Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations. Leinaas andMyrheim [14] proposed how a fermionic wave function can be represented as a function of unordered configurations, which is desirable as the ordering is artificial and unphysical. In this approach, the wave function is a cross-section of a particular...

In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...

We study the chirally symmetric continuum model (CS-CM) of twisted bilayer graphene. The equation on a flat band could be interpreted as Dirac torus in external non-abelian magnetic field. prove that existence implies wave-function has zero and vice verse. found hidden solution CS-CM pole instead zero. Our main result is basis wave functions Landau level From interpretation we show extra bands

We present a comprehensive analysis of natural modes of a planar metamaterial layer (metalayer) formed by arrayed pairs of metallic dogbone-shaped conductors separated by a thin dielectric layer. The in-plane modes are classified based on the symmetric and anti-symmetric current distributions in the pairs. Of particular interest are the anti-symmetric modes, since the anti-symmetric current is ...

it is well known that the matrix exponential function has practical applications in engineering and applied sciences. in this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $x$-form. for instance, $e^{mathbf{a}t}$, $t^{mathbf{a}}$ and $a^{mathbf{a}t}$ will be evaluated by the new formulas in this par...

For the computation of parameters of elliptic filters, the evaluation of elliptic functions is necessary. For this, one can use numerical methods like Landen’s transformation or Darlington’s algorithm. In this paper, Darlington’s algorithm is extended and connected with Landen’s transformation. All formulae are mainly derived for symmetric and antimetric wave digital filters having either an ev...

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.