Related papers: A proof of the lonely runner conjecture
We prove the Aharoni Berger Conjecture
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality…
We prove the explicit formula for the probability of a run of r successes in n trials.
In this note we briefly survey and propose some open problems related to isoparametric theory.
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…
Occlusion is a long-standing problem that causes many modern tracking methods to be erroneous. In this paper, we address the occlusion problem by exploiting the current and future possible locations of the target object from its past…
We consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…
The article provides a counterexample to a conjecture by Blocki-Zwonek.
This paper looks into the problem of pedestrian tracking using a monocular, potentially moving, uncalibrated camera. The pedestrians are located in each frame using a standard human detector, which are then tracked in subsequent frames.…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
In this work the results of a bottleneck experiment with pedestrians are presented in the form of total times, fluxes, specific fluxes, and time gaps. A main aim was to find the dependence of these values from the bottleneck width. The…
Multiple Object Tracking (MOT) has gained increasing attention due to its academic and commercial potential. Although different approaches have been proposed to tackle this problem, it still remains challenging due to factors like abrupt…
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We study the obstacle problem associated with the American chooser option. The obstacle is given by the maximum of an American call option and an American put option, which, in turn, can be expressed as the maximum of the solutions to the…
We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.
Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.
Here we prove some conjectures on the monotony of combinatorial sequences from the recent preprint of Zhi--Wei Sun.
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…