Noncommutative 4-Spheres Based on all Podleś 2-Spheres and Beyond

A wide class of noncommutative spaces, including 4-spheres based on all the quantum 2-spheres and suspensions of matrix quantum groups is described. For each such space a noncommutative vector bundle is constructed. This generalises and clarifies various recent constructions of noncommutative 4-spheres.     

Silicon Carbide Modified Carbon Materials. Formation of Nanocrystalline SiC from Thermochemical Processes in the System Coal Tar Pitch/Poly(carbosilane)

Poly(carbosilane) or PCS, {–CH₂–SiH(CH₃)–} _n , is used as a Si-bearing precursor in combination with a coal tar pitch to study thermally induced transformations toward SiC-modified carbon composites. Following mixing of the components in the molten pitch at 160°C, the mixture is heated under argon atmosphere at 500°C yielding a solid carbonizate that is further subjected to separate pyrolysis experiments at 1300°C or 1650°C. At temperatures up to 500°C, the PCS reacts with suitable pitch components as well as undergoing decomposition reactions. At higher temperatures, clusters of prevailingly nanocrystalline -SiC are confirmed after the 1650°C pyrolysis step with indications that the formation of the compound starts at 1300°C. ²⁹Si MAS NMR, XRD, FT-IR, XPS, and elemental analysis are used to characterize each pyrolysis step, especially, from the viewpoint of transformation of silicon species to silicon carbide in the carbon matrix evolved from the pitch.     

Simulation of the opening and closing of Hsp70 chaperones by coarse-grained molecular dynamics

Heat-shock proteins 70 (Hsp70s) are key molecular chaperones which assist in the folding and refolding/disaggregation of proteins. Hsp70s, which consist of a nucleotide-binding domain (NBD, consisting of NBD-I and NBD-II subdomains) and a substrate-binding domain [SBD, further split into the β-sheet (SBD-β) and α-helical (SBD-α) subdomains], occur in two major conformations having (a) a closed SBD, in which the SBD and NBD domains do not interact, (b) an open SBD, in which SBD-α interacts with NBD-I and SBD-β interacts with the top parts of NBD-I and NBD-II. In the SBD-closed conformation, SBD is bound to a substrate protein, with release occurring after transition to the open conformation. While the transition from the closed to the open conformation is triggered efficiently by binding of adenosine triphosphate (ATP) to the NBD, it also occurs, although less frequently, in the absence of ATP. The reverse transition occurs after ATP hydrolysis. Here, we report canonical and multiplexed replica exchange simulations of the conformational dynamics of Hsp70s using a coarse-grained molecular dynamics approach with the UNRES force field. The simulations were run in the following three modes: (i) with the two halves of the NBD unrestrained relative to each other, (ii) with the two halves of the NBD restrained in an "open" geometry as in the SBD-closed form of DnaK (2KHO), and (iii) the two halves of NBD restrained in a "closed" geometry as in known experimental structures of ATP-bound NBD forms of Hsp70. Open conformations, in which the SBD interacted strongly with the NBD, formed spontaneously during all simulations; the number of transitions was largest in simulations carried out with the "closed" NBD domain, and smallest in those carried out with the "open" NBD domain; this observation is in agreement with the experimentally-observed influence of ATP-binding on the transition of Hsp70's from the SBD-closed to the SBD-open form. Two kinds of open conformations were observed: one in which SBD-α interacts with NBD-I and SBD-β interacts with the top parts of NBD-I and NBD-II (as observed in the structures of nucleotide exchange factors), and another one in which this interaction pattern is swapped. A third type of motion, in which SBD-α binds to NBD without dissociating from SBD-β was also observed. It was found that the first stage of interdomain communication (approach of SBD-β, to NBD) is coupled with the rotation of the long axes of NBD-I and NBD-II towards each other. To the best of our knowledge, this is the first successful simulation of the full transition of an Hsp70 from the SBD-closed to the SBD-open conformation.     

Thermodynamic and structural properties of binary mixtures of some glycols with 2-butoxyethanol at T = (293.15, 298.15 and 303.15) K

Densities and relative permittivities at T = (293.15, 298.15, and 303.15) K in the binary mixtures of 2-butoxyethanol with ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol have been measured as a function of composition. From the experimental data excess molar volumes and deviations in relative permittivity have been calculated over the entire composition range. Both excess molar volumes and relative permittivity deviations have been correlated using Redlich–Kister type polynomial equation by the method of least-squares for the estimation of the binary coefficients and the standard errors. The experimental and calculated quantities were used to analyze the mixing behaviour of the components.     

The doping effect of fluorinated aromatic solvents on the rate of ruthenium-catalysed olefin metathesis

A study concerning the effect of using a fluorinated aromatic solvent as the medium for olefin metathesis reactions catalysed by ruthenium complexes bearing N-heterocyclic carbene ligands is presented. The use of fluorinated aromatic hydrocarbons (FAH) as solvents for olefin metathesis reactions catalysed by standard commercially available ruthenium pre-catalysts allows substantially higher yields of the desired products to be obtained, especially in the case of demanding polyfunctional molecules, including natural and biologically active compounds. Interactions between the FAH and the second-generation ruthenium catalysts, which apparently improve the efficiency of the olefin metathesis transformation, have been studied by X-ray structure analysis and computations, as well as by carrying out a number of metathesis experiments. The optimisation of reaction conditions by using an FAH can be regarded as a complementary approach for the design of new improved ruthenium catalysts. Fluorinated aromatic solvents are an attractive alternative medium for promoting challenging olefin metathesis reactions.     

On convex iterative roots of non-monotonic mappings

Let I be an interval. We consider the non-monotonic convex self-mappings \(f:I\rightarrow I\) such that \(f^2\) is convex. They have the property that all iterates \(f^n\) are convex. In the class of these mappings we study three families of functions possessing convex iterative roots. A function f is said to be iteratively convex if f possesses convex iterative roots of all orders. A mapping f is said to be dyadically convex if for every \(n\ge 2\) there exists a convex iterative root \(f^{1/2^n}\) of order \(2^n\) and the sequence \(\{f^{1/2^n}\}\) satisfies the condition of compatibility, that is \( f^{1/2^n}\circ f^{1/2^n}= f^{1/2^{n-1}}.\) A function f is said to be flowly convex if it possesses a convex semi-flow of f, that is a family of convex functions \(\{f^t,t>0\}\) such that \(f^t\circ f^s=f^{t+s}, \ \ t,s >0\) and \(f^1=f\). We show the relations among these three types of convexity and we determine all convex iterative roots of non-monotonic functions.     

On multiplicatively-additive iteration groups

Aequationes mathematicae - Define on the set $$G:=\mathbb R^+\times \mathbb R$$ the operation $$(t,a)*(s,b)=(ts,tb+a)$$ . $$(G,*)$$ is a non-commutative group with the neutral element...