In this work first we study the properties of nearsemirings to introduce an α-radical. Then we observe the role of near-semirings in generalized linear sequential machines, and we test the minimality through the radical. Introduction Holcombe used the theory of near-rings to study linear sequential machines of Eilenberg [1, 4]. Though the picture of near-rings in linear sequential machines is a...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anoma...

We provide a geometrical construction of the unique slim dense near hexagon with parameters (s, t, t2) = (2, 5, {1, 2}). Using this construction, we construct the rank 3 symplectic dual polar space DSp(6, 2) which is the unique slim dense near hexagon with parameters (s, t, t2) = (2, 6, 2). Both near hexagons are constructed from two copies of the unique generalized quadrangle with parameters (...