i,j(−1) q rkH (D) is the Jones polynomial of L. The groups H (D) were defined as homology groups of a bigraded chain complex. Khovanov proved that the homology groups considered up to isomorphism depend only on the link L. In fact, he showed that any Reidemeister move induces a chain equivalence (of bidegree (0, 0)) between the chain complexes of the two diagrams involved. Khovanov acknowledged...

Let (M, ∆, g) be a sub-Riemannian manifold and x0 ∈ M . Assuming that Chow’s condition holds and that M endowed with the subRiemannian distance is complete, we prove that there exists a dense subset N1 of M such that for every point x of N1, there is a unique minimizing path steering x0 to x, this trajectory admitting a normal extremal lift. If the distribution ∆ is everywhere of corank one, we...

The three-dimensional flow around a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow is studied numerically by solving the full Navier-Stokes equations in a boundary-fitted domain. The main goal of the present study is to provide a complete description of the forces experienced by the bubble (drag, lift and added mass) over a wide range of sliding and shear Reyn...

The complete, historical closed-form steep lifting entry trajectory solution is documented and developed from first principles. The efficacy and accuracy of the solution is assessed for application to aeroassist missions of interest, including aerocapture and entry. Specifically, analytical assessment of the primary assumptions in the solution shows the solution is applicable across a wide rang...

In this work, we introduce a novel method for enhanced particle filtration using shear-modulated inertial migration in straight microchannels. Depending on their size, inertial lift causes particles to migrate toward microchannel walls. Using microchannels with high aspect ratio cross sections, the fluidic shear can be modulated, resulting in preferential equilibration of particles along the lo...

we show that in {bf zf} set theory without choice, the ultrafilter mbox{principle} ({bf up}) is equivalent to several compactness theorems for alexandroff discrete spaces and to rudin's lemma, a basic tool in topology and the theory of quasi-continuous domains. important consequences of rudin's lemma are various lift lemmas, saying that certain properties of posets are inherited by th...

Similar to random sea waves, forces on the offshore structures due to waves are random. These forces can be mainly divided into two components, namely, inline forces and transverse or lift forces. The random nature of lift forces is more complicated than that of inline forces and both should be combined for design purposes. In the present paper, two different approaches have been used to determ...

In this study, a numerical computational fluid dynamics study is conducted in order to predict the aerodynamic forces on the NP car. The turbulent air flow around the car is modeled using the realizable k-ε model. First, results are validated against those presented for the Ahmed’s body. Next, the fluid flow around the car is simulated for different car speeds ( to mph) and fl...

In the popular FOX TV reality show, American Idol, the judges, who are presumably experts in evaluating singing effort, have no voting power when the field is narrowed to the top 24 contestants. It is only the votes of viewers that count. In the 2007 season of the show, one of the judges, Simon Cowell, threatened to quit the show if a contestant, Sanjaya Malakar, who was clearly a low-ability c...

We investigate /xpoint operators for domain equations. It is routine to verify that if every endofunctor on a category has an initial algebra, then one can construct a /xpoint operator from the category of endofunctors to the category. That construction does not lift routinely to enriched categories, using the usual enriched notion of initiality of an endofunctor. We show that by embedding the ...