We prove an extension of Bourgain’s theorem on pinned distances in measurable subset of R2 of positive upper density, namely Theorem 1′ in [1], to pinned non-degenerate k-dimensional simplices in measurable subset of Rd of positive upper density whenever d ≥ k + 2 and k is any positive integer.

A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a repulsive or attractive linear potential too. We find that a pair of mutually symmetric peaks readily gives rise to the spontaneous symmetry breaking (SSB) o...

We present a pinned insect manipulator (IMp) constructed of LEGO® building bricks with two axes of movement and two axes of rotation. In addition we present three variants of the IMp to emphasise the modular design, which facilitates resizing to meet the full range of pinned insect specimens, is fully customizable, collapsible, affordable and does not require specialist tools or knowledge to as...

Given a hypergraph H with m hyperedges and a set X of m pins, i.e. globally fixed subspaces in Euclidean space R, a pinned subspaceincidence system is the pair (H,X), with the constraint that each pin in X lies on the subspace spanned by the point realizations in R of vertices of the corresponding hyperedge of H . We are interested in combinatorial characterization of pinned subspace-incidence ...

Beam-to-beam connections are widely used in steel structures, especially large floor applications and cases where they dictated by architectural restrictions. This type of connection is often designed without rotational restrictions (pinned connections), leading to relatively high bending capacity demands for the connected secondary beam, particularly when larger spans employed. A commonly prac...

A wide dynamic range CMOS image sensor based on a new active pixel structure with a pinned photodiode is proposed and evaluated with device simulations. The proposed pixel device has a linear and a logarithmic characteristics in low and high illumination region, respectively. The technique of direct detection of photodiode potential leads to a wide logarithmic response compared with the convent...