AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

TMS triflate-catalyzed cleavage of prenyl (3-methylbut-2-enyl) ester

[reaction: see text] Prenyl (3-methylbut-2-enyl) ester is catalytically cleaved by TMS triflate affording carboxylic acid and isoprene in high yield under mild conditions with high chemoselectivity without causing epimerization of the neighboring chiral center.     

Asymmetric Diels–Alder reactions in supercritical carbon dioxide catalyzed by rare earth complexes

The rare earth(III) salt catalysed asymmetric Diels–Alder reaction of cyclopentadiene with a chiral dienophile in supercritical carbon dioxide (scCO₂) proceeded rapidly to give the adduct with a higher diastereoselectivity than that in dichloromethane; Yb(ClO₄)₃ gave the endo adduct with value up to 77% de at 40°C, 8 MPa. The chiral rare earth diketonate catalyzed hetero Diels–Alder reaction of the Danishefsky's diene with benzaldehyde gave a higher yield and an enantioselectivity in scCO₂ than that in dichloromethane. Scandium/pybox 8a complex catalysed asymmetric Diels–Alder reaction of 3-crotonoyl-2-oxazolidinone with cyclopentadiene in the presence of MS4A proceeded smoothly in scCO₂ to give the endo adduct 10 in a good yield with up to 88% ee.     

Hydrophobic indicators for two-phase titrations and their application to the determination of silver and pentachlorophenol

The hydrophobic dyes tetrabromophenolphthalein ethyl ester and 2,6-dichlorophenolindo-phenol are proposed as visual indicators for two-phase titrations. The aqueous phase is colourless throughout the titration and these indicators make it possible to detect the end-point of the titration by the colour of one or the other phase. The indicators allow the two-phase titration of the silver(I)-1,10-phenanthroline complex with tetraphenylborate and of pentachlorophenol with tetraphenylphosphonium chloride.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

Inclusion polymerization of 1-chlorobutadiene in a deoxycholic acid canal

Inclusion polymerization of 1-chlorobutadiene was studied using 3α,12α-dihydroxy-5β-cholan-24-oic acid (deoxycholic acid, DCA) as host molecules. It was found that the poly(1-chlorobutadiene) had almost 100% of head to tail, trans-1,4-structure on the basis of ¹³C-NMR and IR spectroscopies. This was the first example of preparing the highly regulated poly(1-chlorobutadiene) by using the inclusion polymerization technique. The polymers obtained were optically active and the maximum value of specific rotation was [α]_D-41.9°. Both the rate constants and the value of activation energy of the elementary reactions of inclusion polymerization of 1-chlorobutadiene were determined by graphical evaluation. The activation energy of propagation and termination was 11.7 and 11.1 kcal/mol, respectively.     

Synthesis and Crystal Structure of p-tert-Butylthiacalix[8]arene: A New Member of Thiacalixarenes

Even though it was obtained in poor yield, p-tert-butylthiacalix[8]arene (TC8A) has been synthesized as a new member of thiacalix[n]arenes by the terephthalate-induced cyclization of a mixture of acyclic oligomers, which was obtained by the reaction between p-tert-butylphenol and sulfur with CaO in ethylene glycol/diphenyl ether system. Slow evaporation of the chloroform solution of TC8A afforded guest-free crystals consisting of TC8A itself. The close-packed crystal structure of TC8A resembles that of p-tert-butylcalix[8]arene (C8A) closely, containing a plated loop molecular structure.This revised version was published online in July 2005 with a corrected issue number.