Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems

MSC 2010: 30A10, 30B10, 30B30, 30B50, 30D15, 33E12

On the Moving Boundary Hitting Probability for the Brownian Motion

2000 Mathematics Subject Classification: 60J65.

Exotic meson decay widths using lattice quantum chromodynamics

Most experiments in particle physics are scattering experiments, the analysis of which leads to masses, scattering phases, decay widths and other properties of one or multi-particle systems. Until the advent of Lattice Quantum Chromodynamics (LQCD) it was difficult to compare experimental results on low energy hadron-hadron scattering processes to the predictions of QCD, the current theory of strong interactions. The reason being, at low energies the QCD coupling constant becomes large and the perturbation expansion for scattering; amplitudes does not converge. To overcome this, one puts the theory onto a lattice, imposes a momentum cutoff, and computes the integral numerically. For particle masses, predictions of LQCD agree with experiment, but the area of decay widths is largely unexplored. ^ LQCD provides ab initio access to unusual hadrons like exotic mesons that are predicted to contain real gluonic structure. To study decays of these type resonances the energy spectra of a two-particle decay state in a finite volume of dimension L can be related to the associated scattering phase shift δ(k) at momentum k through exact formulae derived by Lüscher. Because the spectra can be computed using numerical Monte Carlo techniques, the scattering phases can thus be determined using Lüscher's formulae, and the corresponding decay widths can be found by fitting Breit-Wigner functions. ^ Results of such a decay width calculation for an exotic hybrid( h) meson (JPC = 1-+) are presented for the decay channel h → πa 1. This calculation employed Lüscher's formulae and an approximation of LQCD called the quenched approximation. Energy spectra for the h and πa1 systems were extracted using eigenvalues of a correlation matrix, and the corresponding scattering phase shifts were determined for a discrete set of πa1 momenta. Although the number of phase shift data points was sparse, fits to a Breit-Wigner model were made, resulting in a decay width of about 60 MeV. ^

(Table 1) Salinity and dissolved organic carbon concentration of marine water (ANT-XIX/2) and mangrove porewater (Brazil)

The chemical structure of refractory marine dissolved organic matter (DOM) is still largely unknown. Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR-MS) was used to resolve the complex mixtures of DOM and provide valuable information on elemental compositions on a molecular scale. We characterized and compared DOM from two sharply contrasting aquatic environments, algal-derived DOM from the Weddell Sea (Antarctica) and terrigenous DOM from pore water of a tropical mangrove area in northern Brazil. Several thousand molecular formulas in the mass range of 300-600 Da were identified and reproduced in element ratio plots. On the basis of molecular elemental composition and double-bond equivalents (DBE) we calculated an average composition for marine DOM. O/C ratios in the marine samples were lower (0.36 ± 0.01) than in the mangrove pore-water sample (0.42). A small proportion of chemical formulas with higher molecular mass in the marine samples were characterized by very low O/C and H/C ratios probably reflecting amphiphilic properties. The average number of unsaturations in the marine samples was surprisingly high (DBE = 9.9; mangrove pore water: DBE = 9.4) most likely due to a significant contribution of carbonyl carbon. There was no significant difference in elemental composition between surface and deep-water DOM in the Weddell Sea. Although there were some molecules with unique marine elemental composition, there was a conspicuous degree of similarity between the terrigenous and algal-derived end members. Approximately one third of the molecular formulas were present in all marine as well as in the mangrove samples. We infer that different forms of microbial degradation ultimately lead to similar structural features that are intrinsically refractory, independent of the source of the organic matter and the environmental conditions where degradation took place.

How does problem based learning fit with cognitive load theory?

This paper reports on an investigation with first year undergraduate Product Design and Management students within a School of Engineering. The students at the time of this investigation had studied fundamental engineering science and mathematics for one semester. The students were given an open ended, ill formed problem which involved designing a simple bridge to cross a river. They were given a talk on problem solving and given a rubric to follow, if they chose to do so. They were not given any formulae or procedures needed in order to resolve the problem. In theory, they possessed the knowledge to ask the right questions in order to make assumptions but, in practice, it turned out they were unable to link their a priori knowledge to resolve this problem. They were able to solve simple beam problems when given closed questions. The results show they were unable to visualise a simple bridge as an augmented beam problem and ask pertinent questions and hence formulate appropriate assumptions in order to offer resolutions.

