Related papers: Proof of the orthogonal--Pin duality
In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.
This is a recreational paper showing that certain linked graphs cannot be separated. The proofs employ elementary covering space theory, an appeal to a theorem of Scharlemann (concerning the band sums of two unknots), and a Jones polynomial…
We present, and mathematically describe, a proof-of-principle quantum-optical experiment that seemingly enables superluminal signaling, contrary to the import of the 'no-signaling' theorem.
We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows us to show that there are isomorphisms of chain geometries that arise from antiisomorphisms of the underlying…
We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal…
Green's conjecture is proved for smooth curves C lying on a rational surface S with an anticanonical pencil, under some mild hypotheses on the line bundle L defined by C. Constancy of Clifford dimension, Clifford index and gonality of…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).
Wave-particle duality is one of the most striking and counter-intuitive features of quantum mechanics, illustrating that two incompatible observables cannot be measured simultaneously with arbitrary precision. In this work, we…
This paper has been withdrawn by the author.
We prove several extensions of the Erdos-Fuchs theorem.
We prove that the "minus" version of Lipshitz's double-point enhanced grid homology is a knot invariant through purely combinatorial means.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
We proved that there are infinitely many pairs of twin prime.
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
We give a probabilistic proof of the orbit-counting lemma.
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.