An approximation result for free discontinuity functionals by means of non‐local energies

We approximate, in the sense of Γ‐convergence, free discontinuity functionals with linear growth by a sequence of non‐local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186 (4): 722–744), where there is the proof of the general one‐dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13 (1):135–162), where the n‐dimensional case with ?=Id is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non‐local energies. Copyright © 2008 John Wiley & Sons, Ltd.     

Four-nucleon force using the method of unitary transformation

We discuss in detail the derivation of the leading four-nucleon force in chiral effective field theory using the method of unitary transformation. The resulting four-nucleon force is given in both momentum and configuration space. It does not contain any unknown parameters and can be used in few- and many-nucleon studies.     

Infrared multiple photon dissociation spectroscopy of transition metal oxide cluster cations

Infrared spectra in the range of 530–1400 cm^–1 are presented for tantalum oxide cluster cations (x = 3, 4 and 6). These spectra are obtained via multiple photon dissociation (MPD) spectroscopy of free cluster cations moving in a molecular beam. The IR spectra for are compared to spectra of as well as to the experimental data available for vanadium oxide cluster cations from IR-MPD spectroscopy. For and the IR spectra exhibit very strong similarities (including the band positions), whereas absorption bands in are relatively blue-shifted by about 20–40 cm^–1.     

Theoretical description of the pd → pdη reaction near threshold

The contributions of three different types of driving terms are included in the estimation of the pd → pdη reaction at low energies. Near threshold, it is predicted that a two-step model involving an intermediate pion should be the most important but, as the energy approaches the threshold for η production in the free nucleon-nucleon reaction, a pick-up mechanism with a spectator proton should become dominant. The total cross-sections are underestimated by about a factor of two compared with experimental data but the discrepancies in the angular distributions are more serious, with no sign in the data for the peaks corresponding to the pick-up diagram.     

Single-pion production in pp collisions at 0.95 GeV/c (I)

The single-pion production reactions pp → dπ⁺, pp → npπ⁺ and pp → ppπ⁰ were measured at a beam momentum of 0.95GeV/c ( T _p ≈ 400MeV) using the short version of the COSY-TOF spectrometer. The implementation of a central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements. Thus, all pion production channels were recorded with 1-4 overconstraints. The total and differential cross-sections obtained are compared to previous data and theoretical calculations. Main emphasis is put on the discussion of the ppπ⁰ channel, where we obtain angular distributions different from previous experimental results, however, partly in good agreement with recent phenomenological and theoretical predictions. In particular, we observe very large anisotropies for the π⁰ angular distributions in the kinematical region of small relative proton momenta revealing there a dominance of proton spinflip transitions associated with π⁰ s and d partial waves and emphasizing the important role of π⁰ d-waves.     

Near-threshold η-meson production in the dd↦He η reaction

The dd↦⁴Heη reaction has been investigated near threshold using the ANKE facility at COSY-Jülich. Both total and differential cross-sections have been measured at two excess energies, Q = 2.6 MeV and 7.7 MeV, with a subthreshold measurement being undertaken at Q = - 2.6 MeV to study the physical background. While consistent with isotropy at the lower energy, the angular distribution reveals a pronounced anisotropy at the higher one, indicating the presence of higher partial waves. Options for the decomposition into partial amplitudes and their consequences for the determination of the s-wave ηα scattering length are discussed.     

计算含三角函数无穷积分的新方法

在留数定理及Jordan引理的基础上,提出了一个新的引理,进而发展了计算含三角函数无穷积分的一种新方法.作为应用,计算了几个典型的含三角函数的无穷积分.     

A new class of bilevel generalized mixed equilibrium problems in Banach spaces

A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.     

Single-pion production in pp collisions at 0.95 GeV/c (II)

The single-pion production reactions pp d , pp np and pp pp were measured at a beam momentum of 0.95GeV/c ( T _p 400 MeV) using the short version of the COSY-TOF spectrometer. The central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements from other detector parts. Thus all pion production channels were recorded with 1-4 overconstraints. The main emphasis is put on the presentation and discussion of the np channel, since the results on the other channels have already been published previously. The total and differential cross-sections obtained are compared to theoretical calculations. In contrast to the pp channel we observe in the np channel a strong influence of the excitation. In particular, the pion angular distribution exhibits a (3 cos² + 1) -dependence, typical for a pure s -channel excitation and identical to that observed in the d channel. Since the latter is understood by a s -channel resonance in the ¹ D ₂ pn partial wave, we discuss an analogous scenario for the pn channel.