Molecular composition of organic aerosols in central Amazonia: an ultra-high-resolution mass spectrometry study

The Amazon Basin plays key role in atmospheric chemistry, biodiversity and climate change. In this study we applied nanoelectrospray (nanoESI) ultra-high-resolution mass spectrometry (UHRMS) for the analysis of the organic fraction of PM2.5 aerosol samples collected during dry and wet seasons at a site in central Amazonia receiving background air masses, biomass burning and urban pollution. Comprehensive mass spectral data evaluation methods (e.g. Kendrick mass defect, Van Krevelen diagrams, carbon oxidation state and aromaticity equivalent) were used to identify compound classes and mass distributions of the detected species. Nitrogen- and/or sulfur-containing organic species contributed up to 60 % of the total identified number of formulae. A large number of molecular formulae in organic aerosol (OA) were attributed to later-generation nitrogen- and sulfur-containing oxidation products, suggesting that OA composition is affected by biomass burning and other, potentially anthropogenic, sources. Isoprene-derived organosulfate (IEPOX-OS) was found to be the most dominant ion in most of the analysed samples and strongly followed the concentration trends of the gas-phase anthropogenic tracers confirming its mixed anthropogenic–biogenic origin. The presence of oxidised aromatic and nitro-aromatic compounds in the samples suggested a strong influence from biomass burning especially during the dry period. Aerosol samples from the dry period and under enhanced biomass burning conditions contained a large number of molecules with high carbon oxidation state and an increased number of aromatic compounds compared to that from the wet period. The results of this work demonstrate that the studied site is influenced not only by biogenic emissions from the forest but also by biomass burning and potentially other anthropogenic emissions from the neighbouring urban environments.

An Environment for Rapid Derivatives Design and Experimentation

In the highly competitive world of modern finance, new derivatives are continually required to take advantage of changes in financial markets, and to hedge businesses against new risks. The research described in this paper aims to accelerate the development and pricing of new derivatives in two different ways. Firstly, new derivatives can be specified mathematically within a general framework, enabling new mathematical formulae to be specified rather than just new parameter settings. This Generic Pricing Engine (GPE) is expressively powerful enough to specify a wide range of stand¬ard pricing engines. Secondly, the associated price simulation using the Monte Carlo method is accelerated using GPU or multicore hardware. The parallel implementation (in OpenCL) is automatically derived from the mathematical description of the derivative. As a test, for a Basket Option Pricing Engine (BOPE) generated using the GPE, on the largest problem size, an NVidia GPU runs the generated pricing engine at 45 times the speed of a sequential, specific hand-coded implementation of the same BOPE. Thus a user can more rapidly devise, simulate and experiment with new derivatives without actual programming.

High resolution Thomson Parabola Spectrometer for full spectral capture of multi-species ion beams

We report on the experimental characterisation of laser-driven ion beams using a Thomson Parabola Spectrometer (TPS) equipped with trapezoidally shaped electric plates, proposed by Gwynne et al. [Rev. Sci. Instrum. 85, 033304 (2014)]. While a pair of extended (30 cm long) electric plates was able to produce a significant increase in the separation between neighbouring ion species at high energies, deploying a trapezoidal design circumvented the spectral clipping at the low energy end of the ion spectra. The shape of the electric plate was chosen carefully considering, for the given spectrometer configuration, the range of detectable ion energies and species. Analytical tracing of the ion parabolas matches closely with the experimental data, which suggests a minimal effect of fringe fields on the escaping ions close to the wedged edge of the electrode. The analytical formulae were derived considering the relativistic correction required for the high energy ions to be characterised using such spectrometer.

Nucleophilic addition of Nitrones to Electron deficient acetylenes and related studies

