Related papers: Cluster Convergence Theorem
One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a…
The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is…
We determine bubble tree convergence for a sequence of harmonic maps, with uniform energy bounds, from a compact Riemann surface into a compact locally CAT(1) space. In particular, we demonstrate energy quantization and the no-neck property…
A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a…
The Coupled-Cluster theory is one of the most successful high precision methods used to solve the stationary Schr\"odinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…
Steiner and Schwarz symmetrizations, and their most important relatives, the Minkowski, Minkowski-Blaschke, fiber, inner rotational, and outer rotational symmetrizations, are investigated. The focus is on the convergence of successive…
The current article considers Mayer cluster integrals of n-dimensional hard particles in the n>1 dimensional flat Euclidean space. Extending results from Wertheim and Rosenfeld, we proof that the graphs are completely reducible into 1- and…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a $C_{2}$ cluster algebra, and we find cluster…
To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their…
We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in…
Some general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
In this work, we investigate a very important but unstressed result in the work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton ( J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have calculated the vacuum energy…
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…
We generalize a theorem of Bellow and Calder\'on concerning the a.e. convergence of the convolution powers $\ds \mu^nf(x)=\sum_{k}\mu^n(k)f(T^k x)$ where $T$ is a measure preserving transformation of a probability space and $\mu$ is a…
This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…
In this paper we consider systems of quantum particles in the $4d$ Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the…