Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Immediate extensions of filtered rings

Summary A separated filtered ring has a maximally complete immediate extension. This is an analogue of Krull Theorem from valuation ring theory in the frame of filtered rings.

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Riassunto Un anello separato filtrato ha una immediata estensione massimale completa. Questo risultato è un analogo del teorema di Krull della teoria degli anelli di valutazione nell’ambito degli anelli filtrati.

     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

N‐{3‐[(2‐Ammonioethyl)amino]propyl}ethane‐1,2‐diaminium tris(trifluoromethanesulfonate): a salt of a folded triply protonated tetramine

The structure of a trifluoromethanesulfonate salt of a nontypical triply protonated linear tetramine, C₇H₂₃N₄³⁺·3CF₃SO₃⁻, with a layered crystal structure is presented. One N atom remains unprotonated. The conformation of the cation is enforced by intra‐ and intermolecular hydrogen bonds. The crystal structure is built of ca 10 Å deep layers, within which cations and anions are hydrogen bonded. Each layer is only weakly bound to its neighbours. This study shows a rare example of an unsymmetrically protonated polyamine and the relation between the lack of protonation, intramolecular hydrogen bonding and the conformation of the cation.     

The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

Metallofullerenes

Summary Endohedral and exohedral metallofullerenes, including metal-doped fullerenes, organometallic fullerenes and fullerene metal complexes, are described in the context of their syntheses and properties.     

Chromatographic competitive binding immunoassays: a comparison of the sequential and simultaneous injection methods

Two approaches for performing competitive binding immunoassays by HPLC and other flow-based systems are the simultaneous and sequential injection methods. Both these techniques make use of a column with a limited amount of antibody, onto which is injected a sample and a fixed amount of a labeled analyte analog. An indirect measure of the unlabeled analyte in the sample is then obtained by looking at the amount of analog in either the nonretained or retained peaks. In the simultaneous injection mode, the sample and labeled analog are applied at the same time to the column, while in the sequential mode the sample is injected first, followed by the analog. This results in a difference in the analytical characteristics of these two approaches. This study used chromatographic theory and previous data obtained for injections of human serum albumin (HSA) onto an anti-HSA antibody column to compare the response, detection limits, range, and sensitivity of these methods. Under equivalent conditions, it was found that the sequential method always provided the best lower limit of detection and sensitivity. However, the simultaneous mode had a broader dynamic range and higher upper limit of detection. From these observations, several guidelines were developed regarding the use and selection of such assays for new applications.     

Spectroscopic and photochemical properties of the lichen compound lobaric acid

Lichens synthesize and accumulate photoprotective compounds against possible damage induced by UV radiation in the photobiont. A biological model has been recently formulated that allows the use of lichens to evaluate changes at different UV radiation levels. The thermodynamics, photophysical and photochemical properties of lobaric acid were studied in acetonitrile, ethanol and Brij 35(3%) micelles at different pH values. Also the sun protector factor (SPF) was determined by in vitro methods. Lobaric acid was extracted from Stereoculon alpinum Laur. and characterized by means of standard procedures. Solutions were irradiated in oxygen and under nitrogen conditions with a UV medium pressure lamp. Lobaric acid absorbs at 287, 303 nm, and no fluorescence emission was observed. The maximum value of the molar extinction coefficient (5479.6 M(-1) cm(-1)) was obtained in Brij 35 at pH 12. Solubility is pH dependant and is highest in Brij 35 at pH 12 (4.45 x 10(-4) M). Photoconsumption quantum yields ranged between 10(-4) and 10(-5) in aerobic and anaerobic experimental conditions. Lobaric acid SPF was very low (0.5) compared with homosalate (4.0), (reference solar filter). Two pKa values, 5.05 (carboxylic acid group deprotonation) and 9.75 (phenolic OH deprotonation), were determined.