Hilbert was concerned with fundamental problems of invariant theory: given a linear group, G, acting linearly on the ring of polynomials, S = K[X1, . . . , XN ], we let S be the subring of invariants. Is S nitely generated as an algebra over the eld, K, and if so, what are its generators? Assuming it is nitely generated, that is, that S = K[Y1, . . . , YN ′ ]/I, is it the case that I is nitely ...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

We present here an installation guide, a hand-on mini-tutorial through examples, and the theoretical foundations of the Hilbert++ code.

Space-filling curves, particularly, Hilbert curves, have been extensively used to maintain spatial locality of multi-dimensional data in a wide variety of applications. A window query is an important query operation in spatial (image) databases. Given a Hilbert curve, a window query reports its corresponding orders without the need to decode all the points inside this window into the correspond...