相关论文: The planar Tree Lagrange Inversion Formula

The Proper Forcing Axiom implies all automorphisms of every Calkin algebra associated with an infinite-dimensional complex Hilbert space and the ideal of compact operators are inner. As a means of the proof we introduce the notion of Polish…

A logic of reciprocity between inertial frames in relative uniform motion is investigated. Relativity allows any reference frame to apply Lorentz Transformation while reciprocity would require the relative frame to use Inverse…

We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the Method of Weighted Averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier-Hankel (F-H) integral…

The purpose of this paper is to build an algebraic framework suited to regularise branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the…

We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…

By changing to an orthogonal basis, we give a short proof that the subfactor of the graded algebra of a planar algebra reproduces the planar algebra.

Rational transformations of polynomials are extensively studied in the context of finite fields, especially for the construction of irreducible polynomials. In this paper, we consider the factorization of rational transformations with…

We study whether a Large Language Model can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $…

Let $\mathcal G$ be a separable family of graphs. Then for all positive constants $\epsilon$ and $\Delta$ and for every sufficiently large integer $n$, every sequence $G_1,\dotsc,G_t\in\mathcal G$ of graphs of order $n$ and maximum degree…

An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, $f(T,\phi)$, thus encompassing the cases of $f(T)$ gravity and nonminimally coupled…

We construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases…

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude,…

We investigate the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, in which the connection is not set to zero a priori and compare it with the pure frame theory. We show explicitly that the two formulations…

Let $G$ be a compact Lie group with maximal torus $T$. If $|N_G(T)/T|$ is invertible in the field $k$ then the algebra of cochains $C^*(BG;k)$ is formal as an $A_\infty$ algebra, or equivalently as a DG algebra.

Let us consider an infinite word and $k\geq 1$ an integer. By steps of $k$, we substitute a letter ofthis infinite word by the power of an external letter. The new word obtaining by this process is called $k$ to $k$ substitution of a power…

We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…

This paper is based on the author's talk at the 2012 Workshop on Geometric Methods in Physics held in Bialowieza, Poland. The aim of the talk is to introduce the audience to the Eynard-Orantin topological recursion. The formalism is…

Some time ago we extended our monogenity investigations and calculations of generators of power integral bases to the relative case. Up to now we considered (usually totally real) extensions of complex quartic fields. In the present paper…

A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…