Sentence examples for positive dimensional from inspiring English sources

We denote the edges (resp., faces for ) of by where has positive dimensional Lebesgue measure,,, and,.

The major drawback of these techniques is the exponential explosion of the size of the polynomials needed to represent highly positive dimensional solution sets.

The elimination algorithm combined with an approximate GCD finder appears to be effective in solving polynomial systems for positive dimensional solutions.

For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety.

(1) The condition of being rigidified implies the condition (H^0 (Theta _Y)=0) (else there is a positive dimensional Lie group of biholomorphic self maps), and is obviously implied by the condition of being cohomologically rigidified.

In higher dimensions there are simply connected projective varieties that have a positive dimensional moduli space: already in the case of surfaces, e.g., smooth surfaces in ({mathbb {P}}^3), of degree at least 3, there is an uncountable family of pairwise non isomorphic varieties.

Also, 2-dimensional Riemannian manifolds with positive-dimensional group of isometries were to some extent described in [20], Theorem 5.1], [67].

All Riemann surfaces admitting actions of positive-dimensional groups are well-known (see, e.g., [26], p. 294]), thus we will be interested in the case (Nge 2), although some of the facts stated below apply in the one-dimensional situation as well.

The following non-dimensional parameters are introduced: (26) (27) (28)where is the average value of negative non-dimensional bed stress, is the average value of positive non-dimensional bed stress, is the total average non-dimensional bed stress, is the calculated non-dimensional bed stress at time t, with and corresponding to negative and positive bed stress values, respectively.

And Osgood [6] already gave an example with boundary having positive (2-dimensional) measure.

In papers [19, 24 27] the structure of fractional spaces generated by positive one-dimensional differential and difference operators in Banach spaces was studied.