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.

The stability of slope, both on the slope work and final is a very important aspect stability, in open pit mining activities. inconsistency slopes will result collapse rocks around excavation site. This happens because condition rock when it has not been excavated generally balanced. However, due to discontinuous patterns that occur other than naturally also activities such as excavation, blast...

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.

Introduction The field of cell-death research has matured since pioneering discoveries showed that apoptosis is regulated genetically. Although many of the core caspase-signalling pathways are known, some of the most basic aspects of the biochemistry of mitochondrial apoptosis induction have remained elusive and are, in certain cases, controversial. Research on the metabolic dysfunction that oc...

Although water vapor is the most important greenhouse gas, it is not even agreed whether an increase in its concentration due to global warming will cause more warming or cooling. Warming (a positive feedback) will occur if the biggest effect is to absorb more outgoing long-wave radiation. Cooling (a negative feedback) will occur if the major result is to form more clouds, which would reflect m...

Rockfall in open pit mining using explosives is the most method of operation. Also, addition to technical and economic advantages, this extraction produces effects that can have a negative impact area near quarry. The blasting are such as seismic waves produce vibrations, air overpressure (noise), rock throws toxic gases. If intensity extent these not properly anticipated assessed, serious cons...

In a bivariate data plot, every two points determine an “elementary slope.” For n points with distinct x-values, there are n(n – 1)/2 elementary slopes. These elementary slopes are examined under the two classical regression assumptions: (1) the regressor variable values are fixed and the error is independent and normal, and (2) the data is bivariate normal. For case (1), it is demonstrated tha...