Continuous dependence on the boundary conditions for the Wentzell Laplacian

The solution u of the well-posed problem

Construction of coaxial liquid centrifugal platform for the extraction of active ingredients from natural products

In the classical natural product extraction and separation process, it is tedious and requires large amounts of reagents and time. In this study, an efficient coaxial liquid centrifugal oil-water-oil triple-liquid-phase system with a simple structure and convenient operation was successfully constructed and used to extract flavonoids from Platycladi Cacumen. The results showed that the coaxial liquid centrifugal platform constructed in this study had good stability and 6 ml was the minimum volume of the middle phase for 1000 rpm to stabilize the system. Besides, it was easy to repeat the operation: the relative standard deviations of the extraction yields of flavonoids and sugar in six parallel operations were all less than 10%. Moreover, it was only one-tenth of the time required for this method as traditional liquid-liquid extraction while reducing the use of volatile organic reagents. Finally, the new method was more selective than the traditional method for the extraction of flavonoids. Therefore, this study provides a possibility for the coaxial liquid centrifugal platform to be used in multi-liquid phase systems to achieve the simultaneous extraction of different parts of natural products by different liquid phases. It is expected to provide a reliable reference for further expansion of small-scale experimental operations to industrial production.     

Influence of some minerals on the cellulose thermal degradation mechanisms

The influence of different inorganic salts (MgCl₂, ZnCl₂, NiCl₂ and H₂PtCl₆) on the primary mechanisms of cellulose thermal degradation has been conducted by using thermogravimetric (TG-DTG) and pyrolysis-mass spectrometry (Py-MS) analysis at low heating rate (10°C min-1) from ambient temperature to 500°C. The results clearly demonstrate that the used salts influence the primary degradation mechanisms. Furthermore, we can assume that some inorganic salts could be considered as specific catalysts and some others as inhibitors. MgCl₂ promotes selectively initial low temperature dehydration as observed both by TG and Py-MS. ZnCl₂ strongly changes the thermal behaviour of impregnated sample. The maximum mass loss rate temperature is shifted to lower temperature and on the basis of our results we can conclude that ZnCl₂ acts as catalyst in all primary degradation mechanisms. NiCl₂ and H₂PtCl₆ do not modify significantly the cellulose thermal behaviour but change the composition of both produced gases and liquids suggesting that these minerals catalyse some secondary reactions.     

A Nonlinear Elliptic System Arising in Electron Density Theory

Of concern is the nonlinear system

in R³ Here λ_i,C_j are given positive constants. Such a system arises in spin polarized ground state electron density theory. The parametres λ_:1:, λ_:2 should be such that

where N_1>,N₂ are given positive numbers satisfying where Z is some give positive number. (Here N$sub:1$esub:, N$sub:2$esub:, Z are, respectively, the number of spin up electrons, spin down electrons, and protons in the system.) We establish existence for this problem. Uniqueness remains open.     

Stability estimates for nonlinear hyperbolic problems with nonlinear Wentzell boundary conditions

Of concern is the nonlinear hyperbolic problem with nonlinear dynamic boundary conditions $$\left\{ \begin{array}{lll} u_{tt} ={\rm div} (\mathcal{A} \nabla u)-\gamma (x,u_t), && \quad {\rm in} \; (0, \infty) \times \Omega,\\ u(0, \cdot)=f, \, u_t(0,\cdot)=g, && \quad {\rm in}\; \Omega, \\ u_{tt} + \beta \partial^ \mathcal{A}_\nu u+c(x)u+ \delta (x,u_t)-q \beta \Lambda_{\rm LB} u=0,&& \quad {\rm on} \;(0, \infty ) \times \partial \Omega . \end{array}\right. $$ for t ≥  0 and ${x \in \Omega \subset \mathbb{R}^N}$ ; the last equation holds on the boundary ?Ω. Here ${\mathcal{A}= \{a_{ij}(x)\}_{ij}}$ is a real, hermitian, uniformly positive definite N × N matrix; ${\beta \in C(\partial \Omega)}$ , with β > 0; ${\gamma:\Omega \times \mathbb{R} \to \mathbb{R}; \delta:\partial \Omega \times \mathbb{R} \to \mathbb{R}; \,c:\partial \Omega \to \mathbb{R}; \, q \ge 0, \Lambda_{\rm LB}}$ is the Laplace–Beltrami operator on ?Ω, and ${\partial^\mathcal{A}_\nu u}$ is the conormal derivative of u with respect to ${\mathcal{A}}$ ; everything is sufficiently regular. We prove explicit stability estimates of the solution u with respect to the coefficients ${\mathcal{A},\,\beta,\,\gamma,\,\delta,\,c,\,q}$ , and the initial conditions f, g. Our arguments cover the singular case of a problem with q = 0 which is approximated by problems with positive q.     

