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...

The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication ste...

This paper is a review of the authors’ results on the Dynamical Systems Method (DSM) for solving operator equation (*) F (u)= f . It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F . It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′(u) are imposed. The DSM for solving equation (*) ...

The dependence of the reflectance at the surface on the vertical structure of optical parameters is derived from first principles. It is shown that the depth dependence is a function of the derivative of the round trip attenuation of the downwelling and backscattered light. Previously the depth dependence was usually modeled as being dependent on the round trip attenuation. Using the new relati...

In this work we present a mutilayer approach to the solution of non-stationnary 3D NavierStokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal velocity and a linear (in z) vertical velocity in each layer, possibly discontinuous across layer interfaces. The multilayer approach is deduced by using the variational formulatio...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

This case report describes a modified connective tissue graft wall technique with enamel matrix derivative proposed to treat vertical bony defects. The surgical procedure consisted of coronally advanced flap porcine-derived acellular dermal placed below, acting as buccal soft the defect. patient showed defect between #12 and #13 horizontal bone loss deep infrabony component at mesial area canin...

We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel...

We define the notions of unilateral metric derivatives and “metric derived numbers” in analogy with Dini derivatives (also referred to as “derived numbers”) and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not “metrically differentiable” (in a certain strong sense) is σsymmetrically porous ...