Abstract. We show that the symmetrized product AB + BA of two positive operators A and B is positive if and only if f (A + B) ≤ f (A) + f (B) for all non-negative operator monotone functions f on [0, ∞) and deduce an operator inequality. We also give a necessary and sufficient condition for that the composition f • g of an operator convex function f on [0, ∞) and a non-negative operator monotone function g on an interval (a, b) is operator monotone and give some applications.
We extend the celebrated Löwner-Heinz inequality by showing that if A, B are Hilbert space operators such that A > B 0, thenfor each 0 < r 1. As an application we prove that
Humans have always been seeking greater control over their surrounding objects. Today, with the help of Internet of Things (IoT), we can fulfill this goal. In order for objects to be connected to the internet, they should have an address, so that they can be detected and tracked. Since the number of these objects are very large and never stop growing, addressing space should be used, which can respond to this number of objects. In this regard, the best option is IPv6. Addressing has different methods, the most important of which are introduced in this paper. The method presented in this paper is a hybrid addressing method which uses EPC and ONS IP. The method proposed in this paper provides a unique and hierarchical IPv6 address for each object. This method is simple and does not require additional hardware for implantation. Further, the addressing time of this method is short while its scalability is high, and is compatible with different EPC standards.
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