We extend and unify the proof of a result of L. Lorch (Rend. Sem. Mat. Univ. Politec. Torino 50 (1992), 209–216) by showing that the ratio sgn(ν)Jν+1(|ν|)/Jν(|ν|) increases from −∞ to 1 as ν increases from ν0 (= −0.8375 . . .) to ∞. Here ν0 is the largest zero of Jν(|ν|). One approach is based on an expansion of this ratio involving Rayleigh sums. Another is based on a continued fraction repres...

We study the real x–zeros of the derivative C ν (x) of the cylinder function Cν(x) = Cν(x, α) = cosαJν(x) − sinαYν(x) for ν < 0. For fixed α, 0 ≤ α < π and n = 1, 2, . . ., we show the existence of a number νn in the interval −n+ α/π − 1 < ν < −n+ α/π such that the first positive zero of C ν (x) occurs after the first positive zero of Cν(x) when −n− 1 + α/π < ν < νn and before the first positiv...

In the Standard Model (SM) the transition K to πνν is a Flavor Changing Neutral Current (FCNC) process in which the first order weak decay is forbidden by the GIM mechanism but is allowed, though highly suppressed, in second order due to the differing masses of the up, charm and top quarks in the mediating loops. Theoretically, this decay is sensitive to the CKM matrix element Vtd, which is one...

A general approach to understanding the large mixing seen in atmospheric neutrinos is explained, as well as a highly predictive SO(10) model which implements this approach. It is also seen how bimaximal mixing naturally arises in this scheme. The problem of neutrino mixing should not be looked at in isolation, but as part of the larger " fermion mass problem " , i.e. the problem of understandin...

A proposed experiment to measure KL → πνν̄ at the AGS (E926) is described. It adopts a unique but general strategy of rare decay measurements with two independent rejection criteria, which allows reliable measurements of background levels. The method employs hermetic veto and full kinematic reconstruction using kaon time of flight and kinematic reconstruction of π. Backgrounds are suppressed to ...

This paper is the second of two back-to-back works, whose goal was to generate a more accurate linelist for 5.8 µm absorption band HNO3. Here, we report improved line positions and intensities in ν2 cold which main this region. For this, recorded four high-resolution Fourier transform spectra band, centered at 1709.567 cm−1, under different experimental conditions. Using these spectra, new exte...

Let (Bt; t ≥ 0) be a Brownian motion process starting from B0 = ν and define Xν(t) = ∫ t 0 Bs ds. For a≥ 0, set τa,ν := inf{t : Xν(t) = a} (with inf φ=∞). We study the conditional moments of τa,ν given τa,ν <∞. Using martingale methods, stopping-time arguments, as well as the method of dominant balance, we obtain, in particular, an asymptotic expansion for the conditional mean E(τa,ν | τa,ν <∞)...

and Applied Analysis 3 x ν αx, t ν x, t/|α| for each α/ 0, xi ν x, t ν y, s ≥ ν x y, t s , xii ν x, · : 0,∞ → 0, 1 is continuous, xiii limt→∞ν x, t 0 and limt→ 0ν x, t 1. In this case μ, ν is called an intuitionistic fuzzy norm. Example 1.4 cf. 37 . Let X, ‖·‖ be a normed space, a∗b ab, and a b min a b, 1 for all a, b ∈ 0, 1 . For all x ∈ X and every t > 0 and k 1, 2, consider μk x, t ⎧ ⎨ ⎩ t t...