Visual counting, a task that aims to estimate the number of objects from an image/video, is open-set problem by nature as population can vary in $$[0,+\infty )$$ theory. However, collected data are limited reality, which means only closed set observed. Existing methods typically model this through regression, while they prone suffer unseen scenes with counts out scope set. In fact, counting has...

ANDREEV-THURSTON THEOREM. Let r be a triangulation of S which is not simplicially equivalent to a tetrahedron and let <£: r—»[0, \n\ be given, where T denotes the set of edges of x. Suppose that (A) if eu e2, e3 e r (1) form a closed loop on S and if 2?=i ^(e^^n, then (eif e2, e3) are the three edges of a two-simplex of x; (B) if ex, e2, e3) eA e r (1) form a closed loop on S and if 2?=i <&{e,)...

and Applied Analysis 3 (ii) The scalar C-pseudomonotonicity in Definition 2 is weaker than C-pseudomonotonicity in Definition 1(ii). In fact, for any ξ ∈ C∗ \ {0}, x, y ∈ X, if ⟨ξ(u∗), y − x⟩ ≥ 0, then we have ⟨u∗, y − x⟩ ∉ − intC. Then, it follows from the Cpseudomonotonicity of T that ⟨V∗, y − x⟩ ∈ C, which implies that ⟨ξ(V∗), y − x⟩ ≥ 0. Definition 5. The topological space E is said to be c...

This paper discusses the dynamics computation of closed kinematic chains, especially those found in motions of human gures. A number of e cient dynamics computation algorithms have been established in robotics for open kinematic chains and particular types of closed kinematic chains, such as parallel ve-bar link mechanisms and the Stewart platform. The dynamics computation of closed kinematic c...

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X−E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F -harmonic functions (solutions) wh...

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X − E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F harmonic functions (solutions) w...