The phenoxy/phenol/copper cation: a minimalistic model of bonding relations in active centers of mononuclear copper enzymes

The "bare" complex [Cu(PhOH)(PhO)](+) with a phenol (PhOH) and a phenoxy (PhO) ligand bound to copper is studied both experimentally and computationally. The binding energies and structure of this complex are probed by mass spectrometry, infrared multi-photon dissociation, and DFT calculations. Further, the monoligated complexes [Cu(PhO)](+) and [Cu(PhOH)](+) are investigated for comparison. DFT calculations on the [Cu(PhOH)(PhO)](+) complex predict that a phenolate anion interacts with copper(II) preferentially through the oxygen atom, and the bonding is associated with electron transfer to the metal center resulting in location of the unpaired electron at the aromatic moiety. Neutral phenol, on the other hand, interacts with copper preferentially through the aromatic ring. The same arrangements are also found in the monoligated complexes [Cu(PhO)](+) and [Cu(PhOH)](+). The calculations further indicate that the bond strength between the copper atom and the oxygen atom of the phenoxy radical is weakened by the presence of neutral phenol from 2.6 eV in bare [Cu(PhO)](+) to 2.1 eV in [Cu(PhOH)(PhO)](+).     

Solution of the generalized master equation for an externally driven and environmentally damped two-level system

Using the Generalized Master Equation (GME) we investigate the dynamics of a two-level system which is subjected both to the influence of a thermal reservoir and to an external driving field. The coupling with the phonon reservoir is represented by the usual (energy-conserving) linear-displacements interaction, which makes the model exactly solvable in the absence of the external field. The coupling with the external field is treated within the Rotating Wave Approximation (RWA). We obtain an exact formal solution of the GME and we construct a hierarchical class of weak-driving approximations avoiding usual assumption of a weak coupling to the bath. The populational difference is damped in a nontrivial manner: the relaxation is nonexponential with long-time tail behaviour in the asymptotic region. The evolution is analysed as a function of temperature, the strength of the coupling, the strength of the external field and the detuning. Our model is formally identical to the spin-boson model and our approach gives a systematic improvement of the noninteracting-blip approximation.     

Non-singular dislocation continuum theories: strain gradient elasticity vs. Peierls–Nabarro model

Abstract

Non-singular dislocation continuum theories are studied. A comparison between Peierls–Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analysed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realistic and physical than the corresponding fields of the Peierls–Nabarro model. Strain gradient elasticity of dislocations is a continuum dislocation theory including a weak non-locality within the dislocation core and predicting the size and shape of the dislocation core. The dislocation core is narrower in the strain gradient elasticity dislocation model than in the Peierls–Nabarro model and more evenly distributed in two dimensions. The present analysis shows that for the modelling of the dislocation core structure the non-singular dislocation fields of strain gradient elasticity are the suitable ones.     

Borel classes of sets of extreme and exposed points in

It is known that the sets of extreme and exposed points of a convex Borel subset of are Borel. We show that for there exist convex subsets of such that the sets of their extreme and exposed points coincide and are of arbitrarily high Borel class. On the other hand, we show that the sets of extreme and of exposed points of a convex set of additive Borel class are of ambiguous Borel class . For proving the latter-mentioned results we show that the union of the open and the union of the closed segments of are of the additive Borel class if is a convex set of additive Borel class .

     

On maximal functions for Mikhlin-Hörmander multipliers

Given Mikhlin-Hörmander multipliers , with uniform estimates we prove an optimal bound in L^p for the maximal function and related bounds for maximal functions generated by dilations. These improve the results in [M. Christ, L. Grafakos, P. Honzík, A. Seeger, Maximal functions associated with multipliers of Mikhlin-Hörmander type, Math. Z. 249 (2005) 223-240].     

Crystalline morphology in polymer blends via competition with spinodal decomposition

Miscible polymer blends containing one crystallizable component and exhibiting liquid-liquid phase separation at elevated temperatures [lower critical solution temperature (LCST) behavior] offer an excellent possibility of controlling morphology and thus mechanical properties. For instance, if a homogeneous mixture of dissimilar polymers is allowed to undergo a rapid temperature jump from below LCST to above LCST, spinodal decomposition takes place and a highly interconnected two-phase morphology with uniform domain size (so-called modulated structure) develops. By quenching the phase-separated system below the glass transition temperature after an appropriate time of phase separation, one is able to fix this characteristic morphology [1]. By quenching the phase-separated blend below the melting point of the crystallizable component to different supercooling depths, it is possible to control the number of nuclei and thus the spherulite's size, creating more or less ordered structures.     

Refined comparison theorems for the Dirac equation in d dimensions

A single spin‐1/2 particle obeys the Dirac equation in spatial dimension and is bound by an attractive central monotone potential which vanishes at infinity (in one dimension the potential is even). This work refines the relativistic comparison theorems which were derived by Hall 1 . The new theorems allow the graphs of the two comparison potentials and to crossover in a controlled way and still imply the spectral ordering for the eigenvalues at the bottom of each angular momentum subspace. More specifically in a simplest case we have: in dimension , if , then ; and in dimensions, if , where and , then .

     

Vertex-antimagic labelings of regular graphs

Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, . . . , p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f (x) assigned to the vertex x together with all values f (xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, . . . , r + 1.