On the Fukaya category of a Fano hypersurface in projective space

This paper is about the Fukaya category of a Fano hypersurface \(X \subset \mathbf {CP}^{n}\). Because these symplectic manifolds are monotone, both the analysis and the algebra involved in the definition of the Fukaya category simplify considerably. The first part of the paper is devoted to establishing the main structures of the Fukaya category in the monotone case: the closed–open string maps, weak proper Calabi–Yau structure, Abouzaid’s split-generation criterion, and their analogues when weak bounding cochains are included. We then turn to computations of the Fukaya category of the hypersurface \(X\): we construct a configuration of monotone Lagrangian spheres in \(X\), and compute the associated disc potential. The result coincides with the Hori–Vafa superpotential for the mirror of \(X\) (up to a constant shift in the Fano index 1 case). As a consequence, we give a proof of Kontsevich’s homological mirror symmetry conjecture for \(X\). We also explain how to extract non-trivial information about Gromov–Witten invariants of \(X\) from its Fukaya category.     

Rational design of a cationic polymer network towards record high uptake of 99TcO4-in nuclear waste

99Tc is a long-lived radionuclide present in large amounts as TcO4-anion in used nuclear fuel.Its removal from the waste stream is highly desirable because of i...     

The microwave spectra of cyanamide: Conclusions from a transitions

Microwave spectra have been observed for the species NH₂CN, NHDCN, ND₂CN, ¹⁵NH₂CN, NH₂C¹⁵N, ¹⁵ND₂CN and ND₂C¹⁵N. The nonplanar nature of the molecule is confirmed and the following structural parameters obtained N₁N₂ = 2.506 ± 0.002 Å, N₁C = 1.346 ± 0.005 Å, CN₂ = 1.160 ± 0.005 Å, N₁H = 1.001 ± 0.015 Å, HN?₁H = 113°31′ ± 2°, out of plane angle (see text) = 37°58′ ± 1°. (N₁ is the amino nitrogen atom and N₂ that the cyanide group.)     

A singlet aryl-CF3 carbene: 2-benzothienyl(trifluoromethyl)carbene and interconversion with a strained cyclic allene

Matrix-isolated 2-benzothienyl(trifluoromethyl)carbene was generated by irradiation of the corresponding diazirine, and characterized by IR and UV/vis spectroscopy, in situ trapping, and DFT modeling. Experiments and calculations indicate that the carbene is a ground-state singlet, in contrast to previously characterized aryl(trifluoromethyl)carbenes. The carbene could be interconverted photochemically with a ring-opened thioquinomethide and a highly strained cyclic allene.     

A device to achieve low Reynolds numbers in an open surface water channel

When investigating flow structures, and especially flow transitions, research projects often seek to increase insight using complementary numerical and physical experiments. Obtaining exact Reynolds number correspondence can frequently be difficult in experiments, particularly when relatively low values are required. Often, available test facilities were designed and optimised for a specific velocity range, meaning they have restrictions on the minimum flow velocity. This study describes a device to reduce the flow velocity locally in an open surface water channel. The underlying idea is to divert a controlled fraction of the incoming flow from the working section by increasing the pressure there, resulting in reduced velocity. This idea is realised using a ‘sub-channel’ that can be inserted into the main test chamber, with a variable porosity perforated screen at its downstream end. This study assesses and optimises the flow quality inside this structure, such as usable test section length, uniformity of the velocity profiles and turbulence intensity. The results demonstrate that the device creates high quality low Reynolds number flows, which is exemplified with the canonical circular cylinder in cross-flow.     

Synthesis of tetrafluorinated aromatic amino acids with distinct signatures in 19F NMR

Fluorinated amino acids serve as powerful tools in protein chemistry. We synthesized a series of para-substituted tetrafluorophenylalanines via the regioselective S(NAr) chemistry of the commercially available pentafluorophenylalanine Boc-Z. These novel unnatural amino acids display distinct (19)F NMR signatures, making them powerful tools for analyzing protein-membrane interactions with NMR spectroscopy.     

Generalized Yamaguchi correlation factor for coherent quadratic phase speckle metrology systems with an aperture

In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.