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.     

MRI detection of tumor in mouse lung using partial liquid ventilation with a perfluorocarbon-in-water emulsion

Transverse relaxation time (T(2*))-weighted (1)H-MRI of mouse lungs has been performed using partial liquid ventilation (PLV) with a perfluorocarbon (PFC)-in-water emulsion as a contrast modality for lung MRI. Significant sensitivity enhancement in MRI of mouse lungs has been demonstrated with the protocol. The results show that the T(2*) value in lung is approximately proportional to the infusion dose up to a dose of 5 ml/kg body weight (BW) (4.5 g PFC/kg BW) and becomes essentially constant beyond this dosage. T(2*) maps of lungs have been calculated and T(2*) in lungs is in the range of 10-35 ms with this technique, which is an order of magnitude greater than the T(2*) value of mouse lungs without using a PFC-in-water emulsion. T(2*)-weighted (1)H-MR images of mouse lungs have been obtained with good quality under our experimental conditions. We have applied this technique to detect tumors in mouse lungs. Our technique can detect small lung tumors of B16 melanoma, about 1 mm in diameter, in mice. With its significant MR sensitivity enhancement and technical simplicity, T(2*)-weighted (1)H-MRI using PLV with PFC-in-water emulsion offers a promising approach to investigate lung cancers using rodent models.     

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.     

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.     

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.     

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.     

The Cosmological constant problem

Observational evidence seems to indicate that the expansion of the universe is currently accelerating. Such an acceleration strongly suggests that the content of the universe is dominated by a non-clustered form of matter, the so-called dark energy. The cosmological constant, introduced by Einstein to reconcile General Relativity with a closed and static Universe, is the most likely candidate for dark energy although other options such as a weakly interacting field, also known as quintessence, have been proposed. The fact that the dark energy density is some one hundred and twenty orders of magnitude lower than the energy scales present in the early universe constitutes the cosmological constant problem. We review various aspects of the cosmological constant problem and some interesting scenarios using supersymmetry or extra-dimensions attempting to solve one of the most puzzling issues in physics.     

Evaluation of a new maintenance concept for the preservation of highways

Asphalt roads gradually deteriorate over time and need mendingto remain in a good state. Inspections are performed to obtaininformation about the current state of the road; when the levelof damage reaches the established standards, the road is repairedthrough a maintenance action that is considered most cost-effective.Because of economies of scale, it is to a certain extent economicalto limit the number of maintenance services by integrating neighbouringsegments into a homogeneous section which is completely repaired.In this report we consider the question of whether it is economicallyjustified to adopt a maintenance concept in which the road isoccasionally regenerated from junction to junction with a distanceof several kilometers. The big advantage of junction-to-junctionmaintenance is that it can be done within special road barrierconstructions which reduce the road capacity only slightly,so that the road can be maintained 24 hours a day.