Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Threonine dehydratase deficiency: A probable cause of non‐ketotic hyperglycinaemia

A patient with classical symptoms of non‐ketotic hyperglycinaemia (NKH) is presented. Threonine dehydratase was undetectable in a liver autopsy specimen, which was obtained within 1 h of death and immediately frozen at −70 °C. Activities of four marker enzymes were normal. This represents the first documentation of an inborn error of threonine metabolism and a new explanation of NKH.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147124/1/jimd0053.pd

Using the art practice of play to communicate legged robotics research concepts

The art practice of play uses spontaneity and surprise to communicate meaningful content and inspire critical thinking (1-3). We describe three engineering education outreach efforts that use play to communicate legged robotics research concepts. In the first workshop, Penn engineering students were motivated to learn how to program a legged robot using the narrative of a “dance competition,” with the winning dances to be showcased at the Philadelphia Science Festival. In the second workshop, Philadelphia School District high school students used a poseably programmable legged robot to tell a story by performing a series of behaviors in a set of their own design and documenting the story as a video artwork. Here, there were two narratives: One created by the workshop directors, communicating concepts about complex multi-legged behaviors and gaits, and the other created by the students using the robots to express their ideas. In the final workshop, middle school students created locomoting robots using motors, post-consumer materials, and basic art supplies. The concepts of energy and physical programming were demonstrated using working Trashbots and practiced during an introductory exercise making a vibrating motor from a spinning one. Participants then created a robot of their own design using iterative experimentation. We conclude from these three workshops that play can be used as a vehicle for scientific communication. (1) David Getsy, ed. From diversion to subversion: Games, play, and twentieth-century art, Vol. 16 (Penn State Press, 2011). (2) Nato Thompson and Gregory Scholette, eds. The interventionists: Users\u27 manual for the creative disruption of everyday life (MIT Press, 2004). (3) Diedra Krieger, ‘Plastic Fantastic,’ Gyre Exhibition, Anchorage Museum, Alaska, 2014. For more information: Kod*lab

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

1,8‐Bis(diphenylamino)‐ and 1,8‐Bis(methylphenylamino)naphthalene: Molecular Structure and Dynamic Behavior

The title compounds 2 and 3 have been synthesized from 1,8‐diaminonaphthalene. The molecular structure of 2 has been determined by X‐ray structure analysis and is discussed with regard to the arrangement of the peri‐diphenylamino substituents in the crystalline state and the steric strain in the molecule. NMR studies of 3 reveal two conformational processes. Their nature is discussed and barriers are reported

Accessing Law: An Empirical Study Exploring the Influence of Legal Research Medium

The legal profession is presently engaged in an uncontrolled experiment. Attorneys now locate and access legal authorities primarily through electronic means. Although this shift to an electronic research medium radically changes how attorneys discover and encounter law, little empirical work investigates impacts from the shift to an electronic medium. This Article presents the results of one of the most robust empirical studies conducted to date comparing research processes using print and electronic sources. While the study presented in this Article was modest in scope, the extent and type of the differences that it reveals are notable. Some of the observed differences between print and electronic research processes confirm predictions offered, but never before confirmed, about how the research medium changes the research process. This Article strongly supports calls for the legal profession and legal academy to be more attentive to the implications of the shift to electronic research

Highly conductive molecular junctions based on direct binding of benzene to platinum electrodes

Highly conductive molecular junctions were formed by direct binding of benzene molecules between two Pt electrodes. Measurements of conductance, isotopic shift in inelastic spectroscopy and shot noise compared with calculations provide indications for a stable molecular junction where the benzene molecule is preserved intact and bonded to the Pt leads via carbon atoms. The junction has a conductance comparable to that for metallic atomic junctions (around 0.1-1 Go), where the conductance and the number of transmission channels are controlled by the molecule's orientation at different inter-electrode distances.Comment: 4 pages, 4 figure