Related papers: The lonely runner conjecture holds for nine runner…

In this short note, we will show that the metric of Deligne's pairing is continous.

The jump of the Milnor number of an isolated singularity $f_0$ is the minimal non-zero difference between the Milnor numbers of $f_0$ and one of its deformations $(f_s)).$ We prove that for the singularities in the $X_9$ singularity class…

The most common difference that occurs among the consecutive primes less than or equal to $x$ is called a jumping champion. Occasionally there are ties. Therefore there can be more than one jumping champion for a given $x$. In 1999 A.…

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite number of lines; therefore, no formal proof is possible.

Motivated by the random Lorentz gas, we study deterministic walks in random environment and show that (in simple, yet relevant, cases) they can be reduced to a class of random walks in random environment where the jump probability depends…

In the quarter plane, five lattice path models with unit steps have resisted the otherwise general approach of Fayolle, Rachel, and Kurkova. Here we consider these five models, called the singular models, and prove that the generating…

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

We prove that the approximation conjecture of Luck holds for all amenable groups in the complex group algebra case. This result was previously proved by Dodziuk, Linnell, Mathai, Schick and Yates under the assumption that the group is…

The strong law of large numbers asserts that experimentally obtained mean values, in the limit of number of repetitions of the experiment going to infinity, converges almost surely to the theoretical predictions which are based on a priori…

Combinatorial/probabilistic models for cross-country dual-meets are proposed. The first model assumes that all runners are equally likely to finish in any possible order. The second model assumes that each team is selected from a large…

Multi-view approaches to people-tracking have the potential to better handle occlusions than single-view ones in crowded scenes. They often rely on the tracking-by-detection paradigm, which involves detecting people first and then…

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

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

The aim of this paper is to bring a mathematical justification to the optimal way of organizing one's effort when running. It is well known from physiologists that all running exercises of duration less than 3mn are run with a strong…

In this paper, we investigate the effectiveness of the home team bunting in extra innings of Major League Baseball games when the game is tied in the bottom of the inning. Using methods rooted in causal inference, we show that teams choose…

We consider d independent walkers on Z, m of them performing simple symmetric random walk and r = d -- m of them performing recurrent RWRE (Sinai walk), in I independent random environments. We show that the product is recurrent, almost…

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

In this paper, the abc conjecture is negated under certain conditions

Ranked choice voting is vulnerable to monotonicity failure - a voting failure where a candidate is cost an election due to losing voter preference or granted an election due to gaining voter preference. Despite increasing use of ranked…