Analytical and statistical studies of Rodriguez–Velazquez indices

Journal of Mathematical Chemistry - In this work we perform analytical and statistical studies of the Rodríguez–Velázquez (RV) indices on graphs G. The topological RV(G) indices,...     

Shape-Adaptability and Redox-Switching Properties of a Di-Gold Metallotweezer

The use of a carbazolyl-connected di-gold(I) metallotweezer for the encapsulation of several electron-poor organic substrates, and a planar Au(III) complex containing a CNC pincer ligand, is described. The binding affinity of the receptor depends on the electron-deficient character of the planar guest, with larger association constants found for the more electron-poor guests. The X-ray diffraction molecular structures of two host:guest adducts show that the host approaches its arms in order to facilitate the optimum interaction with the surface of the planar guests, in a clear example of an guest-induced fit conformational arrangement. The electrochemical studies of the encapsulation of N,N’-dimethyl-naphthalenetetracarboxy diimide (NTCDI) show that the redox active guest is released from the receptor upon one electron reduction, thus constituting an example of redox-switchable binding.     

Stability of AgIII towards Halides in Organosilver(III) Complexes

The involvement of silver in two-electron Ag^I/Ag^III processes is currently emerging. However, the range of stability of the required and uncommon Ag^III species is virtually unknown. Here, the stability of Ag^III towards the whole set of halide ligands in the organosilver(III) complex frame [(CF₃)₃AgX]⁻ (X=F, Cl, Br, I, At) is theoretically analyzed. The results obtained depend on a single factor: the nature of X. Even the softest and least electronegative halides (I and At) are found to form reasonably stable Ag^III−X bonds. Our estimates were confirmed by experiment. The whole series of nonradiative halide complexes [PPh₄][(CF₃)₃AgX] (X=F, Cl, Br, I) has been experimentally prepared and all its constituents have been isolated in pure form. The pseudohalides [PPh₄][(CF₃)₃AgCN] and [PPh₄][(CF₃)₃Ag(N₃)] have also been isolated, the latter being the first silver(III) azido complex. Except for the iodo compound, all the crystal and molecular structures have been established by single-crystal X-ray diffraction methods. The decomposition paths of the [(CF₃)₃AgX]⁻ entities at the unimolecular level have been examined in the gas phase by multistage mass spectrometry (MSⁿ). The experimental detection of the two series of mixed complexes [CF₃AgX]⁻ and [FAgX]⁻ arising from the corresponding parent species [(CF₃)₃AgX]⁻ demonstrate that the Ag−X bond is particularly robust. Our experimental observations are rationalized with the aid of theoretical methods. Smooth variation with the electronegativity of X is also observed in the thermolyses of bulk samples. The thermal stability in the solid state gradually decreases from X=F (145 °C, dec.) to X=I (78 °C, dec.) The experimentally established compatibility of Ag^III with the heaviest halides is of particular relevance to silver-mediated or silver-catalyzed processes.     

A macroscopic model for an intermediate state between type‐I and type‐II superconductivity

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type‐I and type‐II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well‐posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi‐implicit time‐discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty–Browder argument are used. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1551–1567, 2015     

Block partitions of sequences

Given a sequence A = (a ₁, …, a _n ) of real numbers, a block B of A is either a set B = {a _i , a _i+1, …, a _j } where i ≤ j or the empty set. The size b of a block B is the sum of its elements. We show that when each a _i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B ₁, …, B _k with |b _i ?b _j | ≤ 1 for every i, j. We extend this result in several directions.     

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M, the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at T _p M and for the so-called 2-stein curvature tensors, the group Sp(1) ? SO(4) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T ², Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined.