Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type zeta function together with related integral representations, differential relations, finite sums, series expansions. Also, present relationship between Laguerre polynomials. Our hypergeometric type involves several known functions including Riemann, Hurwitz, Hurwitz-Lerch, Barnes as particul...

The extended norm-trace function field is a generalization of the Hermitian and norm-trace function fields which are of importance in coding theory. In this paper, we provide explicit bases for certain Riemann-Roch spaces on the extended norm-trace function field. These bases provide explicit generator and parity check matrices for algebraic geometry codes CL ( D, aP∞ + ∑ β∈B aβP0β ) on the ext...

N = 1 supersymmetric QCD is considered using the recently proposed picture of it as the world volume theory of a single M-theory fivebrane with two of its dimensions wrapped on a Riemann surface. The conditions under which a second M-theory brane can be introduced preserving some supersymmetry are analysed. Such configurations represent BPS saturated extended objects in the quantum field theory...

In this article, we introduce the extended Eulerian numbers for a large class of zeta functions, which includes functions associated to function fields, and schemes over finite fields. This construction generalizes defined by Carlitz. We give an asymptotic expansion summatory these numbers. Our main result well known on behavior Riemann function.

In this paper a real analysis approach to stock price modelling is considered. A stock price and its return are defined in a duality to each other provided there exist suitable limits along a sequence of nested partitions of a time interval, mimicking sum and product integrals. It extends the class of stochastic processes susceptible to theoretical analysis. Also, it is shown that extended clas...

We study the geometry of horospheres in Teichmüller space Riemann surfaces genus g with n punctures, where 3g-3+n≥2. show that every C 1 -diffeomorphism to itself preserves is an element extended mapping class group. Using relation between and metric balls, we obtain a new proof Royden’s Theorem isometry group

For a Riemann domain Í2, a connected complex manifold where n (n = dimension) globally defined functions form a local system of coordinates at every point, and an arbitrary holomorphic function / in Í2, the "Riemann surface" Slf, a maximal holomorphic extension Riemann domain for /, is formed from the direct limit of a sequence of Riemann domains. Projective limits are used to construct an enve...

where t>0, o o < x < o o , U(t, x)=(u(t, x), v(t, x)), and the function F(U)= (f(u, v), g(u, v)) is smooth. GLIMM [2] has proved existence of a weak solution provided that the variation of the initial data Uo(x) is small. GLIMM & LAX [3] then improved this result by requiring that the oscillation of Uo(x) be small. SMOLLER [7] has proved the existence of a weak solution provided that Uo(x ) is ...

The inverse scattering problem on half-axis, in other words, in the spherically symmetric case, consists of finding the unknown potential from a suitable class from the scattering data S. The other problem of practical interest is to find this potential from the spectral data dρ(λ). In the literature there are recovery procedures for finding the potential from the spectral or from the scatterin...