the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

in this paper, we investigate duality of modular g-riesz bases and g-riesz basesin hilbert c*-modules. first we give some characterization of g-riesz bases in hilbert c*-modules, by using properties of operator theory. next, we characterize the duals of a giveng-riesz basis in hilbert c*-module. in addition, we obtain sucient and necessary conditionfor a dual of a g-riesz basis to be again a g...

This contribution gives a partial survey over the native spaces associated to (not necessarily radial) basis functions. Starting from reproducing kernel Hilbert spaces and invariance properties, the general construction of native spaces is carried out for both the unconditionally and the conditionally positive definite case. The definitions of the latter are based on finitely supported function...

The problem of model selection is considerably important for acquiring higher levels of generalization capability in supervised learning. In this article, we propose a new criterion for model selection, the subspace information criterion (SIC), which is a generalization of Mallows's C(L). It is assumed that the learning target function belongs to a specified functional Hilbert space and the gen...

It’s well known that the functional Hilbert space H2 over the unit ball Bd ⊂ C , with kernel function K(z, ω) = 1 1−z1ω1−···−zdωd , admits a natural A(Bd)-module structure. We show the rank of a nonzero submodule M ⊂ H2 is infinity if and only if M is of infinite codimension. Together with Arveson’s dilation theory, our result shows that Hilbert modules stand in stark contrast with Hilbert basi...

A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hi...

We generalize Macdonald’s formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to the cohomology of the compactified Jacobian of the curve. The new formula is a consequence of a stronger identity between certain perverse sheaves defined by a family of curves satisfying mild cond...

Reproducing kernel Hilbert spaces and wavelets are both mathematical tools used in system identification and approximation. Reproducing kernel Hilbert spaces are function spaces possessing special characteristics that facilitate the search for solutions to norm minimization problems [3]. As such, they are of interest in a variety of areas including Machine Learning [11]. Wavelets are another mo...

The Hilbert series of the Garsia-Haiman module can be written as a generating function of standard fillings of Ferrers diagrams. It is conjectured by Haglund and Loehr that the Hilbert series of the diagonal harmonics can be written as a generating function of parking functions. In this paper we present a weight-preserving injection from standard fillings to parking functions for certain cases....

This thesis is concerned with Hilbert functions of ideals of finite group orbits, focusing in particular on abelian and metacyclic groups. Conjecture 16 in Section 4 characterizes the Hilbert functions that arise from two-dimensional representations of certain abelian groups, and a proof of the necessity of its conditions is provided. In Section 6, Proposition 18 gives a bound for the Hilbert f...