Flavouring and odorant thiols from renewable natural resources by In-catalysed hydrothioacetylation and lipase-catalysed solvolysis

A chemoenzymatic access to thiol compounds, including ethyl 3-thiobutanoate, 3-thio-p-menthene and 8-thio-p-menthan-2-one, three compounds of interest in flavour and fragrance chemistry presenting various fruity notes, is proposed. It involves an indium(III)-catalysed hydrothioacetylation of renewable precursors followed by an enzymatic solvolysis of the obtained thioesters by lipases in aqueous or organic solvents.     

Weak shock waves and its interaction with characteristic shocks in polyatomic gas

We present Lie symmetry analysis for investigating the shock‐wave structure of hyperbolic differential equations of polyatomic gases. With the application of symmetry analysis, we derive particular exact group invariant solutions for the governing system of partial differential equations (PDEs). In the next step, the evolutionary behavior of weak shock along with the characteristic shock and their interaction is investigated. Finally, the amplitudes of reflected wave, transmitted wave, and the jump in shock acceleration influenced by the incident wave after interaction are evaluated for the considered system of equations.     

Co-Jacobian for Lipschitzian Maps

The notion of co-Jacobian is introduced for locally Lipschitz functions acting between arbitrary normed spaces. The main results of this paper provide a characterization, calculus rules, a mean value theorem, as well as the computation of the co-Jacobian of piecewise smooth functions. Comparisons with known differentiability notions and Mordukhovich’s co-derivatives are derived.     

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

Insights into colloid-mediated trace element release at the soil/water interface

Organic or inorganic colloids play a major role in the mobilization of trace elements in soils and waters. Environmental physicochemical parameters (pH, redox potential, temperature, pressure, ionic strength, etc.) are the controlling factors of the colloidal mobilization. This study was dedicated to follow the colloid-mediated mobilization of trace elements through time at the soil/water interface by means of an experimental approach. Soil column experiments were carried out using percolating synthetic solutions. The percolated solutions were ultrafiltrated with various decreasing cutoff thresholds to separate the different colloidal phases in which the dissolved organic carbon and trace element concentrations were measured. The major results which stem from this study are the following: (i) The data can be divided into different groups of organic compounds (microbial metabolites, fulvic acids, humic acids) with regard to their respective aromaticity and molecular weight. (ii) Three groups of elements can be distinguished based on their relationships with the colloidal phases: the first one corresponds to the so-called "truly" dissolved group (Li, B, K, Na, Rb, Si, Mg, Sr, Ca, Mn, Ba, and V). The second one can be considered as an intermediate group (Cu, Cd, Co, and Ni), while the third group gathers Al, Cr, U, Mo, Pb, Ti, Th, Fe, and rare earth elements (REE) carried by the organic colloidal pool. (iii) The data demonstrate that the fulvic acids seem to be a major organic carrier phase for trace elements such as Cu, Cd, Co, and Ni. By contrast, the trace elements belonging to the so-called colloidal pool were mostly mobilized by humic acids containing iron nanoparticles. Lead, Ti, and U were mobilized by iron nanoparticles bound to these humic acids. Thus, humic substances allowed directly or indirectly a colloidal transport of many insoluble trace elements either by binding trace elements or by stabilizing a ferric carrier phase. (iv) Finally, the results demonstrated also that REE were mostly mobilized by humic substances. The REE normalized patterns showed a middle REE downward concavity. Therefore, as previously shown elsewhere humic substances are a major control of REE speciation and REE fractionation patterns as well since the humic substance/metal ratio was the key parameter controlling the REE pattern shape.     

Weak maximum principle and accessory problem for control problems on time scales

In this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state-endpoints equality constraints. Using the first variation, a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the Dubois–Reymond Lemma to the optimal control setting and time scales. A second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions. The control problem is studied under a controllability assumption, and with or without the shift in the state variable. These two forms of the problem are shown to be equivalent.     

First and second order sufficient conditions for optimal control and the calculus of variations

In this paper we develop first and second order sufficient conditions for optimal control and the calculus of variations problems. Our conditions are derived from the Hamilton-Jacobi approach [15, Thm. 2], which was obtained for the generalized problem of Bolza. We do not require any convexity on the data [7] and [11], or that the control setU is polyhedral [14], or that the control function is in the interior ofU [8]. Instead, we assume a certain inequality which is satisfied in each of the above mentioned cases.The publication of this report has been made possible due to a grant of the Fonds FCAC for the help and support of research.     

Another Jacobi sufficiency criterion for optimal control with smooth constraints

In order to tighten the gap between necessary and sufficient conditions, new second-order sufficient conditions are developed for optimal control problems, where the control set is given by smooth functions. When the control set is polyhedral, our criterion generalizes prior results of the same kind, namely, the Jacobi criterion in Hamiltonian form and that in Lagrangian form (Refs. 1–3).The research of V. Zeidan was supported by NSERC Grant A-8570, which is gratefully acknowledged.     

Numerical study of wave propagation in compressible two‐phase flow

We propose a new model and a solution method for two‐phase two‐fluid compressible flows. The model involves six equations obtained from conservation principles applied to a one‐dimensional flow of gas and liquid mixture completed by additional closure governing equations. The model is valid for pure fluids as well as for fluid mixtures. The system of partial differential equations with source terms is hyperbolic and has conservative form. Hyperbolicity is obtained using the principles of extended thermodynamics. Features of the model include the existence of real eigenvalues and a complete set of independent eigenvectors. Its numerical solution poses several difficulties. The model possesses a large number of acoustic and convective waves and it is not easy to upwind all of these accurately and simply. In this paper we use relatively modern shock‐capturing methods of a centred‐type such as the total variation diminishing (TVD) slope limiter centre (SLIC) scheme which solve these problems in a simple way and with good accuracy. Several numerical test problems are displayed in order to highlight the efficiency of the study we propose. The scheme provides reliable results, is able to compute strong shock waves and deals with complex equations of state. Copyright © 2006 John Wiley & Sons, Ltd.     

锦灯笼果实的化学成分研究

从锦灯笼中分离得到5个甾体类化合物,分别鉴定为酸浆素A(1,alkekengilin A)、酸浆素B(2,alkekengilin B)、酸浆苦素D(3,physalin D)、酸浆苦素P(4,physalin P)、4,7-二去氢新酸浆苦素B(5,4,7-didehydro-neophysalin B).其中酸浆素A(1,alkekengilin A)和酸浆素B(2,alkekengilin B)为新的天然产物.运用现代波谱技术对上述化合物的结构进行了确证.