In this paper, we prove the well-posedness for the fractional NavierStokes equations in critical spaces G −(2β−1) n (R ) and BMO−(2β−1)(Rn). Both of them are close to the largest critical space Ḃ −(2β−1) ∞,∞ (R ). In G −(2β−1) n (R ), we establish the well-posedness based on a priori estimates for the fractional Navier-Stokes equations in Besov spaces. To obtain the well-posedness in BMO−(2β−1)...

B 0 d (t) → DP P time-dependent Dalitz plots, CP-violating angles 2β, 2β + γ, and discrete ambiguities Abstract We study CP-violation in resonant three-body B d → DP P decays, where P P stands for either ¯ Dπ, ¯ DK S , ππ or πK S. Analogously to the B d → 3π channel and the extraction of 2α, the first three channels are shown to measure cos 2β in addition to sin 2β, thus allowing to resolve the...

B 0 d (t) → DP P time-dependent Dalitz plots, CP-violating angles 2β, 2β + γ, and discrete ambiguities Abstract We study CP-violation in resonant three-body B d → DP P decays, where P P stands for either ¯ Dπ, ¯ DK, ππ or πK. Analogously to the B d → 3π channel and the extraction of 2α, the first three channels are shown to measure cos 2β in addition to sin 2β, thus allowing to resolve the β → ...

The time-dependent CP asymmetries in fully reconstructed B0→D(∗)±π∓/ρ∓ decays (new preliminary result), and in partially reconstructed B0→D(∗)±π∓ decays, are measured with the BABAR detector at the PEP-II asymmetric B factory at SLAC, using 232 million Υ (4S) → BB decays. We combine the above results and, using other measurements and theoretical assumptions, we interpret them in terms of the an...

B 0 d (t) → DP P time-dependent Dalitz plots, CP-violating angles 2β, 2β + γ, and discrete ambiguities Abstract We study CP-violation in resonant three-body B d → DP P decays, where P P stands for either ¯ Dπ, ¯ DK S , ππ or πK S. Analogously to the B d → 3π channel and the extraction of 2α, the first three channels are shown to measure cos 2β in addition to sin 2β, thus allowing to resolve the...

The most recent results from the B-factories on the time-dependent CP asymmetries measured in B 0-decays mediated by b → c¯ cs quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin 2β leads to a four-fold ambiguity on the unitarity triangle β which can be reduced to a twofold ambiguity by measuring the sign of the parameter cos 2β. The re...

The most recent results from the B-factories on the time-dependent CP asymmetries measured in B -decays mediated by b → cc̄s quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin 2β leads to a four-fold ambiguity on the unitarity triangle β which can be reduced to a two-fold ambiguity by measuring the sign of the parameter cos 2β. The resu...

The values of sin 2α and sin 2β, where α and β are angles of the unitarity triangle, will be readily measured in a B factory (and maybe also in hadron colliders). We study the standard model constraints in the sin 2α − sin 2β plane. We use the results from recent analyses of fB and τb|Vcb| which take into account heavy quark symmetry considerations. We find sin 2β ≥ 0.15 and most likely sin 2β ...

We consider a l1-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension d of the input variable X is very large (sometimes depending on the number of observations). Estimation of a β-regular regression function f cannot be faster than the slow rate n−2β/(2β+d) . Hopefully, in some situations, f depends only on a few numbers of the coordi...