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.     

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.     

Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [0,1]. These facts hold true, in particular, for covering dimension dim and cohomological dimension dimG, where G is any Abelian group.     

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.     

N‐Acetyl‐l‐tyrosine methyl ester monohydrate at 293 and 123 K

The crystal structure of a protected l ‐tyrosine, namely N‐acetyl‐l ‐tyrosine methyl ester monohydrate, C₁₂H₁₅NO₄·H₂O, was determined at both 293 (2) and 123 (2) K. The structure exhibits a network of O—H...O and N—H...O hydrogen bonds, in which the water molecule plays a crucial role as an acceptor of one and a donor of two hydrogen bonds. Molecules of water and of the protected l ‐tyrosine form hydrogen‐bonded layers perpendicular to [001]. C—H...π interactions are observed in the hydrophobic regions of the structure. The structure is similar to that of N‐acetyl‐l ‐tyrosine ethyl ester monohydrate [Soriano‐García (1993). Acta Cryst. C 49 , 96–97].     

Cationic Heteroconjugation Constants in the OHN+ and NHO+ Systems in Propylene Carbonate: Dependence on Difference in Basicity

Cationic heteroconjugation equilibria of more than ninety systems consisting of substituted pyridines, their N-oxides, and trimethylamine N-oxide, i. e., in systems with mixed hydrogen bridges of type OHN⁺ (NHO⁺) were studied in propylene carbonate. Both experimental systems without proton transfer, BH⁺/B₁, and those with proton transfer, B₁H⁺/B, were explored. The stability of the mixed hydrogen bridges, OHN⁺ (NHO⁺), is compared with that of the OHC⁺-type bridges. The influence of the difference in basicity of the conjugate base of the proton donor and the proton acceptor on the presence of the proton transfer equilibria, and, consequently, the possibility of determination of the cationic heteroconjugation constant values is discussed.     

The thermoelastic behaviour of the orientationally disordered ionic crystals in two dimensions

The anomalous temperature dependence of the elastic constantsc ₁₁ andc ₆₆ and the elastic instability temperatureT _c are obtained in the two-dimensional microscopic model of the alkali cyanides crystals. It has been found, by means of the Michel and Naudts' theory of the translation rotation coupling, that the orientational disorder in the high-temperature phase leads to the critical softening of the shear elastic constantc ₆₆.     

Mechanistic studies on the binding of nitric oxide to a synthetic heme-thiolate complex relevant to cytochrome p450

The synthetic heme-thiolate complex (SR) in methanol binds nitric oxide (k(on) = (2.7 +/- 0.2) x10(6) M(-)(1) s(-)(1) at 25 degrees C) to form SR(NO). The binding of NO to the SR complex in a noncoordinating solvent, such as toluene, was found to be almost 3 orders of magnitude faster than that in methanol. The activation parameters DeltaH(), DeltaS(), and DeltaV() for the formation of SR(NO) in methanol are consistent with the operation of a limiting dissociative mechanism, dominated by dissociation of methanol in SR(MeOH). In the presence of an excess of NO, the formation of SR(NO) is followed by subsequent slower reactions. The substantially negative activation entropy and activation volume values found for the second observed reaction step support an associative mechanism which involves attack of a second NO molecule on the thiolate ligand in the initially formed SR(NO) complex. The following slower reactions are strongly accelerated by a large excess of NO or by the presence of NO(2)(-) in the SR/NO reaction mixture. They can be accounted for in terms of dynamic equilibria between higher nitrogen oxides (NO(x)()) and reactive SR species, which lead to the formation of a nitrosyl-nitrite complex of SR(Fe(II)) as the final product. This finding is clearly supported by laser flash photolysis studies on the SR/NO reaction mixture, which do not reveal simple NO photolabilization from SR(Fe(III))(NO), but rather involve the generation of at least three photoinduced intermediates decaying with different rate constants to the starting material. The species formed along the proposed reaction pathways were characterized by FTIR and EPR spectroscopy. The results are discussed in terms of their relevance for the biological function of cytochrome P450 enzymes and in context of results for the reaction of NO with imidazole- and thiolate-ligated iron(III) hemoproteins.