Nitrones or azomethine-N-oxides are important precursors for the synthesis of several heterocyclic systems. They belong to the allyl anion type 1,3-dipoles and possess unique structural features which make them extraordinarily useful synthons. They behave as 1,3-dipoles in 1,3-dipolar cycloaddition reactions and as electrophiles in reactions with organometallic reagents. These are the two basic reactions given by nitrones. Nitrones also act as ‘spin traps’ in which they react with short-lived radicals to furnish stable nitroxide radicals which can be detected and identified by electron paramagnetic resonance (EPR) spectroscopy. Recently SmI2 catalysed reductive cross-coupling reactions of nitrones have gained significant interest in which the reactions are initiated by single electron transfer (SET) to nitrones. Apart from these reactions, nitrones are also known to participate in reactions which are initiated by the nucleophilic attack of nitrone-oxygen. In our group, we have also explored the nucleophilic character of nitrones through various reactions. The results obtained enabled us to develop a novel two-step one-pot strategy for quinolines and indoles - the heterocycles renowned for their pharmacological applications, from nitrones and electron deficient acetylenes. Using dibenzoylacetylene and phenylbenzoylacetylene as dipolarophiles, we could introduce a desired functional group at a predetermined position of the quinolines or indoles to be synthesised. In this context, the thesis entitled “NUCLEOPHILIC ADDITION OF NITRONES TO ELECTRON DEFICIENT ACETYLENES AND RELATED STUDIES” portrays our attempt to expand the scope of our x novel synthetic protocol using ester functionalised acetylenes: dimethyl acetylenedicarboxylate (DMAD) and methyl propiolate. The thesis is organised in to five chapters. The first chapter briefly describes the different classes of reactions that nitrone functionality can tolerate. The research problem is defined at the end of this chapter. The second chapter describes the synthesis of different nitrones used for the present study. The optimisation and expansion of scope of the novel strategy towards quinoline synthesis is discussed in the third chapter. The fourth chapter portrays the synthesis of indole-3-carboxylates using the novel strategy. In the fifth chapter, the reaction of N-(2,6-dimethylphenyl) and N-(2,4,6-trimethylphenyl)nitrones are discussed. Here we also discuss the mechanistic reinvestigation of Baldwin’s proposal in the isoxazoline-oxazoline rearrangement. The major outcome of the work is given at the end of the thesis. The structural formulae, schemes, tables and figures are numbered chapter-wise since each chapter of the thesis is organized as an independent unit. All new compounds (except two compounds reported in fourth chapter) are fully characterised on the basis of spectral and analytical data and single crystal X-ray analysis on representative examples. Relevant references are included at the end of individual chapters.

Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹.

Cruz, Ângela Maria Paiva. Os paradoxos de Prior e o cálculo proposicional deôntico relevante. Princípios, Natal, v. 4, p. 05-18, 1996.

FX modelling under collateralization

We present the market practice for interest rate yield curves construction and pricing interest rate derivatives. Then we give a brief description of the Vasicek and the Hull-White models, with an example of calibration to market data. We generalize the classical Black-Scholes-Merton pricing formulas, considering more general cases such as perfect or partial collateral, derivatives on a dividend paying asset subject to repo funding, and multiple currencies. Finally we derive generic pricing formulae for different combinations of cash flow and collateral currencies, and we apply the results to the pricing of FX swaps and CCS, and we discuss curve bootstrapping.

Medição do transporte sólido por arrastamento através de sensores acústicos

A quantificação do material sólido transportado (transporte sólido) ao longo de um curso de água é extremamente importante nas mais variadas áreas da engenharia fluvial. O transporte sólido em rios de montanha dá-se maioritariamente por arrastamento no fundo, através de deslizamento, rolamento e saltação dos sedimentos. Ao longo dos tempos foram desenvolvidas várias fórmulas para estimar o transporte sólido por arrastamento, contudo, devido à complexidade dos processos de transporte de sedimentos, bem como a variabilidade espacial e temporal, a previsão de taxas de transporte não foi conseguida exclusivamente através de investigação teórica. Para obter um melhor conhecimento sobre os processos de transporte sólido por arrastamento em rios de montanha, torna-se necessário monitorizá-los com maior precisão possível. Com os avanços na electrónica, novos métodos tecnológicos foram desenvolvidos para resolver a problemática da quantificação do transporte sólido, em detrimento dos atuais métodos tradicionais, que se baseiam na recolha de amostras em campo, para posterior correlação. O objetivo principal da presente dissertação foi o desenvolvimento de um equipamento capaz de estimar/monitorizar continuamente o transporte sólido por arrastamento em rios de montanha, que utilizasse tecnologia de baixo custo. Este equipamento dispõe de um sensor piezolelétrico que realizará medições à vibração causada pelo embate dos sedimentos sobre uma chapa metálica. A energia do sinal resultante dos impactos reverterá em peso. A metodologia usada para a obtenção das medições foi a realização de ensaios laboratoriais, tendo sido dado especial destaque à influência da variação do caudal, bem como da forma dos sedimentos, na intensidade do sinal adquirido.

A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

Shear, shear stress and shearing

New simpler formulae are derived for the shear of a pair of material elements within the context of infinitesimal strain and finite strain. Also, new formulae are derived for shear stress based on the (symmetric) Cauchy stress and for the rate of shear of a pair of material elements within the rate of strain theory. These formulae are exploited to obtain results and to derive new simpler proofs of familiar classical results. In particular, a very simple short derivation is presented of the classical result of Coulomb and Hopkins on the maximum orthogonal shear stress. © 1992.