On quantum toroidal algebra of type A1

In this paper we introduce a new quantum algebra which specializes to the 2-toroidal Lie algebra of type $A_1$. We prove that this quantum toroidal algebra has a natural triangular decomposition, a (topological) Hopf algebra structure and a vertex operator realization.     

The Hopf Algebra Structure of Connes and Kreimer in Epstein–Glaser Renormalization

We show how the Hopf algebra structure of renormalization discovered by Kreimer can be found in the Epstein–Glaser framework without using an analogue of the forest formula of Zimmermann.     

A new method for circular grid analysis in the sheet metal forming test

Computer vision systems are employed to determine the major and minor lengths of deformed elliptic grids while determining a sheet metal's workability. The existing method identifies the ellipse using the least squares analysis. It suffers two drawbacks: assumptions in direct conflict with the observed real-world processes and an undesirable property of orientation dependence. For the remedy, this paper presents a new method that, in addition to achieving the desired property of orientation invariance, discards assumptions that conflict with real-world processes. The proposed method is implemented and tested using simulated and real-world data. Results are reported and compared with those obtained by the existing method.     

Topological Fixed Point Theorems Do Not Hold for Random Dynamical Systems

The aim of this paper is to demonstrate that topological fixed point theorems have no canonical generalization to the case of random dynamical systems. This is done by using tools from algebraic ergodic theory. We give a criterion for the existence of invariant probability measures for group valued cocycles. With that, examples of continuous random dynamical systems on a compact interval without random invariant points, which are an appropriate generalization of fixed points, are constructed.     

Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott(HPS) form.These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector.The perturbing matrix is assumed to be purely imaginary(thus maximally T-violating) and to have a strength in energy scale no greater(but perhaps smaller) than the muon mass.As we shall show,it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O((mμ/mτ)2) ≈ 3.5 × 10?3 from their HPS values.Assuming that(mμ/mτ)2 can be neglected,we derive two simple constraints on the four parameters θ12,θ23,θ31,and δ of the mapping matrix.These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix.We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β;any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.