A leader-follower model and analysis for a two-stage network of oligopolies

This paper is concerned with the existence, uniqueness and computation of leader-follower equilibrium solutions for an industry involved with two major stages of production. We assume that there exists one set of firms performing the first stage of production, which produces a semi-finished product. This semi-finished product is converted to a final good by a second set of firms performing the second stage of production. Furthermore, also competing in the final product market is a third set of firms, which are vertically integrated through the two stages of production and which are assumed to lead the second set of firms by explicitly considering the reaction or response of these latter firms to their own outputs. We model such an industry as a two-stage network of oligopolies, and define equilibrium solutions based on assumed market structures. Our analysis examines the existence and uniqueness of such equilibrium solutions, characterizes the nature of the production strategies of the various firms at an equilibrium, and prescribes algorithms to compute such solutions. This provides the machinery required to perform sensitivity analyses for studying the effects of various mergers or integrations on individual firm profits, and on the industry outputs and prices at equilibrium. The presentation is self-contained, and does not necessarily require any significant prior preparation in economic theory on the part of the reader.This paper is based on work done for the Minerals and Mining Resources Research Institute, under the sponsorship of the Bureau of Mines, Department of the Interior.     

Compatibility and generalised conditional symmetries

It is shown that the determining equations for generalised conditional symmetries (GCSs) of order n, of an evolution equation of arbitrary order, can be found as a consequence of compatibility with an nth-order invariant surface condition. The compatibility technique is demonstrated on a second-order nonlinear diffusion–convection equation with absorption and used to find new GCSs of a linear diffusion equation with nonlinear source.     

Analysis of Selected Macrocyclic Antibiotics by HPTLC with Non-Aqueous Binary Mobile Phases

JPC – Journal of Planar Chromatography – Modern TLC - The retention behavior of selected macrocyclic antibiotics (ery-thromycin, troleandomycin, tylosin, vancomycin, rifamycin B, and...     

Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point

In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R ^k →Y is a C ²-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R ¹ that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ₀)∈X×R ^k and we describe the solution set of the studied equation in a small neighbourhood of this point.     

The type problem for random walks on trees

We consider the question of whether the simple random walk (SRW) on an infinite tree is transient or recurrent. For random-trees (all vertices of distancen from the root of the tree have degreed _n , where {d _n } are independent random variables), we prove that the SRW is a.s. transient if lim inf _n n E(log(d _n-1))>1 and a.s. recurrent if lim sup _n n E(log(d _n-1))<1. For random trees in which the degrees of the vertices are independently 2 or 3, with distribution depending on the distance from the root, a partial classification of type is obtained.Research supported in part by NSF DMS 8710027.     

Influence of Atmospheric Pressure Non-thermal Plasma on Inactivation of Biofilm Cells

The objective of this study is to investigate the bactericidal efficiency of atmospheric pressure non-thermal (cold) dielectric barrier discharge plasma on biofilms of Staphylococcus aureus and Escherichia coli. In general, cold plasma is a mixture of electrons, ions, neutral atoms and molecules. The different particles in cold plasmas exhibit different energies, i.e. electrons are much more energetic than other particles. This feature of cold plasmas allows to produce chemically reactive species at near room temperature that can be used in biological applications. Bacteria inactivation was performed using the air direct plasma (with reactive species, UV light, excited species and electric fields). Discharge power density during the experiment was equal to 70 mW/cm² and plasma dose was regulated by the treatment time. Bacterial biofilms were treated with the non-thermal plasma for 10–300 s. The most effective reduction in the number of S. aureus cells was found after 300 s of treatment and was 2.77 log₁₀ that is 99.83%. When the biofilm of E. coli was used in the experiment, killing of bacteria was independent of the exposure time and the mortality of cells did not exceed 0.48 that is 66.7% kill. The lethal effect on E. coli and S. aureus cells were observed after 300 and 120 s of plasma treatment, respectively but it was necessary to remove the layers of dead cells. The proposed process of removing dead cell layers was carried out due to the probable shielding effect, i.e. dead cells prevent further penetration of active plasma species into the deeper layers of the biofilm. It was shown that the effectiveness of cell destruction by the non-thermal plasma depends on the thickness of biofilm.     

Two Stereoinduction Events in One C−H Activation Step: A Route towards Terphenyl Ligands with Two Atropisomeric Axes

Herein we disclose the synthesis of original chiral scaffolds—ortho‐orientated terphenyls presenting two atropisomeric Ar–Ar axes. These unusual structures were built up by using the C?H activation approach, and remarkably, both chiral axes were controlled with excellent stereoselectivity in a single transformation. During the reaction, not only does atroposelective functionalization of a biaryl precursor occur to establish one stereogenic axis, but an unprecedented atropo‐stereoselective C?H arylation also takes place to generate the second stereogenic element. These enantiomerically pure ortho‐terphenyls show an original tridimensional structure and thus constitute a unique foundation for building up a library of enantiomerically pure bidentate ligands, such as the new ligands S/N‐Biax and diphosphine BiaxPhos.