Let (X,m, H) be a hereditary m-space. A subset of X is said to θ-H-compact relative if for every cover U by m(θ)-open sets X, there exists finite U0 such that \ ∪ ∈ H. We obtain several properties these sets. Also, we define and investigate two kinds strong forms “θ-H-compact X”.

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous. Since this condition is automatically fulfilled in an integral homology sphere, the theorem implies a conjecture of J. Harer, namely, that any fibered link in th...

let x be a random variable from a normal distribution with unknown mean θ and known variance σ2. in many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. as the usual estimator of θ, i.e., x under the linex loss function is inadmissible, finding some competitors for x becomes worthwhile. the only study in the literature considered the problem of min...

Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...

We consider a d-dimensional C∞-manifold M such that M = Mc ∪ M∞, where Mc is relatively compact open submanifold, and M∞ is the noncompact part which is diffeomorphic to (0,∞)×∂M . Here ∂M is a compact manifold without boundary. In the following, we designate a point in M∞ by (r, θ) with r ∈ (0,∞) and θ ∈ ∂M . Often we also denote by θ ∈ ∂M a variables in a local coordinate of ∂M . Let H(θ)dθ b...

The objective of this lecture is to present some of the most fundamental elements of control loops, including open-loop and closed-loop (or feedback) control. There are two basis structures for control of dynamic systems: (a) open-loop control and (b) feedback (or closed-loop) control. These two control structures are shown in Figures 1 and 2. Let us write the equations of motion for a DC motor...