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In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
What are appropriate geometric conditions ensuring that every complete Riemannian 2-cylinder without conjugate points is at?Examples with nonpositive curvature show that one has to assume that the end...
We look at natural foliations on the Painlev´e VI moduli space of regular connections of rank 2 on P1−{t1, t2, t3, t4}. These foliations are fibrations,and are interpreted in terms of the ...
We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.
For simply connected compact exceptional Lie groups G = F4,E6 and E7, we consider two involutions σ, γ and determine the group structure of subgroups G,of G which are the intersection G ∩ G of the ...
Let p and q be two distinct prime numbers, and Xpq/wq be the quotient of the Shimura curve of discriminant pq by the Atkin-Lehner involution wq. We describe a way to verify in wide generality a criter...
1.1. Les classes Xr+1,n(q). — On consid`ere un probl`eme de g´eom´etrie projective com- plexe, auquel nous ont conduits nos travaux r´ecents sur l’alg´ebrisation des tissus de...
Let La(x) be Lebesgue’s singular function with a real parameter a (0 < a < 1, a 6= 1/2). As is well known, La(x) is strictly increasing and has a derivative equal to zero almost everywhere.
Given integers a and m ≥ 2, let Ha(m) be the following set of integral points Ha(m) = {(x, y) : xy ≡ a (mod m), 1 ≤ x, y ≤ m − 1} We improve several previously known upper bounds on va(m), the n...
We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bun...
We study the error in quadrature rules on a compact manifold, XN j=1 !jf (zj) − Z M f(x)dx ≤ cD {zj} V {f} .
This paper defines and investigates a class of meromorphic univalent harmonic functions that are starlike of complex order with respect to conjugate points. The authors obtain convolution and convex c...
We consider the Sturm-Liouville equation on the bounded interval with two singularities in end points. This equation contains one turning point together with discontinuity conditions, moreover the tur...
A modified Mann iteration process for common fixed points of an infinite family of nonexpansive mappings in Banach spaces.

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