Formulae for the number of branch points of one-dimensional orbifolds defined over a non-archimedean local field and uniformisable by discrete projective linear groups are given. They depend only on the uniformising group. The method of equivariant pasting reveals the possible relative position of the branch points.

The problem of testing equality of several binomial proportions to a speci)ed standard is considered. An exact method of testing based on the test statistic considered in Kulkarni and Shah (Statist. Probab. Lett. 25 (1995) 213) is proposed. Exact properties of the exact method and the approximate method due to Kulkarni and Shah are evaluated numerically for the two-sample case. Numerical studie...

Using a calibration method we prove that, if Γ ⊂ Ω is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function uβ which solves { ∆uβ = β(uβ − g) in Ω \ Γ ∂νuβ = 0 on ∂Ω ∪ Γ is in turn discontinuous along Γ and it is the unique absolute minimizer of the nonhomogeneous Mumford-Shah functional

Text line segmentation in handwritten documents is an important step in document processing. We present a new text line segmentation method based on the Mumford-Shah model. The algorithm is script independent. In addition, we use morphing to remove overlaps between neighboring text lines and connect broken ones. Experimental results show the validity of our method.

Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert– Mumford–Kempf from geometric invariant theory. We ded...

This work focuses on a parameter-free joint piecewise smooth image denoising and contour detection. Formulated as the minimization of discrete Mumford–Shah functional estimated via theoretically grounded alternating scheme, bottleneck such variational approach lies in need to fine-tune their hyperparameters, while not having access ground truth data. To that aim, Stein-like strategy providing o...