Related papers: On Generalizations of the Butterfly Theorem
Many practical applications require the analysis of electromagnetic scattering properties of local structures using different sources of illumination. The Optical Theorem (OT) is a useful result in scattering theory, relating the extinction…
In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition…
We state and prove a generalization of the Poincar\'e-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.
This announcement describes a probabilistic approach to cascades which, in addition to providing an entirely probabilistic proof of the Kahane-Peyri\`ere theorem for independent cascades, readily applies to general dependent cascades.…
Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.
This paper develops the theory of a sheaf of normal differential operators to a submanifold Y of a complex manifold X as a generalization of the normal bundle. We show that the global sections of this sheaf play an analogous role for formal…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.
It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.
In this paper, we propose a generalization of a congruence due to Carlitz.
We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.
We prove two generalisations of the Binomial theorem that are also generalisations of the q-binomial theorem. These generalisations arise from the commutation relations satisfied by the components of the co-multiplications of non-simple…