Projects

Students

Next you can find listed the projects I have done so far in different topics of my personal interest.

Equivalence table of spanish grades with the german system - added on August 26, 2016

Abstract: In this report I study how one can develop a reasonable formula to compare the spanish and german systems for the assignation of grades. The complicated part is that the transformation is not linear or affine in the mathematical sense. However, one can determine something nice and simple. The equation is

form

where y is the spanish grade and x the german one.

The Black-Scholes model for European options on two assets - added on June 1, 2016

Abstract: In my bachelor thesis I explore the Black-Scholes model for European options on tow assets. This is a model of Financial Mathematics used in the field of opcion pricing that requires of Partial Differential Equations and Stochastic Calculus to derive the results. I presented my own ones for the case in which one of the assets tends to zero or the modulus of the correlation coefficient is 1, in which case one obtains a degenerated PDE. I also give numerical simulation of the equations obtained with specific values for the parameters and pay-offs.

For instance, the following image corresponds to the value of a perpetual put option on the assets p,q.

perpetual

This image is the numerical solution of the non-linear PDE

nl-pde

The Euler-Lagrange equation and applications - added on June 1, 2016

Abstract: The Euler-Lagrange equation is a powerful tool that appears in several fields such as theoretical physics and applied mathematics. Roughly speaking, it provides an equation for a function that minimizes an integral expression. In this report I give the derivation of the equation following the lines of variational calculus and applications of it.

For instance, the equation for the function that minimizes the surface is given by the PDE

surface_eqn

A numerical solution by using the finite difference method and taking catenary arches on the boundary looks as follows

surface

Geodesics on an ellipsoid - added on June 1, 2016

Abstract: The term geodesic refers in mathematics to the curve on a surface that minimizes the length of arc between two points. A well-known application is the field of Geodesy, which is the study of such curves on the Earth as well as its gravitational field properties. In this report we are going to give a mathematical model for the Earth and derive the equations of a geodesic on its surface. Finally we will calculate distances between pairs of points and introduce the the so-called Two geodetic problems.

An application of the problem is discussed on the report and we calculate the distance between Barcelona and Hamburg by solving the system of ODE

geo_eqns

with the appropriate conditions and calculate the length using the integral expression

arc_len

obtaining the value of L=1198.92 km

World population - added on June 1, 2016

Abstract: In this report we will try to find a mathematical model for the world population’s growth as a function for the time, namely, given a time t, find a population p(t) as accurate to reality as possible. This will allow us to consider a possible growth of the world inhabitants in the forthcoming years and check the stability in the future.

The following image is the simultaneous display of three differenet models for p(t).

worldpop

Cooperation

Here you can find the projects I have done in cooperation with other entities or colleagues.

The Recycling problem - added on June 1, 2016

Abstract: Nowadays, recycling has become a trend-topic in most of first world’s nations. As a matter of fact, several materials can be recycled and there are plenty of benefits, such as reduced consumption of fresh raw materials, reduced energy usage and reduced landfills. Nevertheless, recycling comes with its own costs, such as the collection of items and transfer to the recycling center as well as sorting. Several questions naturally arise, among others:

  • Is recycling worth it compared to sending everything to landfills?
  • Can we also obtain profit from unsorted waste sources?
  • How expensive is recycling if we want to fulfill certain quotas?
  • Do capacities represent a bottle-neck for the recycling process?
  • Is it feasible to remove or build facilities?

In order to answer these questions we are going to derive a mathematical model for the cost-benefit of recycling. Afterwards we will try to see if optimality can be defined in any sense.

Companies

Last but not least, the projects I have done so far for companies. Due to privacy reasons, the projects done for companies are not online.

The summer season 2015 for SNE Hamburg - added on June 1, 2016

Abstract: In this report we are going to give an overview of the Hamburg operation during the summer season 2015. We will compare the weekly values regarding operating profit, revenue and costs with 2014 and discuss them. Aspects that will be taken into account are:

  • Competition in Hamburg;
  • The 2pm FT shift;
  • The German FT shift;
  • Staff costs and SOP;
  • Private tours and groups.

A proposal for the winter season 2015/2016 for SNE Hamburg - added on June 1, 2016

Abstract: In this report we are going to discuss and present possible situations for the Hamburg Operation during the winter season 2015/2016. Facts that will be taken into account are:

  • Competition in Hamburg.
  • 2pm Free Tour shift.
  • Hours of the employees.

Finally, we would like to draw a conclusion about how to set the operation minimizing costs and having a solid employee structure.