The powerful AZ identity is a sharpening of the famous LYM-inequality. More generally, Ahlswede and Zhang discovered a generalization in which the Bollobás inequality for two set families can be lifted to an identity.In this paper, we show another generalization of the AZ identity. The new identity implies an identity which characterizes the deficiency of the Bollobás inequality for an intersecting Sperner family. We also give some consequences relating to Helly families and LYM-style inequalities.

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Designing security model for multi-tenancy applications is challenging, especially when we develop a cloudbased system that must support hierarchical users, multiple access levels and hierarchical service data. In this paper, we present hierarchical multi-tenant pattern to model hierarchical multi-tenancy and security aspects (hierarchical data authentication and authorization) of a cloud-based software system. This pattern proposes a consistent and flexible blueprint to manage multiple tenants, security and service data that require hierarchy based on real world scenarios. We hope that our design pattern will be useful for building both PaaS and SaaS frameworks for software providers as well as normal organizations.

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