In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skew-Frobenius map defined on the quadratic twist of an twisted Edwards curve. Our results show that the Frobenius endomorphism on twisted Edwards curve and the skew-Frobenius endomorphism o...

Fluorescent speckle microscopy (FSM) is a new imaging technique with the potential for simultaneous visualization of translocation and dynamic turnover of polymer structures. However, the use of FSM has been limited by the lack of specialized software for analysis of the positional and photometric fluctuations of hundreds of thousand speckles in an FSM time-lapse series, and for translating thi...

The crystal growth kinetics and interfacial properties of titanium (Ti) are studied using molecular dynamics computer simulation. interactions between the Ti atoms modeled via an embedded atom method potential. First, free solidification (FSM) is used to determine melting temperature Tm at zero pressure where transition from liquid body-centered cubic occurs. From simulations with FSM, kinetic ...

The paper proposes a new model for veriication and high level synthesis (re)using complex units like co-processors. The model is called FSMC (FSM with Co-processors) and is an extension of the FSMD model (FSM with Data path). The veriication method is based on model checking. It permits to analyze the properties and consistency of the whole system and, particularly, the correct (re)use of desig...

We consider the problem of computing regular formal solutions of systems of linear differential equations with analytic coefficients. The classical approach consists in reducing the system to an equivalent scalar linear differential equation and to apply the well-known Frobenius method. This transformation to a scalar equation is not necessarily relevant so we propose a generalization of the Fr...

We express the real period of a family of elliptic curves in terms of classical hypergeometric series. This expression is analogous to a result of Ono which relates the trace of Frobenius of the same family of elliptic curves to a Gaussian hypergeometric series. This analogy provides further evidence of the interplay between classical and Gaussian hypergeometric series.

For a closed Kähler manifold with a Hamiltonian action of a connected compact Lie group by holomorphic isometries, we construct a formal Frobenius manifold structure on the equivariant cohomology by exploiting a natural DGBV algebra structure on the Cartan model. The notion of Frobenius manifolds was introduced by Dubrovin [11, 12]. It gives a coordinate free formulation of solutions to the WDV...

In this paper we apply the Fast Iterative Method (FIM) for solving general Hamilton–Jacobi–Bellman (HJB) equations and we compare the results with an accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be indeed used to solve HJB equations with no relevant modifications with respect to the original algorithm proposed for the eikonal equation, and that it overcomes FSM in...