不同岩蔷薇浸膏挥发性致香成分的SED-GC-MS分析研究

岩蔷薇(cistusladaniferusL.)又名赖百当(labdanum),属半日花科。利用其树脂分泌物及枝叶,通过蒸馏、浸提和萃取等方法,可制得岩蔷薇精油、浸膏、净油、油树脂等各种香原料品种。岩蔷薇的香原料制品是膏香类的极重要品种,主要应用于日化和食品行业,在烟草行业也多有应用。因香料烟香味的主要来源是类赖百当化合物的降解,故被归为烟草的五大类香味物质之一:赖百当类、双萜烯及其降解产物类。这类物质在香料烟中的含量较高,对形成香料烟的特殊香味风格具有重要意义,且在烟草中赖百当仅存在于香料烟中,烤烟、自肋烟中均不存在。赖百当类化合物是香料烟中特有的香气物质,主要成分是冷杉醇、赖百当烯二醇,经调制和醇化转化为多种降赖百当类化合物,其中降龙涎香醚、龙涎香内酯、脱氢龙涎香内酯等都具有强烈的龙涎香香气,对增进卷烟香气和吃味有很好作用。     

2,2′-Bis((di-tert-butylphosphino)methyl)-1,1′-biphenyl (ditbi): a bulky analogue of bisbi. The crystal structure of [Rh2Cl2(1,5-cod)2(μ-ditbi)]

Diphosphine 2,2′-bis(di-tert-butylphosphino)methyl)-1,1′-biphenyl (ditbi) is synthesised by the addition of to 2,2′-bis(bromomethyl)-1,1′-biphenyl, followed by deprotection with diethylamine. Treatment of [Rh₂Cl₂(1,5-cod)₂], with ditbi gives [Rh₂Cl₂(1,5-cod)₂(μ-ditbi)] (2) as confirmed by its X-ray crystal structure determination. Hydroformylation of 1-hexene using [Rh(acac)(CO)₂]/ditbi as catalyst gave n- and iso-heptanal in a ratio of 1:1.     

Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems

Summary A forward error analysis is presented for the Björck-Pereyra algorithms used for solving Vandermonde systems of equations. This analysis applies to the case where the points defining the Vandermonde matrix are nonnegative and are arranged in increasing order. It is shown that for a particular class of Vandermonde problems the error bound obtained depends on the dimensionn and on the machine precision only, being independent of the condition number of the coefficient matrix. By comparing appropriate condition numbers for the Vandermonde problem with the forward error bounds it is shown that the Björck-Pereyra algorithms introduce no more uncertainty into the numerical solution than is caused simply by storing the right-hand side vector on the computer. A technique for computing running a posteriori error bounds is derived. Several numerical experiments are presented, and it is observed that the ordering of the points can greatly affect the solution accuracy.     

The symmetric procrustes problem

The following symmetric Procrustes problem arises in the determination of the strain matrix of an elastic structure: find the symmetric matrixX which minimises the Frobenius (or Euclidean) norm ofAX — B, whereA andB are given rectangular matrices. We use the singular value decomposition to analyse the problem and to derive a stable method for its solution. A perturbation result is derived and used to assess the stability of methods based on solving normal equations. Some comparisons with the standard, unconstrained least squares problem are given.     

Asymmetry through time dependency

Given a single network of interactions, asymmetry arises when the links aredirected. For example, if protein A upregulates protein B and protein Bupregulates protein C, then (in the absence of any further relationships between them) Amay affect C but not vice versa. This type of imbalance is reflected in the associatedadjacency matrix, which will lack symmetry. A different type of imbalance can arise wheninteractions appear and disappear over time. If A meets B today and B meets C tomorrow,then (in the absence of any further relationships between them) A may pass a message ordisease to C, but not vice versa. Hence, even when each interaction is a two-way exchange,the effect of time ordering can introduce asymmetry. This observation is very closelyrelated to the fact that matrix multiplication is not commutative. In this work, wedescribe a method that has been designed to reveal asymmetry in static networks and showhow it may be combined with a measure that summarizes the potential information flowbetween nodes in the temporal case. This results in a new method that quantifies theasymmetry arising through time ordering. We show by example that the new tool can be usedto visualize and quantify the amount of asymmetry caused by the arrow of time.     

