We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation q0 = i q2, q2 = i q0, α ⇀↽ γ. It is shown that the magnetic solution obtained with the help of the procedure used in Ref. [6], can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnet...

A circular holographic display that consists of phase-only spatial light modulators is used to reconstruct images in visible light from digital holograms recorded under infrared (10.6 μm) illumination. The reconstruction yields a holographic digital video display of a three-dimensional ghostlike image of an object floating in space where observers can move and rotate around it.

Supercoiling is introduced into DNAmolecules when the double helix is twisted around its own axis in three-dimensional space. Generally, DNAmolecules are negatively supercoiled inside cells, although the level of supercoiling is not equal throughout the genome and many supercoils may be constrained by bound proteins. Supercoiling increases the free energy of DNA and influences DNA metabolism by...

Let An be the free associative algebra with n generators over C, consider the Lie algebra A1 of its outer derivations (the derivations modulo the inner derivations). Let A0 be its quasi-classical limit, that it the Lie algebra of outer derivations of the free Poisson algebra with n generators over C. Boris Feigin conjectured around 1998 that the Lie algebras A0 and A1 are isomorphic. It turns o...

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation q0 = i q2, q2 = i q0, α ⇀↽ γ. It is shown that the magnetic solution obtained with the help of the procedure used in Ref. [6], can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnet...

We report a realization of three-dimensional (3D) electromagnetic void space. Despite occupying finite volume space, such medium is optically equivalent to an infinitesimal point where waves experience no phase accumulation. The 3D space realized by constructing all-dielectric photonic crystals that the effective permittivity and permeability vanish simultaneously, forming six-fold Dirac-like w...