Self-commutator inequalities in higher dimension

Three natural multi-dimensional substitutes for the self-commutator of a Hilbert space operator are introduced and generalizations of Putnam's inequality to tuples of operators with semidefinite self-commutators are indicated. In addition, a Riesz transform model is developed and investigated.

     

Asymptotic approximation of functions and their derivatives by Müller’s Gamma operators

We obtain the complete asymptotic expansion of the image functions of Müller’s Gamma operators and of their derivatives. All expansion coefficients are explicitly calculated. Moreover, we study linear combinations of Gamma operators having a better degree of approximation than the operators themselves. Using divided differences we define general classes of linear combinations of which special cases were recently introduced and investigated by other authors.     

A complete asymptotic expansion of power means

The complete asymptotic expansion of power means in terms of Bell polynomials is obtained. Some results recently obtained by M. Bjelica are generalized.     

Some remarks on the behaviour of the solution in dynamic processes for rate-type models

This work examines a dynamic problem in the study of semilinear rate-type models for which the plastic rate of deformation depends also on a parameter . The continuous dependence of the solution with respect to is obtained and the problem of finite time stability is also discussed. In the case when is interpreted as the absolute temperature, the dynamic problem is studied in the context of a Cattaneo-type heat law and also using the classical Fourier law. In the case when is interpreted as an internal state variable an existence and uniqueness result is obtained using a fixed point method and the finite time stability is also investigated.     

Construction of multiporphyrin arrays using ruthenium and rhodium coordination to phosphines

The synthesis of linear multiporphyrin arrays with mono- and bisphosphine-substituted porphyrins as ligand donors and ruthenium(II) or rhodium(III) porphyrins as ligand acceptors is described. With appropriate amounts of the building blocks mixed, linear dimeric and trimeric arrays have been synthesized and analyzed by (1)H NMR and (31)P NMR spectroscopy. The Ru/Rh acceptor porphyrins can be located either at the periphery or in the center of the array. Likewise, the monophosphine porphyrins can be positioned at the periphery, thus allowing a high degree of freedom in the overall composition of the arrays. This way, both donor and acceptor porphyrins can act as chain extenders or terminators. One of the trimeric complexes with two nickel and one ruthenium porphyrin has also been analyzed by X-ray crystallography. Attempts have also been made to synthesize higher order arrays by mixing appropriate amounts of the porphyrins; however, from the NMR data it cannot be concluded if monodisperse five, seven, or nine porphyrin arrays are present or if the solutions are composed of a statistical mixture of smaller and larger arrays.     

Colloidal nano-MOFs nucleate and stabilize ultra-small quantum dots of lead bromide perovskites

The development of synthetic routes to access stable, ultra-small (i.e. <5 nm) lead halide perovskite (LHP) quantum dots (QDs) is of fundamental and technological interest. The considerable challenges include the high solubility of the ionic LHPs in polar solvents and aggregation to form larger particles. Here, we demonstrate a simple and effective host–guest strategy for preparing ultra-small lead bromide perovskite QDs through the use of nano-sized MOFs that function as nucleating and host sites. Cr₃O(OH)(H₂O)₂(terephthalate)₃ (Cr-MIL-101), made of large mesopore-sized pseudo-spherical cages, allows fast and efficient diffusion of perovskite precursors within its pores, and promotes the formation of stable, ∼3 nm-wide lead bromide perovskite QDs. CsPbBr₃, MAPbBr₃ (MA⁺ = methylammonium), and (FA)PbBr₃ (FA⁺ = formamidinium) QDs exhibit significantly blue-shifted emission maxima at 440 nm, 446 nm, and 450 nm, respectively, as expected for strongly confined perovskite QDs. Optical characterization and composite modelling confirm that the APbBr₃ (A = Cs, MA, FA) QDs owe their stability within the MIL-101 nanocrystals to both short- and long-range interfacial interactions with the MOF pore walls.

We demonstrate a simple and effective host–guest strategy for preparing ultra-small lead bromide perovskite QDs through the use of nano-sized MOFs that function as nucleating and host sites.     

On Mercury(I) Oxo Compounds — Quasi‐Relativistic Computational and Experimental Studies

About 60 molecular species composed of up to 10 mercury atoms and of oxygen atoms and/or of some other elements or groups (such as halogen, OH₂, OH, H, alkali, NO₃) have been investigated quantum chemically. Different density functional approaches and the ab initio SCF‐MP2 method were applied, comparing different basis sets and different atomic core sizes. It is important not to treat the Hg 5s, p, d as inactive core shells, and to use sufficiently many polarization functions. The shape of the 〉O‐Hg‐Hg‐O〈 units is not favorable concerning the formation of lattices composed of Hg^I, O and OH only. Despite its bulkiness, the OHgHgO units can easily come into contact with each other and then disproportionate. This is prevented in the so‐called ternary M‐Hg^I oxides by the embedded oxometallate (oxoacidic) anions. Furthermore, the Hg^I and Hg^II oxide bond energies are less favorable towards the stability of Hg^I oxo compounds, as compared to Hg halidic or oxoacidic compounds. Both points are not promising concerning the search for Hg^I oxides/hydroxides, although the preparation of such compounds, including spacer groups, by topochemical reactions can still not be excluded. So far, experimental efforts towards the synthesis of such a new class of compounds have only demonstrated that Hg^II is strictly preferred over Hg^I in the formation of solids of binary Hg‐O or ternary A‐Hg‐O composition (A = electropositive metal such as alkali, in contrast to M = transition or semi‐metal). This is so even if compounds containing ‘electron rich Hg^δ— atoms’ (i.e. A‐Hg amalgams) are oxidized under mild conditions.