Gradient estimates for a nonlinear diffusion equation on complete manifolds

Let $(M,g)$ be a complete non-compact Riemannian manifold with the $m$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive smooth bounded solutions to the following nonlinear diffusion equation $$u_t=\Delta u-\nabla\phi\cdot\nabla u-au\log u-bu,$$ where $\phi$ is a $C^2$ function, and $a\neq0$ and $b$ are two real constants. This work generalizes the results of Souplet and Zhang (Bull. London Math. Soc., 38 (2006), pp. 1045-1053) and Wu (Preprint, 2008).Comment: 11 page

Industrial cluster formation in European regions. U.S. cluster templates and Austrian evidence.

The paper will be organized in the following manner. We first provide a concise review of how industrial trade clusters were developed from available I/O coefficients (see box), including how regional industrial data may be embedded within their "templates". Second, we will review the steps taken, using available industrial concordances, that permit regional data from other advanced national industrial systems to be embedded within these templates. Third, we will illustrate the results of applying the U.S. template for the motor vehicle industrial trade cluster to regions in both Austria and North Carolina over 5-10 year time periods. Finally, we will offer some speculative observations about what the results may indicate about regional cluster development in these two regions. (authors' abstract, ed. M.Putz)Series: SRE - Discussion Paper

Comment on ``Periodic wave functions and number of extended states in random dimer systems'

There are no periodic wave-functions in the RDM but close to the critical energies there exist periodic envelopes. These envelopes are given by the non-disordered properties of the system.Comment: RevTex file, 1 page, Comment X. Huang, X. Wu and C. Gong, Phys. Rev. B 55, 11018 (1997

Effects of Warm Up Intensity on Factors Related to Subsequent Performance of Submaximal Exercise

Introduction: Athletes often warm up (WU) prior to exercise to improve performance. However, there are no clear directives regarding the intensity of the WU that is most effective in improving physiological responses related to enhanced aerobic performance. Methods: Nine college-aged men (age, ht, mass, 20.6 yr, 1.7 m, 84.8 kg, respectively) performed WU of varying intensities, 60% ventilatory threshold (VT), 100%VT, and 120%VT prior to performing 5 min of steady state exercise at 80%VT on a cycle ergometer. O2 deficit, RPE, steady state heart rate (HRss), and steady state VO2 (VO2ss) were measured during the exercise bout. Results: There was a significant decrease in O2 deficit as WU intensity increased ((2,9)= 9.15, p = .002, 2=0.53) with the deficit being lowest after WU at 120%VT. RPE were significantly lower after WU at 120%VT than both 60% and 100%VT (=(2,9)=6.88, p=.007, 2=0.46). However, WU intensity did not significantly affect either HRss (F(2,9)=0.48, p=0.63) or VO2ss (F(2,9)=1.10, p=0.36) during the exercise bout. Conclusion: The findings suggest that a higher intensity WU improves factors related to improved aerobic performance, i.e. decreased O2 deficit and RPE, without adversely affecting factors that could lead to a decline in performance, i.e. increased HRss and VO2ss

Generalized M-Fluctuation Tests for Parameter Instability

A general class of fluctuation tests for parameter instability in an M-estimation framework is suggested. The tests are based on partial sum processes of M-estimation scores for which functional central limit theorems are derived under the null hypothesis of parameter stability and local alternatives. Special emphasis is given to parameter instability in (generalized) linear regression models and it is shown that the introduced M-fluctuation tests contain a large number of parameter instability or structural change tests known from the statistics and econometrics literature. The usefulness of the procedures is illustrated using artificial data and data for the German M1 money demand, historical demographic time series from Großarl, Austria, and youth homicides in Boston.Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science

Brief of Michelle M. Wu as Amicus Curiae

Copyright is, above all else, a balancing act. This equity principle is especially important when technology collides with traditional copyright. Market effects are certainly an important feature of that balance but must be weighed against other equitable interests, regardless of their technological form. Literary criticism, second-hand sales, and library lending all have the potential to impact sales but nevertheless are considered social goods that copyright is intended to foster. Controlled digital lending ( CDL ) was established to innovate these core, well-established components of copyright law, allowing libraries to secure their collections and maintain their relevance as physical stewards of knowledge in an increasingly digital age. CDL takes many forms. Many libraries around the United States offer works through CDL subject to their own individual platforms and practices. The arguments offered by Plaintiffs in support of their motion for summary judgment are a broad-based attack on all of them, shoehorning the very concept of CDL into a dispute about the Internet Archive’s individual implementation of it. See, e.g., ECF No. 99 at 1–5. Indeed, they go so far as to generally call digitized copies of physical works “bootleg.” Id. at 1. Amicus respectfully submits that this Court should (1) reject Plaintiffs’ argument in support of their motion that CDL generally does not constitute fair use, and (2) regardless of this Court’s decision on the motions for summary judgment, narrowly construe the parties’ arguments to reach an outcome that has as little effect as possible on the hundreds of unrelated CDL programs at libraries around the country. Amicus addresses three fundamental points for this Court’s consideration and benefit. First, CDL was carefully crafted to balance respect for public and private copyright interests in a digital age. Second, CDL creates enormous benefits for libraries, the users they serve, and society at large that are integral to the fair use analysis. Digital licensing, Plaintiffs’ proposed alternative to CDL, is wholly insufficient to fulfill libraries’ missions and hampers libraries’ ability to serve the public good. Third, this Court should not adopt Plaintiffs’ overbroad attack on CDL. Whatever decision this Court reaches on the particular facts of these plaintiffs against this defendant’s particular CDL program, CDL has many different expressions and applications in libraries all over the United States, serving a diverse set of interests including publishers, authors, users, and libraries themselves. Plaintiffs flatten these distinctions, treating CDL as a monolithic bad and themselves as the monolithic representatives of the interests of copyright holders, when they represent only one profit-focused perspective in the equitable considerations of copyright law (and indeed, only one perspective of publishers). See, e.g., ECF No. 1 at 4–5. Plaintiffs’ motion for summary judgment attacks and denigrates the very concept of CDL, when it just as easily could have been narrowly construed. A wide-reaching holding against CDL — which Plaintiffs request of this Court — would have wide-reaching consequences far beyond the parties, harming the ability of libraries to adequately serve the public in the digital age

On the ergodicity of geodesic flows on surfaces of nonpositive curvature

Let $M$ be a smooth compact surface of nonpositive curvature, with genus $\geq 2$. We prove the ergodicity of the geodesic flow on the unit tangent bundle of $M$ with respect to the Liouville measure under the condition that the set of points with negative curvature on $M$ has finitely many connected components. Under the same condition, we prove that a non closed "flat" geodesic doesn't exist, and moreover, there are at most finitely many flat strips, and at most finitely many isolated closed "flat" geodesics.Comment: 11 pages, 4 figures. Lemma 3.8 is added to correct a gap in the proof of Proposition 3.4. Theorem 1.5 is also adde