Commensurate scale relations are perturbative QCD predictions which relate observable to observable at xed relative scales, independent of the choice of intermediate renormalization scheme or other theoretical conventions. A prominent example is the generalized Crewther relation" which connects the Bjorken and Gross-Llewellyn Smith deep inelastic scattering sum rules to measurements of the e + ...

Let f(x) be a general objective function and let f'x) = h + mf(Ax + d). An analytic estimation of the minimum of one would resemble an analytic estimation of the other in all nontrivial respects. However, the use of a minimization algorithm on either might or might not lead to apparently unrelated sequences of calculations. This paper is devoted to providing a general theory for the affine scal...

Abstract. Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman trans...

This paper describes the system architecture of the Vertica Analytic Database (Vertica), a commercialization of the design of the C-Store research prototype. Vertica demonstrates a modern commercial RDBMS system that presents a classical relational interface while at the same time achieving the high performance expected from modern “web scale” analytic systems by making appropriate architectura...

The present exploratory mixed methods study aimedto develop a scale for assessing critical thinking (CT) ability of Iranian EFL learners. The study wasconducted in three phases. In phase one, the features of CT components were examined in the writingsof 120 participants. A holistic and an analytic scale were developed based on their performance in exploiting the components of CT and the fea...

The expression of effective stress in unsaturated conditions has remained controversial ever since the concept was first proposed 1950s by Bishop. In this paper, based on law thermodynamics, a novel approach is to calculate soil systems applying improved bundled cylindrical capillary model and probability density function particles. provided an for Bishop's coefficient χ. basic assumptions are ...