This paper proposes two ratio and product-type estimators using transformation based on known minimum and maximum values of auxiliary variable. The biases and mean squared errors of the suggested estimators are obtained under large sample approximation. Conditions are obtained under which the suggested estimators are superior to the conventional unbiased estimator, usual ratio and product estim...

The spectral transformation Lanczos method is very popular for solving large scale Her-mitian generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-inner product must be used. This may lead to instabilities and breakdown. In this paper, we suggest a cure for breakdown by use of an implicit restart in the Lanc...

The harmonic polylogarithms (hpl’s) are introduced. They are a generalization of Nielsen’s polylogarithms, satisfying a product algebra (the product of two hpl’s is in turn a combination of hpl’s) and forming a set closed under the transformation of the arguments x = 1/z and x = (1−t)/(1+t). The coefficients of their expansions and their Mellin transforms are harmonic sums. AMS(1991) subject cl...

Abstract. A group of infinite products over low-order rational polynomials evaluated at the sequence of prime numbers is loosely called the HardyLittlewood constants. In this manuscript we look at them as factors embedded in a super-product over primes, semiprimes, 3-almost primes etc. Numerical tables are derived by transformation into series over k-almost prime zeta functions. Alternative pro...

We regard classical phase space as a generalised complex manifold and analyse the B–transformation properties of the ⋆–product of functions. The C–algebra of smooth functions transforms in the expected way, while the C–algebra of holomorphic functions (when it exists) transforms nontrivially. The B–transformed ⋆–product encodes all the properties of phase–space quantum mechanics in the presence...

Various approaches show that software product lines can be implemented using the Model-Driven Engineering concept of successive model refinements. An important aspect of Product-Line Engineering (PLE) is the management of variability. In this paper we propose a strategy to let the model transformation language ATL handle the variability. We consider a transformation sequence that can generate a...