Related papers: The Marker-Steinhorn Theorem

We prove several extensions of the Erdos-Fuchs theorem.

We survey the classical results on the prime number theorem

We present a new, elementary, dynamical proof of the prime number theorem.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We give a new proof of Chen-Lin result with Li-Zhang method.

We determine the complete list of the gaps between successive elements of the multiplication table of the first N integers.

The note clarifies a gap in the proof of the minimum distance for Projective Reed-Muller Codes. The gap was identified by S.Ghorpade and R.Ludhani in a recent article. Here the original thoughts are explained and the gap closed.

We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…

A vector variational principle is proved.

In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

We illustrate the concept of mathematical proof.

We sketch several proofs of F\'ary--Milnor theorem.

In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…

Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The…

A proof of Sendov's conjecture is given.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

We present in this work a new and simple proof of the false centre theorem.