Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Incorporation of silica nanoparticles and polyurethane into hybrid composites for increase of char residue

Journal of Thermal Analysis and Calorimetry - Effect of different chain extenders, silica nanoparticle loading, and using sol–gel method on the thermal properties of polyurethane (PU) hybrid...     

A mild and highly efficient protocol for the one-pot synthesis of primary α-amino phosphonates under solvent-free conditions

Under solvent-free reaction conditions and in the presence of solid LiClO₄ a novel and mild protocol for the one-pot, three-component synthesis of primary α-amino phosphonates from an aldehyde, hexamethyldisilazane and a trialkyl phosphite is described giving high yields and having short reaction times. The same products are obtained in very low yields, when the three-component reaction is carried out under microwave irradiation and in the absence of solid LiClO₄. Examples of some prepared 1-aryl-N,N′-bis(arylidene)methanediamines are also described.     

One-pot diastereoselective synthesis of α-aminonitriles from aldehydes, chiral amines, and trimethylsilyl cyanide under solvent-free conditions

Treatment of aliphatic and aromatic aldehydes with chiral amines and trimethylsilyl cyanide in the absence or in the presence of Lewis acids (including lithium perchlorate) under solvent-free conditions afforded the corresponding α-aminonitriles in good yields and with a diastereoselectivity of 68 to 86%. Published in Russian in Zhurnal Organicheskoi Khimii, 2006, Vol. 42, No. 1, pp. 56–59. The text was submitted by the authors in English.     

Silicon-29 diffusion-ordered NMR spectroscopy (DOSY) as a tool for studying aqueous silicates

The first use of silicon-29 diffusion-ordered NMR spectroscopy (DOSY) is reported, in a study of the speciation of aqueous silicates.     

An ultrasensitive fluorescence sensor for determination of trace levels of copper in blood samples

A novel SBA-15-based fluorescent sensor, SBA-PI: mesoporous SBA-15 structure modified with iminostilbene groups, was designed, synthesized, and characterized by Fourier transform-infrared spectroscopy (FT-IR), ultraviolet–visible spectroscopy, field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDS), thermogravimetric analysis (TGA), low-angle X-ray diffraction techniques (low-angle XRD), and N₂ adsorption–desorption techniques. The SBA-PI as a sensor with a selective behavior for detection of Cu²⁺ comprises iminostilbene carbonyl as the fluorophore group. The SBA-PI sensor displays an excellent fluorescence response in aqueous solutions and the fluorescence intensity quenches remarkably upon addition of Cu²⁺. Other common interfering ions even at high concentration ratio showed either no or very small changes in the fluorescence intensity of SBA-PI in the absence of Cu²⁺. A limit of detection of 8.7 × 10⁻⁹ M for Cu²⁺ indicated that this fluorescence sensor has a high sensitivity and selectivity toward the target copper (II) ion. The fabricated Cu²⁺ sensor was successfully applied for the determination of the Cu²⁺ in human blood samples without any significant interference. With the selective analysis of Cu²⁺ ions down to 0.9 nM in blood, the sensor is a promising and a novel detection candidate for Cu²⁺ and can be applied in the clinical laboratory. A reversibility and accuracy in the fluorescence behavior of the sensor was found in the presence of I^¯ that was described as a masking agent for Cu²⁺.

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