We prove that the support of an $ m dimensional rectifiable varifold with a uniform lower bound on density and bounded generalized mean curvature can be covered \mathscr{H}^{m} almost everywhere by countable union $m$ submanifolds class \mathcal{C}^{2} $. obtain this result using notion arbitrary closed sets originally developed in stochastic geometry extending to our geometric setting techniqu...

Let Fg denote the closed orientable surface of genus g. What is the least order finite group, Gg, for which there is a homomorphism ψ : π1(Fg) → Gg so that no nontrivial simple closed curve on Fg represents an element in Ker(ψ)? For the torus it is easily seen that G1 = Z2 × Z2 suffices. We prove here that G2 is a group of order 32 and that an upper bound for the order of Gg is given by g . The...

This article solves the finite-time bounded tracking control problem for fractional-order systems. Firstly, by taking fractional derivative on state equations and error signals, a system is constructed, signal taken as output vector of system. Secondly, feedback controller introduced into system, disturbance signals desired are combined Thus, original converted input-output finite time stabilit...

The strong stabilizability of linear second order equation is investigated in this paper. It supposed that there exists a feedback law makes the origin closed-loop system globally asymptotically stable. Then control subject to cone-bounded nonlinearity. Well-posedness and stability results under such (nonlinear) are stated. first result proven by using nonlinear semigroups techniques Schauder f...