In 2011 ISO standardized [2] a family of deterministic pseudorandom bit generators MQ—DRBG, based on multivariate quadratic functions satisfying certain properties. The security of the generator could be described in terms of complexity of solving the corresponding system of multivariate quadratic equations. In our previous article [1] we proposed two different techniques for constructing syste...

Laser polishing is a finishing process based on melting material, with the objective of improving surface topography. Some operating parameters must be taken into consideration, such as laser power, feed rate, offset, and overlapping. Moreover, because of its dependence on the primary process, the initial topography has also an impact on the final result. This study describes a quadratic model,...

vector notation and then give two different representations. The first representation is the regular gradient space; it has the advantage of simplicity but contains important singularities. The second one is just a regular vector (p, 4, r) in 3-D with the constraint that p* + q* + r* = 1. (5) This can represent the normal of any plane in 3-D, with the added complexity that Eq. (5), a quadratic ...

The structure theory ([3], [8]) for complete flat homogeneous pseudo-riemannian manifolds reduces the classification to the solution of some systems of quadratic equations. There is no general theory for that, but new solutions are found here by essentially the same construction as that used for isoclinic spheres in Grassmann manifolds [4]. It is interesting to speculate on a possible direct ge...

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

This paper presents the ability of a new group contribution equation of state in the prediction of thermodynamic properties of alcohols, ketones and ethers. This equation of state, called MCORGC, is based on the Chain-Of-Rotators Group Contribution equation considering a NRTL type local composition mixing rule. The group parameters required to predict the thermodynamic properties of the oxygena...

The general equation of state which was found for dense fluids, both compressed liquids and dense supercritical fluids, namely "Linear Isotherm Regularity," is extended to the lower density range, specifically for densities lower than the Boyle density. This new equation of state which is called "ELIR" is shown to be compatible with the equations of state based on statistical-mechanical the...

A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $mathcal{R}_0$, this state can be either endemic ($mathcal{R}_0> 1$), or infection-free ($mathcal{R}_0leq 1$). The global asymptotic stability of ...

In this brief note,  using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove  an existence result for a quadratic  integral equation of Hammerstein type on an unbounded interval in two variables  which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...