We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete

We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative particles with tissue. This model allows for the modeling of inhomogeneities in the body and allows for anisotropic sources modeling distributed radiation—as in brachytherapy—and external beam sources—as in teletherapy. We...

Let K/k be an abelian extension of number fields with a distinguished place of k that splits totally in K. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in K, called the Stark unit, constructed from the values of the L-functions attached to the extension. In this paper, assuming the Stark unit exists, we prove index formulae for it. In a second part, ...

We consider the problem of solving multivariate systems of Boolean polynomial equations: starting from a system of m polynomials of degree at most d in n variables, we want to find its solutions over F2. Except for d = 1, the problem is known to be NP-hard, and its hardness has been used to create public cryptosystems; this motivates the search for faster algorithms to solve this problem. After...

We present a simple numerical method to find the optimal exercise boundary in an American put option. We formulate an intermediate function with the fixed free boundary that has Lipschitz character near optimal exercise boundary. Employing it, we can easily determine the optimal exercise boundary by solving a quadratic equation in time-recursive way. We also present several numerical results wh...

In this paper the stability of quadratic functional equation, f(xy)+f(xy)=2f(x)+2f(y) on class of groups is obtained and also prove that quadratic functional equation may not be stable in any abelian group.

We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z4 × Z5 × Z5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson’s pentagonpentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson’s parametrisation. Th...

Earth-observing satellites, such Landsat, provide many multitemporal images of earth, either water body or land. Using spectral water body characteristics and field measurement, bathymetry (water depth) of the study area can be calculated for each image recorded/acquired at different time. Four multitemporal spatial images were used for generating bathymetry images which were arranged as multil...

Let p ≥ 5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P(p−3)/2 of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.

Let p ≥ 5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.