Dense operators on aKH-module

It is shown that when domain of the modular operator associated with a center-valued weight satisfies certain density condition, the algebra is reduced to the product of a semi-finite algebra and a finite number of properly infinite factors.     

Optimization of headspace solid-phase microextraction for the analysis of specific flavors in enzyme modified and natural Cheddar cheese using factorial design and response surface methodology

A headspace solid-phase microextraction (HS-SPME) combined with gas chromatography-mass spectrometry (GC/MS) method was developed using experimental designs to quantify the flavor of commercial Cheddar cheese and enzyme-modified Cheddar cheese (EMCC). Seven target compounds (dimethyl disulfide, hexanal, hexanol, 2-heptanone, ethyl hexanoate, heptanoic acid, delta-decalactone) representative of different chemical families frequently present in Cheddar cheese were selected for this study. Three types of SPME fibres were tested: Carboxen/polydimethylsiloxane (CAR/PDMS), polyacrylate (PA) and Carbowax/divinylbenzene (CW/DVB). NaCl concentration and temperature, as well as extraction time were tested for their effect on the HS-SPME process. Two series of two-level full factorial designs were carried out for each fibre to determine the factors which best support the extraction of target flavors. Therefore, central composite designs (CCDs) were performed and response surface models were derived. Optimal extraction conditions for all selected compounds, including internal standards, were: 50 min at 55 degrees C in 3M NaCl for CAR/PDMS, 64 min at 62 degrees C in 6M NaCl for PA, and 37 min at 67 degrees C in 6M NaCl for CW/DVB. Given its superior sensitivity, CAR/PDMS fibre was selected to evaluate the target analytes in commercial Cheddar cheese and EMCC. With this fibre, calibration curves were linear for all targeted compounds (from 0.5 to 6 microg g(-1)), except for heptanoic acid which only showed a linear response with PA fibres. Detection limits ranged from 0.3 to 1.6 microg g(-1) and quantification limits from 0.8 to 3.6 microg g(-1). The mean repeatability value for all flavor compounds was 8.8%. The method accuracy is satisfactory with recoveries ranging from 97 to 109%. Six of the targeted flavors were detected in commercial Cheddar cheese and EMCC.     

A magnetically recoverable copper–salen complex as a nano-catalytic system for amine protection via acetylation using thioacetic acid

Research on Chemical Intermediates - A novel copper(II)–salen complex was immobilized on the surface of magnetite nanoparticles using chitosan as a linker. This system exhibits superior...     

Polymeric ionic liquids: a strategy for preparation of novel polymeric materials

A novel polymeric ionic liquid (PIL), bearing high C-N and N-N content, potentially suitable for new safe energetic materials and catalyst supports was introduced. The PIL was prepared by way of radical co-polymerisation of 1-vinyl-3-p-nitrobenzylimidazolium bromide and 1-vinylimidazole at 80°C using azobisisobutyronitrile (AIBN) as an initiator. The PIL thus produced was successfully transformed into NO₃@PIL and N₃@PIL for potential application as safe energetic materials and/or catalyst supports. The polymers were obtained in quantitative yields and were characterised by NMR, FTIR, DSC and TGA data. This study reveals the adequate thermal stability of novel salt-based nitrogen-rich polymeric ionic liquids for application as safe energetic materials and/or supports in heterogeneous catalysis.     

1,2,4,6-Cycloheptatetraenes racemizations: substituent effects via ab initio

Racemizations of three series of non-planar 1-, 4- and 5-X-C₇H₅ cyclic conjugated allenes (1_x, 2_x, and 3_x to 1′_x, 2′_x and 3′_x, respectively) are investigated using ab initio HF, B3LYB and MP2 methods with a 6-31G* basis set (X=H, F, Cl, Br, I, OH, NH₂, CN and NO₂). These three topologically different series of allenes are found to go through their corresponding planar 2-, 3- and 4-X-C₇H₅ singlet carbenic transition states, 1_x–TS, 2_x–TS and 3_x–TS (Series 1: 1_x1_x–TS1′_x; Series 2: 2_x2_x–TS2′_x; Series 3: 3_x3_x–TS3′_x).Frequency calculations show negative force constants for all planar and singlet carbeneic transition states: 1_x–TS, 2_x–TS and 3_x–TS.Based on HF/6-31G*, B3LYP/6-31G* and MP2/6-31g* calculations, the order of substituent effects on energy barrier (ΔG^#) of racemization, increase in the order of: NO₂>CN>H>I>ClBr>OH>F>NH₂ for all three Series 1–3. The height of the energy barrier related to each substituent (X) is highest in Series 3 and lowest in Series 1.Hammet free energy relationships (ρ) found via B3LYP, for Series 1, 2 and 3, are −5.8, −3.4 and −4.1, respectively. Rather similar ρ values are found using HF (−4.3, −4.4 and −4.3). These data indicate that electron-releasing groups highly increase the rate of enantiomeric interconversions.Linearity of the free energy relationships is found to be a function of steric effects. Hence, higher correlation coefficients (R) are found for Hammet free energy relationships for Series 3. This is followed by Series 2, which in turn has a more linear free energy relationship than Series 1 (Series 3>Series 2>Series 1).     

Positive operators on operator algebras

Si dimostra la debole compattezza delle applicazioni lineari positive dalla parte autoaggiunta di un'algebra di von Neumann su uno spazio di Banach parzialmente ordinato, separabile, normale.