Jordanian deformation of the open sℓ(2) Gaudin model

We derive a deformed s?(2) Gaudin model with integrable boundaries. Starting from the Jordanian deformation of the SL(2)-invariant Yang R-matrix and generic solutions of the associated reflection equation and the dual reflection equation, we obtain the corresponding inhomogeneous spin-1/2 XXX chain. The semiclassical expansion of the transfer matrix yields the deformed s?(2) Gaudin Hamiltonians with boundary terms.     

Population dynamics with infinite Leslie matrices: finite time properties

Infinite Leslie matrices, introduced by Demetrius 40 years ago, are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the discrete dynamical system in finite time. We address this problem by appealing to the concept of kneading matrices and kneading determinants. Our analysis is applicable not only to populations models, but also to models of self-reproducing machines and self-reproducing computer programs. The dynamics of these systems can also be described in terms of infinite Leslie matrices.     

Analysis of metabolic pools in broilers chicks

This paper shows the possibility of obtaining new parameters for the mathematical modelling of data on stable isotopes in biological systems and its application in obtaining data on metabolic pools of blood plasma, blood serum, liver and muscle of broilers. This theory states that the modelling of turnover used for studies of isotopic incorporation when the metabolism has a single metabolic pool is feasible by the technique of setting an exponential. However, when the metabolism has more than one metabolic pool, it is necessary to apply the linearization technique, linear regression adjustment and evaluation of the assumptions of regression to obtain the kinetic parameters such as half-life (T_1/2) and isotope exchange rate (k). The application of this technique on carbon-13 data from 100 one-day-old chicks, with the change of diet composed of grains of the photosynthetic cycle of plants from C₄ to C₃, in broilers has enabled the discovery that the liver, blood plasma and blood serum have a single metabolic pool; however, the pectoral muscle has two metabolic pools. For the liver, blood plasma and blood serum, the half-life values were found by the exponential fit being T_1/2?=?1.4 days with the rate of exchange of k?=?0.502, T_1/2?=?2.4 days with k?=?0.293 and T_1/2?=?2.0 days with k?=?0.348, respectively. For the pectoral muscle, after linearization, the half-life values were found for T_1/2(1)?=?1.7 and T_1/2(2)?=?3 days, with exchange rates of k₁?=?0.405 and k₂?=?0.235, representing approximately 66 and 34?%, respectively.     

High pressure studies on hesperitin production with hesperidinase free and immobilized in calcium alginate beads

The use of high pressure for the enzymatic synthesis of pharmacologically interesting molecules is a very important tool. Hesperidin and hesperitin exhibit anti-inflammatory, antimicrobial, antioxidant, and anticarcinogenic properties and prevent bone loss. However, hesperidin has a low bioavailability compared with hesperitin, due to the rutinoside moiety attached to the flavonoid. The aim of this work was the enzymatic production of hesperitin from hesperidin (soluble and insoluble) with hesperidinase free and immobilized in Ca-alginate beads, under high pressure conditions. The work was focused on the optimization of enzyme activity, studying the effects: pressure (50–150 MPa), temperature (35–75 °C), concentration of substrate (100–800 mg/L), and immobilization of hesperidinase. An 18-fold increase in hesperidinase residual activity was observed under high pressure conditions of 100 MPa compared to 0.1 MPa. A higher specificity of the hydrolytic reaction under high pressure (100 MPa) with a two-and three-fold increase in the ratio K _cat/K _M (specificity constant) at 55 °C and 75 °C was observed. A two-fold increase in the maximum activity at 100 MPa was observed with immobilized hesperinase compared to 0.1 MPa. In the second reutilization, almost a four-fold increase was obtained under high pressure conditions in comparison to atmospheric pressure.     

Strong limit theorems for anisotropic random walks on ℤ2

We study the path behaviour of the anisotropic random walk on the two-dimensional lattice ?². Strong approximation of its components with independent Wiener processes is proved. We also give some asymptotic results for the local time in the periodic case.     

