We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other related questions.

16 When increasing the rates of subcritical flow on gentle slopes, the bed successively produces 17 ripples, dunes and flat beds. Antidunes (defined here as all bed undulations for which the 18 surface gravity waves are in phase with the bed profile) appear only in high flow rates and 19 may be found in some extreme natural flow events. Inversely, on steep slopes flume 20 experiment (S≥1% appro...

We study here slopes of periodicity of tilings. A tiling is of slope θ if it is periodic along direction θ but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they coincide with recursively enumerable sets of rationals.

Ring modulators for silicon photonic (SiPho) optical transceivers are extremely thermally sensitive and require thermal tuning stable operation. This is achieved with integrated heaters in this work two aspects of the investigated: firstly, how to model heater-waveguide system a SiPho ring modulator. Secondly, improve energy efficiency by adapting design order minimize power consumed heater. Si...

Abstract This research studies the influence of local weld notch parameters on fatigue crack initiation sites in laser-hybrid butt welds, utilizing high-resolution 3D scans and tests to failure. The suitability different geometric for strength characterization is investigated, current challenges associated with their measurements are highlighted. shapes were found fluctuate significantly, resul...

Several mechanisms have been proposed to explain prolonged epileptiform afterdischarge, elicited by various forms of stimulation in chronically isolated cerebral cortex: (1) loss of a muscarinic inhibitory mechanism 26, (2) decrease in the enzyme activity responsible for inactivating transmitter substance zl, (3) proliferation of axon collaterals 2°, (4) deafferentation of inhibitory stellate c...

Using the Hatcher–Oertel algorithm for finding boundary slopes of Montesinos knots, we prove the Slope Conjecture and the Strong Slope Conjecture for a family of 3-tangle pretzel knots. More precisely, we prove that the maximal degrees of the colored Jones polynomial of such a knot determine a boundary slope as predicted by the Slope Conjecture, and that the linear terms in the degrees correspo...

Motivation: it would be great if we could understand the p-adic variation of the Up-eigenvalues of modular forms as the weights and/or levels varied. (More generally, it would be really great if we could understand how the local p-adic Galois representations attached to automorphic forms behave – for example, even very weak “equidistribution” results here would presumably imply very strong auto...

We show that for certain hyperbolic manifolds all boundary slopes are slopes of π1-injective immersed surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and hyperbolic two-bridge knots.