Related papers: D\'eformations des courbes rationnelles

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].

An technically interesting proof of a known theorem.

We prove that several versions of the Tietze extension theorem for functions with moduli of uniform continuity are equivalent to WKL_0 over RCA_0. This confirms a conjecture of Giusto and Simpson that was also phrased as a question in…

We obtain some results related to Romanoff's theorem.

We construct an example of a continuous centered random process with light tails of finite-dimensional distribution but with heavy tail of maximum distribution.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

We prove a Thom isomorphism theorem for differential forms in the setting of transverse Lie algebra actions on foliated manifolds and foliated vector bundles.

The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a…

We present a counter example to a theorem given by Amir {\em et al.} J. Math. Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the same reference.

This note presents an interesting counterexample to a basic covering problem.

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.

A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.

In this paper, we give a new proof of an arithmetic analogue of the Riemann-Roch Theorem, due originally to Serge Lang. Lang's result was first proved using the lattice point geometry of Minkowski. By contrast, our proof is completely…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

In this short note we give an interpretation of the Kirchheim-Magnani counterexample to metric differentiability in terms of dilatation structures.

This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…

An algebraic deformation theory of coalgebra morphisms is constructed.

In this short note we present a simple counterexample to a nonlinear version of the Krein-Rutman theorem reported in [Nonlinear Anal. 11 (2007), 3084-3090]. Correct versions of this theorem, and related results for superadditive maps are…

We give a counterexample to a recently conjectured variant of the Penrose inequality.