Rigidity of codimension two indefinite spheres

We describe all isometric immersions f:S _n ^s S _s ⁿ +2/S _s ⁿ n–s4, whenever the set of totally geodesic points does not disconnect S _s ⁿ , where S _n ^s denotes the complete n-dimensional indefinite Riemannian space form of constant positive curvature 1 and signature s.     

The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order ¹ and ⁰, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).     

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

Characterisation of raw materials for production of ceramics

The aim of this paper is to characterize some raw materials used for ceramics material production. Five samples of clay have been analyzed. It has been carried out a patterned sampling in a quarry in Rosarno (South Italy). Chemical-physical properties on clay samples are determined. Test pieces have been prepared and physical properties after firing are determined by DSC thermal analysis, XRD analysis and X-ray fluorescence. It is important to note the high amount of Fe₂O₃. The mixture principally contains quartz, illite and oligoclase. It has been observed the colour and the shape after firing: predominant colour is red. In this case the clay has been used in mixtures covered with glazes. The colour of internal clay is hidden by opaque of glazes. The analysed raw materials can be used in a slip for single fired red tiles. The A2sp clay produces best ceramics at 1000°C.     

A convenient two-step synthesis of 6-methylenesubstituted-4-trichloromethyl-2-methylsulfanyl pyrimidines

This work reports a two-step synthetic strategy to obtain a series of 6-methylenesubstituted-4-trichloromethyl-2-methylsulfanylpyrimidines from the cyclization of 5-bromo-4-methoxy-1,1,1-trichloro-pent-3-en-2-ones with 2-methyl-2-pseudothiourea sulfate, followed by nucleophilic substitution of 6-bromomethyl-4-trichloromethyl-2-methylsulfanylpyrimidine with a series of nucleophiles. Alternative strategies to obtain 6-halomethyl-4-trichloro[fluoro]methyl-2-methylsulfanyl pyrimidines have been addressed.     

Determination of fluquinconazole, pyrimethanil, and clofentezine residues in fruits by liquid chromatography with ultraviolet detection

A simple method was developed for the determination of fluquinconazole, pyrimethanil, and clofentezine in whole fruit; peel; and pulp of mango, apple, and papaya. These compounds were extracted from fruit samples with a mixture of ethyl acetate-n-hexane (1 + 1, v/v). An aliquot (2 mL) of the extract was evaporated to near dryness under a stream of nitrogen, and the residue was dissolved with 2 mL methanol. The analysis was performed by means of liquid chromatography with ultraviolet detection at 254 nm using a gradient solvent system. The method was validated with fortified fruit samples at concentration levels of 0.05, 0.10, 0.20, and 0.50 mg/kg. Average recoveries (4-8 replicates) ranged from 80 to 95% with relative standard deviations between 3.5 and 12.7%. Detection limits ranged from 0.03 to 0.05 mg/kg for fruit pulp and 0.03 mg/kg for whole fruit. The quantitation limits ranged from 0.05 to 0.10 mg/kg for fruit pulp and 0.05 mg/kg for whole fruit. The analytical method was applied to fruit samples obtained from local markets.     

Racemization in stepwise solid-phase peptide synthesis at elevated temperatures

The present work is an attempt to assess racemization in stepwise solid-phase peptide synthesis at elevated temperatures (SPPS-ET), a high-speed approach in which peptide elongation occurs at 55-75 °C. This attempt was based on the notion that a high propensity for this side reaction would hamper employment of this alternative approach and would dampen interest in its further development. Simple peptide models were synthesized using customized protocols for classical SPPS or SPPS-ET. Systematic analyses of the resulting crude peptides by reversed-phase HPLC, ion-exchange HPLC, capillary electrophoresis and electrospray ionization mass spectrometry revealed low diastereomeric byproduct contents. These results indicate that, from the standpoint of racemization, classical SPPS and SPPS-ET protocols were equivalent. Therefore, further studies employing SPPS-ET protocols are justified.     

Synthesis of [1,3]dithiole and spiro[1,3]dithiole thiopyran derivatives of the [1,2]dithiolo[1,4]thiazine ring system

We report the synthesis of some new polysulfur-nitrogen heterocycles by cycloaddition reactions to readily available tricyclic condensed 1,2-dithiole-3-thiones. Thus, treatment of bis[1,2]dithiolopyrrole ketothione 1 with diacyl acetylenes gave the bis-aducts 2a-d. On the other hand, cycloaddition of bis[1,2]dithiolo[1,4]thiazine ketothione 3 with 1 equiv of acyl or diacyl acetylenes gave [1,3]dithiolylidenyl[1,2]dithiolo[1,4]thiazines 4a-f in fair to high yields. Catalysis by scandium triflate was used in the reactions that implied the less reactive dipolarophiles. Treatment of 3 with 2 equiv of DBA gave the bis-aduct 5a, and reaction of 4c with DMAD gave the mixed bis-adduct 5b. Cyclic voltammetry of selected examples showed irreversible processes that were influenced by the electrochemical activity of peripheral groups bonded to the heterocyclic system.     

Application of molecular absorption properties of horseradish peroxidase for self-indicating enzymatic interactions and analytical methods

In this paper an in depth study is presented of the use of the horseradish peroxidase (HRP) enzyme as a self-indicating biorecognition reagent in UV-vis molecular absorption spectrometry. The HRP/H2O2 reaction mechanism in the absence of an external substrate has been clarified, and the interaction between HRP and glucose oxidase (GOx) has been studied. It has been demonstrated that GOx can act as a substrate of HRP; in both cases the kinetic constants have been obtained and mathematical models have been developed. Second, the HRP/H2O2 reaction is used to follow a H2O2-producing enzymatic reaction, the glucose reaction with GOx being used as a model. As an application of this, two methodologies have been proposed for glucose determination: with or without previous incubation of glucose with GOx. In both cases mathematical models relating HRP absorbance changes to glucose concentration have been developed and tested; both methods have been optimized, analytically characterized, and tested for glucose determination in samples. The methodology described could be applied to other heme-proteins and to other H2O2-producing enzymatic reactions. The models permit the reaction constants to be calculated. From the analytical chemistry point of view the models allow the prediction of the method sensitivity for other analytes involved in this type of reaction if the kinetic constants are known and can be used in the design of optical sensors.