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

Spontaneous direct bonding of thick silicon nitride

Wafers with LPCVD silicon-rich nitride layers have been successfully direct bonded to silicon-rich nitride and boron-doped silicon surfaces. A chemical - mechanical polishing treatment was necessary to reduce the surface roughness of the nitride before bonding. The measured surface energies of the room-temperature bond were comparable to values found for Si - Si hydrophilic bonding. A mechanism similar to this bonding is suggested for silicon nitride bonding

The surface adhesion parameter: a measure for wafer bondability

A theory is presented which describes the initial direct wafer bonding process. The effect of surface microroughness on the bondability is studied on the basis of the theory of contact and adhesion of elastic solids. An effective bonding energy, the maximum of which is the specific surface energy of adhesion, is proposed to describe the real binding energy of the bonding interface including the influence of the wafer surface microroughness. Both the effective bonding energy and the real area of contact between rough surfaces depend on a dimensionless surface adhesion parameter, &thetas;. Using the adhesion parameter as a measure, three kinds of wafer contact interfaces can be identified with respect to their bondability; viz. the non-bonding regime (&thetas;>&ap;12), the bonding regime (&thetas;<&ap;1), and the adherence regime (1<&thetas;<12). Experimental data are in agreement with this theor

Bound States of the Heavy Flavor Vector Mesons and Y(4008) and Z1+(4050)Z^{+}_1(4050)

The $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and $0^{-+}$ $B^{*}\bar{B}^{*}$ molecules should exist, and the $D^{*}\bar{D}^{*}$ bound states with the same quantum numbers very likely exist as well. However, the CP exotic ($1^{-+}$, $2^{+-}$) $B^{*}\bar{B}^{*}$ and $D^{*}\bar{D}^{*}$ states may not be bound by the one boson exchange potential. We find that the I=0 configuration is more deeply bound than the I=1 configuration, hence $Z^{+}_1(4050)$ may not be a $D^{*}\bar{D}^{*}$ molecule. Although Y(4008) is close to the $D^{*}\bar{D}^{*}$ threshold, the interpretation of Y(4008) as a $D^{*}\bar{D}^{*}$ molecule is not favored by its huge width. $1^{--}$ $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ states can be produced copiously in $e^{+}e^{-}$ annihilation, detailed scanning of the $e^{+}e^{-}$ annihilation data near the $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ threshold is an important check to our predictions.Comment: 17 pages,6 figur

Dominant Strategy Mechanisms with Multidimensional Types

This paper provides a characterization of dominant strategy mechanisms with quasi-linear utilities and multi-dimensional types for a variety of preference domains. These characterizations are in terms of a monotonicity property on the underlying allocation rule.Dominant Strategy, Farkas Lemma, Combinatorial Auctions.

Quark energy loss and shadowing in nuclear Drell-Yan process

The energy loss effect in nuclear matter is another nuclear effect apart from the nuclear effects on the parton distribution as in deep inelastic scattering process. The quark energy loss can be measured best by the nuclear dependence of the high energy nuclear Drell-Yan process. By means of three kinds of quark energy loss parameterizations given in literature and the nuclear parton distribution extracted only with lepton-nucleus deep inelastic scattering experimental data, measured Drell-Yan production cross sections are analyzed for 800GeV proton incident on a variety of nuclear targets from FNAL E866. It is shown that our results with considering the energy loss effect are much different from these of the FNAL E866 who analysis the experimental data with the nuclear parton distribution functions obtained by using the deep inelastic lA collisions and pA nuclear Drell-Yan data . Considering the existence of energy loss effect in Drell-Yan lepton pairs production,we suggest that the extraction of nuclear parton distribution functions should not include Drell-Yan experimental data.Comment: 12 page

The energy spectrum symmetry of Heisenberg model in Fock space

We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry of energy spectrum between its subspace $n$ and the subspace $L-n$ of the Fock space. Our proof is completed by introducing two general quantum operations. One is a flip operation of spin direction and another is a mirror reflection of spin sites.Comment: Revising version, 7 preprint pages, no figures; Published version contains some revisions in Languag