I. The physics of flavor change: The rather convincing evidence that atmospheric neutrinos change from one flavor to another has now been joined by new, very strong evidence that the solar neutrinos do this as well. Neutrino flavor change implies that neutrinos have nonzero masses. That is, there is a spectrum of three or more neutrino mass eigenstates, that are the analogues of the charged-lep...

We consider the " standard " spectrum of the active neutrinos (characterized by strong mass hierarchy and small mixing) with additional sterile neutrino, ν s. The sterile neutrino mixes strongly with the muon neutrino, so that ν µ ↔ ν s oscillations solve the atmospheric neutrino problem. We show that the parametric enhancement of the ν µ ↔ ν s oscillations occurs for the high energy atmospheri...

Abstract. Let u be a solution to the Navier-Stokes equations with viscosity ν in a bounded domain Ω in R, d ≥ 2, and let u be the solution to the Euler equations in Ω. In 1983 Tosio Kato showed that for sufficiently regular solutions, u → u in L∞([0, T ];L(Ω)) as ν → 0 if and only if ν ‖∇u‖2 X → 0 as ν → 0, where X = L([0, T ]× Γcν), Γcν being a layer of thickness cν near the boundary. We show ...

Let L(ν)⊗̂γqY = Lq(ν, Y ) and X⊗̂∆pL(μ) = Lp(μ,X). It is shown that any Lp(μ)-valued measure has finite L2(ν)-semivariation with respect to the tensor norm L(ν)⊗̂∆pL(μ) for 1 ≤ p < ∞ and finite Lq(ν)semivariation with respect to the tensor norm L(ν)⊗̂γqL(μ) whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor no...

This letter presents a combined measurement of the energy spectra atmospheric $\nu_e$ and $\nu_\mu$ in range between $\sim$100 GeV $\sim$50 TeV with ANTARES neutrino telescope. The analysis uses 3012 days detector livetime period 2007--2017, selects 1016 neutrinos interacting (or close to) instrumented volume detector, yielding shower-like events (mainly from $\nu_e+\overline \nu_e$ charged cur...

Abstract: Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2, and let n > 2 be a fixed even integer. Consider a sequence {Fk}k>1 of square integrable random variables, belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k → ∞, we prove that Fk converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k )− 12E(F 3 k ) → 12ν...

Let G = ( V, E ) be a simple graph. A non-empty set D ⊆ V is called global offensive alliance if dominating and for every vertex ν in − , | N [ν] ∩ |≥| |. The number the minimum cardinality of . In this paper, we give constructive characterization trees having unique alliance.

We revisit the Fritzsch-type lepton mass matrix models confronted with new experiments for neutrino mixings. It is shown that the model is viable and leads to a rather narrow range of free parameters. Using empirical mixing information between ν e and ν µ , and between ν µ and ν τ , it is predicted that the mixing angle between ν e and ν τ is in the range 0.04 < |U 13 | < 0.20, consistent with ...

We recall that a probability measure ν on X is said to be μ-stationary if one has μ ∗ ν = ν. It is then said to be μ-ergodic if it is extremal among μ-stationary probability measures. We will say that a probability measure ν on X is homogeneous if it is supported by a closed orbit F of its stabilizer Gν := {g ∈ G | g∗ν = ν}. Such a probability is a finite average of probability measures which a...

We consider a Gaussian type quadrature rule for some classes of integrands involving highly oscillatory functions of the form f (x) = f 1 (x) sin ζ x + f 2 (x) cos ζ x, where f 1 (x) and f 2 (x) are smooth, ζ ∈ R. We find weights σ ν and nodes x ν , ν = 1, 2,. .. , n, in a quadrature formula of the form 1 −1 f (x) dx ≈ n ν=1 σ ν f (x ν) such that it is exact for all polynomials f 1 (x) and f 2 ...