It is well known that increasing functions do not preserve operator order in general; nor decreasing reverse order. However, monotone or do. In this article, we employ a convex approach to discuss preserving conversing functions. As an easy consequence of more general results, find nonnegative constants γ and ψ such A≤B implies f(B)≤f(A)+γ1ℋ andf(A)≤f(B)+ψ1ℋ, for the self-adjoint operators A, B...

Abstract Several properties of subspaces $$J \subset X$$ J ⊂ X in a pair ( X , J ) with quotient lifting different types are derived, giving emphasis to order-preserving for order unit spaces and affine continuous functions on Choquet simplexes.

This paper presents a new method for encryption of color images based on a combination of chaotic systems, which makes the image encryption more efficient and robust. The proposed algorithm generated three series of data, ranged between 0 and 255, using a chaotic Chen system. Another Chen system was then started with different initial values, which were converted to three series of numbers from...

The order of the plaintext remains in the ciphertext, so order-preserving encryption (OPE) scheme is under threat if the adversary is allowed to query for many times. To hide the order in the ciphertext, the only ideal-security OPE scheme (Popa et al., 2013) requires the database server to maintain extra information and realize comparison or range query by user defined functions (UDFs). However...

Due to the increasing demand for cloud services and the threat of privacy invasion, the user is suggested to encrypt the data before it is outsourced to the remote server. The safe storage and efficient retrieval of d-dimensional data on an untrusted server has therefore crucial importance. The paper proposes a new encryption model which offers spatial order-preservation for d-dimensional data ...

The freedom and transparency of information flow on the Internet has heightened concerns of privacy. Given a set of data items, clustering algorithms group similar items together. Clustering has many applications, such as customerbehavior analysis, targeted marketing, forensics, and bioinformatics. In this paper, we present the design and analysis of a privacy-preserving k-means clustering algo...

In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, ω). It is shown that every volume-preserving flow has some 2-forms acting the rôle of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form 1 n−1 H ω where H is the corresponding Hamiltonian...