Related papers: Chang's Conjectures and Easton collapses

We show that the theorem of the three perpendiculars holds in any n-dimensional space form.

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

In this paper we prove the WALA conjecture.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.

In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers…

We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two…

We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of…

We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.

A famous theorem of Kirkman says that there exists a Steiner triple system of order $n$ if and only if $n\equiv 1,3\mod{6}$. In 1973, Erd\H{o}s conjectured that one can find so-called `sparse' Steiner triple systems. Roughly speaking, the…

A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.

We prove that the Eaton-Moreto conjecture is true for the principal blocks of the p-solvable groups

For $E_{b}: y^{2}=x^{3}+b$, we establish Lang's conjecture on a lower bound for the canonical height of non-torsion points along with upper and lower bounds for the difference between the canonical and logarithmic height. In many cases, our…

The article presents the proof of Casas-Alvero conjecture.

We show that the "double circle" order type and some of its generalizations have a compatible triangulation with any other order types with the same number of points and number of edges on convex hull, thus proving another special case of…

Collatz Conjecture sequences increase and decrease in seemingly random fashion. By identifying and analyzing the forms of numbers, we discover that Collatz sequences are governed by very specific, well-defined rules, which we call cascades.

In this short note we present a family of counterexamples to the King's conjecture.