The natural projection from the moduli space of polynomials of degree n is not surjective if n ≥ 4. We give explicit parametric representation of the exceptional set when n = 4 and 5. And we describe degeneration which occurs above the exceptional set when n = 4. Also we show that the preimage of a point generally consists of (n − 2)! points, where (n − 2)! is the maximum when the preimage is a...

We study the time evolution of freely rolling moduli in the context of M-theory on a G2 manifold. This free evolution approximates the correct dynamics of the system at sufficiently large values of the moduli when effects from non-perturbative potentials and flux are negligible. Moduli fall into two classes, namely bulk moduli and blow-up moduli. We obtain a number of non-trivial solutions for ...

We study the $T$-dual completion of four-dimensional $\mathcal{N}=1$ type II effective potentials in presence (non)geometric fluxes. First, we invoke a cohomology version transformations among various moduli, axions, and fluxes appearing IIA IIB supergravities. This leads to some useful observations about significant mixing standard NS-NS with on mirror side. Further, using our $T$-duality rule...

In last years, many modulus sets in the Residue Number System (RNS) for increasing Dynamic Range (DR) and parallelism are presented. Hence, for reach these purposes a new 5-Moduli Set for even n, and its efficient reverse converter design are introduced in this paper. This modulus set contains pair-wise relatively prime, and it offers the maximum feasible DR. New CRT-I and MRC are used to obtai...