Fast algorithms for computing the diameter of a finite planar set

Three algorithms for computing the diameter of a finite planar set are proposed. Although all three algorithms have (O(n ²) worst-case running time, an expected-complexity analysis shows that, under reasonable probabilistic assumptions, all three algorithms have linear expected running time. Experimental results indicate that two of these algorithms perform very well for some distributions, and are competitive with an existing method. Finally, we exhibit situations where these exact algorithms out-perform a published approximate algorithm.Research of the first author was supported by grant NSERC A 2422. Research of the second author was supported by grants NSERC A 9293, FCAC EQ-1678 and a Killam Senior Research Fellowship awarded by the Canada Council     

Limited width parallel prefix circuits

In this paper, we present lower and upper bounds on the size of limited width, bounded and unbounded fan-out parallel prefix circuits. The lower bounds on the sizes of such circuits are a function of the depth, width, and number of inputs. The size requirement of an N input bounded fan-out parallel prefix circuit having limited width W and extra depth k (the difference between allowed and minimum possible depth) is shown to be (N log₂ W/2 ^k + N) for k log₂ W. This implies that insisting on minimum depth causes the circuit size to be nonlinear, while as little as log₂log₂ W of extra depth can possibly reduce the size to linear. Also, we show that there is a clear difference between the two cases of bounded and unbounded fan-out by proving the size of a limited width, unbounded fan-out parallel prefix circuit lies between a lower bound of ((2 + 2^1–k /3)N) and an upper bound of O((2 + 2^1–k )N).Uniform, systolic constructions of limited width parallel prefix circuits are provided here and shown to be asymptotically optimal. By associating the width of the circuit with the number of processors and the fan-out capabilities of the circuit with the interconnection structure of a multiprocessor, time- and processor-efficient algorithms may be developed.     

Effect of curing conditions and ionic additives on properties of fly ash-lime compacts

In the present work the reaction between fly ash and lime in fly ash-lime compacts under water curing and steam curing conditions was studied thoroughly in relation to the processing conditions. Fly ash from different sources were collected, characterized, mixed with lime in different ratios and compacted. The compacts were cured with water and steam separately. The reduction in the free CaO content in these compacts was measured as a function of curing time and curing process. Role of two ionic additives, FeCl₃ and MgCl₂, on the reaction between fly ash and lime was also investigated by measuring the free CaO content. Kinetics of these reactions was studied by determining the reaction order and rate constants with respect to the free CaO content and it was observed that the curing conditions and additives affected the reaction kinetics significantly.     

Hydroformylation of 1-octene using rhodium–phosphite catalyst in a thermomorphic solvent system

The use of a liquid–liquid biphasic thermomorphic or temperature-dependent multicomponent solvent (TMS) system, in which the catalyst accumulates in one of the liquid phases and the product goes preferably to the other liquid phase, can be an enabling strategy of commercial hydroformylation processes with high selectivity, efficiency and ease of product separation and catalyst recovery. This paper describes the synthesis of n-nonanal, a commercially important fine chemical, by the hydroformylation reaction of 1-octene using a homogeneous catalyst consisting of HRh(PPh₃)₃(CO) and P(OPh)₃ in a TMS-system consisting of propylene carbonate (PC), dodecane and 1,4-dioxane. At a reaction temperature of 363 K, syngas pressure of 1.5 MPa and 0.68 mM concentration of the catalyst, HRh(CO)(PPh₃)₃, the conversion of 1-octene and the yield of total aldehyde were 97% and 95%, respectively. With a reaction time of 2 h and a selectivity of 89.3%, this catalytic system can be considered as highly reactive and selective compared to conventional ones. The resulting total turnover number was 600, while the turnover frequency was 400 h^?1. The effects of increasing the concentration of 1-octene, catalyst loading, partial pressure of CO and H₂ and temperature on the rate of reaction have been studied at 353, 363 and 373 K. The rate was found to be first order with respect to concentrations of the catalyst and 1-octene, and the partial pressure of H₂. The dependence of the reaction rate on the partial pressure of CO showed typical substrate inhibited kinetics. The kinetic behavior differs significantly from the kinetics of conventional systems employing HRh(CO)(PPh₃)₃ in organic solvents. Most notable are the lack of olefin inhibition and the absence of a critical catalyst concentration. A mechanistic rate equation has been proposed and the kinetic parameters evaluated with an average error of 5.5%. The activation energy was found to be 69.8 kJ/mol.     

Comparative sorption equilibrium studies of toxic phenols on flyash and impregnated flyash

In the present study, the sorption of toxic phenols, which include phenol, o-cresol, m-cresol, p-cresol, o-nitrophenol, m-nitrophenol and p-nitrophenol, has been investigated. The influences of various factors, such as particle size, impregnation of flyash (IFA), pH and temperature on the sorption capacity have been studied. Equilibrium modelling has been carried out using Langmuir and Freundlich isotherm equations and constants have been calculated under different conditions. Thermodynamic studies have also been carried out and values of standard free energy (ΔG°), enthalpy (ΔH°) and entropy (ΔS°) calculated.     

Comparative sorption kinetic studies of phenolic compounds on fly ash and impregnated fly ash

The factors affecting the rate processes involved in the removal of phenolic compounds, e.g. initial phenol concentration, particle size, impregnation of fly ash (IFA), pH and temperature have been studied. The removal rate of phenols varied in the order p-nitrophenol m-nitrophenol > o-nitrophenol > p-cresol > phenol > m-cresol > o-cresol. The process followed first order rate kinetics. The sorption data generally fit the Lagergren equation and the intraparticle diffusion rate equation from which adsorption rate constants, diffusion rate constants and diffusion coefficients were determined. Intraparticle diffusion was found to be the rate-limiting step. These kinetic parameters were compared for various phenols under different conditions using fly ash (FA) and impregnated fly ash (IFA).     

On separation efficiency

Rising energy costs have renewed interest in energy efficient separations. Such efficiencies can be defined as the free energy of unmixing divided by the work done on and the heat added to the process. The greatest efficiencies occur when the energy cost far exceeds any capital cost. In this limit, rate processes are not important, and efficiency is governed by thermodynamics. Efficiencies for gas absorption and stripping are then typically around 50%. The efficiencies of liquid–liquid extractions are lower, especially when one solute is wanted at higher concentration. The efficiencies of membrane separations are higher, but these require high pressure, normally obtained mechanically. As a result, membrane efficiencies should be reduced by any Carnot efficiency of generating the mechanical energy. These results, which are consistent with earlier estimates for distillation, have implications for carbon dioxide capture as a route to mitigating global warming. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Enhancement in dielectric and ferroelectric properties of lead free Bi0.5(Na0.5K0.5)0.5TiO3 ceramics by Sb-doping

Lead free piezoelectric Bi_0.5(Na_0.5K_0.5)_0.5TiO₃ (pure and 1 wt.%, 2 wt.%, 4 wt.% Sb-doped) ceramics were synthesized away from its MPB. The crystalline nature of the BNKT ceramic was studied by XRD and SEM. Depolarization temperature (T_d) and transition temperature (T_c) were observed through phase transitions in dielectric studies which were found to increase after Sb-doping, thus increasing its usable temperature range. In the study of relaxation behavior, the activation energy for relaxation was found to be 0.33, 0.43, 0.57 and 0.56 eV for pure and Sb-doped samples, respectively. All samples were found to exhibit normal Curie-Weiss law above their T_c. Doping of Sb was found to restrain the diffused character of the pure sample. In P-E loop, Sb-doping was found to increase the ferroelectric properties.Pure and Sb-doped BNKT ceramics exhibited high values of piezoelectric charge coefficient (d₃₃) as 115, 121, 129 and 100 pC/N, respectively.     

A model for planning the product portfolio and launch timings under resource constraints

Product design is increasingly becoming a critical function in many organisations having significant impact on their performance. It aims at the selection of a near-optimal mix of products and attribute-levels to offer in the target market. The standard product portfolio planning approach has focused on selecting optimum product profiles based on part-worth utility data. However, given that product development happens in multiple stages, combining the product definition decisions with the product development feasibility will provide organisations with a more inclusive and global solution. This paper considers a resource-constrained environment with a multi-stage product development cycle and presents an approach for helping an organisation to select the definitions of products for its product portfolio and the feasible launch timings. The proposed framework will aid product managers and researchers to identify and evaluate alternative product definitions using a Mixed Integer Linear Programming model in order to determine the alternatives which best balance product features and product development.