Related papers: Proof of the orthogonal--Pin duality
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
This is a copy of the article by the same authors published in Duke Math. J. (1994).
A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of…
We offer a mathematical proof of consistency for Peano Arithmetic PA formalizable in PA. This result is compatible with Goedel's Second Incompleteness Theorem since our consistency proof does not rely on the representation of consistency as…
In this article we consider orthonormal systems consisting of tensor products of splines. We show some convergence results of the corresponding orthogonal series including a.e. convergence and unconditional convergence in $L^p$ for…
In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.
We give a new proof of Chen-Lin result with Li-Zhang method.
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.
The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lam\'e and Heine-Stieltjes polynomials.
In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.
We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then…
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
This paper is withdrawn. The current main theorem can be proved by using a simple field theory. The main theorem is to placed by another theorem, shortly.