In this paper we find the volume of the intersection of two congruent circular cones whose axes cross at a common point P , with the vertices of the cones equidistant from P . The formula is expressible by elementary functions. The symbol manipulator MACSYMA was used in the derivations. The formula was needed for a practical application. It has not been found in the literature despite a thoroug...

The unsteady, compressible, thin-layer Navier-Stokes equations are used to numerically study the passive control of steady and unsteady supersonic asymmetric flows around circular and noncircular cones. The main computational scheme of the present study is an implicit upwind, flux-difference splitting, finite-volume scheme. Passive control of flow asymmetry is studied by using a vertical fin in...

If instead of elliptical cones, right circular cones are employed, then • • 8 and only the expression for B is changed. In particular for a fixed 8, this causes the 1R. A. Rasmussen and N. E. Head, "Characteristics of High Frequency Sea Reverberation and Their Application to Turbulence Measurement," J. Acoust. Sec. Am. 59, 55-61 (1976). 2E. J. Sullivan and K. A. Kemp, "The Significance'of Beam ...

In this paper, we consider a type of cone-constrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies...

Circular programming problems are a new class of convex optimization problems in which we minimize linear function over the intersection of an affine linear manifold with the Cartesian product of circular cones. It has very recently been discovered that, unlike what has previously been believed, circular programming is a special case of symmetric programming, where it lies between second-order ...

Theoretical analyses are presented for the stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies under small perturbations in an inviscid incompressible flow at high angles of attack and sideslip. The three-dimensional problem of a pair of vortices over slender conical wings and bodies is reduced to a problem in two dimensions by using the conical flow assumpt...