The problem of classifying off-shell representations of the N -extended one-dimensional super Poincaré algebra is closely related to the study of a class of decorated N -regular, N -edge colored bipartite graphs known as Adinkras. In previous work we canonically embedded these graphs into explicitly uniformized Riemann surfaces via the “dessins d’enfants” construction of Grothendieck. The Adink...

We argue that closed string tachyons drive two spacetime topology changing transitions – loss of genus in a Riemann surface and separation of a Riemann surface into two components. The tachyons of interest are localized versions of Scherk-Schwarz winding string tachyons arising on Riemann surfaces in regions of moduli space where string-scale tubes develop. Spacetime and world-sheet renormaliza...

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices. Our approach is based on the finite gap integration method applied to study the Riemann-Hilbert by Kitaev and Korotkin [1], Deift, Its, Kapaev and Zhou [2] and Korotkin, [3]. This permits us to solve the Riemann-Hilbert prob...

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered he...

This is the first in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which describe counter-rotating disks of dust. These disks can serve as models for certain galaxies and accretion disks in astrophysics. We review the Newtonian theory for disks using Riemann-Hilbert methods which can be extended to some extent to the relativistic ...

The Riemann zeta function ζ(s) is defined by ζ(s) = ∑∞ n=1 1 ns for R(s) > 1 and can be extended to a regular function on the whole complex plane deleting its unique pole at s = 1. The Riemann hypothesis is a conjecture made by Riemann in 1859 asserting that all non-trivial zeros for ζ(s) lie on the line R(s) = 12 , which is equivalent to the prime number theorem in the form of π(x)−Li(x) = O(x...

This study aims to prove some midpoint-type inequalities for fractional extended Riemann–Liouville integrals. Crucial equality is proven build new results. Using this equality, several are established via differentiable convex functions and the proposed operators. To be more specific, well-known Hölder, Jensen, power mean integral employed in demonstrated inequalities. Additionally, many remark...

In this paper we first briefly review the semi-analytical method [20] for solving the Derivative Riemann Problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection...

Consider a junction with n incoming and m outgoing roads. Along each road, the flow of traffic is described through the continuum model displaying phase transitions introduced in [5]. This note provides a Riemann solver for the resulting Riemann problem at the junction. 2000 Mathematics Subject Classification: 35L65, 90B10.

In this paper we introduce an abstract integral which includes both product integrals and additive integrals. Thus our theory of Riemann integration embraces both the product integrals of Volterra [l, 2, 3](2), Birkhoff [3], and Masani [l] and the classical additive integrals of Riemann [l] and Stieltjes [l]. Similarly our theory of Lebesgue integration includes the Lebesgue product integrals o...