We show that the singular values m of the fractional integration operator of order > 0 acting from weighted L 2 spaces of functions deened on the interval (?1; 1) or (0; 1) may, in both cases, have asymptotics m ? or m ?=2 , as m ! 1, depending on the speciic choice of weight functions. Some questions of singular value decompositions are also investigated for Riesz potential operators in weight...

Kriging (Gaussian process, spatial correlation) metamodels approximate the Input/Output (I/O) functions implied by the underlying simulation models; such metamodels serve sensitivity analysis and optimization, especially for computationally expensive simulations. In practice, simulation analysts often know that the I/O function is monotonic. To obtain a Kriging metamodel that preserves this kno...

In the past few years, many scholars gave much attention to use of q-calculus in geometric functions theory, and they defined new subclasses analytic harmonic functions. While using symmetric function very little work has been published so far. this research, with help fundamental concepts q-Salagean differential operator for functions, we define a class connected Janowski SH0˜m,q,A,B. First, i...