Two-point Taylor expansions in the asymptotic approximation of double integrals. Application to the second and fourth Appell functions

The main difficulty in Laplace's method of asymptotic expansions of double integrals is originated by a change of variables. We consider a double integral representation of the second Appell function F₂(a,b,b^′,c,c^′;x,y) and illustrate, over this example, a variant of Laplace's method which avoids that change of variables and simplifies the computations. Essentially, the method only requires a Taylor expansion of the integrand at the critical point of the phase function. We obtain in this way an asymptotic expansion of F₂(a,b,b^′,c,c^′;x,y) for large b, b^′, c and c^′. We also consider a double integral representation of the fourth Appell function F₄(a,b,c,d;x,y). We show, in this example, that this variant of Laplace's method is uniform when two or more critical points coalesce or a critical point approaches the boundary of the integration domain. We obtain in this way an asymptotic approximation of F₄(a,b,c,d;x,y) for large values of a,b,c and d. In this second example, the method requires a Taylor expansion of the integrand at two points simultaneously. For this purpose, we also investigate in this paper Taylor expansions of two-variable analytic functions with respect to two points, giving Cauchy-type formulas for the coefficients of the expansion and details about the regions of convergence.     

Papers by Selected Lecturers at the 11th International Symposium on Non-thermal/Thermal Plasma Pollution Control Technology & Sustainable Energy (ISNTPT 11)

Plasma Chemistry and Plasma Processing -     

Molecular symmetry effects on the stability of highly ordered smectic phases

In an effort to control the phase ranges of highly ordered smectic phases, we examined the impact of molecular symmetry on phase behaviour of a series of 12 symmetrical and unsymmetrical 4,4′-dialkanoyloxybiphenyl derivatives. Combined differential scanning calorimetry, polarised optical microscopy, and X-ray diffraction studies indicated that the compounds studied formed smectic F liquid crystals, and in some cases, G phases at lower temperatures. Although the clearing temperatures were largely unaffected by molecular symmetry, the transitions from the SmF liquid crystals to more ordered phases were consistently lowered upon reducing the molecular symmetry. As a result, unsymmetrical molecules had broader mesophases than their higher symmetry isomers, suggesting a strategy for tuning the phase behaviour of these highly ordered lamellar phases, which have been widely targeted for organic semiconductors.     

Microwave-assisted purification of HIPCO carbon nanotubes

A very easy way for improving the purity of carbon nanotubes using a domestic multimode microwave oven is reported, in which selective burning of metal particles helps remove most of the iron content.     

An invariance principle for one large particle with collisions

Summary The convergence to the brownian motion of a stochastic process obtained by a onedimensional mechanical system, subject to random initial conditions, is proven.

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Sommario Si dimostra la convergenza al moto browniano di un processo stocastico ottenuto da un sistema meccanico unidimensionale, soggetto a condizioni iniziali aleatorie.

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Presented at the ?VII Congresso Nazionale dell'Associazione Italiana di Meccanica Teorica ed Applicata? (AIMETA), Trieste, October 84. Work realized within the activities of C.N.R., Gruppo Nazionale Fisica Matematica with partial support of M.P.I.     

Determination of insecticides in honey by matrix solid-phase dispersion and gas chromatography with nitrogen-phosphorus detection and mass spectrometric confirmation

A multiresidue method was developed for the determination of 12 organophosphorus insecticides (diazinon, parathion methyl, fenitrothion, pirimiphosmethyl, malathion, fenthion, chlorpyrifos, quinalphos, methidathion, ethion, azinphosmethyl, coumaphos), one carbamate (pirimicarb), and one amidine (amitraz) in unifloral and multifloral honeys. The analytical procedure was based on the matrix solid-phase dispersion of honey on a mixture of Florisil and anhydrous sodium sulfate in small glass columns and subsequent extraction with a low volume of hexane-ethyl acetate (90 + 10, v/v), assisted by sonication. The insecticide residues were determined by capillary chromatography with nitrogen-phosphorus detection and confirmed by mass spectrometry. Average recoveries at the 0.05-0.5 microg/g levels were >80% for organophosphorus insecticides and about 60% for the other insecticides, pirimicarb and amitraz, with relative standard deviations <10%. The detection limit for the different insecticides ranged between 6 and 15 microg/kg. The main advantages of the proposed method are that extraction and cleanup are performed in a single step with a low volume of organic solvent. The method is simple, rapid, and less laborious than conventional methods. Several Spanish honeys were analyzed with the proposed method and no residues of the studied insecticides were found.     

Degradation of Single‐Layer and Few‐Layer Graphene by Neutrophil Myeloperoxidase

Biodegradability of graphene is one of the fundamental parameters determining the fate of this material in vivo. Two types of aqueous dispersible graphene, corresponding to single‐layer (SLG) and few‐layer graphene (FLG), devoid of either chemical functionalization or stabilizing surfactants, were subjected to biodegradation by human myeloperoxidase (hMPO) mediated catalysis. Graphene biodegradation was also studied in the presence of activated, degranulating human neutrophils. The degradation of both FLG and SLG sheets was confirmed by Raman spectroscopy and electron microscopy analyses, leading to the conclusion that highly dispersed pristine graphene is not biopersistent.