A sequence $(x_n)_{; ; ; ; ; n \geq 0}; ; ; ; ; $ of positive real numbers is log-convex if the inequality $x_n^2 \leq x_{; ; ; ; ; n-1}; ; ; ; ; x_{; ; ; ; ; n+1}; ; ; ; ; $ is valid for all $n \geq 1$. We show here how the problem of establishing the log-convexity of a given combinatorial sequence can be reduced to examining the ordinary convexity of related sequences. The new method is then used to prove that the sequence of Motzkin numbers is log-convex.
This paper reviews the state of art of e-health applications and technologies. These solutions usually are proprietary and lack interoperability between them. Our approach describes a system architecture that provides capabilities to integrate different telecare, telemedicine and domotic services in a smart home gateway hardware independent. We propose a rule system to define the user behaviour and monitor relevant events. Several use cases and data model for the system are presented.
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