Stochastic predator–prey model with Allee effect on prey

We study a predator–prey model with the Allee effect on prey and whose dynamics is described by a system of stochastic differential equations assuming that environmental randomness is represented by noise terms affecting each population. More specifically, we consider a term that expresses the variability of the growth rate of both species due to external, unpredictable events. We assume that the intensities of these perturbations are proportional to the population size of each species. With this approach, we prove that the solutions of the system have sample pathwise uniqueness and bounded moments. Moreover, using an Euler–Maruyama-type numerical method we obtain approximated solutions of the system with different intensities for the random noise and parameters of the model. In the presence of a weak Allee effect, we show that long-term survival of both populations can occur. On the other hand, when a strong Allee effect is considered, we show that the random perturbations may induce the non-trivial attracting-type invariant objects to disappear, leading to the extinction of both species. Furthermore, we also find the Maximum Likelihood estimators for the parameters involved in the model.     

Synthesis of Cephalexin in Aqueous Medium with Carrier-bound and Carrier-free Penicillin Acylase Biocatalysts

The use of very high substrate concentrations favors the kinetically controlled synthesis of cephalexin with penicillin acylase (PA) not only by Michaelian considerations, but also because water activity is depressed, so reducing the rates of the competing reactions of product and acyl donor hydrolysis. Commercial PGA-450, glyoxyl agarose immobilized (PAIGA) and carrier-free cross-linked enzyme aggregates of penicillin acylase (PACLEA) were tested in aqueous media at concentrations close to the solubility of nucleophile and at previously determined enzyme to nucleophile and acid donor to nucleophile ratios. The best temperature and pH were determined for each biocatalyst based on an objective function considering conversion yield, productivity, and enzyme stability as evaluation parameters. Stability was higher with PAIGA and specific productivity higher with PACLEA, but best results based on such objective function were obtained with PGA-450. Yields were stoichiometric and productivities higher than those previously reported in organic medium, which implies significant savings in terms of costs and environmental protection. At the optimum conditions for the selected biocatalyst, operational stability was determined in sequential batch reactor operation. The experimental information gathered is being used for a technical and economic evaluation of an industrial process for enzymatic production of cephalexin in aqueous medium.     

An accurate calibration method for high pressure vibrating tube densimeters in the density interval (700 to 1600) kg · m−3

A calibration procedure of vibrating tube densimeters for density measurement of liquids in the intervals (700 to 1600) kg · m^?3, (283.15 to 323.15) K, and (0.1 to 60) MPa is presented. It is based on the modelization of the vibrating tube as a thick-tube clamped at one end (cantilever) whose stress and thermal behaviour follows the ideas proposed in the Forced Path Mechanical Calibration model (FPMC). Model parameters are determined using two calibration fluids with densities certified at atmospheric pressure (dodecane and tetracholoroethylene) and a third one with densities known as a function of pressure (water). It is applied to the Anton Paar 512P densimeter, obtaining density measurements with an expanded uncertainty less than 0.2 kg · m^?3 in the working intervals. This accuracy comes from the combination of several factors: densimeter behaves linearly in the working density interval, densities of both calibration fluids cover that interval and they have a very low uncertainty, and the mechanical behaviour of the tube is well characterized by the considered model. The main application of this method is the precise measurement of high density fluids for which most of the calibration procedures are inaccurate.     

Excess molar properties for binary systems of alkylimidazolium-based ionic liquids + nitromethane. Experimental results and ERAS-model calculations

Density, isobaric molar heat capacity, and excess molar enthalpy were experimentally determined at atmospheric pressure for a set of binary systems ionic liquid + nitromethane. The studied ionic liquids were: 1-butyl-3-methylimidazolium tetrafluoroborate, 1-hexyl-3-methylimidazolium tetrafluoroborate, 1-butyl-3-methylpyridinium tetrafluoroborate, 1-ethyl-3-methylimidazolium ethylsulfate, 1-butyl-3-methylimidazolium methylsulfate, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate, and 1-butyl-3-methylimidazolium trifluoromethanesulfonate. Density and heat capacity were obtained within the temperature range (293.15 to 318.15) K whereas excess molar enthalpy was measured at 303.15 K; excess molar volume and excess molar isobaric heat capacity were calculated from experimental data. The ERAS-model was applied in order to study the microscopic mechanisms involved in the mixing process. Although the studied compounds are not self-associated, ERAS-model describe adequately the experimental results if cross-association between both compounds is considered.     

