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Suppose you have a data matrix comprised of several stock options over a set period of time. How do you choose the optimal collection of stocks such that you maximize your returns for a given level of risk? What Markowitz found was an elegant equation. What we realized rather quickly is there does not exist a closed form solution to this problem. Instead we use the tried and tested linear approximation. By transforming this problem into Matrix multiplication, we are able to quickly and (with desired accuracy) approximate the optimal solution, using only linear algebra.

The use of Customer Relationship Managers to foster customers’ loyalty has become one of the most common business strategies in the past years. However, CRM solutions do not fill the “abundance of happily ever-after relationships” that business needs, and each client's perception is different in the buying process. Therefore, the experience must be precise, in order to extend the loyalty period, of a customer as much as possible. One of the economic sectors in which CRM's have improved this experience is retailing, where the personalized attention to the customer is a key factor among others. However, brick and mortar experiences are not enough to be aware in how environmental changes could affect the industry trends in the long term. A base unified theoretical framework must be taken into consideration, in order to develop an adaptable model for constructing or implementing CRM’s into companies. Thanks to this approximation, the information is complemented and the final outcome will increment the quality in any Marketing/Sales initiative. The goal of this article is to explore the different factors grouped by three main domains within the impact of the service quality, from consumer’s perspective in both on-line and off-line retailing sector. Secondly, we plan to go a step forward and extract base guidelines about previous analysis for designing CRM’s solutions focused on the loyalty of the customers for an specific retailing sector and its product: Sports Running Shoes. Furthermore, we design and develop a structured survey and give it to a diverse group of users, with questions that evaluate the contrast an influence of service quality, customer satisfaction and customer loyalty in both on-line and off-line environments.

The impact crater of a small metal ball of 63.7 grams (0.0637kg) is dropped from 8 different heights, ranging from 0.20m to 0.90m was observed. A mean was measured for the craters diameter. Using the equation E=mg$\Delta$h given that we have m, and g is a constant of 9.81 we can find the kinetic energy of the ball on impact. The relationship between crater diameter, D, and impact energy, E, is given by D=kE$^n$ where K is constant and n is found by the gradient of the graph and is also constant. This can be modified to give $\log D = n\log E + \log k$.

The goal of this project is to explore both the theory behind the Extended Kalman Filter and the way it was used to localize a four-wheeled mobile-robot. This can be achieved by estimating in real-time the pose of the robot, while using a pre-acquired map through Laser Range Finder (LRF). The LRF is used to scan the environment, which is represented through line segments. Through a prediction step, the robot simulates its kinematic model to predict his current position. In order to minimize the difference between the matched lines from the global and local maps, a update step is implemented. It should be noted that every measurement has associated uncertainty that needs to be taken into account when performing each step of the Extended Kalman Filter. These uncertainties, or noise, are described by covariance matrices that play a very important role in the algorithm. Since we are dealing with an indoor structured environment, mainly composed by walls and straight-edged objects, the line segment representation of the maps was the chosen method to approach the problem.

Description of results of fieldwork at Pocono Environmental Education Center with students from Malcolm X Shabazz High School, May 2005.

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