A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Theoretical study of (e,2e) triple differential cross sections of pyrimidine and tetrahydrofurfuryl alcohol molecules using multi-center distorted-wave method

We report theoretical studies of electron impact triple differential cross sections of two bio-molecules,pyrimidine and tetrahydrofurfuryl alcohol,in the coplanar asymmetric kinematic conditions with the impact energy of 250 eV and ejected electron energy of 20 eV at three scattering angles of-5°,-10°,and-15°.Present multi-center distorted-wave method well describes the experimental data,which was obtained by performing(e,2e)experiment.The calculations show that the secondary electron produced by the primary impact electron is strongly influenced by the molecular ionic multi-center potential,which must be considered when the low energy electron interacts with DNA analogues.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Cobalt-Catalyzed Regio- and Stereoselective Hydroboration of Allenes

An efficient pincer-ligand-based cobalt-complex-catalyzed allene hydroboration affording Z-allylic boronates is described. The reaction demonstrates an excellent regio- as well as Z-stereoselectivity and a wide substrate scope that tolerates many functional groups. Based on solvent-assisted electrospray ionization mass spectrometry (SAESI-MS) studies, a rationale for the cobalt-catalyzed hydroboration involving the highly selective insertion of an allene into the Co−H bond to form Z-allylic cobalt intermediates is proposed.     

Air-Stable Hexagonal Bipyramidal Dysprosium(III) Single-Ion Magnets with Nearly Perfect D6h Local Symmetry

Eight-coordinated Dy^III centres with D_6h symmetry are expected to act as high-performance single-molecule magnets (SMMs) due to the simultaneous fulfilment of magnetic axiality and a high coordination number (a requisite for air stability). But the experimental realization is challenging due to the requirement of six coordinating atoms in the equatorial plane of the hexagonal bipyramid; this is usually too crowded for the central Dy^III ion. Here a hexaaza macrocyclic Schiff base ligand and finetuned axial alkoxide/phenol-type ligands are used to show that a family of hexagonal bipyramidal Dy^III complexes can be isolated. Among them, three complexes possess nearly perfect D_6h local symmetry. The highest effective magnetic reversal barrier is found at 1338(3) K and an open hysteresis temperature of 6 K at the field sweeping rate of 1.2 mT s⁻¹; this represents a new record for D_6h SMMs.     

Rhodium‐Catalyzed Stitching Polymerization of 1,5‐Hexadiynes and Related Oligoalkynes

A new mode of polymerization, rhodium‐catalyzed stitching polymerization, has been developed for the synthesis of π‐conjugated polymers with bridged repeating units from nonconjugated 1,5‐hexadiynes containing both terminal and internal alkyne moieties as monomers. The polymerization proceeded smoothly with a high degree of stitching efficiency under mild conditions, and 1,5,9‐decatriyne and 1,5,9,13‐tetradecatetrayne monomers could also be employed. The present polymerization strategy would be particularly beneficial for the synthesis of polymers consisting of a repeating unit that is difficult to prepare as a stable monomer because it does not require the use of a preformed bridged π‐conjugated monomer.