Bogomolov multipliers for some pp-groups of nilpotency class 2

The Bogomolov multiplier $B_0(G)$ of a finite group $G$ is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of $G$. The triviality of the Bogomolov multiplier is an obstruction to Noether's problem. We show that if $G$ is a central product of $G_1$ and $G_2$, regarding $K_i\leq Z(G_i), i=1,2$, and $\theta:G_1\to G_2$ is a group homomorphism such that its restriction $\theta\vert_{K_1}:K_1\to K_2$ is an isomorphism, then the triviality of $B_0(G_1/K_1), B_0(G_1)$ and $B_0(G_2)$ implies the triviality of $B_0(G)$. We give a positive answer to Noether's problem for all $2$-generator $p$-groups of nilpotency class $2$, and for one series of $4$-generator $p$-groups of nilpotency class $2$ (with the usual requirement for the roots of unity).Comment: This is the revised version which appeared in Acta Math. Sinica (English Series). arXiv admin note: text overlap with arXiv:1304.189

A contribution to the knowledge of the species Rafalskia olympica (KULCZYNSKI, 1903) (Opiliones, Phalangiidae, Phalangiinae)

Balkan populations of Rafalskia olympica (KULCZYNSKI, 1903) are distinguished as separate subspecies Rafalskia olympica bulgarica ST ARI::GA, 1963 novo stat. Certain novel details of the R. olympica female body structure are presented. It is stated that Metaplatybunus drenskii SILHAVY, 1965 is not a synonym of R. olympica

Quasi-2D dynamic jamming in cornstarch suspensions: visualization and force measurements

We report experiments investigating jamming fronts in a floating layer of cornstarch suspension. The suspension has a packing fraction close to jamming, which dynamically turns into a solid when impacted at a high speed. We show that the front propagates in both axial and transverse direction from the point of impact, with a constant ratio between the two directions of propagation of approximately 2. Inside the jammed solid, we observe an additional compression, which results from the increasing stress as the solid grows. During the initial growth of the jammed solid, we measure a force response that can be completely accounted for by added mass. Only once the jamming front reaches a boundary, the added mass cannot account for the measured force anymore. We do not, however, immediately see a strong force response as we would expect when compressing a jammed packing. Instead, we observe a delay in the force response on the pusher, which corresponds to the time it takes for the system to develop a close to uniform velocity gradient that spans the complete system.Comment: 7 pages, 7 figure

Digital optical phase conjugation of fluorescence in turbid tissue

We demonstrate a method for phase conjugating fluorescence. Our method, called reference free digital optical phase conjugation, can conjugate extremely weak, incoherent optical signals. It was used to phase conjugate fluorescent light originating from a bead covered with 0.5 mm of light-scattering tissue. The phase conjugated beam refocuses onto the bead and causes a local increase of over two orders of magnitude in the light intensity. Potential applications are in imaging, optical trapping, and targeted photochemical activation inside turbid tissue

A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1-dimensional and 2-dimensional systems