Enumerating Rational Curves: The Rational Fibration Method

A new method to approach enumerative questions about rational curves on algebraic varieties is described. The idea is to reduce the counting problems to computations on the Néron-Severi group of a ruled surface. Applications include a short proof of Kontsevich's formula for plane curves and the solution of the analogous problem for the Hirzebruch surface F₃.     

A solver for the stochastic master equation applied to gene regulatory networks

An important driver of gene regulatory networks is noise arising from the stochastic nature of interactions of genes, their products and regulators. Thus, such systems are stochastic and can be modelled by the chemical master equations. A major challenge is the curse of dimensionality which occurs when one attempts to integrate these equations. While stochastic simulation techniques effectively address the curse, many repeated simulations are required to provide precise information about stationary points, bifurcation phenomena and other properties of the stochastic processes. An alternative way to address the curse of dimensionality is provided by sparse grid approximations. The sparse grid methodology is applied and the application demonstrated to work efficiently for up to 10 proteins. As sparse grid methods have been developed for the approximation of smooth functions, a variant for infinite sequences had to be developed together with a multiresolution analysis similar to Haar wavelets. Error bounds are provided which confirm the effectiveness of sparse grid approximations for smooth high-dimensional probability distributions.     

Approximation of functionally graded plates with non-conforming finite elements

In this paper rectangular plates made of functionally graded materials (FGMs) are studied. A two-constituent material distribution through the thickness is considered, varying with a simple power rule of mixture. The equations governing the FGM plates are determined using a variational formulation arising from the Reissner–Mindlin theory. To approximate the problem a simple locking-free Discontinuous Galerkin finite element of non-conforming type is used, choosing a piecewise linear non-conforming approximation for both rotations and transversal displacement. Several numerical simulations are carried out in order to show the capability of the proposed element to capture the properties of plates of various gradings, subjected to thermo-mechanical loads.     

Lebesgue decomposition by σ-null-additive set functions using ideals

Using V. Ficker’s and P. Capek’s algebraic approach by ideals a Lebesgue decomposition theorem for a wide class of non-additive set functions called null-additive set functions is obtained. In special cases decompositions theorems for ⊕-decomposable measures andk-triangular set functions are obtained.     

Electrochemical behavior of dopamine at a 3,3′-dithiodipropionic acid self-assembled monolayers

Monolayers of 3,3′-dithiodipropionic acid (DTDPA) were prepared on a polycrystalline gold electrode through a self-assembly procedure to produce a gold 3,3′-dithiodipropionic acid self-assembled monolayer (AuDTDPA) modified electrode. The characterization of the AuDTDPA electrode was investigated by cyclic voltammetry and ac impedance using the [Fe(CN)₆]^3−/4− redox couple. The electrochemical behavior of DA on the modified electrode AuDTDPA was studied by cyclic and square-wave voltammetries, using phosphate buffer as supporting electrolyte. The oxidation peak current for DA increases linearly with concentration in the range of 0.35 × 10⁻⁵ to 3.4 × 10⁻⁵ mol L⁻¹. The performance of the AuDTDPA modified electrode was evaluated for the electroanalytical determination of dopamine (DA) in a pharmaceutical formulation. The AuDTDPA modified electrode showed a stable behavior and the presence of surface-COOH groups avoided the passivation of the electrode surface during the dopamine oxidation.     

Intermediate free radicals in the oxidation of wastewaters

The cleaning action on wastewater as obtained through oxidation methods has been investigated by means of EPR spectroscopy to achieve qualitative and quantitative information on the radicals produced upon utilising peracetic acid and hydrogen peroxide with and without UV irradiation. The DEPMPO spin trap was employed to detect hydroxyl and carbon-centred short living radicals during water disinfection, either in the absence or in the presence of UV-C irradiation. Moreover, three different kinds of water (wastewater, demineralized water, distilled water) were analysed in order to assess the contribution of Fenton reactions to the radical production. The spectroscopic results are discussed in relation to the efficiency of the different oxidising agents and UV irradiation in wastewater disinfection evaluated as Escherichia coli, faecal and total coliforms inactivation.     

Synthesis and reactivity of 1-methyl-3-phenyl-4-diazo-5-benzoylamidopyrazole. A potential antitumor agent

The title compound 2 was prepared in excellent yield by diazotation of the parent amino derivative. Compound 2 was found to react with a variety of acyclic and cyclic active methylene compounds to yield the corresponding pyrazolo-4-ylhydrazones.     

Selective sequential dissolution for the determination of inorganic indium compounds in the particulate matter of emissions and workplace air.

A speciation method was developed for the determination of inorganic indium compounds in the particulate matter of emissions and from the workplace, based on selective sequential extractions. The main inorganic indium compounds that are expected to be present in the atmospheric particulate matter involving the industrial production of indium and in the manufacture of indium compounds were separated and determined. The procedure has been tested on standard reference materials. The indium recovery was in the range 93 - 105%.     

Pressure broadening of hydrogen sulfide

Microwave measurements of the self-broadening parameters of four pure rotational transitions of H₂S have been carried out in the millimeter and submillimeter wavelength region. The resulting parameters are (in MHz torr^-1): 1_1.0?1_0.1, 7.18±0.5; 2_2.0?2_1.1, 6.78±0.5; 2_1.1?2_0.2, 9.10±0.5; 3_3.0?3_2.1, 7.76 ±0.5. In addition. Anderson theory calculations have been carried out for these transitions and are found to be in good agreement.     

Excitation,inversion, and relaxation mechanisms of the HCN FIR discharge laser

Millimeter/submillimeter rotational absorption spectroscopy has been used as a diagnostic probe of a cw HCN discharge laser. This sensitive technique allowed in situ absolute population measurements of a number of vibrational states of HCN (including the upper lasing state) and other pertinent molecules. This unique set of data, which was obtained under a variety of discharge and laser conditions, is directly related to excitation, inversion, and relaxation processes. Along with elucidating several fundamental aspects of inversion and relaxation these results also strongly indicate that the primary laser excitation mechanism is near-resonant energy transfer from vibrationally excited nitrogen, N₂ (v=1), to the fundamental symmetric stretching mode of hydrogen cyanide, HCN(100), and subsequent thermal population exchange between HCN (100) and the upper laser state, HCN (110).Work supported by ARO Contract DAAG-29-83-K-0078