Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is Qt i=0(1 + q ) for the types BN , DN , whereas for the case of type CN , more isotro...

We give simple exact descriptions of the null controllable regions for general linear systems with saturating actuators. The description is in terms of a set of extremal trajectories of the anti-stable subsystem. For lower order systems or systems with only real eigenvalues, this description is further simpli6ed to result in explicit formulae for the boundaries of the null controllable regions....

In this paper we study controllability properties for semilinear degenerate parabolic equations with nonlinearities involving the first derivative in a bounded domain of R. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of ’regional null controllability’, showing that we can drive the solution to rest at time T on a subset of the sp...

Abstract. In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form ∂y ∂n + β y = 0. We consider distributed controls with support in a small set and nonregular coefficients β = β(x, t). For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classi...

The subjects for this study were male bar patrons in three Texas cities. Linear discriminant analysis was utilized to test the null hypothesis between each pair of subject groups on self-esteem, personal competence, self-acceptance, purpose in life, powerlessness, normlessness, social isolation, alienation, status concern, social responsibility, age, occupation, marital status, education, and a...

Recently it was discovered that null hypersurfaces can develop caustics outside the event horizon of super-entropic Kerr-AdS black holes, in contrast to usual case. In this work we explore a few more examples hole spacetimes which such exterior develop. If closed curve is present, e.g., case Taub-NUT and "transunital" spacetimes, then coincides with hypersurface caustic (NHC) minimal separation...

For any asymptotically at spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two...

For any asymptotically flat spacetime with a suitable causal structure obeying Penrose's cosmic censorship conjecture (weak form) and satisfying conditions guaranteeing focus-ing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two u...

In this paper, a new method was proposed for the navigation of a mobile robot in an unknown dynamic environment. The robot could detect only a limited radius of its surrounding with its sensors and it went on the shortest null space (SNS) toward the goal. In the case of no obstacle, SNS was a direct path from the robot to goal; however, in the presence of obstacles, SNS was a space around the r...