and Applied Analysis 3 4. The ε-Method for Resonant Centers We recall in this section the ε-method developed in [23] which we apply here to resonant centers. We consider system (2) which we write into the form ?̇? = P (x, y) = px + F 1 (x, y) , ?̇? = Q (x, y) = −q y + F 2 (x, y) , (5) where F 1 (x, y) and F 2 (x, y) are analytic functions without constant and linear terms, defined in a neighborho...

The CP–violating ratio ε/ε constitutes a fundamental test for our understanding of flavour–changing phenomena. The present experimental world average,1 Re (ε/ε) = (19.3 ± 2.4) · 10, provides clear evidence for a non-zero value and, therefore, the existence of direct CP violation. The theoretical prediction has been rather controversial since different groups, using different models or approxima...

We present a pedagogical and phenomenological introduction to the study of cosmic microwave background (CMB) polarization to build intuition about the prospects and challenges facing its detection. Thomson scattering of temperature anisotropies on the last scattering surface generates a linear polarization pattern on the sky that can be simply read off from their quadrupole moments. These in tu...

The Standard Model (SM) prediction for the ratio ε′/ε appears to be significantly below the experimental data. Also εK in the SM tends to be below the data. Any new physics (NP) removing these anomalies will first of all have impact on flavour observables in the K meson system, in particular on rare decays K+ → π+νν̄, KL → π0νν̄, KL → μ+μ− and KL → π0`+`− and ∆MK . Restricting the operators contr...

We consider tensor product random fields Yd, d∈N, whose covariance functions are Gaussian kernels with a given sequence of length scale parameters. investigate the growth average case approximation complexity nYd(ε) Yd for arbitrary fixed ε∈(0,1) and d→∞. Namely, we find criteria boundedness depending on d nYd(ε)→∞ when d→∞ any ε∈(0,1). In latter obtain necessary sufficient conditions following...