A new optimization formulation for simulating multiphase flow in porous media is introduced. A locally mass-conservative, mixed finite-element method is employed for the spatial discretization. An unconditionally stable, fully-implicit time discretization is used and leads to a coupled system of nonlinear equations that must be solved at each time step. We reformulate this system as a least squ...

FIGURE 1 Two-dimensional representation of a spherical structure presenting a morphological particularity on a portion of its surface . AB, arc corresponding to the cross-section of the cap of the sphere presenting the characteristic ; OA = OB = R; 0, angle defining the cap ; v, vector defining the secant planes. S I and S2 are two-dimensional representation of secant planes which intersect (S2...

Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geome...

This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than...

Many in the mathematical community believe that the secant method arose from Newton’s method using a finite difference approximation to the derivative, most likely because that is the way that it is taught in contemporary texts. However, we were able to trace the origin of the secant method all the way back to the Rule of Double False Position described in the 18th-century B.C. Egyptian Rhind P...

A well known theorem of Helly [l] asserts that if $ is a finite family of convex subsets of En in which each re + 1 members have a common point, then there is a point common to all members of g. In this connection, Vincensini [5; 6] has raised the following question: For «^2 and Ogrgn-1, is there an integer k = k(n, r) such that if § is an arbitrary finite family of convex subsets of En in whic...

in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...