Badly Approximable Matrices and Diophantine Exponents

Doklady Mathematics - This paper is a survey of results concerning different kinds of Diophantine exponents. Special attention is paid to the transference principle and the generalization of the...     

Proof of the Faugère criterion for the F5 algorithm

The validity of the Faugère criterion for the F5 algorithm is established.     

Transference inequalities for multiplicative diophantine exponents

We prove inequalities for multiplicative analogues of Diophantine exponents; these inequalities are similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly approximable and establish some inequalities connecting multiplicative exponents with ordinary ones.     

Investigation of the electrode potential drop at a molybdenum electrode in a flow of argon seeded with potassium

The results of an experimental investigation of the operation of an electrode in argon containing 0.15% of potassium at temperatures from 1400 to 1800 °C and a pressure of 1 atmosphere when the gas and the electrode are in thermal equilibrium are presented. The current-voltage characteristics obtained are compared with the theory of electrode processes developed previously [1, 2]. Good agreement is obtained between the theoretical and experimental data.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 132–136, July–August, 1970.     

Probing four orders of magnitude of the diffusion time in porous silica glass with unconventional NMR techniques

The combined use of two unconventional NMR diffusometry techniques permits measurements of the self-diffusion coefficient of fluids confined in porous media in the time range from 100 microseconds to seconds. The fringe field stimulated echo technique (FFStE) exploits the strong steady gradient in the fringe field of a superconducting magnet. Using a standard 9.4 T (400 MHz) wide-bore magnet, for example, the gradient is 22 T/m at 375 MHz proton resonance and reaches 60 T/m at 200 MHz. Extremely short diffusion times can be probed on this basis. The magnetization grid rotating frame imaging technique (MAGROFI) is based on gradients of the radio frequency (RF) field. The RF gradients not necessarily need be constant since the data are acquired with spatial resolution along the RF gradient direction. MAGROFI is also well suited for unilateral NMR applications where all fields are intrinsically inhomogeneous. The RF gradients reached depend largely on the RF coil diameter and geometry. Using a conic shape, a value of at least 0.3 T/m can be reached which is suitable for long-time diffusion measurements. Both techniques do not require any special hardware and can be implemented on standard high RF power NMR spectrometers. As an application, the influence of the tortuosity increasing with the diffusion time is examined in a saturated porous silica glass.     

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.     

On the ray method for Biot media

This paper is devoted to an investigation of wave propagation in a Biot porous medium, which consists of elastic and fluid phases. The space-time ray expansion of solutions of dynamic equations for a Biot medium is constructed (in the anisotropic inhomogeneous case). In the inhomogeneous isotropic case, a Rytov law analog is derived similarly to elasticity theory. Bibliography: 3 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 112–131.