Exceptional sets for Diophantine inequalities

We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed

Web-Based Training Program for New Custom Decoration Apparel Franchisees

Effective franchise training is essential in the expansion of a franchised business. With advances in internet connections, web applications and multimedia capabilities, training for new and existing franchisees can now take place online in the form of web-based e-learning. In addition to potentially increasing the overall effectiveness of the franchisee training, web-based training also eliminates some of the challenges of traditional, face-to-face franchise training like travel expenses, time, and the availability of human resources. The purpose of this project was to develop an asynchronous web-based training program for new or potential franchisees in the custom decorated apparel industry. The ADDIE model was used to guide the development of the training program and curriculum, which was then evaluated and critiqued by a panel of subject matter experts

The community school director - a changing role

The Community School Director in the local school or town has one of the key roles in the delivery and implementation of the community education concept