On idempotents of a class of commutative rings

Abstract

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results.     

Intermolecular Carbonyl–olefin Metathesis with Vinyl Ethers Catalyzed by Homogeneous and Solid Acids in Flow

The carbonyl–olefin metathesis reaction has experienced significant advances in the last seven years with new catalysts and reaction protocols. However, most of these procedures involve soluble catalysts for intramolecular reactions in batch. Herein, we show that recoverable, inexpensive, easy to handle, non-toxic, and widely available simple solid acids, such as the aluminosilicate montmorillonite, can catalyze the intermolecular carbonyl–olefin metathesis of aromatic ketones and aldehydes with vinyl ethers in-flow, to give alkenes with complete trans stereoselectivity on multi-gram scale and high yields. Experimental and computational data support a mechanism based on a carbocation-induced Grob fragmentation. These results open the way for the industrial implementation of carbonyl–olefin metathesis over solid catalysts in continuous mode, which is still the origin and main application of the parent alkene–alkene cross-metathesis.     

Ferrocenyl‐Coupled N‐Heterocyclic Carbene Complexes of Gold(I): A Successful Approach to Multinuclear Anticancer Drugs

Four gold(I) carbene complexes featuring 4‐ferrocenyl‐substituted imidazol‐2‐ylidene ligands were investigated for antiproliferative and antivascular properties. They were active against a panel of seven cancer cell lines, including multidrug‐resistant ones, with low micromolar or nanomolar IC₅₀ (72 h) values, according to their lipophilicity and cellular uptake. The delocalized lipophilic cationic complexes 8 and 10 acted by increasing the reactive oxygen species in two ways: through a genuine ferrocene effect and by inhibiting the thioredoxin reductase. Both complexes gave rise to a reorganization of the F‐actin cytoskeleton in endothelial and melanoma cells, associated with a G1 phase cell cycle arrest and a retarded cell migration. They proved antiangiogenic in tube formation assays with endothelial cells and vascular‐disruptive on real blood vessels in the chorioallantoic membrane of chicken eggs. Biscarbene complex 10 was also tolerated well by mice where it led to a volume reduction of xenograft tumors by up to 80 %.     

Friction oscillator excited by moving base and colliding with a rigid or deformable obstacle

The dynamics of non-smooth oscillators has not yet sufficiently been investigated, when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest of this type of systems, an effort is made in this paper to lighten the behaviour of a single-degree-of-freedom oscillator colliding with an obstacle and excited by a moving base, which transfers energy to the system via friction. The different nature of discontinuities arising in the combined problem of friction and impact has been recognized and discussed. Closed-form solutions are presented for both transient and steady-state response, assuming Coulomb's friction law and a rigid stop-limiting motion. Furthermore, a deformable (hysteretic) obstacle has been considered, and its influence on the response has been investigated.     

Experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics

Analytical and experimental investigations are performed in order to characterize the dynamic behaviour of a non-smooth rotational oscillator, which exhibits multiple discontinuity boundaries in the phase space. The physical system consists of a rotating body subjected to an elastic restoring force and in contact with one or two rough discs rotating with constant driving velocities. The presence of multiple discontinuity boundaries caused by frictional contacts leads to non-standard bifurcations that are studied by means of a simple mechanical model.A test set-up has then been built to investigate the correctness of modelling of the friction force and the validity of the proposed model for technical applications: the experimental measurements qualitatively and quantitatively capture the basic scenarios anticipated by the model while a strong robustness of the phenomena pointed out by the theoretical analyses has been revealed in the experiments.     

An efficient coarse-grained approach for the electron transport through large molecular systems under dephasing environment

Dephasing effects in electron transport in molecular systems connected between contacts average out the quantum characteristics of the system, forming a bridge to the classical behavior as the size of the system increases. For the evaluation of the conductance of the molecular systems which have sizes within this boundary domain, it is necessary to include these dephasing effects. These effects can be calculated by using the D’Amato-Pastawski model. However, this method is computationally demanding for large molecular systems since transmission functions for all pairs of atomic orbitals need to be calculated. To overcome this difficulty, we develop an efficient coarse-grained model for the calculation of conductance of molecular junctions including decoherence. By analyzing the relationship between chemical potential and inter-molecular coupling, we find that the chemical potential drops stepwise in the systems with weaker inter-unit coupling. Using this property, an efficient coarse-grained algorithm which can reduce computational costs considerably without losing the accuracy is derived and applied to one-dimensional organic systems as a demonstration. This model can be used for the study of the orientation dependence of conductivity in various phases (amorphous, crystals, and polymers) of large molecular systems such as organic semiconducting materials.