We prove local integral (entropy) estimates for nonnegative solutions of the fourth order degenerate parabolic equation u t + div(u n ru) = 0 in space dimensions two and three. These estimates enable us to show that solutions have nite speed of propagation if n 2 (1 8 ; 2) and that the support cannot shrink if the growth exponent n is larger than 3=2. In addition, we prove decay estimates for s...

Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by Hassler Whitney [Geometric integration theory, Princeton Univ. Press, Princeton, NJ, 1957] and by geometric measure theorists because we extend the class of integrable domains. Let oi be an «-form defined on Rm . We s...

An improved high-resolution gravimetric geoid model covering the four main islands of Japan (Hokkaido, Honshu, Shikoku, and Kyushu) was developed on a 1 × 1.5 arc-minute grid from EGM2008, GOCO02S/EGM2008, and terrestrial gravity data. A modified form of the Stokes-Helmert scheme was applied for the determination of the geoid using an empirically determined optimal spherical cap size. Handling ...

A (coordinate) gauge of general type is introduced where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour C. For a special class of contours the gauge condition reduces to k µ (x)A µ (x) = 0 where k µ (x) is a tangent vector to the contour C. A simple proof of the nonabelian Stokes theorem is given demonstrating the advantage...

Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven’s formula connecting ellipsoidal and sphero-conal harmonics is generalize...

A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour C. For a special class of contours the gauge condition reduces to k µ (x)A µ (x) = 0 where k µ (x) is a tangent vector to the contour C. It is shown, that this gauge is advantageous to give a simple proof of the nonabelian Stoke...

Abstract The material of the work is an integral element problem determining stress-strain state various types arrays, including forms recess. In current problem, stress determined in plastic zone near ellipsoidal recess for a compressible mass. There no pressure inside recess, and at considerable distance there compression by mutually perpendicular forces. A solution obtained case first approx...

changing altimetry information from satellites on the surface of seas and oceans, into anomaly gravity for example free air anomaly, is a fundamentally new method presented by researches. the determination of the free air gravity anomaly over the earth’s marine regions has led to a major improvement in our understanding of plate tectonic processes relating to oceanic ridges, the formation of ma...