Intrauterine diagnosis of hydranencephaly by magnetic resonance

Magnetic resonance imaging (MRI) was used to confirm an ultrasound diagnosis of hydranencephaly in utero. MRI provided an accurate anatomical assessment, influencing the pregnancy management. The result supports previous reports suggesting that MRI may be a useful complement to ultrasonography in intrauterine diagnoses.     

General transformation theory of Lagrangian mechanics and the Lagrange group

The general transformation theory of Lagrangian mechanics is revisited from a group-theoretic point of view. After considering the transformation of the Lagrangian function under local coordinate transformations in configuration spacetime, the general covariance of the formalism of Lagrange is discussed. Next, the group of Lagrange (for alln-dimensional Lagrangian systems) is introduced, and some important features of this group, as well as of its action on the set of Lagrangians, are briefly examined. Only finite local transformations of coordinates are considered here, and no variational transformation of the action is required in this study. Some miscellaneous examples of the formalism are included.     

The multiplicative product (\delta (x_0 - \left| x \right|)/\left| x \right|^{(n - 2)/2} )(\delta (x_0 + \left| x \right|)/\left| x \right|^{(n - 2)/2} )

In this paper we give a sense to the distributional multiplicative product $(\delta (x_o - \left| x \right|)/\left| x \right|^{(n - 2)/2} )(\delta (x_o + \left| x \right|)/\left| x \right|^{(n - 2)/2} )$ . For the case n=4 we obtain a formula which is used for a perturbative calculation of Green function in quantum field theories. As an application of our product, we show the calculation of the self-energy of the theory of $\lambda \emptyset ^4 $ .     

Dicationic electrophiles from olefinic amines in superacid

This paper describes the superacid-catalyzed chemistry of olefinic amines and related compounds. A variety of olefinic amines are found to react with benzene in CF(3)SO(3)H (triflic acid) to give addition products in good yields (75-99%), including the pharmaceutical agents fenpiprane and prozapine. A general mechanism is proposed that invokes the formation of reactive, dicationic electrophiles and the direct observation of a diprotonated species is reported from low-temperature NMR experiments. This chemistry is also used to conveniently prepare functionalized polystyrene beads having pendant amine groups.     

An efficient preparation of stereospecific β-hydroxy nitriles

The cyanide-ring opening of thionocarbonates with NaCN in DMF and TBACN in THF is described. This reaction occurred regioselectively to afford β-hydroxy nitrile with preserved stereochemistry of the hydroxy group in high yield.     

Enzymatic metabolism of ergosterol by cytochrome p450scc to biologically active 17alpha,24-dihydroxyergosterol

We demonstrate the metabolism of ergosterol by cytochrome P450scc in either a reconstituted system or isolated adrenal mitochondria. The major reaction product was identified as 17alpha,24-dihydroxyergosterol. Purified P450scc also generated hydroxyergosterol as a minor product, which is probably an intermediate in the synthesis of 17alpha,24-dihydroxyergosterol. In contrast to cholesterol and 7-dehydrocholesterol, cleavage of the ergosterol side chain was not observed. NMR analysis clearly located one hydroxyl group to C24, with evidence that the second hydroxyl group is at C17. 17alpha,24-Dihydroxyergosterol inhibited cell proliferation of HaCaT keratinocytes and melanoma cells. Thus, in comparison with cholesterol and 7-dehydrocholesterol, the 24-methyl group and the C22-C23 double bond of ergosterol prevent side chain cleavage by P450scc and change the enzyme's hydroxylase activity from C22 and C20, to C24 and C17, generating bioactive product.