Related papers: The Rosenberg-Strong Pairing Function
Peca suggested in a recent paper on the arxiv to consider binary butterfly trees and their Horton-Strahler numbers. The trees are obtained by glueing two binary trees together in a special way; the results are again binary trees but with a…
Pairing correlations play a very important role in atomic nuclei. Although several effective pairing interactions have been used in mean field calculations for nucleons, little is known about effective pairing interactions for hyperons.…
These notes are a written version of my talk given at the CARMA workshop in June 2017, with some additional material. I presented a few concepts that have recently been used in the computation of tree-level scattering amplitudes (mostly…
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions, is strongly bounded.
We present here a more general version of the balanced pair algorithm. This version works in the reducible case and terminates more often than the standard algorithm. We present examples to illustrate this point. Lastly, we discuss the…
The aim of this work is to outline in some detail the use of combinatorial algebra in planar quantum field theory. Particular emphasis is given to the relations between the different types of planar Green's functions. The key object is a…
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…
We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…
In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
Using the functor of Baumslag rationalization of groups we construct a functor on the category of all (non necessarily simply connected) spaces that extends the classical rationalization of simply connected spaces. We study this functor and…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…
A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the BCS approach, directly incorporates corrections due to particle number conservation. The functional is…
Cantor's ternary function is generalized to arbitrary base-change functions in non-integer bases. Some of them share the curious properties of Cantor's function, while others behave quite differently.
We construct a symmetric invertible binary pairing function $F(m,n)$ on the set of positive integers with a property of $F(m,n)=F(n,m)$. Then we provide a complete proof of its symmetry and bijectivity, from which the construction of…
We study the statistics of pairs from the sequence $(n^\alpha)_{n\in\mathbb{N}^*}$, for every parameter $\alpha \in \, ]0,1[$. We prove the convergence of the empirical pair correlation measures towards a measure with an explicit density.…
In his groundbreaking work on pair correlation, Montgomery analyzed the distribution of the differences $\gamma'-\gamma$ between ordinates $\gamma$ of the nontrivial zeros of the Riemann zeta function, assuming the Riemann Hypothesis. In…
Strong functors and monads are ubiquitous in Computer Science. More recently, comonads have demonstrated their use in structuring context-dependent notions of computation. However, the dualisation of ``being strong'' property passed somehow…
Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.