Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.

Gravity-fed drip irrigation design procedure for a single-manifold subunit

Abstract: A simple procedure was developed for the design of low-cost, gravity-fed, drip irrigation single-manifold subunits in hilly areas with laterals to one or both sides of the manifold. The allowable pressure head variation in the manifold and laterals is calculated individually for different pressure zones, and the manifold subunit design is divided into independent processes for laterals and manifold. In the manifold design, a two-stage optimal design method is used. In the first design stage, the pipe cost is minimized and a set of optimal manifold pipe diameters is obtained. In the second design stage, a partial list of available diameters is prepared based on the calculated optimal diameters, and the lengths for available diameters and pressure head of every lateral location along the manifold are calculated. The size of each of the pressure sections is determined according to the pressure head distribution along the manifold. Using the proposed methodology, the minimum manifold pipe cost is obtained, and the target emission uniformity is satisfied for gravity-fed drip irrigation subunits.

A further improvement of the Quantitative Subspace Theorem

Abstract: In 2002, Evertse and Schlickewei [11] obtained a quantitative version of the so-called Absolute Parametric Subspace Theorem. This result deals with a parametrized class of twisted heights. One of the consequences of this result is a quantitative version of the Absolute Subspace Theorem, giving an explicit upper bound for the number of subspaces containing the solutions of the Diophantine inequality under consideration. In the present paper, we further improve Evertse’s and Schlickewei’s quantitative version of the Absolute Parametric Subspace Theorem, and deduce an improved quantitative version of the Absolute Subspace Theorem. We combine ideas from the proof of Evertse and Schlickewei (which is basically a substantial refinement of Schmidt’s proof of his Subspace Theorem from 1972 [22]), with ideas from Faltings’ and Wustholz’ proof of the Subspace Theorem [14]. A new feature is an “interval result,” which gives more precise information on the distribution of the heights of the solutions of the system of inequalities considered in the Subspace Theorem.

Screen conformal half-lightlike submanifolds

Abstract: We study some properties of a half-lightlike submanifold M, of a semi-Riemannian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM) . We prove some results on symmetric induced Ricci tensor and null sectional curvature of this class.

Kinematics for rolling a Lorentzian sphere

Abstract: We derive the equations of motion for the n-dimensional Lorentzian sphere (one-sheet hyperboloid) rolling, without slipping and twisting, over the affine tangent space at a point. Both manifolds are endowed with semi-Riemannian metrics, induced by the Lorentzian metric on the embedding manifold which is the generalized Minkowski space. The kinematic equations turn out to be a nonlinear control system evolving on a connected subgroup of the Poincare group. The controls correspond to the choice of the curves along which the Lorentzian sphere rolls. Controllability of this rolling system will be proved by showing that the corresponding distribution is bracket-generating.

Integrable random matrix ensembles

Abstract: We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner–Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to the integrability of the underlying system. Formulae for spacing distributions and level compressibility are obtained for various instances of such ensembles.