The ν-support vector classification (ν-SVC) algorithm was shown to work well and provide intuitive interpretations, e.g., the parameter ν roughly specifies the fraction of support vectors. Although ν corresponds to a fraction, it cannot take the entire range between 0 and 1 in its original form. This problem was settled by a non-convex extension of ν-SVC and the extended method was experimental...

We show that the Hurwitz zeta function, ζ(ν, a), and the Legendre chi function, χν(z), defined by ζ(ν, a) = ∞ ∑ k=0 1 (k + a)ν , 0 < a ≤ 1, Re ν > 1, and χν(z) = ∞ ∑ k=0 z2k+1 (2k + 1)ν , |z| ≤ 1, Re ν > 1 with ν = 2, 3, 4, . . . , respectively, form a discrete Fourier transform pair. Many formulae involving the values of these functions at rational arguments, most of them unknown, are obtained...

Exclusive and inclusive (ν µ , µ −), (ν e , e −) cross-sections and µ −-capture rates are calculated for 12 C and 16 O using the consistent random phase approximation (RPA) and pairing model. After a pairing correction is introduced to the RPA results the flux-averaged theoretical (ν µ , µ −), (ν e , e −) cross-sections and µ −-capture rates in 12 C are in good agreement with experiment. In par...

The super-Kamiokande collaboration have used multi-ring events to discriminate between the ν µ → ν τ and ν µ → ν s solutions to the atmospheric neutrino anomaly. We show that the effect of systematic uncertainties in cross sections are so significant that the usefulness of multi-ring data to distinguish between these two solutions is doubtful.

In the present paper, by Haagerup theorem, we show that if A ∈ Mn is a non scalar strictly positive matrix and 0 < ν < 1 be a real number such that ν 6= 12 , then there exists X ∈ Mn such that ‖AνXA1−ν‖ > ‖νAX + (1− ν)XA‖.

The recent observation of the purely leptonic decay B → τντ at the B factories permits a sizeable contribution from a charged Higgs boson (H). Such a H would also contribute to the decays D s → μ νμ and D ± s → τ ντ , which are being measured with increasing precision at CLEO-c. We show that the branching ratios of D s → μ νμ and D s → τ ντ could be suppressed by up to 10% from the Standard Mod...

Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν − , ν+). In this note, we show that there are ending laminations ν+ such that for any choice of ν − , the punctured torus group is transcendental as a subgroup of PSL2C.

This Article contains a typographical error in Equation (2). () () = − −). ν ν ν ν + + + G 1 1 M N e h 2 1 1 bg tg bg tg 2 should read: 1 bg tg bg tg 2 In addition, the Acknowledgements section is incomplete.

According to the composite fermion theory, the interacting electron system at filling factor ν is equivalent to the non-interacting composite fermion system at ν = ν/(1 − 2mν), which in turn is related to the non-interacting electron system at ν. We show that several eigenstates of non-interacting electrons at ν do not have any partners for interacting electrons at ν, but, upon composite fermio...

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.