A simplified method of computing the process of opening of a parachute

We propose a simplified method of determining the integral characteristics of the opening of a parachute which makes it possible to compute the maximal stress on a parachute and the trajectory parameters of the motion of the load in the region of the opening of the parachute, and to determine the size of the portion of the canopy at the time of maximal stress.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 38–41.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

Coverings of topological loops

In this paper, we show that in some cases, no proper covering of a locally compact group topologically generated by left translations of a topological loop can occur as the group topologically generated by left translations of a topological loop. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 22, Algebra and Geometry, 2004.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Contact Interaction of Two Elastic Wedges

We consider the problem of contact of two elastic wedges and assume that only the vertices of the wedges touch before loading. After loading, the edges of both wedges come in contact near their common vertex. We reduce the constructed system of dual integral equations to a Fredholm integral equation of the second kind with difference kernel given on the semiaxis. We analytically solve the Fredholm equation by reducing it to the boundary-value Riemann problem for analytic functions. We obtain an analytic expression for contact stresses.     

Dynamical Characteristics of Traveling Wave Packets of Total Electron Content Disturbances

Using the COPHASE method and the GPS interferometry method for travelling ionospheric disturbances, we analyze in detail the spatio-temporal properties of travelling wave packets (TWP) of total electron content (TEC) disturbances. The analysis is performed on the example of a clearest TWP manifestation observed in California, USA, in October 18, 2001, using the GLOBDET technique, developed at the Institute of Solar-Terrestrial Physics of the Siberian Branch of RAS for global detection and monitoring of natural and technogenic ionospheric disturbances on the basis of TEC variations retrieved from the global network of GPS receivers. In the time domain, TWPs are quasi-periodic TEC oscillations of duration about 1 h, period of 10–20 min, and amplitude exceeding that of the background TEC fluctuations by at least one order of magnitude. The velocity and direction of TWP motion are similar to those of mid-latitude mesoscale travelling ionospheric disturbances, as obtained earlier from the analysis of phase parameters of HF radio signals and the signals of geostationary satellites and discrete space radio sources.     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

Optical background measurement in a potential site for the NEMO KM undersea neutrino telescope

We describe the measurement of the deep sea optical background in some sites south of Capo Passero, Sicily. A continuous flux of about 440 photons cm ^-2 s ^-1 in the wavelength interval 440-550 nm is estimated due to the decays of the ⁴⁰K contained in the sea water. Bioluminescence light bursts are also observed and an example of time evolution is reported. All the measurements were accomplished using a deep sea module also described in this article. Received: 20 April 2002 / Published online: 26 July 2002     

On mechanical characteristics of nanocrystals

The dependence of the elastic moduli of a nanocrystal on its size is investigated theoretically with reference to a two-dimensional single-crystal strip. It is shown that the uncertainty (of a fundamental nature) in the size of a nanocrystal causes the determination of many of its mechanical characteristics to be ambiguous. It is found that the Cauchy-Green relations are modified and the elastic-constant tensor ceases to be symmetric; the size and shape of a nanocrystal render its mechanical properties more anisotropic. For a single-crystal strip, the Poisson ratio decreases and the Young modulus increases with decreasing thickness of the strip; in the case of a very thin crystal film (two atomic layers thick), these elastic moduli can differ from their macroscopic values by a factor of two. The size effects which make the continuum elasticity theory inapplicable to nanocrystals are estimated. The size effects that occur when the molecular dynamics method is applied for modeling macroscopic objects are also discussed.