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...     

An Efficient and Facile Synthesis of Quinoxaline Derivatives Catalyzed by KHSO4 at Room Temperature

Summary. A facile synthesis of quinoxaline derivatives catalyzed by KHSO₄ in very high yields at room temperature is reported.     

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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SnCl4 and SbCl5 promoted aromatization of enamines

Aromatic amines have been synthesized efficiently from enamines using SnCl₄ and SbCl₅ in CH₂Cl₂ at room temperature.     

Adsorptive Behavior of Methylene Blue onto Sawdust of Sour Lemon,Date Palm,and Eucalyptus as Agricultural Wastes

In the present study, to remove methylene blue (MB) from aqueous solution, some agricultural residues and cheap bioadsorbents such as sawdust of palm trees, eucalyptus, and sour lemon were used. To do this, significant parameters like contact time, temperature, pH, initial concentration, and adsorbent dosage were checked. The results affirmed that the best conditions for MB adsorption from aqueous solution were obtained such as the temperature of 25?°C, pH of 8, adsorbent dosage of 2g/L, contact time of 120?minutes, and dye concentration of 5?mg/l which under these conditions the adsorption efficiencies determined were 95.8, 93.4, and 92.8% using sawdust of palm tree, eucalyptus, and sour lemon, respectively. Also, the equilibrium behavior of adsorbents showed that the Freundlich model could better predict the adsorption behavior of the process due to having a larger correlation coefficient (R²). The maximum biosorption capacities by Langmuir isotherm model were also obtained 54, 53.5, and 52.4?mg/g for sawdust of palm trees, eucalyptus, and lemon, respectively, which were significant amounts. In addition, kinetic behavior of adsorption showed that pseudo-second-order model can describe the kinetics of the adsorption process better than the pseudo-first-order model. Moreover, kinetic, equilibrium, and thermodynamic behaviors of adsorption affirmed that the biosorption process was desirable, physisorption, spontaneous, and exothermic.