This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for margina...

The surface alignment of lyotropic chromonic liquid crystals can not only be planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is d...

AIMS Isolation of the genes relative to PCB biodegradation and identification of the bph gene function in Rhodococcus sp. R04. METHODS AND RESULTS A 8.7-kb fragment carrying the biphenyl catabolic genes bphABCD was isolated from the gene library in Rhodococcus sp. R04. Based on the deduced amino acid sequence homology, seven bph genes, bphA1A2A3A4, bphB, bphC and bphD, were thought to be resp...

The substitution of aqua ligands of mononuclear Pt(II) complexes of the general form [Pt(H(2)O)(N,N-bis(2-pyridylmethyl)-N(CH(2))(n)-CH(3); -NC(CH(3))(3); -NH](CF(3)SO(3))(2), n = 1 (bpea); 2 (bppa); 3 (bpba); 5 (bpha), 9 (bpda) -NC(CH(3))(3) (bpbta) and -NH (bpma) by thiourea nucleophiles was investigated under pseudo first-order conditions as a function of concentration and temperature using ...

X. Zhao and co-workers develop on page 4035 a new biocompatible hydrogel system that is extremely tough and stretchable and can be 3D printed into complex structures, such as the multilayer mesh shown. Cells encapsulated in the tough and printable hydrogel maintain high viability. 3D-printed structures of the tough hydrogel can sustain high mechanical loads and deformations.

Three-dimensional (3D) printing is a rapidly evolving technology with several potential applications in the diagnosis and management of cardiac disease. Recently, 3D printing (i.e. rapid prototyping) derived from 3D transesophageal echocardiography (TEE) has become possible. Due to the multiple steps involved and the specific equipment required for each step, it might be difficult to start impl...

Conventional education results in unsatisfactory morphological understanding of acetabular fractures due to lack of three-dimensional (3D) details and tactile feedback of real fractures. Virtual reality (VR) and 3D printing (3DP) techniques are widely applied in teaching. The purpose of this study was to identify the effect of physical model (PM), VR and 3DP models in education of morphological...

We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker–Planck equation and the Burgers equation are considered as examples. Using reducibility of them to the one-dimensional linear heat equation, we construct complete hierarchies of local and potential conservati...