Unbounded subnormal weighted shifts on directed trees

A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established. An approach to this issue via consistent systems of probability measures is invented. The role played by determinate Stieltjes moment sequences is elucidated. Lambert’s characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi-analytic vectors, which is a new phenomenon in this area.     

Permeability Tensor for Heterogeneous Porous Medium of Fibre Type

A theoretical model which allows us to determine the permeability of a fibrous porous medium is proposed. Fibres are assumed to be parallel and nonuniform in space and material with a low volume fraction of fibres is considered. The model includes two geometric parameters: the diameter of fibres and the diameter of caverns or fissures inside the bundle of fibres. The tensor of permeability of the porous medium is determined based upon a generalized cell model. The components of permeability tensor depend on two parameters which are determined using experimental data and least-squares approximation. The influence of the geometric parameters on components of permeability tensor is discussed.     

On unbounded composition operators in L^2-spaces

Fundamental properties of unbounded composition operators in \(L^2\) -spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert’s characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied.     

Metathesis of silicon-containing olefins: IX. Synthesis of 1-(trimethylsilyl)-1-alkenes by olefin metathesis

1-(Trimethylsilyl)-1-alkenes of general formula CH₃(CH₂)_nCH?CHSi(CH₃)₃, where n = 3–15, have been prepared by a novel method, viz. by an effective cross-metathesis of vinyltrimethylsilane with 1-alkenes catalyzed by RuCl₂(PPh₃)₃. Excess of 1-alkene in the reaction mixture gave 1-(trimethylsilyl)-1-alkenes in good yields of up to 60% (in terms of vinylsilane). The products were identified by NMR spectroscopic (¹H, ¹³C NMR) and GC MS methods.     

Conductance of substituted amine perchlorates and picrates in N-methyl-2-pyrrolidinone at 25°C

Conductance measurements of 16 perchlorates and picrates of substituted ammonium cations have been made in N-methyl-2-pyrrolidinone (NM-2-Py) at 25°C. To aid in the estimation of ionic conductances, measurements of tetrabutyl-ammonium tetraphenylborate were also included. The data were analyzed by both the full Pitts equation and the expanded Pitts equation in order to obtain limiting molar conductances _o and the ion association constants K _A . The results showed that pyridinium perchlorate and piperidinium, 2,4-dimethyl-pyridinium, 2,4,6-trimethylpyridinium picrates and tetrabutylammonium tetraphenylborate appear to be completely dissociated in NM-2-Py. The values of K _A for the other salts range from 1 to 36 dm³-mol^–1. Limiting molar conductances for the cation were based on the Coplan-Fuoss assumption.On leave 1973–1975 from University of Gdask, Poland.     

Sur les solutions d'une équation fonctionnelle,III

Sans résumé

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Prestress for maximum strength

The problem of designing prestress to maximize elastic capacity is treated analytically. Our formulation models structures comprised of a one-material elastic continuum, subject to a single deterministic load configuration.The equations needed to predict the optimal prestress design are derived. They are shown to comprise necessary and sufficient conditions for global maximum strength in the unconstrained design problem. The theory is demonstrated on the design of prestress for a thick-walled cylinder.     

Multielemental Analysis of Bee Pollen,Propolis, and Royal Jelly Collected in West-Central Poland

Beehive products possess nutritional value and health-promoting properties and are recommended as so-called “superfoods”. However, because of their natural origin, they may contain relevant elemental contaminants. Therefore, to assess the quality of bee products, we examined concentrations of a broad range of 24 selected elements in propolis, bee pollen, and royal jelly. The quantitative analyses were performed with inductively coupled plasma-mass spectrometry (ICP-MS) and inductively coupled plasma optical emission spectrometry (ICP-OES) techniques. The results of our research indicate that bee products contain essential macronutrients (i.e., K, P, and S) and micronutrients (i.e., Zn and Fe) in concentrations depending on the products’ type. However, the presence of toxic heavy metals makes it necessary to test the quality of bee products before using them as dietary supplements. Bearing in mind that bee products are highly heterogenous and, depending on the environmental factors, differ in their elemental content, it is necessary to develop standards regulating the acceptable levels of inorganic pollutants. Furthermore, since bees and their products are considered to be an effective biomonitoring tool, our results may reflect the environment’s condition in west-central Poland, affecting the health and well-being of both humans and bees.     

Hyperexpansive completion problem via alternating sequences; an application to subnormality

Truncations of completely alternating sequences are entirely characterized. The completely hyperexpansive completion problem is solved for finite sequences of (positive) numbers in terms of positivity of attached matrices. Solutions to the problem are written explicitly for sequences of two, three, four, five and six numbers. As an application, an explicit solution of the subnormal completion problem for five numbers is given.