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We investigate the determinantal representation by exploiting the limiting expression for the generalized inverseAT,S(2). We show the equivalent relationship between the existence and limiting expression ofAT,S(2)and some limiting processes of matrices and deduce the new determinantal representations ofAT,S(2), based on some analog of the classical adjoint matrix. Using the analog of the classical adjoint matrix, we present Cramer rules for the restricted matrix equationAXB=D,  R(X)⊂T,  N(X)⊃S∼.

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Network function virtualization (NFV) is a new way to provide services to users in a network. Different from dedicated hardware that realizes the network functions for an IoT application, the network function of an NFV network is executed on general servers, and in order to achieve complete network functions, service function chaining (SFC) chains virtual network functions to work together to support an IoT application. In this paper, we focus on a main challenge in this domain, i.e., resource efficient provisioning for social IoT application oriented SFC requests. We propose an online SFC deployment algorithm based on the layered strategies of physical networks and an evaluation of physical network nodes, which can efficiently reduce bandwidth resource consumption (OSFCD-LSEM) and support the security and privacy of social IoT applications. The results of our simulation show that our proposed algorithm improves the bandwidth carrying rate, time efficiency, and acceptance rate by 50%, 60%, and 15%, respectively.