Related papers: On Generalizations of the Butterfly Theorem
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all…
We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline structures in Section 8. A transparent proof of Desargues…
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
This is a survey on recent results on the Loewner theory in one and several complex manifolds
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…
Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…
Two theorems on the theory of cluster expansions for an abstract polymer system are reported.
The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its…
In this chapter we briefly review the basics of the theory of stellar evolution.
A generalization of the law of total covariance is presented and proved.
We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the butterfly decomposition we obtain a one-to-one…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
An algebraic deformation theory of dialgebra morphisms is obtained.
We give the converse to Dirichlet's theorem on primes in arithmetic progressions by generalizing an old result of Guinand.
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
We present a generalization of Descartes' theorem for the family of polytopal sphere packings arising from uniform polytopes. The corresponding quadratic equation is expressed in terms of geometric invariants of uniform polytopes which are…
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal,…