Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Q2Q^2 Independence of QF2/F1QF_2/F_1, Poincare Invariance and the Non-Conservation of Helicity

A relativistic constituent quark model is found to reproduce the recent data regarding the ratio of proton form factors, $F_2(Q^2)/F_1(Q^2)$. We show that imposing Poincare invariance leads to substantial violation of the helicity conservation rule, as well as an analytic result that the ratio $F_2(Q^2)/F_1(Q^2)\sim 1/Q$ for intermediate values of $Q^2$.Comment: 13 pages, 7 figures, to be submitted to Phys. Rev. C typos corrected, references added, 1 new figure to show very high Q^2 behavio

Delta M_K and epsilon_K in the left-right supersymmetric model

We perform a complete analysis of $\Delta S=2$ processes in the kaon system and evaluate $\Delta M_K$ and $\epsilon_K$ in the left-right supersymmetric model. We include analytic expressions for the contributions of gluinos, neutralinos and charginos. We obtain general constraints on off-diagonal mass terms between the first two generations of both down-type and up-type squarks. In the down-squark sector, we compare the results with gluino-only estimates. In the up-squark sector, we find a complete set of bounds on all combinations of chirality conserving or chirality flipping parameters. Finally, we comment on the size of the bounds obtained by imposing left-right symmetry in the squark sector.Comment: 22 pages, 1 figure and 4 table

New low-stress PECVD poly-SiGe layers for MEMS

Thick poly-SiGe layers, deposited by plasma-enhanced chemical vapor deposition (PECVD), are very promising structural layers for use in microaccelerometers, microgyroscopes or for thin-film encapsulation, especially for applications where the thermal budget is limited. In this work it is shown for the first time that these layers are an attractive alternative to low-pressure CVD (LPCVD) poly-Si or poly-SiGe because of their high growth rate (100-200 nm/min) and low deposition temperature (520/spl deg/C-590/spl deg/C). The combination of both of these features is impossible to achieve with either LPCVD SiGe (2-30 nm/min growth rate) or LPCVD poly-Si (annealing temperature higher than 900/spl deg/C to achieve structural layer having low tensile stress). Additional advantages are that no nucleation layer is needed (deposition directly on SiO/sub 2/ is possible) and that the as-deposited layers are polycrystalline. No stress or dopant activation anneal of the structural layer is needed since in situ phosphorus doping gives an as-deposited tensile stress down to 20 MPa, and a resistivity of 10 m/spl Omega/-cm to 30 m/spl Omega/-cm. With in situ boron doping, resistivities down to 0.6 m/spl Omega/-cm are possible. The use of these films as an encapsulation layer above an accelerometer is shown

FAPRI 2004 U.S. and World Agricultural Outlook

Crop Production/Industries, Livestock Production/Industries,

FAPRI 2006 U.S. and World Agricultural Outlook

The FAPRI 2006 U.S. and World Agricultural Outlook presents projections of world agricultural production, consumption, and trade under average weather patterns, existing farm policy, and policy commitments under current trade agreements and custom unions. Despite continued high energy prices, world economic growth is expected to remain strong in the coming decade, above 3% per annum. Other major drivers of the 2006 baseline include new bio-energy policies in several large countries, EU sugar policy reform, sanitary and phytosanitary (SPS) shocks in livestock and poultry markets, and movements in the exchange rate.Crop Production/Industries, International Relations/Trade, Livestock Production/Industries,

Nonlinear Realization of Chiral Symmetry on the Lattice

We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.Comment: 34 pages, 2 figures, revised version to be published in J. High Energy Phys. (changes in the 1st paragraph, additional descriptions on the nature of the coordinate singularities in Sec.2, references added

FAPRI 2005 U.S. and World Agricultural Outlook

Crop Production/Industries, Livestock Production/Industries,

A calculation of the QCD phase diagram at finite temperature, and baryon and isospin chemical potentials

We study the phases of a two-flavor Nambu-Jona-Lasinio model at finite temperature $T$, baryon and isospin chemical potentials: $\mu_{B}=(\mu_{u}+\mu_{d})/2$, $\mu_{I}=(\mu_{u}-\mu_{d})/2$. This study completes a previous analysis where only small isospin chemical potentials $\mu_{I}$ were consideredComment: 21 pages, 13 figures included, two more refernces adde