Critical exponents for semilinear equations of mixed elliptic‐hyperbolic and degenerate types

For semilinear Gellerstedt equations with Tricomi, Goursat or Dirichlet boundary conditions we prove Pohozaev type identities and derive non existence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic hyperbolic or degenerate settings where the power is one less than the critical exponent in a relevant Sobolev imbedding. © 2002 Wiley Periodicals, Inc.     

Model based soft-sensor for on-line determination of substrate

A software sensor for on-line determination of substrate was developed based on a model for fed-batch alcoholic fermentation process and on-line measured signals of ethanol, biomass, and feed flow. The ethanol and biomass signals were obtained using a colorimetric biosensor and an optical sensor developed in previous works that permitted determination of ethanol at a concentration of 0–40 g/L and biomass of 0–60 g/L. The volume in the fermentor could be continuously calculated using the total measured signal of the feed flow. The results obtained show that the model used is adequate for the proposed software sensor and determines continuously the substrate concentration with efficiency and security during the fermentation process.     

Expanding the Scope of Atropisomeric Monodentate P‐Donor Ligands in Asymmetric Catalysis: Hydrogen‐Transfer Reduction of α,β‐Unsaturated Acid Derivatives by Rhodium/Ph‐binepine Catalysts

A range of α,β‐unsaturated acids and esters have been selectively reduced to the corresponding saturated acid derivatives by hydrogen transfer. As the reducing agent, formic acid was used in the presence of Rh^I complexes formed with the powerful chiral ligand Ph‐binepine ( 1 ), an axially chiral binaphthalene‐type monodentate P‐donor ligand. Very high stereoselectivities (up to 97% ee) were obtained in the case of itaconic acid ( 2a ).     

Pyrolytic synthesis of long strands of large diameter single-walled carbon nanotubes at atmospheric pressure in the absence of sulphur and hydrogen

We describe the synthesis of cm-long strands consisting of single-walled carbon nanotube ropes. The method involves the thermolysis of ferrocene (FeCp₂)–alcohol solutions under an Ar atmosphere at 800–950 °C. The tubes within strands could exhibit large diameters (2–3.5 nm OD) in high yields by either increasing the ferrocene concentration in the alcohol solution or by increasing the pyrolysis temperature. We noted that the nanotube material with the highest degree of crystallinity was produced at 950 °C, and as the ferrocene concentration in the alcohol solution increases (e.g., 1.2 wt%), the tubes tend to be metallic. This method appears to be simple, safer and more efficient than others reported in the literature because it does not require vacuum, sulphur agents, relatively high temperatures or large amounts of H₂.     

Reactive oxygen species (ROS) generation inhibited by aporphine and phenanthrene alkaloids semi-synthesized from natural boldine

Four phenanthrene and one aporphine alkaloids semi-synthesized from boldine were evaluated for their inhibitory effect on reactive oxygen species (ROS) generation. ROS generation by neutrophils stimulated with N-formyl-methionyl-leucyl-phenylalanine was inhibited in a concentration dependent manner. Alkaloids exerted similar inhibitory effect in the hypoxanthine-xanthine oxidase system than in stimulated neutrophils, which could be attributed to a direct ROS scavenging activity. None of the alkaloids assayed had any effect on xanthine oxidase activity. Therefore the synthesized alkaloids might constitute an alternative therapy in inflammation disorders in which ROS generation is involved.     

Ab initio molecular electrostatic potentials

The ab initio isopotential map of guanine is given and compared to that of adenine. It shows that in contrast to the situation in adenine, the most basic site of guanine is N₇ with a secondary potential minimum at O₆. These results as well as those concerning the secondary out-of-plane attractive regions over the NH₂ group and C₈ H bonds of the two molecules are discussed in connection with the available experimental knowledge concerning the bonding of alkylating carcinogens and mutagens.     

Engineering multiphoton states for linear optics computation

Transformations achievable by linear optical components allow to generate the whole unitary group only when restricted to the one-photon subspace of a multimode Fock space. In this paper, we address the more general problem of encoding quantum information by multiphoton states, and elaborating it via ancillary extensions, linear optical passive devices and photodetection. Our scheme stems in a natural way from the mathematical structures underlying the physics of linear optical passive devices. In particular, we analyze an economical procedure for mapping a fiducial 2-photon 2-mode state into an arbitrary 2-photon 2-mode state using ancillary resources and linear optical passive N-ports assisted by post-selection. We found that adding a single ancilla mode is enough to generate any desired target state. The effect of imperfect photodetection in post-selection is considered and a simple trade-off between success probability and fidelity is derived.     

Infrared studies of small azobenzene peptides: unexpectedly slow reactions on the time range of minutes

Infrared absorption experiments on light-triggered azobenzene peptides have been performed below and above the freezing point of the solvent dimethyl sulfoxide (DMSO). Even 20 K below the freezing point, illumination of the azobenzene chromophore resulted in IR absorption changes indicative of light-induced structural rearrangements of the peptide. In addition, new conformational states could be found at low temperature, which involve the formation of additional hydrogen bonds. In one sample the new low-temperature state survived melting and reheating and disappeared at 298 K only on the time scale of 10 min. The observations indicate that at low temperatures the peptide, together with traces of water present in the sample, forms a shell in the vicinity of the chromophore that facilitates internal motion even in the rigid cage of frozen DMSO.     

A rheological phase diagram of additives for cement formulations

A detailed rheological study of aqueous solutions of methylhydroxyethylcellulose has been carried out in the presence of different acrylate-based graft polymer used as additive contents. Both polymer components are used in cement formulations to improve the flow performances of the concretes, but no physicochemical studies can be easily found in the literature. The content of the graft polymer has been varied between 0.1 and 2.7 wt% in an aqueous solution with a fixed content of 6.5 wt% of methylhydroxyethylcellulose. Creep curves were performed at different stresses in order to build up the flow curves for the various solutions. We found that the addition of the graft polymer triggers a phase transition, which is made more dramatic by the presence of an external flow. A “flow-phase diagram” has been obtained, which could be used as a guide for determining the critical conditions for the onset of the flow-induced instability.     

Order conditions for partitioned Runge-Kutta methods

We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations.