 7, and 9 is similar to the histidine functional materials; however, the self‐assemblies do not become stable after the addition of Cu²⁺, indicating that the imidazole plays a crucial role in metal‐ion coordination that locks the micelles. The reversibility of the histidine‐copper complex locking mechanism is demonstrated by the addition of acid to protonate the imidazole and destabilize the polymer self‐assemblies. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1964–1973     

A modified approach for the site-selective direct C-6 arylation of benzylated uracil

An efficient methodology is reported for the regioselective C-6 arylation of protected uracil via the palladium catalyzed CH functionalization of 1-(4-methoxybenzyl)-3-methylpyrimidine-2,4(1H,3H)-dione with (hetero)aryl halides and boronic acids. Utilization of the Pd(OAc)₂/Xantphos catalytic system with a stoichiometric amount of CuI and DBU as the base was vital for the success of this protocol. The methodology is facile and compatible with aryl bromides, iodides and boronic acids and hence affords broad substrate scope and diversity.