Strong closed range estimates: necessary conditions and applications

Necessary and sufficient conditions for strong comparability of multicomponent systems

In this article we analyze the stochastic comparison of continuous time Markov chains with state space E = {0, 1, 2, . . .} used as models for N−component systems. Although the conditions for comparability of such processes are known in the theory, they involve a huge family of sets which makes their checking a difficult task. We show how, under some assumptions on the transitions allowed in th...

New necessary conditions for Lipschitz strong local minimizers

We derive a set of new necessary conditions for Lipschitz strong local minimizers. These conditions restrict the behavoir of the L gradient of the minimizer at its discontinuities. We show by way of examples that the derived conditions are independent of one another.

Some Applications of Strong Product

Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...

Necessary and Sufficient Conditions for the Pointwise Convergence of Nearest Neighbor Regression Function Estimates

where (v,1, ..., v,,) is a given probability vector, and (Xt(x), Yl(x)), ..., (X.(x), Y,(x)) is a permutation of (X1, I71) . . . . , (X, , Y,) according to increasing values of IlXi-x[I, x e R a. When [IXi-xll = H X j x l [ but i < j , X i is said to be closer to x than X~. The consistency properties of m, for special choices of the weight vector (v,,, ..., v,,,) are discussed in Cover (1968), ...

Necessary Conditions to Attain Performance Bounds on Structure and Motion Estimates of Rigid Objects