π-Complemented Algebras Through Pseudocomplemented Lattices

For an ideal I of a nonassociative algebra A, the ??-closure of I is defined by $\overline{I} = {\rm Ann}({\rm Ann} (I))$ , where Ann(I) denotes the annihilator of I, i.e., the largest ideal J of A such that IJ?=?JI?=?0. An algebra A is said to be ??-complemented if for every ??-closed ideal U of A there exists a ??-closed ideal V of A such that A?=?U????V. For instance, the centrally closed semiprime ring, and the AW ^?-algebras (or more generally, boundedly centrally closed C ^?-algebras) are ??-complemented algebras. In this paper we develop a structure theory for ??-complemented algebras by using and revisiting some results of the structure theory for pseudocomplemented lattices.     

Homogeneous nearly K?hler manifolds

The structure of nearly K?hler manifolds was studied by Gray in several articles, mainly in Gray (Math Ann 223:233?C248, 1976). More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a complete strict nearly K?hler manifold is locally a Riemannian product of homogeneous nearly K?hler spaces, twistor spaces over quaternionic K?hler manifolds and six-dimensional (6D) nearly K?hler manifolds, where the homogeneous nearly K?hler factors are also 3-symmetric spaces. In the present article, we show some further properties relative to the structure of nearly K?hler manifolds and, using the lists of 3-symmetric spaces given by Wolf and Gray, we display the exhaustive list of irreducible simply connected homogeneous strict nearly K?hler manifolds. For such manifolds, we give details relative to the intrinsic torsion and the Riemannian curvature.     

Dynamic transition from modelike patterns to turbulentlike patterns in a broad-area Nd:YAG laser

We report the first experimental observation to our knowledge of a dynamic transition from modelike patterns to completely disordered patterns in a large-aspect-ratio Nd:YAG laser. Recordings of near-field patterns with an integration time as small as 1 ns allow us to follow the evolution of the transverse intensity profile along the output pulse of the laser.     

New stibines containing acetal and formyl group: Platinum complex and unexpected oxastibol derivative

A new tertiary stibine ligand (1) containing acetal group at the ortho-position has been synthesized. This new stibine was then complexed with to obtain trans-PtCl₂L₂ (2) where stibine acts as a monodentate ligand. The acetal was hydrolyzed in a slightly acidic medium and forms a very new stibine (3) containing formyl group at the ortho-position. When (3) was reduced with NaBH₄ an unusual oxastibol (4) derivative was obtained under the experimental conditions used.All the compounds were characterized by IR, mass, ¹H, ¹³C, COSY and HETCOR NMR spectroscopy. The molecular structures of (2), (3) and (4) were determined. Compound (3) crystallizes in two different polymorphs (3a) and (3b) and both the polymorphs show hypervalent antimony with three Sb?O interactions and the molecule exists in O-cis-exo configuration. Compound (4) shows intramolecular Sb?O interactions. To the best of our knowledge this is the first report on organoantimony compounds containing carbonyl groups though their phosphorus and bismuth analogues are well known. Compound (2) shows helicoidal chirality, which is a very new concept in antimony chemistry     

Multicomponent synthesis of acylated short peptoids with antifungal activity against plant pathogens

In this article, we describe the synthesis of a small library of short peptoids composed of four glycine residues and acylated with a fatty acid that showed a remarkable in vitro activity against two fungal plant pathogens. Their straightforward synthesis implied two consecutive Ugi reactions and can be efficiently extended to the construction of highly diverse libraries.     

Entropy–Based Diversification Approach for Bio–Computing Methods

Nature–inspired computing is a promising field of artificial intelligence. This area is mainly devoted to designing computational models based on natural phenomena to address complex problems. Nature provides a rich source of inspiration for designing smart procedures capable of becoming powerful algorithms. Many of these procedures have been successfully developed to treat optimization problems, with impressive results. Nonetheless, for these algorithms to reach their maximum performance, a proper balance between the intensification and the diversification phases is required. The intensification generates a local solution around the best solution by exploiting a promising region. Diversification is responsible for finding new solutions when the main procedure is trapped in a local region. This procedure is usually carryout by non-deterministic fundamentals that do not necessarily provide the expected results. Here, we encounter the stagnation problem, which describes a scenario where the search for the optimum solution stalls before discovering a globally optimal solution. In this work, we propose an efficient technique for detecting and leaving local optimum regions based on Shannon entropy. This component can measure the uncertainty level of the observations taken from random variables. We employ this principle on three well–known population–based bio–inspired optimization algorithms: particle swarm optimization, bat optimization, and black hole algorithm. The proposal’s performance is evidenced by solving twenty of the most challenging instances of the multidimensional knapsack problem. Computational results show that the proposed exploration approach is a legitimate alternative to manage the diversification of solutions since the improved techniques can generate a better distribution of the optimal values found. The best results are with the bat method, where in all instances, the enhanced solver with the Shannon exploration strategy works better than its native version. For the other two bio-inspired algorithms, the proposal operates significantly better in over 70% of instances.