In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions defining nonlinear connection (N–connection) structures. They geometrically unify and develop the concepts of Riemann–Cartan manifolds and Lagrange–Finsler sp...

Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being discretization Euclidian time. Convergence time-continuum limit is shown various discretized actions. The focus integral representation partition function and expectation values in canonical ensemble. connection to grand-canonical integral, number differences, dis...

We construct tame differential calculi coming from toral actions on a class of $\mathrm{C}^*$-algebras. Relying the existence unique Levi-Civita connection such calculus, we prove version Bianchi identity. A Gauss-Bonnet theorem for canonical calculus rank two is studied.

We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds–style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this “language parameter” is made explicit, it reveals...

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be...

We investigate the special class of formulas made up of arbitrary but finite combinations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such formulas, we describe two essentially distinct families of canonical formula-encodings for integers, respectively deduced from the decimal encoding and the fund...

In [1] a balanced canonical form for continuoustime lossless systems was presented. This form has a tridiagonal dynamical matrix A and the useful property that the corresponding controllability matrix K is upper triangular. In [2], this structure is also derived from a LC ladder. In this paper, a connection is established between Ober’s canonical form and a Schur algorithm built from angular de...

Abstract We give a complete classification of left invariant para-Kähler structures on four-dimensional simply connected Lie groups up to an automorphism. As application we discuss some curvatures properties the canonical connection associated these as flat, Ricci flat and existence solitons.

Stokes’ manifolds, also known as wild character varieties, carry a natural Poisson structure. Our goal is to provide explicit log-canonical coordinates for this structure on the manifolds of polynomial connections rank 2, thus including second Painlevé hierarchy. This construction provides linearization first discovered by Flaschka and Newell then rediscovered generalized Boalch. We show that, ...