Robust control systems synthesis is generally recast as a class of robust feasibility problems which is to find a solution satisfying a set of parameter-dependent convex constraints for all possible parameter values. For this class of the problems, a stochastic ellipsoid method with multiple cuts each of which corresponds to each of the constraint is proposed, where a new update rule is present...

Equal-time comparison. Stochastic light culling has a trade-off between the performance and quality, which is controlled by the user-specified parameter δ. Therefore, our ellipsoid-based approach can render higher-quality images than the sphere-based approach when comparing at the same computation time. Fig. 2 shows the equal-time comparison between the bounding sphere and our bounding ellipsoi...

We give a new proof of the complete integrability of the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose non-parameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperbolic metric inside the ellipsoid (Klein’s model). Mathematics Subject Classi...

In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi–infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality res...

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

No. title/pages date update file name 1 A note on the elliptic integrals and elliptic functions ellipsoid-may04.tex 3 A note on " Potential flow of a second order fluid over a sphere or an ellipse " ellipse-wang-joseph-apr27.tex 4 A note on flows of a second order fluid around an ellipsoid ellipse-may31a.tex 5 A note on flows of a second order fluid around an ellipsoid of revolution/11pages

This paper compares two different local surface shape description methods. The general goal of surface shape description methods is to classify different surface shapes from range data. One well-known method to classify patches of various shapes is the HK classification space [2, 1, 10]. Another way to classify patches is the SC method introduced by Koenderink [9]. This paper presents several e...

Computational fluid dynamics (CFD) is a powerful numerical tool that is becoming widely used to simulate many processes in the industry. In this work study of the stirred tank with 7 types of concave blade with CFD was presented. In the modeling of the impeller rotation, sliding mesh (SM) technique was used and RNG-k-ε model was selected for turbulence. Power consumption in various speeds in th...