Separability and distance

Translated from Matematicheskie Zametki, Vol. 50, No. 5, pp. 18–22, November, 1991.     

Some negative results on multiplier sequences of the first kind

It is proved that the composition of a polynomial with a multiplier sequence of the first kind may lead to a diminishing of the number of real roots of this polynomial and that the reciprocals of the moments of a nonnegative function on [0, 1] need not form a multiplier sequence of the first kind. On the basis of these facts one establishes the inaccuracy of the solution, obtained by T. Craven and G. Csordas, to S. Karlin's problem on the characterization of linear transformations that do not increase the number of zeros and also the incorrectness of M. Kostova's certain results, given in L. Iliev's monograph Laguerre entire functions (Sofia, 1987).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 305–309, March, 1992.     

Preparation of a 99mTc-labeled graft polymer and its in vitro and in vivo evaluation

Journal of Radioanalytical and Nuclear Chemistry - The aim of this study is the synthesis of a novel 99mTc-labeld graft polymer and the biological evaluation of its in vitro and in vivo properties....     

Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space C w 0

For an arbitrary function , we determine the general form of a linear continuous functional on the space C _w ⁰ . The criterion for denseness of polynomials in the space established by Hamburger in 1921 is extended to the spaces C _w ⁰ .     

Biodistribution of GdCl3 and Gd-DTPA and their influence on proton magnetic relaxation in rat tissues

The biodistribution and relative molar effectiveness of the ionic (GdCl3) and chelated (Gd-DTPA) forms of gadolinium (Gd) to enhance proton relaxation rates in rat kidney, liver and spleen were evaluated. Rats were given intravenous injections of either GdCl3 (100 mumol/kg) or Gd-DTPA (178 mumol/kg). Gd-DTPA was primarily contained in the vascular compartment and was quickly accumulated in the kidney after injection with a relaxivity of 4.3 sec-1 (mumol/g kidney)-1. It was eliminated quickly from the body with only 2% of the injected dose remaining after 120 min. After GdCl3 injection, Gd was found primarily in liver and spleen. It accumulated continuously reaching 72% of the injected does in these two tissues after 120 min. Despite this continuous increase in tissue Gd concentration, the relaxation rates showed saturation in liver and spleen. The results suggest that after GdCl3 was injected it distributed either in a protein bound form that was effective at causing relaxation or in a colloid form that was not effective. The biodistribution of GdCl3 was such that it was determined by the phagocytic action of the recticuloendothelial system on a colloid. The biodistribution and tissue relaxivity of Gd-DTPA suggest it will be a useful vascular MRI contrast agent. However, the usefulness of GdCl3 as an MRI contrast agent is limited not only by its acute toxicity but also by its saturable effect on tissue relaxation rates. Consequently, GdCl3 has only a modest influence on tissue relaxivity.     

On geometric properties of the generating function for the Ramanujan sequence

The Ramanujan sequence \(\{\theta _{n}\}_{n \ge 0}\), defined as \(\theta _{0}= {1}/{2}\), \({n^{n}} \theta _{n}/{n !} = {e^{n}}/{2} - \sum _{k=0}^{n-1} {n^{k}}/{k !}\, \), \(n \ge 1\), has been studied on many occasions and in many different contexts. Adell and Jodrá (Ramanujan J 16:1–5, 2008) and Koumandos (Ramanujan J 30:447–459, 2013) showed, respectively, that the sequences \(\{\theta _{n}\}_{n \ge 0}\) and \(\{4/135 - n \cdot (\theta _{n}- 1/3 )\}_{n \ge 0}\) are completely monotone. In the present paper, we establish that the sequence \(\{(n+1) (\theta _{n}- 1/3 )\}_{n \ge 0}\) is also completely monotone. Furthermore, we prove that the analytic function \((\theta _{1}- 1/3 )^{-1}\sum _{n=1}^{\infty } (\theta _{n}- 1/3 ) z^{n} / n^{\alpha }\) is universally starlike for every \(\alpha \ge 1\) in the slit domain \(\mathbb {C}\setminus [1,\infty )\). This seems to be the first result putting the Ramanujan sequence into the context of analytic univalent functions and is a step towards a previous stronger conjecture, proposed by Ruscheweyh et al. (Israel J Math 171:285–304, 2009), namely that the function \((\theta _{1}- 1/3 )^{-1}\sum _{n=1}^{\infty } (\theta _{n}- 1/3 ) z^{n} \) is universally convex.     

Majorization of regular measures and weights with finite and positive critical exponent

For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω.     

Representation of measures with polynomial denseness in , , and its application to determinate moment problems

It has been proved that algebraic polynomials are dense in the space , , iff the measure is representable as with a finite non-negative Borel measure and an upper semi-continuous function such that is a dense subset of the space    as equipped with the seminorm . The similar representation ( ) with the same and ( , and is also a dense

subset of ) corresponds to all those measures (supported by ) that are uniquely determined by their moments on ( ). The proof is based on de Branges' theorem (1959) on weighted polynomial approximation. A more general question on polynomial denseness in a separable Fréchet space in the sense of Banach has also been examined.

     

Electrolytic precipitation of natural uranium on stainless steel cathode

Electrolytic precipitation of natural uranium has been studied on stainless stell cathode from ammonium acetate and ammonium oxalate media with the aim to prepare a radiation source suitable for α-spectrometry. Modification of parameters—having an important role at the precipitation—has been investigated, data of the two media were compared and the most optimal conditions determined.