where both m(·) and σ(·) are unknown functions defined over R, the data {(Xt, Yt)}t=1 are weakly dependent stationary time series, and et is an error process with zero mean and unit variance. Suppose that {mθ(·)|θ ∈ Θ} is a family of parametric specification to the regression function m(x) where θ ∈ R is an unknown parameter belonging to a parameter space Θ. This paper considers testing the val...

Let {p θ , θ ∈ Θ} be a family of probability densities with respect to µ where Θ is an open subinterval (finite, infinite or semi-infinite) of the real line. The Fisher Information for this family is defined by: I(θ) := E θ ∂ ∂θ log p θ (X) 2 Note that the densities p θ can be on arbitrary spaces; the only condition for defining I(θ) is that θ is real. The function ∂ ∂θ log p θ (X) is called th...

This article provides a regularity criterion for the surface quasigeostrophic equation with supercritical dissipation. This criterion is in terms of the norm of the solution in a Orlicz-Morrey space. The result shows that, if a weak solutions θ satisfies Z T 0 ‖∇θ(·, s)‖ α α−r M L2 logP L 1 + ln(e+ ‖∇⊥θ(·, s)‖L2/r ) ds <∞, for some 0 < r < α and 0 < α < 1, then θ is regular at t = T . In view o...

Open charm production at HERA has developed as a precision testing ground for fixed order (FO) NLO pQCD calculations as well as for other QCD inspired models. The bulk of the available data is on inclusive charmed particle production cross sections for several species. I will focus on reviewing the status of the comparison of the data with FO NLO pQCD calculations trying to identify the open is...

and Applied Analysis 3 where bi t , rj t , aik t , cil t , djk t , ejl t , ejl t i, k 1, 2, . . . ,N; j, l 1, 2, . . . ,M are assumed to be continuous ω-periodic functions and the delays τik, δjk, ηil, ξjl are assumed to be positive constants. The system 1.3 is supplemented with the initial condition: xi θ φi θ , yj θ ψi θ , θ ∈ −τ, 0 , φi 0 > 0, ψi 0 > 0, 1.4

Let A be an arc on the boundary of the unit disk U. We prove an asymptotic formula for the probability that there is a percolation cluster K for critical site percolation on the triangular grid in U which intersects A and such that 0 is surrounded by K ∪ A. Motivated by questions raised by Langlands et al [LPSA94] and by M. Aizenman, J. Cardy [Car92, Car] derived a formula for the asymptotic pr...

We prove that classical Hecke operators on Maass forms are a special case of completely positive maps on II1 factors, associated to a pair of isomorphic subfactors. This representation induces several matrix inequalities on the eigenvalues of the Hecke operators Maass forms. In particular the family of eigenvalues corresponding to an eigenvector is a completely bounded multiplier of the Hecke a...

ν = q · P M = E − E′ is the lepton’s energy loss in the nucleon rest frame (in earlier literature sometimes ν = q · P ). Here, E and E′ are the initial and final lepton energies in the nucleon rest frame. Q2 = −q2 = 2(EE′−−→k · −→k ′)−m2 −m2 ′ where m (m ′) is the initial (final) lepton mass. If EE′ sin2(θ/2) m2 , m2 ′ , then ≈ 4EE′ sin2(θ/2), where θ is the lepton’s scattering angle with respe...

In this paper, we prove the existence of at least three solutions to the following Kirchhoff nonlocal fractional equation:  M (∫ Rn×Rn |u(x)− u(y)| K(x− y)dxdy − ∫ Ω |u(x)|dx ) ((−∆)u− λu) ∈ θ(∂j(x, u(x)) + μ∂k(x, u(x))), in Ω, u = 0, in R \ Ω, where (−∆) is the fractional Laplace operator, s ∈ (0, 1) is a fix, λ, θ, μ are real parameters and Ω is an open bounded subset of R, n > 2s, with L...

Let f∗(z) = ∞ ∑ j=0 aj z j be a convergent series in which {aj}j=0 are known real numbers. In this paper, by referring to Osler’s lemma [8], we obtain explicit forms of the two bivariate series ∞ ∑ j=0 an j+m r j cos(α+ j)θ and ∞ ∑ j=0 an j+m r j sin(α+ j)θ, where r, θ are real variables, α ∈ R, n ∈ N and m ∈ {0, 1, . . . , n − 1}. With some illustrative examples, we also show how to obtain the...