Any p, q ∈ R2 together with the origin determine a pinned triangle. We prove that any finite set S contained in an irreducible algebraic curve C of degree d in R2 determines Ωd(|S| 4/3) distinct pinned triangle areas, unless C is a line, or an ellipse or hyperbola centered at the origin. This improves the bound Ω(|S|5/4) obtained by Charalambides [1]. The proof is based on that of Pach and De Z...

In the past, stability of an undamped clamped-pinned pipe conveying fluid has been always considered numerically leading to controversial results. Païdoussis (2004) has shown that a numerical stability analysis of a clamped-pinned pipe requires exceptionally large number of vibration modes to obtain the correct dynamical behaviour. In this paper, analytical proof of stability of a clamped-pinne...

The fine control of the exchange coupling strength and blocking temperature ofexchange bias systems is an important requirement for the development of magnetoresistive sensors with two pinned electrodes. In this paper, we successfully tune these parameters in top- and bottom-pinned systems, comprising 5 nm thick Co40Fe40B20 and 6.5 nm thick Ir22Mn78 films. By inserting Ru impurities at differen...

California's boldness stemmed in part from the attitude of its governor, Arnold Schwarzenegger, a Republican who has been outspoken in his determination to combat global warming. " There are some issues in the world that are simply so compelling, whether in the United States or in the United Kingdom, that demand us to put aside our partisan differences and attack them head on, " Schwarzenegger ...

Rotating vortices are easily pinned to any defects in excitable media. Moderate advective fields cannot remove the pinned vortices. We have found and tested experimentally a mechanism for unpinning a vortex. To unpin a vortex, we created additional waves close to its core. A vortex can be unpinned when a new created wave is pinned to the same obstacle and has a topological defect. This mechanis...

In this paper, we study the controllability of networks with different numbers of communities and various strengths of community structure. By means of simulations, we show that the degree descending pinning scheme performs best among several considered pinning schemes under a small number of pinned nodes, while the degree ascending pinning scheme is becoming more powerful by increasing the num...

Pinning of spiral waves by defects in cardiac muscle may cause permanent tachycardia. We numerically study the removal of a pinned spiral by a localized stimulus at the boundary of a two-dimensional excitable medium. It is shown that target waves may be generated by an external local force, and then the target waves will interact with the pinned spiral. When the external force is appropriately ...

Answering a question of Kechris, I show that the equality of countable sets of reals is not the smallest unpinned equivalence relation.