Almost strong properness

Properness without Elementaricity

We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary sub-models of some (H(χ),∈). This leads to forcing notions which are “reasonably” definable. We present two specific properties materializing this intuition: nep (non-elementary properness) and snep (Souslin non-elementary properness) and al...

Properness for Scaled Gauged Maps

We prove properness of moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet [42] and Schmitt [48]. The proof combines a git construction of Schmitt [48], properness for twisted stable maps by Abramovich-Vistoli [1], a variation of a boundedness argument due to Ciocan-Fontanine-Kim-Maulik [13], and a removal of singularities for bundles on surfaces in Colliot-Thél...

Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence

On Almost Everywhere Strong Convergence of Multidimensional Continued Fraction Algorithms

We describe a strategy which allows one to produce computer assisted proofs of almost everywhere strong convergence of Jacobi-Perron type algorithms in arbitrary dimension. Numerical work is carried out in dimension three to illustrate our method. To the best of our knowledge this is the rst result on almost everywhere strong convergence in dimension greater than two.

Almost Everywhere Strong Summability of Two-dimensional Walsh-fourier Series

A BMO-estimation of two-dimensional Walsh-Fourier series is proved from which an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series is derived.