Charles Micchelli, Yuesheng Xu and Haizhang Zhang* ([email protected]), Ann Arbor, MI 48109. Optimal Learning of Bandlimited Functions from Localized Sampling. Motivated by the celebrated Shannon sampling theorem, we consider the recovery of a bandlimited function from its localized sampling. The intrinsic approximation error is formulated. In the univariate case, we obtain its upper bound and...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

The Pearcey process is a universal point in random matrix theory and depends on parameter [Formula: see text]. Let text] be the variable that counts number of points this fall interval In note, we establish following global rigidity upper bound: where arbitrary. We also obtain similar bound for maximum deviation points, central limit theorem individual fluctuations. proof short combines recent ...

We use an upper bound on Jacobsthal’s function to complete a proof of a known density result. Apart from the bound on Jacobsthal’s function used here, the proof we are completing uses only elementary methods and Dirichlet’s Theorem on the infinitude of primes in arithmetic progressions.

This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and modern equivariant moving frame a framework dubbed involutive frames. As an attestation fruitfulness our framework, we obtain new, constructive intuitive proof Lie-Tresse theorem (Fundamental basis theorem) first general upper bound on minimal number generating differential invariants for Li...

In this paper, we describe some bounds and inequalities relating h-index, g-index, e-index, and generalized impact factor. We derive the bounds and inequalities relating these indexing parameters from their basic definitions and without assuming any continuous model to be followed by any of them. We verify the theorems using citation data for five Price Medalists. We observe that the lower boun...

Convex polytopes are the d-dimensional analogues of 2-dimensional convex polygones and 3-dimensional convex polyhedra. A polytope is a bounded convex set in R d that is the intersection of a finite number of closed halfspaces. The faces of a polytope are its intersections with supporting hyperplanes. The/-dimensional faces are called the i-faces and f i ( P ) denotes the number of i-faces of a ...

Given r > 2, we establish a good upper bound for the number of multivariate polynomials (with as many variables and with as large degree as we wish) with integer coefficients mapping the “cube” with real coordinates from [−r, r] into [−t, t]. This directly translates to a nice statement in logic (more specifically recursion theory) with a corresponding phase transition case of 2 being open. We ...

We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this paper, we revisit a known upper bound obtained by taking the minimum value on a regular grid, and a known lower bound based on Pólya’s representation theorem....