Chaos in duopoly pricing

The dynamics of two competing firms in a market is studied in terms of Cournot's duopoly theory. Assuming iso-elastic demand and constant unit production costs the iterative mapping

for the outputs of the two firms ensues. The two constants are the unit production costs. The fixed point, the Cournot equilibrium, has earlier been assumed to be the only interesting feature of this model. It is, however, shown that the model can produce persistent motion, periodic or chaotic.     

Luminescence of heterogeneous dimers of certain polymethine dyes in dichloroethane

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 5, pp. 881–884, November, 1991.     

Coherent backscattering of light from saturated atoms

We survey recent progress achieved in understanding the impact of inelastic processes on coherent backscattering of light from cold atoms that are saturated by a powerful laser field.     

Colossal magnetoresistance manganites: A new approach

Manganites of the LA_1−x Ca _x MnO₃ family show a variety of new and poorly understood electronic, magnetic and structural effects. Here we outline a new approach recently proposed by us, where we argue that due to strong Jahn-Teller (JT) coupling with phonons the twofold degeneratee _g states at the Mn sites dynamically reorganize themselves into localised, JT polaronsl with exponentially small inter-site hopping, and band-like, nonpolaronic statesb, leading to anew 2-band model for manganites which includes strong Coulomb and Hund’s couplings. We also discuss some results from a dynamical mean-field theory treatment of the model which explains quantitatively a wide variety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physical conditions on the relative energies and occupation of thel andb states. We argue that this microscopic coexistence of the two types of electronic states, and their relative occupation and spatial correlation is the key to manganite physics. Dedicated to Professor C N R Rao on his 70th birthday     

Evaluation of the probability of bankruptcy for a model of insurance company

We study the problem of evaluation of the probability of ruin of an insurance company for infinitely many steps in the case where the company can invest its capital to bank deposits at any time. As a distribution of the amounts of claims to the insurance company, we use the gamma-distribution with the parameters n and α. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 447–457, April, 2007.     

Copolymers of acrylic acid with urea

Composition and rheological characteristics of aqueous solutions of acrylic acid/urea copolymers were studied, including the composition dependences of the equivalent conductivity and viscosity.     

A new mean field SA-SA' critical point in a symmetry breaking field

We consider a S_A-S_A' critical point in the presence of a symmetry-breaking external magnetic (electric) field with a positive magnetic (dielectric) anisotropy or a dislocation layer. Via a renormalization group analysis of the model hamiltonian, we show that the upper critical dimensions below which mean-field theory breaks down is d_c = 2·5. Thus the S_A-S_A' transition in three dimensions becomes mean-field like in the presence of a symmetry-breaking field. We estimate the reduced temperature region where we can expect to see the mean field S_A-S_A' critical point in the presence of a magnetic field or a dislocation layer.