Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

The subgroup identification problem for finitely presented groups

We introduce the subgroup identification problem, and show that there is a finitely presented group G for which it is unsolvable, and that it is uniformly solvable in the class of finitely presented locally Hopfian groups. This is done as an investigation into the difference between strong and weak effective coherence for finitely presented groups.Comment: 11 pages. This is the version submitted for publicatio

Poster 312 Efficacy of Combined Intra‐articular Facet Joint and Transforaminal Epidural Steroid Injection in the Management of Symptomatic Lumbosacral Lateral Recess Stenosis: A Retrospective Analysis

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147060/1/pmr2s280a.pd

Cervical Transforaminal Epidural Injection in the Management of a Stinger

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146907/1/pmr273.pd

Analysis of Reforming Gas Combustion in Internal Combustion Engine

Abstract The present paper deals with the study of the combustion of reforming gas in a small size Internal Combustion Engine. Therefore, mathematical models of both reforming process and internal combustion engine were implemented. In particular, steams reforming of glycerol to produce synthesis gas and spark ignition four strokes ICE were studied. The reforming process mathematical model was verified using experimental data. Synthesis gas was used to feed the ICE with different syngas and engine configuration. On the basis of the comparison with the experimental results, it is possible to state that the mathematical model is validated. Engine performance and pollutant emission evaluation was carried out using the integrated mathematical models with reference to the engine running on standard commercial fuel. The results highlight a reduction in engine performance and, at the same time a reduction of pollutant emissions in terms of CO and CO 2

Emerging giant resonant exciton induced by Ta-substitution in anatase TiO2_{2}: a tunable correlation effect

Titanium dioxide (TiO$_2$) has rich physical properties with potential implications in both fundamental physics and new applications. Up-to-date, the main focus of applied research is to tune its optical properties, which is usually done via doping and/or nano-engineering. However, understanding the role of $d$-electrons in materials and possible functionalization of $d$-electron properties are still major challenges. Herewith, within a combination of an innovative experimental technique, high energy optical conductivity, and of the state-of-the-art {\it ab initio} electronic structure calculations, we report an emerging, novel resonant exciton in the deep ultraviolet region of the optical response. The resonant exciton evolves upon low concentration Ta-substitution in anatase TiO$_{2}$ films. It is surprisingly robust and related to strong electron-electron and electron-hole interactions. The $d$- and $f$- orbitals localization, due to Ta-substitution, plays an unexpected role, activating strong electronic correlations and dominating the optical response under photoexcitation. Our results shed light on a new optical phenomenon in anatase TiO$_{2}$ films and on the possibility of tuning electronic properties by Ta substitution

Design and Implementation of a State-Driven Operating System for Highly Reconfigurable Sensor Networks

Due to the low-cost and low-power requirement in an individual sensor node, the available computing resources turn out to be very limited like small memory footprint and irreplaceable battery power. Sensed data fusion might be needed before being transmitted as a tradeoff between procession and transmission in consideration of saving power consumption. Even worse, the application program needs to be complicated enough to be self-organizing and dynamically reconfigurable because changes in an operating environment continue even after deployment. State-driven operating system platform offers numerous benefits in this challenging situation. It provides a powerful way to accommodate complex reactive systems like diverse wireless sensor network applications. The memory usage can be bounded within a state transition table. The complicated issues like concurrency control and asynchronous event handling capabilities can be easily achieved in a well-defined behavior of state transition diagram. In this paper, we present an efficient and effective design of the state-driven operating system for wireless sensor nodes. We describe that the new platform can operate in an extremely resource constrained situation while providing the desired concurrency, reactivity, and reconfigurability. We also compare the executing results after comparing some benchmark test results with those on TinyOS