The equivalence principle

For the example of the motion of an accelerated charge it is shown that an inertial frame of reference in which there is a homogeneous static gravitational field with strength g is physically inequivalent to a uniformly accelerated frame of reference moving with acceleration-g with respect to the inertial frame of reference. It follows from this that the equivalence principle does not hold in the usual formulation. The widely held opinion that such a principle is the basis of the general theory of relativity is not entirely correct. Einstein's theory of gravitation is based on an equivalence principle of a deeper content, which takes the form that the metric fieldg of a Riemannian space is declared to be a gravitational field. Such is the natural formulation of the equivalence principle at which Einstein subsequently arrived.Institute of High Energy Physics; Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 1, pp. 121–140, April, 1994.     

Solution of Goursat problem for the Maxwell-Bloch system

A formal method of solving the initial—boundary-value problem in the quadrantx0,t0 for the Maxwell-Bloch system of equations is presented in terms of the inverse scattering problem.Institute of Mathematics, Urals Branch, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 29–37, January, 1994.     

3-Instantons et réseaux de quadriques

Sans résumé     

Divergence in 3-manifold groups

The divergence of the fundamental group of compact irreducible 3-manifolds satisfying Thurston's geometrization conjecture is calculated. For every closed Haken 3-manifold group, the divergence is either linear, quadratic or exponential, where quadratic divergence occurs precisely for graph manifolds and exponential divergence occurs when a geometric piece has hyperbolic geometry. An example is given of a closed 3-manifoldN with a Riemannian metric of nonpositive curvature such that the divergence is quadratic and such that there are two geodesic rays in the universal coverN whose divergence is precisely quadratic, settling in the negative a question of Gromov's.Partially supported by NSF grant DMS-9200433.     

Survey of linear programming for standard and nonstandard Markovian control problems. Part II: Applications

This paper deals with some applications of Markov decision models for which the linear programming method is efficient. These models are replacement models (with the optimal stopping problem as special case), separable models (including the inventory model as special case) and the multi-armed bandit model. In the companion paper Survey of linear programming for standard and nonstandard Markovian control problems. Part I: Theory, general linear programming methods are discussed. These linear programming formulations are the starting point for the efficient methods that will be derived for the special models.     

On a triangulation consistent with covering

If to every point x of a convex polyhedron M Eⁿ there corresponds an open ball with center at x and radius f(x), where f is any positive function, then M can be split into simplexes so that every simplex is covered by those balls whose centers lie at the vertices of the simplexes.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 110–114, 1992.     

Magnetic field value in the weak energy release region of the solar corona

Spectrographic data from observations of the polarized weak steplike (with relatively sharp growth t 3 sec and slow decay t 10² sec) solar continuum radioemission are analyzed below. The main results are found using a sweeping spectrograph in the 8–12 GHz frequency range (sweep rate 1 sample per second and frequency resolution 120 MHz) and using the RT-22 radio telescope at the Crimean Astrophysical Observatory (angular resolution 4–6). In a series of events at the leading edge of the continuum a narrow-band frequency drifting emission termed blip-type is found. The degree of continuum circular polarization (p<10%) is low compared to that of the narrow-band component (p20%). Both components of the aforementioned events should be radiating on the second harmonic of the local plasma frequency in the context of a plasma generating mechanism. Based on the model proposed and using the observed degree of circular polarization of each component, we can estimate the strength of the magnetic field within the area of the source and the width of the angular spectrum from the radiating plasma turbulence. The results of analysis of the real microwave events are given below.Radiophysical Research Institute, Nizhnii Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 7, pp. 874–882, July, 1994.