Related papers: A proof of the lonely runner conjecture

In this work we present a "vision" model for blind people, preferentially for those ones of birth origin. The model should be implemented using the available computational resources at the moment. The model uses a simulation of an optical…

For the general obstacle problem, we prove by direct methods an epiperimetric inequality at regular and singular points, thus answering a question of Weiss (Invent. Math., 138 (1999), 23--50). In particular at singular points we introduce a…

A vector variational principle is proved.

This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…

Two variable speed of light models and their physical consequences are investigated.

We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.

In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…

We prove some theorems about self-avoiding walks attached to an impenetrable surface (i.e. positive walks) and subject to a force. Specifically we show the force dependence of the free energy is identical when the force is applied at the…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

Handling object interaction is a fundamental challenge in practical multi-object tracking, even for simple interactive effects such as one object temporarily occluding another. We formalize the problem of occlusion in tracking with two…

A survey of reinforced random walk, with emphasis on the linear case.

The accurate visual tracking of a moving object is a human fundamental skill that allows to reduce the relative slip and instability of the object's image on the retina, thus granting a stable, high-quality vision. In order to optimize…

New cases of the multiplicity conjecture are considered.

We prove some constructive results that on first and maybe even on second glance seem impossible.

The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…

In this paper the circulant Hadamard conjecture is proved.

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

Recurrent Neural Network, Long Short-Term Memory, and Transformer have made great progress in predicting the trajectories of moving objects. Although the trajectory element with the surrounding scene features has been merged to improve…

We provide a short proof of the 1-dimensional flat chain conjecture.

The phenomenon of convection is found in a wide variety of settings on different scales -- from applications in the cooling technology of laptops to heating water on a stove, and from the movement of ocean currents to describing…