the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the earth’s surface. downward continuation is a...

We experimentally and theoretically investigate the shapes of contact lines on the surfaces of micrometer-sized polystyrene ellipsoids at the water-air interface. By combining interferometry and optical trapping, we directly observe quadrupolar symmetry of the interface deformations around such particles. We then develop numerical solutions of the partial wetting problem for ellipsoids, and use...

Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function disco...

We study a class of left-invertible operators which we call weakly concave operators. It includes the and some subclasses expansive strict $m$ -isometries with $m > 2$ . prove Wold-type decomposition for also obtain Berger–Shaw-type theorem analytic finitely cyclic The proofs these results rely heavily on spectral dichotomy provides fairly close relationship, written in terms reciprocal auto...

There is a common example in convex geometry and Banach space geometry: the unique ellipsoid with largest volume associated each symmetric body K called John ellipsoid. In this paper, we will give some results of operator problem Gaussian measure, mainly continuity measure existence operator.

For the year of past most three-dimensional objects are represented and mapped with spherical function. Since the mapping preserves important criteria such as geometrical information of a 3D object, the representation of a 3D shape in a suitable way is an important matter for 3D object retrieval. In many circumstances, spherical surface fitting to a 3D shape does not approximate very well, beca...

Methods for simulation from multivariate Gaussian distributions restricted to be from outside an arbitrary ellipsoidal region are often needed in applications. A standard rejection algorithm that draws a sample from a multivariate Gaussian distribution and accepts it if it is outside the ellipsoid is often employed: however, this is computationally inefficient if the probability of that ellipso...

Given a linear isometry A0 : Rn → Rn of finite order on Rn , a general 〈A0〉-invariant closed subset M of Rn is considered with Lipschitz boundary. Under suitable topological restrictions the existence of A0-invariant geodesics of M is proven.

In this paper, we establish some inequalities among the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual. 2000 Mathematics Subject Classification. 52A40, 52A20.