Iteration Method for Solving the Problem of Determining the Coefficient and the Source in the Heat Equation

Differential Equations - We consider an initial–boundary value problem for the heat equation in which the heat conduction coefficient and one of the functions occurring in the source depend...     

To the spectral theory of Krein systems

We consider the Krein systems. For the set of Stummel class coefficients, we establish the criterion in terms of these coefficients for the system to satisfy the Szegö-type estimate on the spectral measure.     

To the problem of energy recuperation in gyrotrons

A relatively high level of the minimal electron energy at the gyrotron output even at very large spread in pitch factor is explained. An estimation of the recuperation efficiency, which can be obtained due to this effect, is given.     

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22     

Charge transfer states in GeO2-doped silicate fiber-optic waveguides and their role in second-harmonic generation

The concentration dependence of the broad-band luminescence arising in GeO₂-doped silicate fiber-optic waveguides is measured and interpreted. The spectra obtained show that electronic excitations of a new type that are absent in pure silicate glass — charge transfer excitons — arise in the doped system. Under the action of light an electron can be transferred both from a Ge center into the host and between Ge centers. Self-organization of these excitations in the field of a light wave (orientational ordering of their dipole moments) results in the appearance of a macroscopic electric field that destroys the initial centrosymmetry of the system and allows second-harmonic generation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 737–740 (25 November 1998)     

Traveling-wave solutions and their application to inverse problems of sorption dynamics

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 67–74, 1994.