Uniform convergence of basic Fourier–Bessel series on a q-linear grid

We study Fourier–Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The convergence results are illustrated with specific examples of expansions in q-Fourier–Bessel series.

     

Use of radial basis function networks and near-infrared spectroscopy for the determination of total nitrogen content in soils from Sao Paulo State

Total nitrogen has been determined by using a model developed between the conventional chemical measurements and diffuse reflectance spectra in the near-infrared region. Samples (244) from different types of soils with total nitrogen contents ranging from 0.20 to 13.60% (m/m) were modeled by partial least-squares regression (PLS), multi-layer perceptron feed-forward networks (MLP) and radial basis function networks (RBFN). The RBFN model produced a better square error of prediction (SEP) of 0.048 and R(2) = 0.93 in a procedure that is simpler, faster and less dependent on the initial conditions.     

On the covariantization of the chiral constraints

We show that a complete covariantization of the chiral constraint in the Floreanini-Jackiw necessitates an infinite number of auxiliary Wess-Zumino fields other-wise the covariantization is only partial and unable to remove the nonlocality in the chiral boson operator. We comment on recent works that claim to obtain covariantization through the use of Batalin-Fradkin-Tyutin method, that uses just one Wess-Zumino field.     

A study of π andK production in proton-uranium and oxygen-uranium interactions at 22 GeV/A using decay muons

The like-sign dimuons copiously recorded in the NA 38 experiment both inp-U and O?U reactions at 200 GeV/nucleon are interpreted as resulting from decays of π andK mesons in comparable proportions. The ++/?? ratio is large (?1.7) and ascribed to theK ⁺ being more copiously produced than theK ^?. Both the average transverse momentum and the ++/?? ratio are comparable forp-U and O?U reactions, and both increase only slightly with the transverse energyE _T .     

Electron energy loss measurements on PbF2, PbCl2, PbBr2 and PbI2

The results of electron energy loss measurements on polycrystalline films of PbF₂, PbC1₂, PbBr₂ and PbI₂ are present and the calculated dielectric functions are discussed in relation to their band structures and optical data.     

Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at sqrt[S(NN)] =2.76 TeV with the ATLAS detector at the LHC

By using the ATLAS detector, observations have been made of a centrality-dependent dijet asymmetry in the collisions of lead ions at the Large Hadron Collider. In a sample of lead-lead events with a per-nucleon center of mass energy of 2.76 TeV, selected with a minimum bias trigger, jets are reconstructed in fine-grained, longitudinally segmented electromagnetic and hadronic calorimeters. The transverse energies of dijets in opposite hemispheres are observed to become systematically more unbalanced with increasing event centrality leading to a large number of events which contain highly asymmetric dijets. This is the first observation of an enhancement of events with such large dijet asymmetries, not observed in proton-proton collisions, which may point to an interpretation in terms of strong jet energy loss in a hot, dense medium.     

A Faber–Krahn Inequality for Solutions of Schrödinger’s Equation on Riemannian Manifolds

We consider a bounded open set with smooth boundary \(\Omega \subset M\) in a Riemannian manifold (M, g), and suppose that there exists a non-trivial function \(u\in C({\overline{\Omega }})\) solving the problem

$$\begin{aligned} -\Delta u=V(x)u, \,\, \text{ in }\,\,\Omega , \end{aligned}$$

in the distributional sense, with \(V\in L^\infty (\Omega )\), where \(u\equiv 0\) on \(\partial \Omega .\) We prove a sharp inequality involving \(||V||_{L^{\infty }(\Omega )}\) and the first eigenvalue of the Laplacian on geodesic balls in simply connected spaces with constant curvature, which slightly generalises the well-known Faber–Krahn isoperimetric inequality. Moreover, in a Riemannian manifold which is not necessarily simply connected, we obtain a lower bound for \(||V||_{L^{\infty }(\Omega )}\) in terms of its isoperimetric or Cheeger constant. As an application, we show that if \(\Omega \) is a domain on a m-dimensional minimal submanifold of \({\mathbb {R}}^n\) which lies in a ball of radius R, then

$$\begin{aligned} ||V||_{L^{\infty }(\Omega )}\ge \left( \frac{m}{2R}\right) ^{2}. \end{aligned}$$

     

Riemann and Dirichlet Type Problems for Hyperanalytic Functions in Fractal Domains

In this paper we are interested in finding solvability conditions for Riemann and Dirichlet type boundary value problems with generalized Hölder-continuous boundary data in the case of hyperanalytic functions defined in a domain of the complex plane bounded by an h-summable closed curve.