Related papers: Filter convergence and decompositions for vector l…
In analogy with the classical theory of filters, for finitely complete categories, we provide the concepts of filter, G-neighborhood (short for \Grothendieck-neighborhood") and cover-neighborhood of a point, with the aim of studying…
We derive a path counting formula for two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves a problem of finding an explicit…
Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of singular vector pairs. The singular vector tuples of a…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
We extend almost everywhere convergence in Wiener-Wintner ergodic theorem for $\sigma$-finite measure to a generally stronger almost uniform convergence and present a larger, universal, space for which this convergence holds. We then extend…
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
With the help of Van der Corput lemmas, decay estimates are proven for Fourier transforms of mixed homogeneous hypersurface measures with densities that can be quite irregular. The primary results are local in nature, but can be extended to…
Previously, a method has been developed to find the best colour filter for a given camera which results in the new effective camera sensitivities that best meet the Luther condition. That is, the new sensitivities are approximately linearly…
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
The Dedekind-Birkhoff theorem for finite-height modular lattices has previously been generalized to complete modular lattices using the theory of regular coverings. In this paper, we investigate regular coverings in lattices of filters and…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N < 6 or p > 2^N. Let G act rationally on a finitely generated…
In 1950 Maharam asked whether every disintegration of a $\sigma$-finite measure into $\sigma$-finite measures is necessarily uniformly $\sigma$-finite. Over the years under special conditions on the disintegration, the answer was shown to…
We consider the possible gain in the measurement of lensing shear from imaging data in multiple filters. Galaxy shapes may differ significantly across filters, so that the same galaxy offers multiple samples of the shear. On the other…
Consider a measurable space with an atomless finite vector measure. This measure defines a mapping of the $\sigma$-field into an Euclidean space. According to the Lyapunov convexity theorem, the range of this mapping is a convex compactum.…
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…