Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Grobner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set F of polynomials with ...

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

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...

the main purpose of this research is to describe emergent approach of grounded theory methodology and then compare it with systematic approach. to do so, after describing emergent approach, it compare it with systematic one surrounding 5 axis: coding processes; sampling processes; paradigms; literature review and rigor considerations. the findings show that emergent approach in comparison with ...

plato in theory of philosopher-king believes that all of the members of ideal city-state, whether ruler or citizens, will attain happiness if the philosopher is the ruler. but there are paradoxes in the theory and the bases of the happiness are unstable too. in other words, plato in his theory presents hierarchical dualities (intelligible/visible world, episteme/ doxa,true/ untrue or shadow, …)...