相关论文: Recent developments of the DDVV Conjecture

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

We present some new results on the cohomology of a large scope of SL\_2-groups in degrees above the virtual cohomological dimension; yielding some partial positive results for the Quillen conjecture in rank one. We combine these results…

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…

In this review, I discuss briefly theoretical scenarios concerning the interpretation of recent results from indirect and direct dark matter searches, with emphasis on the former.

We summarise the main results from a number of our recent articles on the subject of probabilistic temperature forecasting.

We provide new sufficient conditions under which Ryser's conjecture holds.

Some recent developments in the theory of quantum spin systems are reviewed.

More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres.

We present a relative form of the Toponogov comparison theorem.

This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…

We extend a recent breakthrough result relating expectation thresholds and actual thresholds to include some rainbow versions.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

I review the current status of lattice QCD results. I concentrate on new analytical developments and on numerical results relevant to phenomenology.

We develop the theory of versal deformations of dialgebras and describe a method for constructing a miniversal deformation of a dialgebra.

The paper presents a counterexample to the Hodge conjecture.

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.

This is a survey recent works on topological extensions of the Tutte polynomial.

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

In this note we present a collection of attempts of some researchers to prove or disprove whether the Zeraoulia sequences convergent. Even nowdays convergence of Zeraoulia sequences still open.