Multiple boundary peak solutions for some singularly perturbed Neumann problems

We consider the problem \left \{ \begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega, \end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>$is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as \varepsilon approaches zero, at a critical point of the mean curvature function H(P), P \in \partial \Omega . It is also known that this equation has multiple boundary spike solutions at multiple nondegenerate critical points of H(P) or multiple local maximum points of H(P). In this paper, we prove that for any fixed positive integer$K$there exist boundary$K-peak$solutions at a local minimum point of$H(P)$. This implies that for any smooth and bounded domain there always exist boundary$K-peak$ solutions. We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions. Then we use a maximizing procedure to obtain multiple boundary spikes

Local sourcing of multinational enterprises in China

Purpose – Local sourcing from indigenous firms by multinational enterprises (MNEs) is an important channel through which the former may benefit from the positive externalities generated by the latter. The purpose of this study is to analyze the extent and determinants of local sourcing of MNEs. Design/methodology/approach – Employing a survey dataset covering 493 multinational subsidiaries in China during 1999-2005, this paper applies the two-limit Tobit model. Findings – It is found that an MNE's local sourcing decision is influenced by its strategies, characteristics such as size and learning ability and country-of-origin. More specifically, export-orientation strategy, joint venture strategy and networking with local suppliers positively affect local sourcing. Small and autonomous subsidiaries tend to source more locally. Age has a non-linear effect. The importance of these determinants varies with regions. Research limitations/implications – Aiming at capacity building and competitiveness of indigenous firms, the Chinese government has initiated local content requirement. This study shows that such policy intervention could be counterproductive. The creation of a more competitive business environment by the government could promote more linkages. Originality/value – Given its critical role in economic development, local sourcing by MNEs has attracted much attention. Only limited research has been carried out on FDI linkage effects in China, and the location effect on FDI linkages has not been examined. This study aims to fill the gap by using Chinese survey data

k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions

We show that hard-scattering factorization is violated in the production of high-p_T hadrons in hadron-hadron collisions, in the case that the hadrons are back-to-back, so that k_T factorization is to be used. The explicit counterexample that we construct is for the single-spin asymmetry with one beam transversely polarized. The Sivers function needed here has particular sensitivity to the Wilson lines in the parton densities. We use a greatly simplified model theory to make the breakdown of factorization easy to check explicitly. But the counterexample implies that standard arguments for factorization fail not just for the single-spin asymmetry but for the unpolarized cross section for back-to-back hadron production in QCD in hadron-hadron collisions. This is unlike corresponding cases in e^+e^- annihilation, Drell-Yan, and deeply inelastic scattering. Moreover, the result endangers factorization for more general hadroproduction processes.Comment: 10 pages. V. 2: Title change, misprints and minor corrections, as in journal versio

Performance Analysis of a Dual-Hop Cooperative Relay Network with Co-Channel Interference

This paper analyzes the performance of a dual-hop amplify-and-forward (AF) cooperative relay network in the presence of direct link between the source and destination and multiple co-channel interferences (CCIs) at the relay. Specifically, we derive the new analytical expressions for the moment generating function (MGF) of the output signal-to-interference-plus-noise ratio (SINR) and the average symbol error rate (ASER) of the relay network. Computer simulations are given to confirm the validity of the analytical results and show the effects of direct link and interference on the considered AF relay network

Near-ionization-threshold emission in atomic gases driven by intense sub-cycle pulses

We study theoretically the dipole radiation of a hydrogen atom driven by an intense sub-cycle pulse. The time-dependent Schr\"odinger equation for the system is solved by ab initio calculation to obtain the dipole response. Remarkably, a narrowband emission lasting longer than the driving pulse appears at a frequency just above the ionization threshold. An additional calculation using the strong field approximation also recovers this emission, which suggests that it corresponds to the oscillation of nearly-bound electrons that behave similarly to Rydberg electrons. The predicted phenomenon is unique to ultrashort driving pulses but not specific to any particular atomic structure.Comment: 8 pages, 2 figure