Iranian Journal of Mathematical Sciences and Informatics
Year:2010 | Volume:5 | Issue:1|Papers Count:7

Let V and W be two real vector spaces and let ~ be a relation on both V and W. A linear function T : V ® W is said to be a linear preserver (respectively strong linear preserver) of ~ if Tx ~ Ty whenever x ~ y (respectively Tx ~ Ty if and only if x ~ y). In this paper we characterize all linear functions T : Mn,m ® Mn, k which preserve or strongly preserve multivariate and directional majorization.

In this paper using the Clifford algebra over R4 and its matrix representation, we construct Clifford scaling functions and Clifford wavelets. Then we compute related mask functions and filters, which arise in many applications such as quantum mechanics.

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P-1 is a ring. In fact, it is proved that P-1 = (P : P) if and only if P is not invertible. Furthermore, if P is invertible, then R = (P : P) and P is a principal ideal of R.

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should have.

In this paper, we establish new cebysev type integral inequalities involving functions whose derivatives belong to Lp spaces via certain integral identities.

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.