On the twistor space of a quaternionic contact manifold

In this note, we prove that the CR manifold induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard.     

A dynamic model for road protection against flooding

This paper focuses on the problem of identifying optimal protection strategies to reduce the impact of flooding on a road network. We propose a dynamic mixed-integer programming model that extends the classic concept of road network protection by shifting away from single-arc fortifications to a more general and realistic approach involving protection plans that cover multiple components. We also consider multiple disruption scenarios of varying magnitude. To efficiently solve large problem instances, we introduce a customised GRASP heuristic. Finally, we provide some analysis and insights from a case study of the Hertfordshire road network in the East of England. Results show that optimal protection strategies mainly involve safeguarding against flooding events that are small and likely to occur, whereas implementing higher protection standards are not considered cost-effective.     

Structure and ion exchange properties of a new cobalt borate with a tunnel structure "templated" by Na+

The new anhydrous borate Na2Co2B12O21 has been synthesized by flux methods and studied by single-crystal X-ray diffraction (space group I2/a with a = 17.1447(15) A, b = 4.5530(5) A, c = 19.4408(15) A, beta = 103.212(5) degrees , V = 1477.4(2) A3, Z = 4). Refinement of its structure reveals it is the first metaborate exhibiting a tunnel network, with internal dimensions of 4.5 x 8.8 A2. Further single-crystal diffraction studies show that the Na+ ions within the tunnels are exchangeable with Li+ along with the absorption of water molecules to form Li2(H2O)2Co2B12O21, making this compound a unique non-siliceous zeotype.     

Quantum-limited noise performance of a mode-locked laser diode

Low-noise operation of a 9-GHz hybridly mode-locked laser diode is demonstrated. The integrated timing jitter was 47 fs (10 Hz to 10 MHz) and 86 fs (10 Hz to 4.5 GHz), with a pulse width of 6.7 ps. The noise performance as a function of filter bandwidth and oscillator noise is also addressed.     

Ground state of magnetic dimers on metal surfaces

We present model studies of the ground state for magnetic dimers on metal surfaces. We find it can be neither ferromagnetic nor antiferromagnetic, but is often canted for nearest neighbors. Thus, the system cannot be described using bilinear exchange. We give a criterion which can be used quite generally to interrogate the local stability of ferromagnetically or antiferromagnetically aligned dimers, and which also may be used to infer the canting angle when canted states are stable.     

Low temperature solid-state NMR experiments of half-integer quadrupolar nuclides: caveats and data analysis

Solid-state NMR spectroscopy of half-integer quadrupolar nuclides has received a lot of interest recently with the advent of new methodologies and higher magnetic fields. We present here the extension of our previous low temperature method to an 18.8T system. This new probe entailed a total redesign including a cross coil and variable capacitors that are operational at cryogenic temperatures. The limitations to sensitivity are also discussed; including a new diode network, the utilization of a cryogenic band pass filter, and the consequences of the RF profiles of the coil. Further, details of the spectroscopy of quadrupolar nuclei in a protein are discussed, such as the observation of the outer transitions and how to distinguish them from the desired +/-1/2 transition.     

An alternate proof of Cohn's four squares theorem

While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques.