Applications of Operational Research in Marketing

The pricing and selling of industrial products are considered in sections on decision theory, bidding and personal selling. It is suggested that the marketing of consumer durables and semi-durables can be studied by means of models which use aggregate data but that consumer panel data are needed for modelling consumer expendable markets. Finally, some problems which might be suboptimized are indicated.     

Conversion of free radicals upon annealing of x-irradiated single crystal of cholest-4-EN-3-one

Single crystals of the steroid cholest-4-en-3-one were irradiated at 68K and studied at 68 and 300 K using X-band ESR and ENDOR. At 68 K, two A- and B-types of radicals were detected. The A-type radical was identified as the one formed by attachment of an electron to the O₃ oxygen atom. The B-type was probably formed on the aliphatic part of the molecule. Upon heating in the temperatures ranging from 90–100 K both types of radicals undergo a conversion. The radical A converts into neutral one and becomes like a radical formed in single crystal of cholest-4-en-3-one. Explanation of the radical B conversion would need more research. From ESR and ENDOR data collected for three planes of single     

Type,fixed point iteration,and mean value theorems

A function is said to be of ‘type k’ near zero if it behaves roughly like x^k there. This notion is defined precisely, then it is used to obtain modifications of the Newton and Halley iteration schemes. It also gives an idea of the location of the constants c which arise in various mean value theorems.     

Classroom note: The number c in Cauchy's average value theorem

The location of the number c arising from Cauchy's Average Value Theorem is described when the size of the interval is small.     

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with the two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of non-adiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the non-adiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero as the extinction condition is reached. Prospects of further work are also discussed.     

Multiplexed Electrochemical Cancer Diagnostics With Automated Microfluidics

Microfluidic platforms can lead to miniaturisation, increased throughput and reduced reagent consumption, particularly when the processes are automated. Here, a programmable microcontroller is used for automation of a microfluidic platform configured to electrochemically determine the levels of 8 proteins simultaneously in complex liquid samples. The platform system is composed of a programmable Arduino microcontroller that controls inexpensive valve actuators, pump, magnetic stirrer and electronic display. The programmable microcontroller results in repeatable timing for each step in a complex assay protocol, such as sandwich immunoassays. Application of the platform is demonstrated using a multiplexed electrochemical immunoassay based on capture at the electrode surface of magnetic particles labelled with horseradish peroxidase and detection antibody. The multiplexed assay protocol is completed in less than 30 mins and results in detection of eight proteins associated with prostate cancer. The approach presented can be used to automate and simplify high‐throughput screening campaigns, such as detection of multiple biomarkers in patient samples.     

Palladium-catalyzed stereoselective formation of alpha-O-glycosides

A novel method for palladium-catalyzed stereoselective formation of alpha-O-glycosides has been developed. This strategy relies on the palladium-biaryl phosphine catalyst-glycal donor complexation to control the anomeric selectivity. It does not depend on the nature of the protecting groups on the substrates, thus eliminating the need for cumbersome protecting group manipulations.     

Comparison of basis set effects and the performance of ab initio and DFT methods for probing equilibrium fluctuations

The electronic absorption and emission spectra of large molecules reflect the extent and timescale of electron-vibration coupling and therefore the extent and timescale of relaxation/reorganization in response to a perturbation. In this paper, we present a comparison of the calculated absorption and emission spectra of NADH in liver alcohol dehydrogenase (LADH), using quantum mechanical/molecular mechanical methods, in which we vary the QM component. Specifically, we have looked at the influence of basis set (STO-3G, 3-21G*, 6-31G*, CC-pVDZ, and 6-311G**), as well as the influence of applying the DFT TD-B3LYP and ab initio TD-HF and CIS methods to the calculation of absorption/emission spectra and the reorganization energy (Stokes shift). The ab initio TD-HF and CIS methods reproduce the experimentally determined Stokes shift and spectral profiles to a high level of agreement, while the TD-B3LYP method significantly underestimates the Stokes shift, by 45%. We comment on the origin of this problem and suggest that ab initio methods may be naturally more suited to predicting molecular behavior away from equilibrium geometries.     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.