Optimal pricing and quantity of products with two offerings

This paper analyzes the decision of a firm offering two versions of a product, a deluxe and a regular. While both products satisfy the same market, the deluxe version is sold at a high price relative to its cost and is aimed at the high end of the demand curve. The regular version is sold at a low price relative to its cost and is targeted to customers at the low end of the demand curve. This two-offering strategy is especially popular with book publishers where a paperback book is introduced some time after the hardbound version is introduced. The time between the introduction of the two versions of the product is accompanied by a downward shift in the demand curve due to customers losing interest in the product or satisfying their demand from a secondary used market. We solve a profit maximization model for a firm using a two-offering strategy. The model is solved for linear and exponential deterioration in demand, which is assumed to be deterministic. Also, a model with linear deterioration in demand, which is assumed to be stochastic, is solved. The results indicate that substantial improvements in profit can be obtained by using the two-offering strategy. Numerical sensitivity analysis and examples are used to illustrate the results.     

The Spectrum of a Parametrized Partial Differential Operator Occurring in Hydrodynamics

A partial differential operator associated with natural oscillationsof an incompressible fluid in the neighbourhood of an ellipticalflow is considered. The differentiation is only taken with respectto the angular variable, and thus the operator becomes a familyof ordinary differential operators parametrized by the radialvariable. It is shown that the spectra of these ordinary differentialoperators completely determine the spectrum of the given operatorwhich turns out to have a kind of skeleton structure.     

Local times of fractional Brownian sheets

 Let be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field B ^H defined by

A Third Arc-Sine Theorem

As well as the arc-sine laws for the time spent positive beforetime 1 and the time at which the maximum over [0, 1] occurs,Paul Lévy also established a third arc-sine law for Brownianmotion; this relates to the time of the last visit to zero beforetime 1. For random walks, analogues of the first two of thethese results are well known. Here it is shown that for anyrandom walk satisfying Spitzer's condition there is an analogueof the third, but care has to be taken in its formulation. Anassociated conditional uniform law and some applications tostable processes are also given. 2000 Mathematics Subject Classification60G50.     

Crystal structure and magnetic properties of dinuclear iron(III) complex with ONNO-donor ligand

A new dinuclear Fe(III) complex, [Fe(5-MeOL1)(OH)_0.86(CH₃O)_0.14]₂?2(CH₃OH), [H₂-5-MeOL1 = N,N′-bis(5-methoxy-2-hydroxybenzylidene)-2,2-dimethylpropane-1,3-diamine], 1 has been synthesized and characterized by single crystal structure analysis. The structure of 1 consists of two Fe(III) centers with one tetradentate schiff base ligand (N₂O₂) which are bridged by dihydroxo/dimethoxo groups to yield a Fe₂O₂ core. Complex 1 exhibits weak antiferromagnetic exchange interaction between Fe(III) ions with J = ?0.21 cm^–1.     

A numerical approximation for Volterra’s population growth model with fractional order

This paper presents a numerical scheme for approximate solutions of the fractional Volterra’s model for population growth of a species in a closed system. In fact, the Bessel collocation method is extended by using the time-fractional derivative in the Caputo sense to give solutions for the mentioned model problem. In this extended of the method, a generalization of the Bessel functions of the first kind is used and its matrix form is constructed. And then, the matrix form based on the collocation points is formed for the each term of this model problem. Hence, the method converts the model problem into a system of nonlinear algebraic equations. We give some numerical applications to show efficiency and accuracy of the method. In applications, the reliability of the technique is demonstrated by the error function based on accuracy of the approximate solution.     

Photosensitization of Staphylococcus aureus with malachite green isothiocyanate: inactivation efficiency and spectroscopic analysis

The potential of malachite green isothiocyanate as a photosensitizer for the inactivation of bacteria has been evaluated. Samples of Staphylococcus aureus are treated with the dye and exposed to continuous-wave red light from a filtered xenon lamp. Reduction in cell viability is seen to increase with radiation dose, whilst non-photosensitized samples are largely unaffected with exposure. The mechanism of photosensitization and the subsequent inactivation is addressed. UV-Vis and Fourier-transform infrared absorption spectrometry have been applied to this biological system, revealing the rapid hydrolysis of the isothiocyanate group of the dye and the transition to the colourless carbinol base when in solution. On binding to Staphylococcus aureus via a complexation mechanism, the dye is seen to be stabilized in its cationic form. Involvement of the excited triplet state of the photosensitizer is suggested and identification of reduced dye photoproducts is made following irradiation.