Cristiana J. Silva
Mathematical models for HIV infection and TB-HIV/AIDS co-infection
Two population mathematical models are proposed for HIV infection and TB-HIV/AIDS co-infection. The respective basic reproduction numbers are
computed, equilibria and stability are studied. A case study is presented for the HIV model and optimal control theory is applied to the TB-HIV/AIDS
co-infection model.
computed, equilibria and stability are studied. A case study is presented for the HIV model and optimal control theory is applied to the TB-HIV/AIDS
co-infection model.
Marisa L. Toste
Convolutional Codes over Rings
We will start this talk by briefly presenting the area
of error correcting codes. This is one of the most interesting
areas of applied mathematics and is used in most of digitally
represented data, as CD players, TV, satellites, mobiles. This
is due to the fact that in real life applications errors occur and we need
to correct them. After presenting the basic ideas of this area we introduce the main
topic of this talk, namely convolutional codes over finite rings. In particular
we focus on the ring Zrp. Classical convolutional codes over finite
fields are a well-known class of codes widely used in mobiles and satellite
communications. Convolutional codes are codes that require memory to encode the data.
Convolutional codes over finite rings have been recently discovered to be
the most optimal codes for code modulation. However these codes are more involved
than standard codes over fields. From a mathematical point of view,
they can be seen as R[x] - submodules of R[x]n,
where R is a finite ring and R[x] is the ring
of polynomials over R. We will introduce this powerful class
of codes and their main properties. We shall conclude the presentation
by presenting some novel results on convolutional codes over finite rings
which are Maximum Distance Separable.
Simão Pedro Silva Santos
Higher-order variational problems of Herglotz type with time delay
We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Namely, we deduce a higher-order Euler--Lagrange and DuBois--Reymond necessary optimality condition as well as a higher-order Noether type theorem for delayed variational problems of Herglotz type.