A queueing system with random server capacity and multiple control

The authors study queueing, input and output processes in a queueing system with bulk service and state dependent service delay. The input flow of customers, modulated by a semi-Markov process, is served by a single server that takes batches of a certain fixed size if available or waits until the queue accumulates enough customers for service. In the latter case, the batch taken for service is of random size dependent on the state of the system, while service duration depends both on the state of the system and on the batch size taken. The authors establish a necessary and sufficient condition for equilibrium of the system and obtain the following results: Explicit formulas for steady state distribution of the queueing process, intensity of the input and output processes, and mean values of idle and busy periods. They employ theory of semi-regenerative processes and illustrate the results by a number of examples. In one of them an optimization problem is discussed.     

Photonic crystal waveguides with ultra-low group velocity

We present a novel photonic crystal waveguide, which leads to a large increase in group index while maintaining a simple design. We report group index values up to 850 with large bandwidth. Through a study of the group velocity dispersion, we show that our structure is ideally suited for dispersion compensation applications.     

Stability aspect of magnetized hybrid nanofluid with suction and injection phenomenon: Modified thermal model

Nanoparticles with ultra-high thermal efficiency and stability have dynamic applications in numerous eras of thermal sciences, including energy production, heat transmission devices, cooling and heating systems, manufacturing applications, aircraft, and solar energy, among others. This study's primary objective is to investigate the mathematical modeling using a Tiwari and Das nanofluid model, taking into account the effects of magnetic, suction/injection, and thermal radiation, as well as the stability analysis of a hybrid nanofluid containing copper ($Cu$) and alumina ($A{l}_2{O}_3$) nanoparticles in a water-based liquid. Using similarity transformations, self-similarity solutions of the system of governing ordinary differential equations (ODEs) were obtained, and the resulting ODEs were simulated using implementations of the three-stage Lobatto IIIa technique. The numerical results indicate that the energy characteristics such as thermal conductivity increase rapidly when copper nanomaterials are used. It is also noticed that the combination of both nano-materials results in an excellent energy enhancement. For the solution validation, novel stability performances for the obtained simulations are determined.     

Spectrophotometric determination of tranexamic acid with chloranil

Tranexamic acid is reacted with aqueous alcoholic chloranil, buffered at pH 9, to give a complex with maximum absorption at 346 nm and with an apparent molar absorptivity of 15.7 x 10(3) l.mole(-1).cm(-1). A(max) is linearly related to concentration over the range 2-10 mug ml . When applied to tablets labelled as containing 500 mg each, the mean found was 496 +/- 4 mg. The results were comparable with those of the traditional formol titration method for amino-acids.     

Kinetics and mechanisms of diels-alder addition of tetracyanoethylene to anthracene derivatives—II : Solvent effects

The effect of change of solvent on the rate of Diels-Alder addition of tetracyanoethylene (TCNE) to anthracene has been investigated using solvents CCl₄, CHCl₃ and CH₂Cl₂. Solvent effects were measured on the intermediate complex and on the starting materials from solubility measurements. From this, solvent effects on the transition state alone can be evaluated. These effects were remarkable similar to those measured for both the initial state and the intermediate complex suggesting an “early” transition state having a structure similar to that of the intermediate. From the correlation of ΔG_t^≠ (the free energy of transfer from CCl₄ to another solvent for the transition state alone) with the solubility parameter δ², the molar volume of the transition state can be estimated. The result again suggests that the transition state is more “factor” than product-like.     

Association of metal cations with alkanes: Na(CH4)+ versus Cu(CH4)+ as molecular models

Summary Ab initio molecular orbital calculations give small stabilization energies for the various Na(CH₄)⁺ adducts (less than 4 kcal mol^–1), but predict a stronger binding for the copper compounds (about 13 kcal mol^–1). The different behaviour of Na⁺ and Cu⁺, already present at the SCF level, is reinforced by electron correlation. This can be attributed to an important contribution of the dispersion energy to the binding energy of the copper ion: about 40% of the total, including basis set superposition corrections.Dedicated to Mrs A. Pullman     

Assessment of various kinetic models for the pyrolysis of a microgranular cellulose

The kinetics of pyrolysis of a micro-crystalline cellulose in nitrogen were studied from TGA and DTG data, obtained with two different modes of heating: a dynamic mode at constant heating rates between 1 and 11 °C/min and an isothermal mode at various temperatures, kept constant between 280 and 320 °C. In isothermal mode, it appeared very clearly that the mass depletion shows a sigmoid profile characteristic of an auto-accelerated reaction process. This behaviour is consistent with kinetics of nuclei-growth, well represented by the models of Avrami-Erofeev (A-E) and of Prout-Tompkins (P-T) type. All the other kinetic models commonly applied to the thermal decomposition of solids revealed unsatisfactory. The TGA and DTG data were, thus, found ideally simulated from a reaction scheme consisting in two parallel reactions, termed 1 and 2, each one described by the kinetic law: dx/dt=−A^−E/RTxⁿ(1−0.99x)^m. Reaction 1 is related to the bulk decomposition of cellulose and is characterised by the set of parameters: E₁=202 kJ/mol; n₁=1; m₁=0.48. Reaction 2 is related to the slower residual decomposition, which takes place over approximately 350 °C and affects only 16% by weight of the raw cellulose. With m₂ constrained to 1, the optimised parameters of this reaction were: E₂=255 kJ/mol; n₂=22. Finally, the proposed model allowed to correctly fit not less than to 10 sets of ATG-DTG data, isothermal and dynamic.     

Finding strong defining hyperplanes of Production Possibility Set

Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. Data Envelopment Analysis models implicitly use PPS to evaluate relative efficiency of Decision Making Units (DMUs). Although DEA models can determine the efficiency of a DMU, they cannot present efficient frontiers of PPS. In this paper, we propose a method for finding all Strong Defining Hyperplanes of PPS (SDHP). They are equations that form efficient surfaces. These equations are useful in Sensitivity and Stability Analysis, the status of Returns to Scale of a DMU, incorporating performance information into the efficient frontier analysis and so on.