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...

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...

This article describes the method of construction the Gröbner basis based on the information in the Anick’s resolution.

The principal result described in this report is the design and implementation of a parallel version of Buchberger's algorithm. Its correctness is stated and some experimental results are given. The first parts are devoted to a partial review of Grobner bases, of Buchberger's algorithm which computes them, and of some of their applications.

This paper discusses a result by Fliess about input-output equations [or polynomial systems with time delays, and strengthens the result somewhat. The proof given is more detailed and opens the way [or constructive methods [or determining the input-output behavior. Some such methods based on Grobner bases are described in detail. Furthermore, some connections with observability are exploited.

Grabner basis is olle of the most important tools ill recent symbolic algebraic computations. Howe\'er, computing a Grobncr basis fo r the given polynomial ideal is lIot easy and it is lIot numcric.. . l1y stable if polynomials have inexact coefficients. I n this paper, we study what we should get for computing a Grabner basis with inexact coefficients alld introduce a naive method to compute a...