Maximum Principle for Elliptic and Parabolic Equations

Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.

The Development of Calibrants through Characterization of Volatile Organic Compounds from Peroxide Based Explosives and a Non-target Chemical Calibration Compound

Detection canines represent the fastest and most versatile means of illicit material detection. This research endeavor in its most simplistic form is the improvement of detection canines through training, training aids, and calibration. This study focuses on developing a universal calibration compound for which all detection canines, regardless of detection substance, can be tested daily to ensure that they are working with acceptable parameters. Surrogate continuation aids (SCAs) were developed for peroxide based explosives along with the validation of the SCAs already developed within the International Forensic Research Institute (IFRI) prototype surrogate explosives kit. Storage parameters of the SCAs were evaluated to give recommendations to the detection canine community on the best possible training aid storage solution that minimizes the likelihood of contamination. Two commonly used and accepted detection canine imprinting methods were also evaluated for the speed in which the canine is trained and their reliability. As a result of the completion of this study, SCAs have been developed for explosive detection canine use covering: peroxide based explosives, TNT based explosives, nitroglycerin based explosives, tagged explosives, plasticized explosives, and smokeless powders. Through the use of these surrogate continuation aids a more uniform and reliable system of training can be implemented in the field than is currently used today. By examining the storage parameters of the SCAs, an ideal storage system has been developed using three levels of containment for the reduction of possible contamination. The developed calibration compound will ease the growing concerns over the legality and reliability of detection canine use by detailing the daily working parameters of the canine, allowing for Daubert rules of evidence admissibility to be applied. Through canine field testing, it has been shown that the IFRI SCAs outperform other commercially available training aids on the market. Additionally, of the imprinting methods tested, no difference was found in the speed in which the canines are trained or their reliability to detect illicit materials. Therefore, if the recommendations discovered in this study are followed, the detection canine community will greatly benefit through the use of scientifically validated training techniques and training aids.

Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.

Modelling of a Stirling engine with parabolic dish for thermal to electric conversion of solar energy

Stirling engines with parabolic dish for thermal to electric conversion of solar energy is one of the most promising solutions of renewable energy technologies in order to reduce the dependency from fossil fuels in electricity generation. This paper addresses the modelling and simulation of a solar powered Stirling engine system with parabolic dish and electric generator aiming to determine its energy production and efficiency. The model includes the solar radiation concentration system, the heat transfer in the ther- mal receiver, the thermal cycle and the mechanical and electric energy conversion. The thermodynamic and energy transfer processes in the engine are modelled in detail, including all the main processes occur- ring in the compression, expansion and regenerator spaces. Starting from a particular configuration, an optimization of the concentration factor is also carried out and the results for both the transient and steady state regimes are presented. It was found that using a directly illuminated thermal receiver with- out cavity the engine efficiency is close to 23.8% corresponding to a global efficiency of 10.4%. The com- ponents to be optimized are identified in order to increase the global efficiency of the system and the trade-off between system complexity and efficiency is discussed.

Thermal decomposition of the synthetic hydrotalcite iowaite

The thermal stability and thermal decomposition pathways for synthetic iowaite have been determined using thermogravimetry in conjunction with evolved gas mass spectrometry. Chemical analysis showed the formula of the synthesised iowaite to be Mg6.27Fe1.73(Cl)1.07(OH)16(CO3)0.336.1H2O and X-ray diffraction confirms the layered structure. Dehydration of the iowaite occurred at 35 and 79°C. Dehydroxylation occurred at 254 and 291°C. Both steps were associated with the loss of CO2. Hydrogen chloride gas was evolved in two steps at 368 and 434°C. The products of the thermal decomposition were MgO and a spinel MgFe2O4. Experimentally it was found to be difficult to eliminate CO2 from inclusion in the interlayer during the synthesis of the iowaite compound and in this way the synthesised iowaite resembled the natural mineral.

Raman spectroscopic study of the metatellurate mineral : Xocomecatlite Cu3TeO4(OH)4

The mineral xocomecatlite is a hydroxy metatellurate mineral with Te6+O4 units. Tellurates may be subdivided according to their formula into three types of tellurate minerals: type (a) (AB)m(TeO4)pZq, type (b) (AB)m(TeO6).xH2O and (c) compound tellurates in which a second anion including the tellurite anion, is involved. The mineral Xocomecatlite is an example of the first type. Raman bands for xocomecatlite at 710, 763 and 796 cm-1 and 600 and 680 cm-1 are attributed to the ν1 (TeO4)2- symmetric and ν3 antisymmetric stretching mode. Raman bands observed at 2867 and 2926 cm-1 are assigned to TeOH stretching vibrations and enable estimation of the hydrogen bond distances of 2.622 Å (2867 cm-1), 2.634 Å (2926 cm-1) involving these OH units. The hydrogen bond distances are very short implying that they are necessary for the stability of the mineral.

Tris[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]aluminium(III)-tris[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]iron(III) (3/1)

In the title compound, [Al(C8H4F3O2S)3]3[Fe(C8H4F3O2S)3], the metal centre is statistically occupied by AlIII and FeIII cations in a 3:1 ratio. The metal centre is within an octahedral O6 donor set defined by three chelating substituted acetoacetonate anions. The ligands are arranged around the periphery of the molecule with a mer geometry of the S atoms.

2,4-Diodoaniline

The structure of the title compound C6H6I2N shows a weak intermolecular amine-amine N--H...N hydrogen-bonding interaction giving a helical chain which extends along the axis. An intramolecular N-H...I hydrogen bond is also observed.

