On Robin's criterion for the Riemann Hypothesis

Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality sum_{d|n}d=5041, where gamma denotes the Euler(-Mascheroni) constant. We show by elementary methods that if n>=37 does not satisfy Robin's criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that n must be divisible by a fifth power >1. As a consequence we infer that RH holds true if and only if every natural number divisible by a fifth power >1 satisfies Robin's inequality.Comment: 15 pages. Corrected version. In the first version in Theorem 5 (main result) it was falsely asserted that n must be superabundant, invalidating the proof. An alternative proof is provided in this version, some typos have been corrected, and the presentation has been improve

Testing hypotheses of the cause of peripheral thinning of the Greenland Ice Sheet: is land-terminating ice thinning at anomalously high rates?

Recent observations have shown that the periphery of the Greenland ice sheet (GrIS) is thinning rapidly and that this thinning is greatest around marine-terminating outlet glaciers. Several theories have been proposed which provide a link between climate and ice thinning. We present surface elevation change (<i>dh/dt</i>) data from NASA's Program for Arctic Regional Climate Assessment (PARCA) laser altimetry surveys for fourteen and eleven of the largest outlet glaciers in Southern Greenland from 1993 to 1998 and 1998 to 2006 respectively to test the applicability of these theories to the GrIS. <br><br> Initially, outlet glacier <i>dh/dt</i> data are compared with data from concurrent surveys over inland ice (slow flowing ice that is not obviously draining into an outlet glacier) to confirm the effect of ice flow on surface thinning rates. Land-terminating and marine-terminating outlet glacier <i>dh/dt</i> data are then compared from 1993 to 1998 and from 1998 to 2006. Finally, ablation anomalies (the difference between the "normal" ablation rate from 1970 to 2000 and the ablation rate in the time period of interest) calculated with a positive degree day model are compared to both marine-terminating and land-terminating outlet glacier <i>dh/dt</i> data. <br><br> Our results support earlier conclusions that certain marine-terminating outlet glaciers have thinned much more than land-terminating outlet glaciers during both time periods. Furthermore we show that these differences are not limited to the largest, fastest-flowing outlet glaciers – almost all marine-terminating outlet glaciers are thinning more than land-terminating outlet glaciers. There was a four fold increase in mean marine-terminating outlet glacier thinning rates below 1000 m elevation between the periods 1993 to 1998 and 1998 to 2006, while thinning rates of land-terminating outlet glaciers remained statistically unchanged. This suggests that a change in a controlling mechanism specific to the thinning rates of marine-terminating outlet glaciers occurred in the late 1990s and that this change did not affect thinning rates of land-terminating outlet glaciers. <br><br> Thinning rates of land-terminating outlet glaciers are statistically the same as ablation anomalies, while thinning rates of marine-terminating outlet glaciers are not. Thinning of land-terminating outlet glaciers therefore seems to be a response to changes in local mass balance (principally increases in air temperature) while thinning of marine-terminating outlet glaciers is principally controlled by ice dynamics. The mechanism by which this dynamic thinning occurs is still not clear although its association with marine-terminating outlet glaciers suggests perturbations at marine termini (calving) as the likely cause

Analysis of Countermovement Vertical Jump Force-Time Curve Phase Characteristics in Athletes

The purposes of this dissertation were to examine the phase characteristics of the countermovement jump force-time curve between athletes based on jumping ability, examine the influence of maximal muscular strength on the countermovement jump force-time curve phase characteristics of athletes, and to examine the behavior of the countermovement jump force-time curve phase characteristics over the course of a training process in athletes of varying strength levels. The following are the major findings of these dissertations. The analysis of athletes by jumping ability suggested that proficient jumpers are associated with greater relative phase magnitude and phase impulse throughout the phases contained in the positive impulse of the countermovement jump force-time curve. Additionally, phase duration was not found to differ between athletes based on jumping ability or between male and female athletes. The analysis of athletes based on maximal muscular strength suggested that only unweighted phase duration differs between strong and less-strong athletes. Interestingly, in both investigations based on jumping ability and maximal strength indicated the relative shape of the stretching phase representing the rise in positive force was related to an athlete’s jumping ability (jump height). The results of the longitudinal analysis of countermovement jump force-time phase characteristics identified that these variables can be frequently assessed throughout a training process to provide information of regarding an athlete performance state. Furthermore, based on the contrasting behaviors of many of the countermovement jump force-time curve phase characteristics over time, an athlete’s level of muscular strength may influence how these characteristics are expressed in the context of a training process

Tort Law - Products Liability - Settlements - Contribution

The Pennsylvania Supreme Court found that a manufacturer was independently liable under products liability for the failure to warn of a known defect in a component part. The court also held that a settlement by one joint tort-feasor -reduced the verdict amount only by the settling defendant\u27s pro-rata share, and that the non-settling joint tort-feasor owed its full pro-rata share to the plaintiff. Walton v Avco Corp., ___ Pa ___ ,610 A2d 454 (1992)

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the $q$-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.Comment: 4 pages and 5 figure

Facies and local roodel for the aluvial deposits in the rio Mero basin and Sada peninsula (A Coruña, Galicia, NW Spain)

[Resumen] Los depósitos aluviales de la cuenca del río Mero y península de Sada se originaron en dos tipos diferenciados de ambientes fluviales; - Corrientes fluviales de tipo trenzado. - Cursos I conos torrenciales Dichos ambientes pueden ser reconocidos gracias a las asociaciones de facies que presentan habiéndose identificado cuatro asociaciones diferentes (proximales, medias, distales y de curso yI o cono torrencial). La sedimentación se desarrolló en un contexto temporal con alternancia de periodos con predominio de procesos alocíclicos opuestos a periodos con mayor importancia de procesos autocíclicos ambos caracterizados por dos tipos diferentes de disección. El producto de esta alternancia dió como resultado secuencias grano y energía decreciente separadas por hiatos erosivos en los que se produciría el aterrazamiento de los depósitos. Cronologicamente los depésitos sedimentarios de la cuenca del Mero corresponderían, a la falta de datos más precisos el registro del transito Terciario- Cuaternario en esta zona.[Abstract] Aluvial deposits of Mero basin and Sada peninsula was generated under two different kinds of fluvial environments: - Braided type fluvial currents. - Torrential fan/currents. This ennvironments can be recognized by their facies associations. Four facies associations have been recognized (proximal, middle, distal and torrential currents Ifan association). Sedimentation was developed on a temporal context whith alociclicautociclic processes periodes characterized by two different kinds of dissection. The result of this, was energy and fining-upwards sequences construction limited by erosiva hiatus. During erosive hiatus was produced the deposits trenchment. This deposits can be, by lack of more precise data, the Terciary-Quaternary age record in this zone