Generating-line method, which is based on the generating process of spherical involute curve, is a new processing theory of cutting ideal spherical involute gears. Based on the principle of the new method, this paper expands the traditional geometrical relationship into the cutting geometry of generating-line method, and proposes the base-cone parameters with their formulas to provide necessary...

We study the formation of singularities for the mean curvature flow of monotone Lagrangians in C. More precisely, we show that if singularities happen before a critical time then the tangent flow can be decomposed into a finite union of area-minimizing Lagrangian cones (Slag cones). When n = 2, we can improve this result by showing that connected components of the rescaled flow converge to an a...

The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well–known assumptions of Filippov’s existence theorem (about solutions of differential inclusions), every epi-Lipschitzian initial compact set K ⊂ RN preserves this regularity for a short time, i.e. θF (t, K) is also epi-Lipschitzian for all small t >...

— A point P on a smooth hypersurface X of degree d in PN is called a star point if and only if the intersection of X with the embedded tangent space TP (X) is a cone with vertex P . This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in P3. We generalize results on the configuration space of total inflection points on plane curv...

The paper is concerned with the optimal design problems for the fourth order variational inequalities. Namely, the first order necessary optimality conditions are derived for the class of optimization problems under consideration. The differential stability of metric projection in the Sobolev space HQ{Q) onto the cone of nonnegative elements is considered by Mignot [9]. Mignot derived the form ...

We introduce and study the random non-compact metric space called the Brownian plane, which is obtained as the scaling limit of the uniform infinite planar quadrangulation. Alternatively, the Brownian plane is identified as the Gromov-Hausdorff tangent cone in distribution of the Brownian map at its root vertex, and it also arises as the scaling limit of uniformly distributed (finite) planar qu...

Abstract. We give examples of complex hyperplane arrangements A for which the top characteristic variety, V1(A), contains positive-dimensional irreducible components that do not pass through the origin of the algebraic torus (C∗)|A|. These examples answer several questions of Libgober and Yuzvinsky. As an application, we exhibit a pair of arrangements for which the resonance varieties of the Or...

In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex problem, it is well known that involve the support function of tangent set. propose two approaches establishing case. first approach, extend concept so applicable to general problems, whereas in second introduce notion directional regular cone and apply classical results ...

With the aid of some novel complementarity constraint quali cations, we derive some simpli ed primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simpli ed results, which rely heavily on a careful dissection and im...