MOP-phosphonites: a novel ligand class for asymmetric catalysis

Chiral phosphonite ligands (S,R(b))-5a, (S,S(b))-5b, (R,R(b))-6a and (R,S(b))-6b are introduced, comprising a MOP-type backbone with a binol-based binaphthyl group bound to the phosphorus. Their reaction with [Pd(η(3)-C(4)H(7))Cl](2) affords η(3)-methallylpalladium chloride complexes 7a/b and 8a/b which have been isolated and structurally characterised. Solid-state and solution studies indicate subtle differences in their coordination behaviour, which ultimately affects their efficacy in the asymmetric hydrosilylation of styrene.     

The numerical stability of barycentric Lagrange interpolation

The Lagrange representation of the interpolating polynomialcan be rewritten in two more computationally attractive forms:a modified Lagrange form and a barycentric form. We give anerror analysis of the evaluation of the interpolating polynomialusing these two forms. The modified Lagrange formula is shownto be backward stable. The barycentric formula has a less favourableerror analysis, but is forward stable for any set of interpolatingpoints with a small Lebesgue constant. Therefore the barycentricformula can be significantly less accurate than the modifiedLagrange formula only for a poor choice of interpolating points.This analysis provides further weight to the argument of Berrutand Trefethen that barycentric Lagrange interpolation shouldbe the polynomial interpolation method of choice.     

Google PageRank as mean playing time for pinball on the reverse web

It is known that the output from Google’s PageRank algorithm may be interpreted as (a) the limiting value of a linear recurrence relation that is motivated by interpreting links as votes of confidence, and (b) the invariant measure of a teleporting random walk that follows links except for occasional uniform jumps. Here, we show that, for a sufficiently frequent jump rate, the PageRank score may also be interpreted as a mean finishing time for a reverse random walk. At a general step this new process either (i) remains at the current page, (ii) moves to a page that points to the current page, or (iii) terminates. The process is analogous to a game of pinball where a ball bounces between pages before eventually dropping down the exit chute. This new interpretation of PageRank gives another view of the principle that highly ranked pages will be those that are linked into by highly ranked pages that have relatively few outgoing links.     

Numerical methods for nonlinear stochastic differential equations with jumps

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method. The second method, CSSBE, arises from the introduction of a compensated, martingale, form of the Poisson process. We show that both methods are amenable to rigorous analysis when a one-sided Lipschitz condition, rather than a more restrictive global Lipschitz condition, holds for the drift. Our analysis covers strong convergence and nonlinear stability. We prove that both methods give strong convergence when the drift coefficient is one-sided Lipschitz and the diffusion and jump coefficients are globally Lipschitz. On the way to proving these results, we show that a compensated form of the Euler–Maruyama method converges strongly when the SDE coefficients satisfy a local Lipschitz condition and the pth moment of the exact and numerical solution are bounded for some p>2. Under our assumptions, both SSBE and CSSBE give well-defined, unique solutions for sufficiently small stepsizes, and SSBE has the advantage that the restriction is independent of the jump intensity. We also study the ability of the methods to reproduce exponential mean-square stability in the case where the drift has a negative one-sided Lipschitz constant. This work extends the deterministic nonlinear stability theory in numerical analysis. We find that SSBE preserves stability under a stepsize constraint that is independent of the initial data. CSSBE satisfies an even stronger condition, and gives a generalization of B-stability. Finally, we specialize to a linear test problem and show that CSSBE has a natural extension of deterministic A-stability. The difference in stability properties of the SSBE and CSSBE methods emphasizes that the addition of a jump term has a significant effect that cannot be deduced directly from the non-jump literature.This work was supported by Engineering and Physical Sciences Research Council grant GR/T19100 and by a Research Fellowship from The Royal Society of Edinburgh/Scottish Executive Education and Lifelong Learning Department.     

Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

We are interested in the strong convergence of Euler-Maruyama type approximations to the solution of a class of stochastic differential equations models with highly nonlinear coefficients, arising in mathematical finance. Results in this area can be used to justify Monte Carlo simulations for calibration and valuation. The equations that we study include the Ait-Sahalia type model of the spot interest rate, which has a polynomial drift term that blows up at the origin and a diffusion term with superlinear growth. After establishing existence and uniqueness for the solution, we show that an appropriate implicit numerical method preserves positivity and boundedness of moments, and converges strongly to the true solution.