The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices

Two recent methods (Shanno, 1978; Toint, 1980) for revisingestimates of sparse second derivative matrices in quasi-Newtonoptimization algorithms reduce to variable metric formulae whenthere are no sparsity conditions. It is proved that these methodsare equivalent. Further, some examples are given to show thatthe procedure may make the second derivative approximationsworse when the objective function is quadratic. Therefore theconvergence properties of the procedure are sometimes less goodthan the convergence properties of other published methods forrevising sparse second derivative approximations.     

Spectral Response of a Stochastic Oscillator under Impacts

An approximate analytical procedure is presented to estimate theresponse spectrum of an oscillator with elastic impacts under a Gaussian whitenoise excitation. The proposed approach is based on a perturbation analysis ofthe problem and on the use of the stochastic averaging principle. The basicidea is to replace the initial system by a more regular system obtained byapproximating the nonlinear restoring force by a Chebychev polynomial, and thento construct for this regular system two approximations: one for the flowand one for the stationary distribution of the response amplitude. Ananalytical approximation of the response spectrum can then be derived fromthese results. Predictions from this analytical approximation are compared with corresponding digital simulation estimates and with the ones obtained from theconventional equivalent linearization method.     

Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals

We address the issue of out-of-plane losses in two-dimensional (2D) photonic crystals (PC) etched through a GaAs monomode waveguide clad with standard GaAlAs alloys. We correlate experimental transmission of PCs with two kinds of loss simulation results. The first kind is 2D and introduces an ad hoc imaginary index in the air holes to account for the losses [see (Benisty et al. Appl. Phys. Lett. 76, 532, 2000)]. The second kind is a novel exact three-dimensional calculation inspired by grating-Fourier analysis that provides quantitatively unprecedented agreement with experimental measurements taking into account hole depth as a limiting parameter. We conclude that, in revision to the conclusions of the above reference, the experimental losses are not the intrinsic ones, being larger by a factor of 5 to 10 due to insufficient hole depth. The transition occurs at a critical etch depth shown to be here around 700 nm. We thus predict, for holes deeper than 700 nm, much improved crystals with very low transmission losses and microresonators with ultra-high quality factors.     

Potentiometrische Titration von organischen Verbindungen als sehr schwache S?uren mit Lithiumdiisopropylamid

Zusammenfassung Zahlreiche organische Verbindungen wie Phenylharnstoffderivate, Anilide, Phenyl- und Alkylcarbamate können als sehr schwache Säuren angesehen werden. Mit Ausnahme der phenoxysubstituierten Carbamate, die einer O-CO-Bindungsspaltung unterliegen, können derartige Substanzen mit einer Lösung von Lithiumdiisopropylamid in THF potentiometrisch titriert werden. Mit einer Indicatorelektrode aus Wolfram und einer Silber/Silberchloridelektrode werden Potentialsprünge erhalten, die sich über mehrere 100mV erstrecken und eine genaue Auswertung erlauben.

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Potentiometric titration of organic compounds as very weak acids with lithium diisopropylamide

Summary Numerous organic compounds, such as phenylureas, anilides, alkyl- and phenylcarbamates, can be regarded as very weak acids. Except the phenoxy substituted carbamates these compounds can be titrated potentiometrically by a solution of lithium diisopropylamide in tetrahydrofuran. Carbamates with a phenoxy group undergo a fission of the O-CO-binding during the titration. The system with an indicator electrode of tungsten and a silver/silver chloride electrode gives distinct inflexions over a range of some 100mV.

     

1, 4-Dimethylcyclohex-3-enyl Methyl Ketone

An improved one-step synthesis of the title compound is described, the optical activity of the natural product is confirmed, and the NMR. spectral behaviour is explained.     

The role of new eudesmane-type sesquiterpenoid and known eudesmane derivatives from the red alga Laurencia obtusa as potential antifungal–antitumour agents

A new eudesmane sesquiterpenoid, eudesma-4(15),7-diene-5,11-diol (1) along with the known trinor-sesquiterene, teuhetenone (2), and a seco-eudesmane sesquiterpene, chabrolidione B (3), have been isolated from the Red Sea red alga Laurencia obtusa. The chemical structures were elucidated on the basis of extensive spectroscopic analysis. The antifungal and cytotoxic activities of the isolated metabolites were tested against several fungi, yeast and human mammary carcinoma cell line (MCF-7). Compounds 1 and 3 showed a much better activity [minimum inhibitory concentration (MIC): 2.9 μM] than that of amphotericin B (MIC: 4.6 μM). Interestingly, compound 2, the least active antifungal compound, retained the high anticancer activity against MCF-7 (22 μM) in comparison with cisplatin (59 μM), which was determined by employing lactate dehydrogenase assay. Compounds 1–3 are recorded here for the first time from algal flora. The chemotaxonomic importance of the isolated metabolites was discussed.     

Coupled ab initio potential energy surfaces for the two lowest 2A′ electronic states of the C2H molecule

Realistic two-valued potential energy surfaces for the reaction C(³P) + CH(X²Π) → C₂ + H have been constructed from a set of high level ab initio data describing the first two ²A′ electronic states of the C₂H system. These states have linear equilibrium configurations, known as the X ²Σ⁺ and A²Π states, and are coupled by a conical intersection. They lead to the formation of C₂(X¹Σ⁺ _g) and C₂(a³Π_u) considering an adiabatic dissociation process. The ab initio calculations are of the multireference configuration interaction variety and were carried out using a polarized triple-zeta basis set. Using the ab initio adiabatic energies and the matrix elements of the dipole moment, a 2 × 2 diabatic representation of the electronic Hamiltonian was built. Each element of this Hamiltonian matrix was expressed within the double many-body expansion (DMBE) scheme which is based, in this case, on the extended Hartree-Fock approximate correlation energy model (EHFACE). The analytical adiabatic potential energy surfaces are then obtained as the eigenvalues of this matrix, and display correctly the Σ/Π conical intersection. Moreover, the non-adiabatic couplings given by our analytical model are compared with the ab initio ones, and good qualitative agreement is observed.