Conformal Maps to Multiply-Slit Domains and Applications

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [Tee and Trefethen, 2006] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to 'enlarge the region of analyticity' in the solution: an idea which can be extended to other numerical methods based upon global polynomial interpolation. Here we show how such maps can be rapidly computed in both periodic and nonperiodic geometries, and apply them to some challenging differential equations

A rational spectral collocation method with adaptively transformed Chebyshev grid points

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Padé approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plan close to [-1,1]

Enhancing the personal identification number input as a means of identification signature

The process of typing the personal identification number (PIN) can be broken down into quantifiable components, such as latency time, keypress force, keypress duration and keypress displacement which can be evaluated and used to verify the identity of a person. The keypress pattern is called the PIN signature. As the PIN signature is like the written signature that differs slightly with every execution, a neural-fuzzy application is devised to verify the PIN signature input against the reference profile

Pin signature verification using wavelet transform

The personal identification number signature (PIN signature) is a method of remembering and typing the PIN using the de facto standard numeric keypad format. The PIN signature affords a second level security in that it enhances the PIN with additional information on the user, i.e. the profile of its input. The PIN signature reference profile can be viewed as a signal vector and can thus be enhanced and verified as to its physiological characteristics using wavelet transform. The result of this analysis is presented

Self awareness curiculum activities and effectiveness to youth

This article discusses the self-consciousness of youth in co-curricular activities forming their personality. In addition, this article also discussed the core curriculum which has been outlined by the Ministry of Education (MOE) to adolescents who are still studying in higher education institutions as well as the effectiveness of the curriculum in shaping the personality of adolescents including studies that have been done in connection with extra-curricular activities. This article also touched on the education system nowadays

Dietary dairy product intake and incident type 2 diabetes: a prospective study using dietary data from a 7-day food diary

The consumption of specific dairy types may be beneficial for the prevention of diabetes. Abstract: The aim of this study was to investigate the association between total and types of dairy product intake and risk of developing incident type 2 diabetes, using a food diary. Methods: A nested case-cohort within the EPIC-Norfolk Study was examined, including a random subcohort (n=4,000) and cases of incident diabetes (n=892, including 143 cases in the subcohort) followed-up for 11 years. Diet was assessed using a prospective 7-day food diary. Total dairy intake (g/day) was estimated and categorised into high-fat (≥3.9%) and low-fat (<3.9% fat) dairy, and by subtype into yoghurt, cheese and milk. Combined fermented dairy product intake (yoghurt, cheese, sour cream) was estimated and categorised into high- and low-fat. Prentice-weighted Cox regression HRs were calculated. Results: Total dairy, high-fat dairy, milk, cheese and high-fat fermented dairy product intakes were not associated with the development of incident diabetes. Low-fat dairy intake was inversely associated with diabetes in age- and sex-adjusted analyses (tertile [T] 3 vs T1, HR 0.81 [95% CI 0.66, 0.98]), but further adjustment for anthropometric, dietary and diabetes risk factors attenuated this association. In addition, an inverse association was found between diabetes and low-fat fermented dairy product intake (T3 vs T1, HR 0.76 [95% CI 0.60, 0.99]; ptrend=0.049) and specifically with yoghurt intake (HR 0.72 [95% CI 0.55, 0.95]; ptrend=0.017) in multivariable adjusted analyses. Conclusions/interpretation: Greater low-fat fermented dairy product intake, largely driven by yoghurt intake, was associated with a decreased risk of type 2 diabetes development in prospective analyses. These findings suggest that the consumption of specific dairy types may be beneficial for the prevention of diabetes, highlighting the importance of food group subtypes for public health messages

Non-metricity with bounday terms: f(Q,C)f(Q,C) gravity and cosmology

We formulate $f(Q,C)$ gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar $Q$ we incorporate in the Lagrangian the boundary term $C$ of its difference from the standard Levi-Civita Ricci scalar $\mathring R$. We extract the general metric and affine connection field equations, we apply them in a cosmological framework, and making two gauge choices we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.Comment: minor changes, references adde