Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page

Renormalization group flows and continual Lie algebras

We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z_n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.Comment: latex, 73pp including 14 eps fig

The Bayh-Dole Act of 1980 and University–Industry Technology Transfer: A Model for Other OECD Governments?

Recent initiatives by a number of OECD governments suggest considerable interest in emulating the Bayh-Dole Act of 1980, a piece of legislation that is widely credited with stimulating significant growth in university--industry technology transfer and research collaboration in theUS. We examine the effects of Bayh-Dole on university--industry collaboration and technology transfer in the US, emphasizing the lengthy history of both activities prior to 1980 and noting the extent to which these activities are rooted in the incentives created by the unusual scale and structure (by comparison with Western Europe or Japan) of the US higher education system. Efforts at “emulation” of the Bayh-Dole policy elsewhere in the OECD are likely to have modest success at best without greater attention to the underlying structural differences among the higher education systems of these nations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43108/1/10961_2004_Article_5384361.pd

Trends and transitions in the institutional environment for public and private science

The last quarter-century bore witness to a sea change in academic involvement with commerce. Widespread university-based efforts to identify, manage, and market intellectual property (IP) have accompanied broad shifts in the relationship between academic and proprietary approaches to the dissemination and use of science and engineering research. Such transformations are indicators of institutional changes at work in the environment faced by universities. This paper draws upon a fifteen-year panel (1981–1995) of university-level data for 87 research-intensive US campuses in order to document trends and transitions in relationships among multiple indicators of academic and commercial engagement. The institutional environment for public and private science is volatile, shifting in fits and starts from a situation conducive to organizational learning through high volume patenting to a more challenging arrangement that links indiscriminate pursuit of IP with declines in both the volume and impact of academic science. The pattern and timing of these transitions may support an enduring system of stratification that offers increasing returns to first-movers while limiting the opportunities available to universities that are later entrants to the commercial realm. Unpacking the systematic effects of university research commercialization requires focused attention on the sources and trajectories of profound institutional change.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42839/1/10734_2004_Article_2916.pd

Growth analysis in the potato crop under different irrigation levels

Conduziu-se um experimento na Fazenda São Manoel, localizada em São Manuel, SP, pertencente à Faculdade de Ciências Agronômicas da Universidade Estadual Paulista, com o objetivo de avaliar os efeitos de diferentes lâminas de irrigação no crescimento da cultura da batata (Solanum tuberosum ssp. tuberosum), cultivar Aracy. O ensaio foi instalado em um Latossolo Vermelho-Escuro, textura arenosa, sob uma cobertura de plástico. O delineamento experimental utilizado foi o de blocos ao acaso, com cinco tratamentos, cinco coletas de plantas para fins de análise de crescimento, e quatro repetições. Os tratamentos consistiam em irrigar a batata quando a tensão da água no solo atingia 15, 35, 55, 75 e 1.500 kPa. O aumento nas lâminas de irrigação induz incremento no índice de área foliar, na duração da área foliar, na taxa de crescimento relativo e na taxa assimilatória líquida. _________________________________________________________________________________________ ABSTRACT: An experiment was carried out at Fazenda São Manoel, pertaining to the Faculdade de Ciências Agronômicas of the Universidade Estadual Paulista, São Manuel, SP, Brazil, to evaluate irrigation levels in the potato (Solanum tuberosum ssp. tuberosum) growth, cv. Aracy. This work was installed in a sandy Dark-Red Latosol, under a plastic cover. The experimental design was an entirely randomized block composed by irrigation in the potato plots when the soil water potential has reached 15, 35, 55, 75 and 1,500 kPa, and five plant sampling time with four replicates. It was found that higher irrigation levels led to increase of the leaf area index, leaf area duration, relative growth rate and net assimilation rate

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR