This paper is an attempt is made to obtain Generating functions of modified Bessel Function. We can find number of generating functions for various special function and orthogonal polynomials by the application of group-theoretic method introduced by Louis Weisner.The process may also lead to some new generating functions for corresponding special functions. Bessel Function and orthogonal polyn...

Imposing a total-order on a 2-D discrete random eld induces an orthogonal decomposition of the random eld into two components: A purely-indeterministic eld and a deterministic one. The purely-indeterministic component is shown to have a 2-D whiteinnovations driven moving-average representation. The 2-D deterministic random eld can be perfectly predicted from the eld's \past" with respect to the...

In the upcoming article eight new members of the dynamical systems of class C and F are investigated via numerical integration. Although four configurations of the state matrices are familiar with the chaos generation the others are hypothetic and complete the study. The aim of this paper is to discover and describe different canonical representations for a given set of the differential equatio...

We study the dynamics of a homogeneous, isotropic, and positively curved universe in presence SU(2) gauge field or triplet mutually orthogonal vector fields. In case we use previously known ansatz for gauge-field configuration, but without non-abelian symmetries is more nontrivial develop new ansatz. particular consider axion-SU(2) inflation with fields having U(1)$\times$U(1)$\times$U(1) symme...

In 2011, Aaronson gave a striking proof, based on quantum linear optics, showing that the problem of computing the permanent of a matrix is #P-hard. Aaronson’s proof led naturally to hardness of approximation results for the permanent, and it was arguably simpler than Valiant’s seminal proof of the same fact in 1979. Nevertheless, it did not prove that computing the permanent was #P-hard for an...

The irreducibility of a representation of a real Lie algebra may depend on whether the representation space is a real or complex Hilbert space. The unitary projective representations of the Poincare group on complex Hilbert spaces were studied by Wigner and many others. Although the Poincare group has a real Lie algebra, we do not know of any study of the orthogonal projective representations o...

Motion and form encoding are closely coupled in the visual system. A number of physiological studies have shown that neurons in the striate and extrastriate cortex (e.g., V1 and MT) are selective for motion direction parallel to their preferred orientation, but some neurons also respond to motion orthogonal to their preferred spatial orientation. Recent psychophysical research (Mather, Pavan, B...

A unified electrodynamic approach to the guided wave excitation by external sources in the waveguiding structures with bianisotropic media is developed. Effect of electric, magnetic, and magneto-electric losses in such media manifests itself in the special form of eigenmode orthogonality referred to as the quasi-orthogonality relation. It reflects the existence of the cross-power flow Pkl and l...