Chebyshev approximation with respect to a vanishing weight function

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

Integration with Respect to a Vector Measure and Function Approximation

The integration with respect to a vector measure may be applied in order to approximate a function in a Hilbert space by means of a finite orthogonal sequence {fi} attending to two different error criterions. In particular, if ∈ R is a Lebesgue measurable set, f ∈ L2( ), and {Ai} is a finite family of disjoint subsets of , we can obtain a measure μ0 and an approximation f0 satisfying the follow...

Orthogonal Polynomials Related to the Oscillatory-chebyshev Weight Function

L(p) = ∫ 1 −1 p(x)x(1− x2)−1/2eiζxdx, ζ ∈ R. Since the weight function alternates in sign in the interval of orthogonality, the existence of orthogonal polynomials is not assured. A nonconstructive proof of the existence is given. The three-term recurrence relation for such polynomials is investigated and the asymptotic formulae for recursion coefficients are derived. AMS Mathematics Subject Cl...

Decision criteria in risk analysis : an application of stochastic dominance with respect to a function

LIFTING MODULES WITH RESPECT TO A PRERADICAL

Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplusN_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting moduleis $tau_M$-lifting.