Lifting is a procedure for deriving valid inequalities formixed-integer sets from valid inequalities for suitable restrictions of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used to solve such problems with branch-and-cut algorithms. Here we generalize the theory of lifting to conic i...

We propose a new threshold signature scheme based on conic curve. The security of the proposed threshold signature scheme is based on the difficulty of computing the DLP in conic curve groups. It can resist some of the known attacks. Since an exciting characteristic of conic is both encoding and decoding over conic are easily implemented, it can be used in the mobile payment system with the lim...

We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces (= the set of points w...

During the last two decades, major developments in convex optimization were focusing on conic programming, primarily, on linear, conic quadratic and semidefinite optimization. Conic programming allows to reveal rich structure which usually is possessed by a convex program and to exploit this structure in order to process the program efficiently. In the paper, we overview the major components of...

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...

We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp′(z)) ∈ D ⇒ p(z) ≺ q(z), where D and q( ) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q( ). Also, we find the best dominant of the differential subordination p(z)+ (zp′(z)/(βp(z)+γ)) ≺ pk(z), when the functio...

The most frequently observed focal conic domains (FCD's) in lamellar phases are those based on confocal paris of ellipse and hyperbola. Experimentally, the eccentricity of the ellipse takes a broad range of values 0</=e<1. We present an analytical expression for the curvature energy of a FCD that is valid in the entire range 0</=e<1. Generally, the curvature energy of an isolated FCD reaches a ...