The first goal of this short note is to answer a question posed by Thomas Craven in [3]. To explain the question we need to recall some definitions. A field K is called split Rolle (or for brevity SR) field if for any polynomial f(x) ∈ K[x] which splits completely in K its derivative f (x) also splits completely in K. For any field L there is the unique (up to L−isomorphism) smallest SR-field K...

The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...

In this paper, the behavior of a continuous flow in the vicinity of a closed positively .invariant subset in a metric space is investigated. The main theorem in this part in some sense generalizes previous results concerning classification of the flow near a compact invariant set in a locally compact metric space which was described by Ura-Kimura (1960) and Bhatia (1969). By applying the obtain...

Let iX, T) be a transformation group with compact Hausdorff phase space X. The points x and y of A" are said to be proximal provided, whenever ß is a member of the unique compatible uniformity of X, there exists i£ T such that (x/, yt) GßIf x and y are not proximal, they are said to be distal. Let P denote the proximal relation in X. P is a reflexive, symmetric, T invariant relation, but is not...

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

For long-term pharmacokinetic studies in humans as well as in experimental animals, an analysis of strontium (Sr) with a low detection limit and high sensitivity is necessary. The data presented here describe the optimization of the furnace program and sample handling for measuring Sr in plasma by using graphite furnace atomic absorption spectrophotometry. The method was validated and applied t...

cardiomyocytes from wild-type and GRK2 knockout (GRK2KO) mice without (sham) or with myocardial infarction (MI). In cardiac myocytes isolated from unstressed wild-type and GRK2KO hearts, myocyte contractions and Ca transients were similar, but GRK2KO myocytes had lower sarcoplasmic reticulum (SR) Ca content because of increased sodium-Ca exchanger activity and inhibited SR Ca ATPase by local pr...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

Let E be a compact subset of C and w ≥ 0 a weight function on E with w > 0 on a non-pluripolar subset of E. To (E, w) we associate a canonical circular set Z ⊂ C. We obtain precise relations between the weighted pluricomplex Green function and equilibrium measure of (E, w) and the pluricomplex Green function and equilibrium measure of Z. These results, combined with an appropriate form of the B...

In loop quantum gravity in the connection representation, the quantum configuration space A/G, which is a compact space, is much larger than the classical configuration space A/G of connections modulo gauge transformations. One finds that A/G is homeomorphic to the space Hom(L∗, G))/Ad. We give a new, natural proof of this result, suggesting the extension of the hoop group L∗ to a larger, compa...