Elliptic operators with general Wentzell boundary conditions,analytic semigroups and the angle concavity theorem

We prove a very general form of the Angle Concavity Theorem, which says that if (T (t)) defines a one parameter semigroup acting over various L^p spaces (over a fixed measure space), which is analytic in a sector of opening angle θ_p, then the maximal choice for θ_p is a concave function of 1 – 1/p. This and related results are applied to give improved estimates on the optimal L^p angle of ellipticity for a parabolic equation of the form ?u /?t = Au, where A is a uniformly elliptic second order partial differential operator with Wentzell or dynamic boundary conditions. Similar results are obtained for the higher order equation ?u /?t = (–1)^{m +l}A^mu, for all positive integers m.     

Studies on pyrrolidinones. synthesis of N-(2-nitrobenzyl)pyroglutamic acid

While methyl N-(4-nitrobenzyl)pyroglutamate can be obtained from methyl N-trimethylsilylpyroglutamate, the best way to obtain methyl N-(2-nitrobenzyl)pyroglutamate is to react 4-nitro benzyl bromide with the iminoether derived from methyl pyroglutamate.     

Fischer subspaces of Hermitian manifolds

The finite groups generated by 3-transpositions, studied by B.Fischer [5]have a geometrical interpretation given by F.Buekenhout [1] under the name of Fischer spaces.This geometrical concept allows us to study the Fischer subgroups of primitive groups classified by Fischer, and in particular those of unitary groups PSU(n,4), symplectic groups PSp(n,2), orthogonal groups PO(n,2) and symmetric groups Sym(n).This problem is linked to the determination of groups of projectivities generated by clations in characteristic 2 studied by Wagner [9] and McLaughlin[8], and is related to Kantor's work [7] on classical groups generated by long root elements, and to Enright's recent note on Fi₂₂ and Fi₂₃ [5].     

Heterologous Expression of Aldehyde Dehydrogenase in <Emphasis Type="Italic">Lactococcus lactis</Emphasis> for Acetaldehyde Detoxification at Low pH

Aldehyde dehydrogenase (E.C. 1.2.1.x) can catalyze detoxification of acetaldehydes. A novel acetaldehyde dehydrogenase (istALDH) from the non-Saccharomyces yeast Issatchenkia terricola strain XJ-2 has been previously characterized. In this work, Lactococcus lactis with the NIsin Controlled Expression (NICE) System was applied to express the aldehyde dehydrogenase gene (istALDH) in order to catalyze oxidation of acetaldehyde at low pH. A recombinant L. lactis NZ3900 was obtained and applied for the detoxification of acetaldehyde as whole-cell biocatalysts. The activity of IstALDH in L. lactis NZ3900 (pNZ8148-istALDH) reached 36.4 U mL^?1 when the recombinant cells were induced with 50 ng mL^?1 nisin at 20 °C for 2 h. The IstALDH activity of recombinant L. lactis cells showed higher stability at 37 °C and pH 4.0 compared with the crude enzyme. L. lactis NZ3900 (pNZ8148-istALDH) could convert acetaldehyde at pH 2.0 while the crude enzyme could not. Moreover, the resting cells of L. lactis NZ3900 (pNZ8148-istALDH) showed a 2.5-fold higher activity and better stability in catalyzing oxidation of acetaldehyde at pH 2.0 compared with that of Escherichia coli expressing the IstALDH. Taken together, the L. lactis cells expressing recombinant IstALDH are potential whole-cell biocatalysts that can be applied in the detoxification of aldehydes.