Synthesis, Characterization, and Fluxional Behaviour of Binuclear Palladium Complexes with a Half-A-Frame Structure

Summary.  Partial removal of chloride anions from the dimer [Pd(η³-2-CH₃*C₃H₄)(μ-Cl)]₂ with AgTf(Tf = CF₃SO₃) followed by addition of dppm affords [Pd₂(η³-Me*C₃H₄)₂(μ-Cl)(μ-dppm)]Tf (1). The substitution of Cl⁻ by X⁻ (X = pz, SC₆F₅, S _py ) using the appropriate salts yields the new derivatives [Pd₂(η³-Me*C₃H₄)₂(μ-X)(μ-dppm)]Tf (2–4). All complexes exhibit a dinuclear half-A-frame structure with two isomers present in solution. The isomers differ in the relative orientation of the two allyl groups (cis or trans). The isomer interconversion was studied by variable temperature ¹H NMR spectroscopy. The molecular structures of 2 and 4 were solved by X-ray diffraction studies. A distorted boat conformation of the seven- or six-membered metallacycle was found in both cases. Received June 7, 2000. Accepted June 20, 2000     

Splitting Potential and the Poincaré-Melnikov Method for Whiskered Tori in Hamiltonian Systems

Summary. We deal with a perturbation of a hyperbolic integrable Hamiltonian system with n+1 degrees of freedom. The integrable system is assumed to have n -dimensional hyperbolic invariant tori with coincident whiskers (separatrices). Following Eliasson, we use a geometric approach closely related to the Lagrangian properties of the whiskers, to show that the splitting distance between the perturbed stable and unstable whiskers is the gradient of a periodic scalar function of n phases, which we call splitting potential. This geometric approach works for both the singular (or weakly hyperbolic) case and the regular (or strongly hyperbolic) case, and provides the existence of at least n+1 homoclinic intersections between the perturbed whiskers. In the regular case, we also obtain a first-order approximation for the splitting potential, that we call Melnikov potential. Its gradient, the (vector) Melnikov function, provides a first-order approximation for the splitting distance. Then the nondegenerate critical points of the Melnikov potential give rise to transverse homoclinic intersections between the whiskers. Generically, when the Melnikov potential is a Morse function, there exist at least 2 ⁿ critical points. The first-order approximation relies on the n -dimensional Poincaré-Melnikov method, to which an important part of the paper is devoted. We develop the method in a general setting, giving the Melnikov potential and the Melnikov function in terms of absolutely convergent integrals, which take into account the phase drift along the separatrix and the first-order deformation of the perturbed hyperbolic tori. We provide formulas useful in several cases, and carry out explicit computations that show that the Melnikov potential is a Morse function, in different kinds of examples. Received January 18, 1999; final revision received October 25, 1999; accepted December 12, 1999     

Orlicz-Pettis Polynomials on Banach Spaces

 We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between these polynomials and the corresponding linear operators. (Received 17 May 1999; in revised form 6 October 1999)     

6‐Amino‐3‐methyl‐5‐nitro­so­pyrimi­dine‐2,4(1H,3H)‐dione forms a three‐dimensional hydrogen‐bonded framework structure

Molecules of the title compound, C₅H₆N₄O₃, are linked into a single three‐dimensional framework by a two‐centre N—H⃛O hydrogen bond [H⃛O = 1.92 Å, N⃛O = 2.785 (2) Å and N—H⃛O = 168°], a two‐centre N—H⃛H hydrogen bond [H⃛N = 2.19 Å, N⃛N = 3.017 (2) Å and N—H⃛N = 157°] and the intermolecular component of an effectively planar three‐centre N—H⃛(O)₂ hydrogen bond [H⃛O = 2.03 and 2.31 Å, N⃛O = 2.645 (2) and 2.957 (2) Å, N—H⃛O = 126 and 130°, and O⃛H⃛O = 101°].     

The Participation of 3,3,3-Trichloro-1-nitroprop-1-ene in the [3 + 2] Cycloaddition Reaction with Selected Nitrile N-Oxides in the Light of the Experimental and MEDT Quantum Chemical Study

The regioselective zw-type [3 + 2] cycloaddition (32CA) reactions of a series of aryl-substituted nitrile N-oxides (NOs) with trichloronitropropene (TNP) have been both experimentally and theoretically studied within the Molecular Electron Density Theory (MEDT). Zwitterionic NOs behave as moderate nucleophiles while TNP acts as a very strong electrophile in these polar 32CA reactions of forward electron density flux, which present moderate activation Gibbs free energies of 22.8–25.6 kcal·mol⁻¹ and an exergonic character of 28.4 kcal·mol⁻¹ that makes them irreversible and kinetically controlled. The most favorable reaction is that involving the most nucleophilic MeO-substituted NO. Despite Parr functions correctly predicting the experimental regioselectivity with the most favorable O-CCCl₃ interaction, these reactions follow a two-stage one-step mechanism in which formation of the O-C(CCl₃) bond takes place once the C-C(NO₂) bond is already formed. The present MEDT concludes that the reactivity differences in the series of NOs come from their different nucleophilic activation and polar character of the reactions, rather than any mechanistic feature.     

