The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

Non-word repetition in adolescents with Specific Language Impairment and Autism plus Language Impairments: a qualitative analysis

Non-word repetition (NWR) was investigated in adolescents with typical development, Specific Language Impairment (SLI) and Autism Plus language Impairment (ALI) (n = 17, 13, 16, and mean age 14;4, 15;4, 14;8 respectively). The study evaluated the hypothesis that poor NWR performance in both groups indicates an overlapping language phenotype (Kjelgaard & Tager-Flusberg, 2001). Performance was investigated both quantitatively, e.g. overall error rates, and qualitatively, e.g. effect of length on repetition, proportion of errors affecting phonological structure, and proportion of consonant substitutions involving manner changes. Findings were consistent with previous research (Whitehouse, Barry, & Bishop, 2008) demonstrating a greater effect of length in the SLI group than the ALI group, which may be due to greater short-term memory limitations. In addition, an automated count of phoneme errors identified poorer performance in the SLI group than the ALI group. These findings indicate differences in the language profiles of individuals with SLI and ALI, but do not rule out a partial overlap. Errors affecting phonological structure were relatively frequent, accounting for around 40% of phonemic errors, but less frequent than straight Consonant-for-Consonant or vowel-for-vowel substitutions. It is proposed that these two different types of errors may reflect separate contributory mechanisms. Around 50% of consonant substitutions in the clinical groups involved manner changes, suggesting poor auditory-perceptual encoding. From a clinical perspective algorithms which automatically count phoneme errors may enhance sensitivity of NWR as a diagnostic marker of language impairment. Learning outcomes: Readers will be able to (1) describe and evaluate the hypothesis that there is a phenotypic overlap between SLI and Autism Spectrum Disorders (2) describe differences in the NWR performance of adolescents with SLI and ALI, and discuss whether these differences support or refute the phenotypic overlap hypothesis, and (3) understand how computational algorithms such as the Levenshtein Distance may be used to analyse NWR data.

A review of Islamic mutual funds’ financial performance and investment style in Muslim and non-Muslim countries

Islamic finance has grown beyond its reputation of providing small-scale banking options and now provides investment and financing options for complex large-scale commercial transactions. Islamic investments are one area that has attracted the attention of investors due to its performance, especially during the economic downturn. The Shari’ah compliance nature of Islamic funds provides an opportunity for those Muslim investors to be part of the global investment sector who have previously been reluctant to invest in conventional mutual funds. The fact that the funds’ managers are prohibited from investing in activities such as weapons production, alcohol production and interest-bearing finance operations, makes Islamic mutual funds also attractive for those Non-Muslim investors who wish to invest ethically. Today there are hundreds of Islamic equity indices offered by Dow Jones, FTSE, MSCI and S&P. Despite the growing importance of Islamic funds, there have been limited studies exploring the performance of Islamic funds worldwide. Due to very limited data sets and not too rigorous analytical methods, these existent studies have neither investigated Islamic funds’ financial performance in noticeable detail nor analysed the investment style of more than six funds. For instance, relevant questions such as the financial performance of Islamic mutual funds’ beyond their investment styles or a difference in performance between funds from Muslim and non-Muslim countries have nearly not been investigated at all. Very recently, a study by Hoepner, Rammal and Rezec (2011) analysed the financial performance and investment style of 262 Islamic equity funds from 20 countries in five regions (Africa, Asia-Pacific, Europe, Gulf Cooperative Council-GCC, and North America). As comparison, previous studies did not even analyse 60 funds. Hoepner et al.’s study sampled a period of two decades and was therefore able to test the performance of the funds during economic booms as well as economic downturns. The findings of the study provide new insights into the performance of Islamic mutual funds in Muslim and Western markets and during financial crisis.