Column completion of a pair of matrices

Given a pair of matrices (AB) it is well known that its invariant factors and its controllability indices form a complete set of invariants for the Γ-equivalence [11] or block similarity [5]. How do they vary by adding columns to B? This problem was solved in [12] when B = 0; here we give a complete answer for this question.     

C60 Based Hybrid Nanocomposites Obtained in the Presence of Ultrasounds

Since their discovery, fullerenes in general and buckminsterfullerene C₆₀ in particular, became a subject of great interest for studies. Being compatible with the sol–gel process, one of the promising approaches is to incorporate the fullerene molecules in sol–gel oxide matrices. Great part of studies deals with SiO₂ sol–gel oxide as the optimal matrix for entrapment of organic molecules. C₆₀-doped silica matrices used through our present study have been prepared by sol–gel processing, using different alkoxide precursors, as a silicon oxide source: tetraethoxysilane (a), methyltriethoxysilane (b), phenyltriethoxysilane (c) and a mixture of phenyltriethoxysilane and tetraethoxysilane (d). C₆₀-to-Si molar ratio was chosen to be 1.0 × 10^?3:1 for all materials synthesized, final oxide composition remaining unchanged in all cases. The effect of ultrasounds on the gelation process was established by preparing two series of samples, either via sonication or in the absence of ultrasound processing. The properties of the resulted materials were also established. The prepared samples were characterized by XRD, IR, RPE and UV-VIS spectrometry. All methods have put in evidence the embedment of the fullerene into the silica matrix.     

Two-step electrochemical annulation for the assembly of polycyclic systems

[reaction: see text] A two-step electrochemical annulation has been developed for the preparation of fused furans. The process involves an initial conjugate addition of a furyethyl cuprate and trapping of the enolate as the corresponding silyl enolether. The second step of the annulation involves the anodic coupling of the furan and the silyl enol ether to form a six-membered ring.     

Bridged synthons from tetrabromocyclopropene: studies on the rearrangement of the primary Diels-Alder adduct with 2,5-dimethylfuran

The reaction of tetrabromocyclopropene and furan leads directly to 8-oxabicyclo[3.2.1]octadiene derivatives. It has been proposed that this involves an initial Diels-Alder reaction followed by rearrangement of the primary adduct. We have, for the first time, isolated a primary adduct and established through X-ray crystallographic analysis that the adduct is the product of an exo-selective addition. Kinetic studies suggest the intermediacy of charged intermediates during the rearrangement.     

Reactions of TFDA with ketones. synthesis of difluoromethyl 2,2-difluorocyclopropyl ethers

The sequential reaction of 2 equiv of difluorocarbene (generated from trimethylsilyl fluorosulfonyldifluoroacetate (TFDA) by treatment with catalytic fluoride ion) with a series of electron-rich aromatic ketones and alpha,beta-unsaturated ketones leads to the formation of difluoromethyl 2,2-difluorocyclopropyl ethers in good yield.     

Microstructure and mechanical characteristics of hydroxyapatite coatings on Ti/TiN/Si substrates synthesized by pulsed laser deposition

We synthesized by pulsed laser deposition a bilayer of Ti/TiN on Si(100) wafers which was coated in a next step with hydroxyapatite (samples labelled HA-1). Some of the structures were further thermally treated in a water vapour jet (samples labelled HA-2). In SEM, the HA surface looked rough, with micronic droplets. TEM and SAED investigations revealed a compact organization of HA crystals in the case of the HA-1 sample, while two regions (one compact and one porous) were identified for the HA-2 sample, with triclinic HA crystals within the 500 nm range. In XTEM, at the Si/TiN border, a 2–3 nm SiO₂ layer was visible, whereas at the TiN/Ti border there was a smooth transition from fcc (111) TiN to hcp (100) Ti. The HA crystals were elongated normal to the surface. According to Berkovich indentation qualitative analyses, the sample HA-1 was more homogeneous and harder but brittle. Scratch tests confirmed quantitatively that HA-1 was more resistant and adherent than HA-2 films. In the first case, the big droplets only were removed by the indenter, while the HA-2 films were delaminated on large areas as a result of wedge spallation failure.     

Shaping distinct magnetic interactions in molecular compounds

Oxalates containing various 3d transitional elements and positive NH₄ or negative OH groups were newly synthesized. Each above-mentioned component has directly influenced the structure, the electronic or interaction properties, while some unexpected behaviors were revealed by various magnetic and Mössbauer measurements. The main magnetic parameters, the long-range anti-ferromagnetic couplings observed at very low temperature and, particularly the uncompensated moment are discussed in detail. The induced lower spin states for bivalent ions and especially the anti-parallel arrangement of the spins belonging to trivalent and bivalent iron inside the molecule are also emphasized.     

Operators with N-threshold for uncertainty management

In this paper we present a pair of operators (t-norm, t-conorm) dual with a strong negation with n-thresholda ₁, …,a _n ∈(0, 1),a ₁<a ₂< …<a _n . In this way we obtain an extension of operators with threshold, that are obtained forn=1. The new pair is obtained from given one.     

Anion mediated,tunable isoguanosine self-assemblies: decoding the conformation influence and solvent effects

Systematic investigations were performed with various substituted groups at C8 purine and ribose. A series of isoG analogs, C8-phenyl substituted isoG were synthesized and applied for Cs⁺ coordination. The structural proximity between purine and ribose limited pentaplex formation for C8-phenyl substituted isoG derivatives. Based on this observation, deoxy isoG derivative with modification on ribose (tert-butyldimethylsilyl ether) was applied to assemble with the Cs⁺ cation. Critical solvent (CDCl₃ and CD₃CN) and anion (BPh₄⁻, BARF⁻, and PF₆⁻) effects were revealed, leading to the controllable formation of various stable isoG pentaplexes, including singly charged decamer, doubly charged decamer, and 15-mer, etc. Finally, the X-ray crystal structure of [isoG₂₀Cs₃]³⁺(BARF⁻)₃ was successfully obtained, which is the first example of multiple-layer deoxy isoG binding with the Cs⁺ cation, providing solid evidence of this new isoG ionophore beyond two-layer sandwich self-assembly.

The first example of multiple-layer deoxy isoG self-assembly was characterized by X-ray crystal structure. Critical solvent and anion effects were revealed, leading to the controllable formation of various stable isoG assemblies.     

On the Computation of the Third Order Terms of the Series Defining the Center Manifold for a Scalar Delay Differential Equation

When computing the third order terms of the series of powers of the function whose graph is the center manifold, at an equilibrium point of a scalar delay differential equation with a single constant delay r > 0, some problems occur at the term w_2,1z²[`(z)].{w_{2,1}z^2\overline{z}.} More precisely, in order to determine the values at 0, respectively −r of the function w _2,1(.), an algebraic system of equations must be solved. We show that the two equations are dependent, hence the system has an infinity of solutions. Then we show how we can overcome this lack of uniqueness and provide a formula for w _2,1(0).