‎This paper presents some results of an annihilated element in Banach algebra‎, ‎and in specific case‎, ‎for any square matrix‎. The developed method significantly improves the computational aspects of transformations calculus and especially for finding powers and roots of any annihilated element‎. ‎An example is given to compare the proposed method with some other methods to show the efficienc...

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on RN . The Dunkl operators are denoted by Tj for 1 ≤ j ≤ N, and the Laplacian ∆κ = ∑j=1 T2 j . This paper finds the homogeneous harmonic polynomials annihilated by all Tj for j > 2. The structure constants with respect to the Gaussian and sphere inner...

We prove that the smallest cardinality of a maximal packing in any tree is at most the cardinality of an R-annihilated set. As a corollary to this result we point out that a set of parameters of trees involving packing, perfect neighbourhood, R-annihilated, irredundant and dominating sets is totally ordered. The class of trees for which all these parameters are equal is described and we give an...

We point out that the mutual annihilation of an electron-hole pair at a tunnel barrier leads to teleportation of the state of the annihilated electron to a second, distant electron--if the latter was previously entangled with the annihilated hole. We propose an experiment, involving low-frequency noise measurements on a two-dimensional electron gas in a high magnetic field, to detect teleportat...

CNR-ISTM, Istituto di Scienze e Tecnologie Italy. E-mail: [email protected] Center for Materials Crystallography, Aarh Aarhus, Denmark Dipartimento di Chimica, Università degl Milano, Italy † Electronic supplementary information (E methods and on the developed source co spin density reconstruction (ESI_2); 3D orbital densities and of total spin dens (Fig. S1–S3); maps of s(r) and Vs(r) [CASSC...