Distribution of Zinc Oxide Nanocrystals in a Polymer Film

The structure of polymer films modified with zinc oxide nanocrystals was studied by the optical absorption and small-angle X-ray scattering methods. Small-angle X-ray scattering allows determination of the nanoparticle size distribution function, which is the decisive factor in predicting the optical properties of heterophase materials, including filled polymer films. The optical absorption spectrum of an acrylate polymer film doped with 1.6 wt % zinc oxide nanocrystals approaches the ideal absorber spectrum, which allows this material to be recommended for use as a protective color filter.     

Synthesis and transformations of 3-allyl-7,10-dimethyl-2-sulfanylidene-2,3,5,6-tetrahydrospiro[benzo[<Emphasis Type="Italic">h</Emphasis>]quinazoline-5,1′-cyclopentan]-4(1<Emphasis Type="Italic">H</Emphasis>)-one

Ethyl 4′-amino-5′,8′-dimethyl-1′H-spiro[cyclopentane-1,2′-naphthalene]-3′-carboxylate reacted with allyl isothiocyanate to give 3-allyl-7,10-dimethyl-2-sulfanylidene-2,3,5,6-tetrahydrospiro[benzo[h]quinazoline- 5,1′-cyclopentan]-4(1H)-one. Reactions of the latter with alkyl halides and hydrazine hydrate and subsequent transformations of the products afforded a series of new benzo[h]quinazoline derivatives containing an allyl group in the 3-position.     

Evaluation of the biosafety of cyanoacrylate adhesive in vitro

This paper considers the evaluation of the biosafety of cyanoacrylate adhesive in vitro on human multipotent mesenchymal stem cells. This adhesive is intended for medical use, in particular, for X-ray and endovascular interventions. A toxicity study was carried out in a culture of multipotent mesenchymal stem cells isolated from human subcutaneous fat. As a result of the work, the concentration of cyanoacrylate adhesive in lipiodol was chosen, which has the lowest toxicity.     

On 3-generated lattices with a completely modular element among generators

We consider a lattice generated by three elements, one of which is completely modular. The free lattice with this property is proved to be finite. It is not modular and contains exactly 39 elements. We have also found a finite set of defining relations for the generating elements of this lattice.     

Students as toolmakers: refining the results in the accuracy and precision of a trigonometric activity

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This research has demonstrated how two classroom activities based on tool-making can enhance student measurement and application of accuracy and precision considerations through a trigonometric activity investigating arctan.     

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.     

On weak* convergent sequences in duals of symmetric spaces of <Emphasis Type="Italic">τ</Emphasis>-measurable operators

It is shown that the pre-dual of a σ-finite von Neumann algebra has property (k) in the sense of Figiel, Johnson and Pelczyński [12]. This resolves in the affirmative an open question raised in [12]. It is shown further that a weakly sequentially complete symmetric space E of τ-measurable operators affiliated with a semifinite σ-finite von Neumann algebra has property (k).     

Rigged modules I: Modules over dual operator algebras and the Picard group

In a previous paper we generalized the theory of $W^{?}$-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak^?-rigged modules. At that time we promised a forthcoming paper devoted to other aspects of the theory. We fulfill this promise in the present work and its sequel “Rigged modules II”, giving many new results about weak^?-rigged modules and their tensor products. We also discuss the Picard group of weak* closed subalgebras of a commutative algebra. For example, we compute the weak Picard group of $H^{\infty }(\mathbb{D})$, and prove that for a weak* closed function algebra A, the weak Picard group is a semidirect product of the automorphism group of A, and the subgroup consisting of symmetric equivalence bimodules.