We show that the problem of testing whether a given set of n+k rational vectors in Rn forms a Hilbert basis can be solved in polynomial time if k is fixed.

For an integral polyhedral cone C = pos{a, . . . , a}, a ∈ Z, a subset B(C) ⊂ C ∩ Z is called a minimal Hilbert basis of C iff (i) each element of C∩Z can be written as a non-negative integral combination of elements of B(C) and (ii) B(C) has minimal cardinality with respect to all subsets of C ∩ Z for which (i) holds. We give a tight bound for the so-called height of an element of the basis wh...

Caspian kutum fish (Rutilus frisii) wild broodstocks were caught by gillnet during their upstream migration and subjected to short-time confinement stress and their physiological responses have been examined. Thirty fish (average weight of 1217.6 g) were divided into three experimental groups CO (control), OV (ovaprim) and CO+OV (cortisol+ovaprim) and placed into rearing tanks (10 fish tank-1; ...

For certain subsets S and T of A = { · · · , (0, 2), (0, 1), (0, 0), (1, 0), (2, 0), · · · } and factor spaces C S [X, Y ], C +S,T [X, Y, Z,W ] and C − S,T [X, Y, Z,W ], bitableaux bases are constructed that are indexed by pairs of standard tableaux and sequences in the collections ΥψS and ΥψT . These bases give combinatorial interpretations to the appropriate Hilbert series of these spaces as ...

The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and conjecturally, for all simply connected surfaces).

We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L 2-martingales which have wavelet bases.

This paper proposes a new class of Hilbert pairs of almost symmetric orthogonal wavelet bases. For two wavelet bases to form a Hilbert pair, the corresponding scaling lowpass filters are required to satisfy the half-sample delay condition. In this paper, we design simultaneously two scaling lowpass filters with the arbitrarily specified flat group delay responses at ω = 0, which satisfy the hal...

In this paper it is investigated how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give ba...

We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar to frames in a Hilbert space, we show that for any two approximate Schauder frames for a Banach space, every weaving is an approximate Schauder frame if and only if there is a uniform constant C ≥ 1 such that every weaving is a C-approximate Schauder frame. We also study weaving Schauder bases, where it i...

Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equation...