If an algebraic surface F of order J > ^ 4 has a double line (either nodal or cuspidal), the anomaly A of the plane sections C of a tangent cone to F is A = (1/6) v(v — 4) (v — 5). As is evident from this expression for A, plane curve systems C associated with a surface having a double line are anomalous only for v^6. When z> = 3, the above formula yields A = l. However, a cubic surface with a ...

By means of (1.2) and (1.3) each matrix S ∈ SL(2,C) is associated with some matrix S ∈ SO(1, 3,R) so that we can write S = φ(S), see [1], [2], and [3] for detailed description of this construction. Let M be a space-time manifold, i. e. a four-dimensional orientable manifold equipped with a pseudo-Euclidean Minkowski-type metric g and carrying a special smooth geometric structure which is called...

This paper focuses on the study of the second-order directional derivative of a symmetric matrix-valued function of the form F (X) = Pdiag[f(λ1(X)), · · · , f(λn(X))]P . For this purpose, we first adopt a direct way to derive the formula for the second-order directional derivative of any eigenvalue of a matrix in Torki [13]; Second, we establish a formula for the (parabolic) second-order direct...

A basic algorithm for the minimization of a differentiable convex function (in particular, a strictly convex quadratic function) defined on the convex hull of m points in R is outlined. Each iteration of the algorithm is implemented in barycentric coordinates, the number of which is equal tom. The method is based on a new procedure for finding the projection of the gradient of the objective fun...

A nose cone is the conically shaped tip part of a missile, bomb or aircraft, used to regulate behavior oncoming airflow and minimize drag. In this study, effects different designs on trajectory impact angle smart fire extinguishing ammunition were investigated. For purpose, three types with profiles designed: spherically blunted conic cone, tangent ogive truncated cone. virtual wind tunnel was ...

We prove the existence of a solution to the Monge-Ampère equation detHess(φ) = 1 on a cone over a thrice-punctured two-sphere. The total space of the tangent bundle is thereby a Calabi-Yau manifold with flat special Lagrangian fibers. (Each fiber can be quotiented to three-torus if the the affine monodromy can be shown to lie in SL(3,Z)⋉ R .) Our method is through Baues and Cortés’s result that...

We study the evolution of complete, noncompact, convex hypersurfaces in Rn+1 by inverse mean curvature flow. establish long-time existence solutions, and we provide characterization maximal time terms tangent cone at infinity initial hypersurface. Our proof is based on an a priori pointwise estimate solution from below aperture supporting infinity. The strict convexity solutions shown means vis...

We show, in this first part, that the maximal number of singular points a normal quartic surface $X \subset \mathbb {P}^{3}_{K}$ defined over an algebraically closed field K characteristic 2 is at most 16. produce examples with 14, respectively 12, and show that, under several geometric assumptions ( $\mathfrak S_{4}$ -symmetry, or behaviour Gauss map, structure tangent cone one P, separability...