The relationship between the Jordan forms of the matrix products AB and BA for some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1. We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.

We investigate the bifurcations and basins of attraction in the Bogdanov map, a planar quadratic map which is conjugate to the Hénon area-preserving map in its conservative limit. It undergoes a Hopf bifurcation as dissipation is added, and exhibits the panoply of mode locking, Arnold tongues, and chaos as an invariant circle grows out, finally to be destroyed in the homoclinic tangency of the ...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

Given two finite p-local finite groups and a fusion preserving morphism between their Sylow subgroups, we study the question of extending it to a continuous map between the classifying spaces. The results depend on the construction of the wreath product of p-local finite groups which is also used to study p-local permutation representations.

Recently, Hu and Jia presented an efficient attack on the GGH13 map. They show that the MPKE and WE based on GGH13 with public tools of encoding are not secure. Currently, an open problem is to fix GGH13 with functionality-preserving. By modifying zero-testing parameter and using switching modulus method, we present a new construction of multilinear map from ideal lattices. Our construction mai...

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products {a, b, c} = (abc + cba)/2. These include especially isometries and disjointness preserving operators.

We prove that the stationarity and the ergodicity of a quantum source {ρ[1,m]}m=1 are preserved by any trace-preserving completely positive linear map of the tensor product form E⊗m, where a copy of E acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.

Financial firms make up a substantial fraction of the domestic equity market. A number of studies subsequently used different conceptual and methodological approaches to model equity return of financial services firms. Movement of the stock price as the consequence of the movement of the micro and macroeconomic factors is strongly supported by the literature review. Amman Stock Exchange in Jord...