About Bianchi I with VSL

In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Lambda, but taking into account the effects of a $c$-variable into the curvature tensor. We study the model under the assumption,div(T)=0. These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC) and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS approaches bring us to obtain all the quantities depending on \int c(t)dt. Therefore, in order to study their behavior we impose some physical restrictions like for example the condition q<0 (accelerating universe). In this way we find that $c$ is a growing time function and Lambda is a decreasing time function whose sing depends on the equation of state, w, while the exponents of the scale factor must satisfy the conditions $\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$ $\forall\omega$, i.e. for all equation of state$,$ relaxing in this way the Kasner conditions. The behavior of $G$ depends on two parameters, the equation of state $\omega$ and $\epsilon,$ a parameter that controls the behavior of $c(t),$ therefore $G$ may be growing or decreasing.We also show that through the Lie method, there is no difference between to study the field equations under the assumption of a $c-$var affecting to the curvature tensor which the other one where it is not considered such effects.Nevertheless, it is essential to consider such effects in the cases studied under the SS, MC, and KSS hypotheses.Comment: 29 pages, Revtex4, Accepted for publication in Astrophysics & Space Scienc

Pricing multiple exercise American options by linear programming

We consider the problem of computing the lower hedging price of American options of the call and put type written on a non-dividend paying stock in a non-recombinant tree model with multiple exercise rights. We prove using a simple argument that an optimal exercise policy for an option with h exercise rights is to delay exercise until the last h periods. The result implies that the mixedinteger programming model for computing the lower hedging price and the optimal exercise and hedging policy has a linear programming relaxation that is exact, i.e., the relaxation admits an optimal solution where all variables required to be integral have integer values. © Springer International Publishing Switzerland 2017

Recent development of respiratory rate measurement technologies

Respiratory rate (RR) is an important physiological parameter whose abnormity has been regarded as an important indicator of serious illness. In order to make RR monitoring simple to do, reliable and accurate, many different methods have been proposed for such automatic monitoring. According to the theory of respiratory rate extraction, methods are categorized into three modalities: extracting RR from other physiological signals, RR measurement based on respiratory movements, and RR measurement based on airflow. The merits and limitations of each method are highlighted and discussed. In addition, current works are summarized to suggest key directions for the development of future RR monitoring methodologies

An Integer Programming Model for Pricing American Contingent Claims under Transaction Costs

American Contingent Claims, Transaction Costs, Mixed-integer Programming, Linear Programming, Martingales, Incomplete Markets, Pricing, Hedging, Dividends,