Novel synthesis of new 1,2,4‐trithioles by reductive coupling of benzoyldithioacetic acid derivatives mediated by Sml2

1,2,4‐trithioles 2a–e are readily obtained in good yields by dimerization of benzoyldithioacetic acid derivatives using samarium diiodide as a promotor under very mild conditions. The structures of compounds 2a–e were determined by IR, ¹H, and ¹³C NMR spectroscopies using heteronuclear multiple bond correlation, heteronuclear multiple quantum correlation, and nuclear Overhauser enhancement spectroscopy experiments, mass spectrometry, and, in the case of 2a, the structure was confirmed by single‐crystal X‐ray diffraction studies. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:329–335, 2000     

A Comprehensive Experimental and Theoretical Study on the [{(η5-C5H5)2Zr[P(µ-PNEt2)2P(NEt2)2P]}]2O Crystalline System

The structure of tetraphosphetane zirconium complex C₅₂H₁₀₀N₈OP₁₀Zr₂ 1 was determined by single crystal X-ray diffraction analysis. The crystal belongs to the monoclinic system, space group P21/c, with a = 19.6452(14), b = 17.8701(12), c = 20.7963(14)Å, α = γ = 90°, β = 112.953(7)°, V = 6722.7(8)Å3, Z = 4. The electronic structure of the organometallic complex has been characterized within the framework of Quantum Chemical Topology. The topology of the Electron Localization Function (ELF) and the electron density according to the Quantum Theory of Atoms in Molecules (QTAIM) show no covalent bonds involving the Zr atom, but rather dative, coordinate interactions between the metal and the ligands. This is the first reported case of a Zr complex stabilized by an oxide anion, anionic cyclopentadienyl ligands and rare tetraphosphetane anions.     

Smartphone-Based Colorimetric Method to Quantify Iron Concentration and to Determine the Nanoparticle Size from Suspensions of Magnetic Nanoparticles

Advanced uses of smartphones are changing lifestyles, and may have a great impact in materials science in the near future. In this work, the use of these devices to develop fast, simple, and cheap methods to characterize magnetic nanoparticle suspensions is tested. A series of dilutions of a wide library of magnetic nanoparticles, composed of iron oxide materials in the range between 3 and 43 nm, with two different shapes and four different coatings is prepared. The colloid color is analyzed using the RGB (red, green, blue) color model. Ratios of these parameters are correlated with the suspension iron concentration and with the nanoparticles average size. A linear relationship between the color (in particular the G/R ratio) and both the colloid iron content and the particles size is found. The link between these parameters allows the development of two new methods to determine either the concentration or the particle size of magnetic nanoparticle suspensions just by acquiring images from suspensions of iron oxide magnetic nanoparticles with a smartphone.     

Multi-Class Classification of Medical Data Based on Neural Network Pruning and Information-Entropy Measures

Medical data includes clinical trials and clinical data such as patient-generated health data, laboratory results, medical imaging, and different signals coming from continuous health monitoring. Some commonly used data analysis techniques are text mining, big data analytics, and data mining. These techniques can be used for classification, clustering, and machine learning tasks. Machine learning could be described as an automatic learning process derived from concepts and knowledge without deliberate system coding. However, finding a suitable machine learning architecture for a specific task is still an open problem. In this work, we propose a machine learning model for the multi-class classification of medical data. This model is comprised of two components—a restricted Boltzmann machine and a classifier system. It uses a discriminant pruning method to select the most salient neurons in the hidden layer of the neural network, which implicitly leads to a selection of features for the input patterns that feed the classifier system. This study aims to investigate whether information-entropy measures may provide evidence for guiding discriminative pruning in a neural network for medical data processing, particularly cancer research, by using three cancer databases: Breast Cancer, Cervical Cancer, and Primary Tumour. Our proposal aimed to investigate the post-training neuronal pruning methodology using dissimilarity measures inspired by the information-entropy theory; the results obtained after pruning the neural network were favourable. Specifically, for the Breast Cancer dataset, the reported results indicate a 10.68% error rate, while our error rates range from 10% to 15%; for the Cervical Cancer dataset, the reported best error rate is 31%, while our proposal error rates are in the range of 4% to 6%; lastly, for the Primary Tumour dataset, the reported error rate is 20.35%, and our best error rate is 31%.