相关论文: A Short Proof of the Poincar\'e Conjecture

This is a survey on Kawaguchi-Silverman conjecture.

This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.

We provide a proof of the Borwein Conjecture using analytic methods.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

We provide a self-contained proof to so-called Martio's conjecture in the class of mappings of bounded length distortion. Unlike the earlier proofs, our proof is not based on the modulus of continuity estimate of Martio from 1970.

We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.

We give a proof of some small weight and level cases of Serre's conjecture.

Many invariants of finitely generated positive cancelative commutative semigroups can be studied from their Poincar\'e series. We offer and present several closed formulas for them. Moreover, those formulas have elementary proofs and are…

The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…

We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.

We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…

We consider the operation to crush a subset of a manifold to one-point when the result of the crushing also be a manifold. Then the Poincare conjecture is split to two problems; for any closed orientable 3-manifold which is not homeomorphic…

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.