the gravity method is one of the first geophysical techniques used in oil and gas exploration. an algorithm is developed for a fast quantitative interpretation of gravity data generated by geometrically simple but also the estimated depths and other model parameters of a buried structure. following abdelrahman et al (1989). the general gravity anomaly expression produced by a sphere, an infinit...

Methods are presented to derive with the aid of the computer mathematics software system SageMath the Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box starting from its algebraic expressions. Motivation to this work were the results of recent articles [4, 5, 6] which we have verified and extended in an original way, to our knowledge, n...

In this paper, we discuss semide$nite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the S-procedure. This formulation leads to convex optimization problems that can be essentially solved in O(n)—n being the size ...

We develop several tools to derive quadratic equations from algebraic S-boxes and to prove their linear independence. By applying them to all known almost perfect nonlinear (APN) power functions and the inverse function, we can estimate the resistance against algebraic attacks. As a result, we can show that APN functions have different resistance against algebraic attacks, and especially S-boxe...

Michaelis-Menten equation is a basic equation of enzyme kinetics and gives an acceptable approximation of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to MichaelisMenten curve (15). This curve is derived from Quasi-Steady-State Assumption(QSSA), which has been proved always t...

We consider the nonlinear biharmonic Schr\"odinger equation $$i\partial_tu+(\Delta^2+\mu\Delta)u+f(u)=0,\qquad (\text{BNLS})$$ in critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $\mu=0$ or $-1$, $0<s<\min\{\fc N2,8\}$ and $f(u)$ is a function that behaves like $\lambda\left|u\right|^{\alpha}u$ with $\lambda\in\mathbb{C},\alpha=\frac{8}{N-2s}$. prove existence uniqueness of global solutions t...