Sodium 2-nitrocinnamate dihydrate: a one-dimensional hydrogen-bonded coordination polymer

The title compound catena-poly[aqua-mu3-2-nitrocinnamato], [Na(C9H6NO4)(H2O)2]n, the sodium salt of trans-2-nitrocinnamic acid, is a one-dimensional coordination polymer based on six-coordinate octahedral NaO6 centres comprising three facially-related monodentate carboxylate O-atom donors from separate ligands (all bridging)[Na-O, 2.4370(13)-2.5046(13)A] and three water molecules (two bridging, one monodentate) [Na-O, 2.3782(13)-2.4404(17)A]. The structure is also stabilized by intra-chain water-O-H...O(carboxylate) and O-H...O(nitro) hydrogen bonds.

4-(2-Hydroxyethyl) anilinium 3,5-dinitrobenzoate

In the title compound, C8H12NO+ C7H3N2O6-, the anilinium and hydroxyl protons of the cation result in N-H...O, N-H..(O,O) and O-H...O hydrogen-bonding interactions with carboxylate O atom acceptors, forming a two-dimensional network structure. An intermolecular C-H...O interaction is also present.

4-Chloroanilinium 2-carboxy-4,5-dichlorobenzoate

The structure of the 1:1 proton-transfer compound of 4-chloroaniline with 4,5-dichlorophthalic acid (DCPA), viz. C6H7ClN+ C8H3Cl2O4-, has been determined at 130 K. The non-planar hydrogen phthalate anions and the 4-chloroanilinium cations form two-dimensional O-H...O and N-H...O hydrogen-bonded substructures which have no peripheral extension. Between the sheets there are weak \p--\p associations between alternating cation--anion aromatic ring systems [shortest centroid separation, 3.735(4)A].

1,10-phenanthrolin-1-ium 2-carboxy-4,5-dichlorobenzoate

In the structure of the 1:1 proton-transfer compound of 1,10-phenanthroline with 4,5-dichlorophthalic acid, C12H9N2+ C8H3Cl2O4-, determined at 130 K, the 1,10-phenanthroline cation and the hydrogen 4,5-dichlorophthalate anion associate through a single N-H...O(carboxyl) hydrogen bond giving discrete units which have no extension except through a number of weak cation C-H...O(anion) associations and weak cation--anion aromatic ring pi-pi interactions [minimum centroid separation, 3.6815(12)A]. The anions are essentially planar [maximum deviation 0.214(1)A (a carboxyl O)] with the syn-related H atom of the carboxyl group forming a short intramolecular O-H...O(carboxyl) hydrogen bond.

Zero- one- and two-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, nicotinamide and isonicotinamide

The structures of the anhydrous 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, 3-(aminocarboxy) pyridine (nicotinamide) and 4-(aminocarbonyl) pyridine (isonicotinamide), namely 2-aminopyrimidinium 2-carboxy-4,5-dichlorobenzoate C4H6N3+ C8H3Cl2O4- (I), 3-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate C6H7N2O+ C8H3Cl2O4- (II) and the unusual salt adduct 4-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate 2-carboxymethyl-4,5-dichlorobenzoic acid (1/1/1) C6H7N2O+ C8H3Cl2O4-.C9H6Cl2O4 (III) have been determined at 130 K. Compound (I) forms discrete centrosymmetric hydrogen-bonded cyclic bis(cation--anion) units having both R2/2(8) and R2/1(4) N-H...O interactions. In compound (II) the primary N-H...O linked cation--anion units are extended into a two-dimensional sheet structure via amide-carboxyl and amide-carbonyl N-H...O interactions. The structure of (III) reveals the presence of an unusual and unexpected self-synthesized methyl monoester of the acid as an adduct molecule giving one-dimensional hydrogen-bonded chains. In all three structures the hydrogen phthalate anions are

Development of a colorimetric assay for heparanase activity suitable for kinetic analysis and inhibitor screening

The role that heparanase plays during metastasis and angiogenesis in tumors makes it an attractive target for cancer therapeutics. Despite this enzyme’s significance, most of the assays developed to measure its activity are complex. Moreover, they usually rely on labeling variable preparations of the natural substrate heparan sulfate, making comparisons across studies precarious. To overcome these problems, we have developed a convenient assay based on the cleavage of the synthetic heparin oligosaccharide fondaparinux. The assay measures the appearance of the disaccharide product of heparanase-catalyzed fondaparinux cleavage colorimetrically using the tetrazolium salt WST-1. Because this assay has a homogeneous substrate with a single point of cleavage, the kinetics of the enzyme can be reliably characterized, giving a Km of 46 μM and a kcat of 3.5 s−1 with fondaparinux as substrate. The inhibition of heparanase by the published inhibitor, PI-88, was also studied, and a Ki of 7.9 nM was determined. The simplicity and robustness of this method, should, not only greatly assist routine assay of heparanase activity but also could be adapted for high-throughput screening of compound libraries, with the data generated being directly comparable across studies.

An Improved Synthetic Route to the Potent Angiogenesis Inhibitor Benzyl Manα(1→3)-Manα(1→3)-Manα(1→3)-Manα(1→2)-Man Hexadecasulfate

An improved synthetic route to α(1→3)/α(1→2)-linked mannooligosaccharides has been developed and applied to a more efficient preparation of the potent anti-angiogenic sulfated pentasaccharide, benzyl Manα(1→3)-Manα(1→3)-Manα(1→3)-Manα(1→2)-Man hexadecasulfate, using only two monosaccharide building blocks. Of particular note are improvements in the preparation of both building blocks and a simpler, final deprotection strategy. The route also provides common intermediates for the introduction of aglycones other than benzyl, either at the building block stage or after oligosaccharide assembly. The anti-angiogenic activity of the synthesized target compound was confirmed via the rat aortic assay.