Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

The evolution of the mass-metallicity relation in SDSS galaxies uncovered by astropaleontology

We have obtained the mass-metallicity (M-Z) relation at different lookback times for the same set of galaxies from the Sloan Digital Sky Survey, using the stellar metallicities estimated with our spectral synthesis code STARLIGHT. We have found that this relation steepens and spans a wider range in both mass and metallicity at higher redshifts. We have modeled the time evolution of stellar metallicity with a closed-box chemical evolution model, for galaxies of different types and masses. Our results suggest that the M-Z relation for galaxies with present-day stellar masses down to 10^10 M_sun is mainly driven by the history of star formation history and not by inflows or outflows.Comment: Accepted for publication in MNRA

Stellar populations of bulges at low redshift

This chapter summarizes our current understanding of the stellar population properties of bulges and outlines important future research directions.Comment: Review article to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing. 34 pages, 12 figure

Optimal design of water treatment processes

Predicted water shortages assign water treatment a leading role in improving water resources management. One of the main challenges associated with the processes remains early stage design of techno-economically optimised purification. This work addresses the current gap by undertaking a whole-system approach of flowsheet synthesis for the production of water at desired purity at minimum overall cost. The optimisation problem was formulated as a mixed-integer non-linear programming model. Two case studies were presented which incorporated the most common commercial technologies and the major pollution indicators, such as chemical oxygen demand, dissolved organic carbon, total suspended solids and total dissolved solids. The results were analysed and compared to existing guidelines in order to examine the applicability of the proposed approach

Cinema-going trajectories in the digital age

The activity of cinema-going constantly evolves and gradually integrates the use of digital data and platforms to become more engaging for the audiences. Combining methods from the fields of Human Computer Interaction and Film Studies, we conducted two workshops seeking to understand cinema audiences’ digital practices and explore how the contemporary cinema-going experience is shaped in the digital age. Our findings suggest that going to the movies constitutes a trajectory during which cinemagoers interact with multiple digital platforms. At the same time, depending on their choices, they construct unique digital identities that represent a set of online behaviours and rituals that cinemagoers adopt before, while and after cinema-going. To inform the design of new, engaging cinemagoing experiences, this research establishes a preliminary map of contemporary cinema-going including digital data and platforms. We then discuss how audiences perceive the potential improvement of the experience and how that would lead to the construction of digital identities

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

The epidemiology of chronic pain in Libya: a cross-sectional telephone survey.

BACKGROUND: Chronic pain is a public health problem although there is a paucity of prevalence data from countries in the Middle East and North Africa. The aim of this study was to estimate the prevalence of chronic pain and neuropathic pain in a sample of the general adult population in Libya. METHODS: A cross-sectional telephone survey was conducted before the onset of the Libyan Civil War (February 2011) on a sample of self-declared Libyans who had a landline telephone and were at least 18 years of age. Random sampling of household telephone number dialling was undertaken in three major cities and interviews conducted using an Arabic version of the Structured Telephone Interviews Questionnaire on Chronic Pain previously used to collect data in Europe. In addition, an Arabic version of S-LANSS was used. 1212 individuals were interviewed (response rate = 95.1 %, mean age = 37.8 ± 13.9 years, female = 54.6 %). RESULTS: The prevalence of chronic pain ≥ 3 months was 19.6 % (95 % CI 14.6 % to 24.6 %) with a mean ± SD duration of pain of 6 · 5 ± 5 · 7 years and a higher prevalence for women. The prevalence of neuropathic pain in the respondents reporting chronic pain was 19 · 7 % (95 % CI 14 · 6-24 · 7), equivalent to 3 · 9 % (95 % CI 2 · 8 to 5 · 0 %) of the general adult population. Only, 71 (29 · 8 %) of respondents reported that their pain was being adequately controlled. CONCLUSIONS: The prevalence of chronic pain in the general adult population of Libya was approximately 20 % and comparable with Europe and North America. This suggests that chronic pain is a public health problem in Libya. Risk factors are being a woman, advanced age and unemployment. There is a need for improved health policies in Libya to ensure that patients with chronic pain receive effective management