In this paper, two protocols are presented for private intersection detection of moving objects’ trajectories. Assuming that the movement trajectory an object can be described by a time-dependent polynomial function, problem finding points is simplified to common roots corresponding polynomials. Thereafter, GrObner Basis used design novel secure protocol Another also designed based on distance ...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal I in a polynomial ring a monomial ideal in≺I, in some special situations the monomial ideal in≺I is square free. On the other hand given any monomial ideal I of a polynomial ring S, we can define the toric K[I] ⊂ S. In this paper we will study toric rings defined by Segre embed...

Quantum sensors may provide extremely high sensitivity and precision to extract key information in a quantum or classical physical system. A fundamental question is whether sensor capable of uniquely inferring unknown parameters system for given structure the admissible measurement on sensor. In this paper, we investigate capability class which consist either single qubit two qubits. coupled sp...

This paper presents an explicit bound on the number of primitive elements that are linear combinations of generators for field extensions. It is well known that every finite separable extension of an arbitrary field has a primitive element; that is, there exists a single element in the extension field which generates that field over the ground field. This is a fundamental theorem in algebra whi...