Inner-product encryption (IPE) provides fine-grained access control and has attractive applications. Agrawal, Freeman, and Vaikuntanathan (Asiacrypt 2011) proposed the first IPE scheme from lattices by twisting the identity-based encryption (IBE) scheme by Agrawal, Boneh, and Boyen (Eurocrypt 2010). Their IPE scheme supports inner-product predicates over Rμ , where the ring is R = Zq . Several ...

The calculus of generalized p-forms,−1 p n, is developed further. On an n-dimensional manifold with metric, M, a (Hodge) star operator, inner product, co-differential and Laplacian operators are introduced. The inner product and Lie derivative with respect to vector fields on M are defined. Applications are made to Hamiltonian mechanics, field theories and Einstein’s vacuum equations. PACS numb...

We study divisibilities between bounded holomorphic quasi-inner functions in H∞ and operator-valued bounded holomorphic quasi-inner functions in H∞(Ω, L(K)) where Ω is a bounded finitely connected region. Furthermore, we characterize these divisibilities by using rationally-invariant subspaces.

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum infere...

in this note first by considering the notion of general fuzzy automata (for simplicity gfa), we define the notions of direct product, restricted direct product and join of two gfa. also, we introduce some operations on (fuzzy) sets and then prove some related theorems. finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given gfa....

A mapping f : M → N between Hilbert C∗-modules approximately preserves the inner product if ‖〈f(x), f(y)〉 − 〈x, y〉‖ ≤ φ(x, y), for an appropriate control function φ(x, y) and all x, y ∈ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert C∗modules on more general restricted domains. In particular, we investigate some asympt...

Th. M. Rassias 1984 proved that the norm defined over a real vector space X is induced by an inner product if and only if for a fixed integer n ≥ 2, ∑ni 1 ‖xi − 1/n ∑n j 1 xj‖ ∑n i 1 ‖xi‖ − n‖ 1/n ∑ni 1 xi‖ holds for all x1, . . . , xn ∈ X. The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation ∑n i 1 f ...