We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale by scale. The crucial cancellations of resonances are shown to follow from the Ward identities expressing the translation invariance of the corresponding fie...

A novel method for correlation analysis using scale-dependent Rényi entropies is described. The method involves calculating the entropy of a data distribution as an explicit function of the scale of a d-dimensional partition of d-cubes, which is dithered to remove bias. Analytic expressions for dithered scale-local entropy and dimension for a uniform random point set are derived and compared to...

objective: the present study aimed to investigate the effects of spiritual well-being and family protective factors on the family strength in a propositional structural model. methods: the research population consisted of all the married people of the isfahan, iran, in 2012 with preschool-aged children and in the first decade of marriage with at least eight grades of educational level. three hu...

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level m...

Decision.The Analytic Hierarchy Process AHP, introduced by Thomas Saaty 1980, is an. Synthesizing the results, the AHP helps to capture both subjective and.Saaty The AHP: How to make a decision properties or features of the alternatives being compared, and the alternatives themselves are gradually layered in the.INTRODUCTION. The Analytic Hierarchy Process AHP is due to Saaty 1980 and is often ...

One of the crucial features of tropical convection is the observed variability on multiple spatiotemporal scales, ranging from cumulus clouds on the daily time scale over a few kilometers to intraseasonal oscillations over planetary scales. The diurnal cycle of tropical convection is a significant process but its large-scale impact is not well understood. Here we develop a multi-scale analytic ...

The present study intended to evaluate EFL students' performance on a traditional method of writing assessment in comparison to an alternative assessment technique by taking into account the effects of teacher and peer feedback. Moreover, the attitudes of the participants regarding assessment procedures and activities were focused in this study. To this end, thirty male and female language lear...

In this paper we break the scale invariance of the primordial power spectrum of curvature perturbations of inflation. Introducing a singular behaviour due to spontaneous symmetry breaking in the inflaton potential, we obtain fully analytic expressions of scale dependent oscillation and a modulation in power on small scale in the primordial spectrum. And we give the associated cosmic microwave b...