Investigating the potassium interactions with the palytoxin induced channels in Na+/K+ pump

K(+) has been appointed as the main physiological inhibitor of the palytoxin (PTX) effect on the Na(+)/K(+) pump. This toxin acts opening monovalent cationic channels through the Na(+)/K(+) pump. We investigate, by means of computational modeling, the kinetic mechanisms related with K(+) interacting with the complex PTX-Na(+)/K(+) pump. First, a reaction model, with structure similar to Albers-Post model, describing the functional cycle of the pump, was proposed for describing K(+) interference on the complex PTX-Na(+)/K(+) pump in the presence of intracellular ATP. A mathematic model was derived from the reaction model and it was possible to solve numerically the associated differential equations and to simulate experimental maneuvers about the PTX induced currents in the presence of K(+) in the intra- and extracellular space as well as ATP in the intracellular. After the model adjusting to the experimental data, a Monte Carlo method for sensitivity analysis was used to analyze how each reaction parameter acts during each experimental maneuver involving PTX. For ATP and K(+) concentrations conditions, the simulations suggest that the enzyme substate with ATP bound to its high-affinity sites is the main substate for the PTX binding. The activation rate of the induced current is limited by the K(+) deocclusion from the PTX-Na(+)/K(+) pump complex. The K(+) occlusion in the PTX induced channels in the enzymes with ATP bound to its low-affinity sites is the main mechanism responsible for the reduction of the enzyme affinity to PTX.     

On the Drazin index of regular elements

It is known that the existence of the group inverse a ^# of a ring element a is equivalent to the invertibility of a ² a ⁻ + 1 − aa ⁻, independently of the choice of the von Neumann inverse a ⁻ of a. In this paper, we relate the Drazin index of a to the Drazin index of a ² a ⁻ + 1 − aa ⁻. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.      

Improved Enzyme Stability in Lipase-Catalyzed Synthesis of Fatty Acid Ethyl Ester from Soybean Oil

In this work, we describe the optimization of the ethanolysis of soybean oil by the enzyme Lipozyme™ TL-IM in the lipase-catalyzed biodiesel synthesis and the improvement of the enzyme stability over repeated batches. The studied process variables were: reaction temperature, substrate molar ratio, enzyme content, and volume of added water. Fractional factorial design was used to analyze the variables so as to select those with higher influence on the reaction and then perform a central composite design to find the optimal reaction conditions. The optimal conditions found were: temperature, 26 °C; substrate molar ratio, 7.5:1 (ethanol/oil); enzyme content, 25% in relation to oil weight; and added water, 4% in relation to oil weight. Under these conditions, the yield conversion obtained was 69% in 12 h. The enzyme stability assessment in repeated batches was carried out by washing the immobilized enzyme with different solvents (n-hexane, water, ethanol, and propanol) after each batch. In the treatment with n-hexane, around 80% of the enzyme activity still remains after seven cycles of synthesis, suggesting its economical application on biodiesel production.     

Photobiological properties of hydroxy-substituted flavothiones

Flavothione (FT) and a series of 18 hydroxy- and methoxy-substituted flavothiones were screened for photobiological activity. The 5-hydroxy-substituted compounds (group 3) and the methoxy-substituted flavothiones were inactive. FT and the remaining hydroxy-substituted compounds, all displayed photobiological activity. Among these, the 3-hydroxy-substituted compounds (group 2) were the most efficient photosensitizers overall in spite of their concurrent fast photodegradation. FT and all other hydroxyflavothiones, not substituted in the 3- or 5-positions (group 1), were inefficient compared with group 2. Detailed photobiological tests were carried out for four flavothiones of groups 1 and 2. The biological tests included fungi, several strains of Escherichia coli, Salmonella typhimurium and mammalian cells. In addition, the ability of these flavothiones to perform lipid peroxidation was evaluated. FT and 6-hydroxyflavothione (group 1) induce DNA damage via H-atom abstraction from the lowest n, pi* triplet state of the thione (oxygen independent). For 3-hydroxy and 3,6-dihydroxyflavothione (group 2), both DNA and the membrane are targets. The mechanism likely involves both energy transfer and electron transfer from the lowest pi, pi* triplet state to oxygen, to form singlet oxygen and the superoxide anion. Some of these compounds could be considered as models for environmentally safe photopesticides.     

Effect of impurities in the large Au-Au distances in gold nanowires

Experimentally obtained atomically thin gold nanowires have presented exceedingly large Au-Au interatomic distances before they break. Since no theoretical calculations of pure gold nanowires have been able to produce such large distances, we have investigated, through ab initio calculations, how impurities could affect them. We have studied the effect of H, B, C, N, O, and S impurities on the nanowire electronic and structural properties, in particular how they affect the maximum Au-Au bond length. We find that the most likely candidates to explain the distances in the range of 3.6 A and 4.8 A are H and S impurity atoms, respectively.