Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schr\"odinger Equations

We consider the existence and stability of real-valued, spatially antiperiodic standing wave solutions to a family of nonlinear Schr\"odinger equations with fractional dispersion and power-law nonlinearity. As a key technical result, we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations, i.e. that its kernel is generated by the translational and gauge symmetries of the governing evolution equation. In the process, we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional Schr\"odinger operators on $\mathbb{R}$ with real-valued, periodic potentials as well as a Sturm-Liouville type oscillation theory for the higher antiperiodic eigenfunctions.Comment: 46 pages, 2 figure

The recovery of microwave scattering parameters from scatterometric measurements with special application to the sea

As part of an effort to demonstrate the value of the microwave scatterometer as a remote sea wind sensor, the interaction between an arbitrarily polarized scatterometer antenna and a noncoherent distributive target was derived and applied to develop a measuring technique to recover all the scattering parameters. The results are helpful for specifying antenna polarization properties for accurate retrieval of the parameters not only for the sea but also for other distributive scenes

Toward RADSCAT measurements over the sea and their interpretation

Investigations into several areas which are essential to the execution and interpretation of suborbital observations by composite radiometer - scatterometer sensor (RADSCAT) are reported. Experiments and theory were developed to demonstrate the remote anemometric capability of the sensor over the sea through various weather conditions. It is shown that weather situations found in extra tropical cyclones are useful for demonstrating the all weather capability of the composite sensor. The large scale fluctuations of the wind over the sea dictate the observational coverage required to correlate measurements with the mean surface wind speed. Various theoretical investigations were performed to establish a premise for the joint interpretation of the experiment data. The effects of clouds and rains on downward radiometric observations over the sea were computed. A method of predicting atmospheric attenuation from joint observations is developed. In other theoretical efforts, the emission and scattering characteristics of the sea were derived. Composite surface theories with coherent and noncoherent assumptions were employed

Field trial for assessment of avian influenza vaccination effectiveness in Indonesia

The aim of this field study was to determine the efficacy of vaccination against highly pathogenic avian influenza (HPAI) virus strain H5N1 in Indonesia. A limited, prototype clinical trial was performed using a standardised treatment group, in which poultry flocks were vaccinated at least twice with a selected H5N1 vaccine, and a control group comprising flocks treated with nonstandardised procedures chosen by the farmer. Each group consisted of six flocks comprising either layers or native chickens. Haemagglutination inhibition (HI) antibody levels were determined by regular serum sampling, and outbreak surveillance relied on non-Al-vaccinated sentinel birds. After three vaccinations high antibody titres were produced in the treatment group, and the percentage of layers with an HI titre > 40 was approximately 90%. Although no conclusions can be drawn regarding reduction of virus transmission, this study demonstrated that 11 farms remained free from Al during the observation period, and that a surveillance programme based on differentiating infected from vaccinated animals (DIVA) can be implemented

Controlling the magnetic state of the proximate quantum spin liquid α-RuCl₃ with an optical cavity

Harnessing the enhanced light-matter coupling and quantum vacuum fluctuations resulting from mode volume compression in optical cavities is a promising route towards functionalizing quantum materials and realizing exotic states of matter. Here, we extend cavity quantum electrodynamical materials engineering to correlated magnetic systems, by demonstrating that a Fabry-Pérot cavity can be used to control the magnetic state of the proximate quantum spin liquid α-RuCl3. Depending on specific cavity properties such as the mode frequency, photon occupation, and strength of the light-matter coupling, any of the magnetic phases supported by the extended Kitaev model can be stabilized. In particular, in the THz regime, we show that the cavity vacuum fluctuations alone are sufficient to bring α-RuCl3 from a zigzag antiferromagnetic to a ferromagnetic state. By external pumping of the cavity in the few photon limit, it is further possible to push the system into the antiferromagnetic Kitaev quantum spin liquid state

Recent developments in the rapid analysis of plants and tracking their bioactive constituents

Natural products chemistry has witnessed many new developments in the last 5 years like extractions with subcritical water and ionic liquids, LC/HRMS and LC/SPE/cryo-NMR, UHPLC, TLC/MS, MS-based preparative HPLC, comprehensive chromatography (GC × GC, LC × LC), high-throughput screening, introduction of monolithic columns, miniaturisation, and automated structure identification. Nevertheless identifying bioactive constituents in complex plant extracts remains a tedious process. The classical approach of bioassay guided fractionation is time-consuming while off-line screening of extracts does not provide information on individual compounds and sometimes suffers from false positives or negatives. One way out of this is by coupling chromatography with chemical or biochemical assays, so called high resolution screening. An example is the development of HPLC on-line assays for antioxidants. By the post-column addition of a relatively stable coloured radical like DPPH¿ or ABTS¿+, radical scavengers are detected as negative peaks because in a reaction coil they reduce the model radical to its reduced, non-coloured form. When combined with LC/DAD/MS and LC/SPE/NMR, reliable identification of active constituents becomes possible without the necessity of ever isolating them in a classical sense. Also for finding leads for new drugs, combining HPLC with biochemical assays is interesting but technically more difficult. Most enzymes do not work at the organic modifier concentrations commonly encountered in RP-HPLC and the reaction time is often longer requiring dilution and lengthy coils respectively. Therefore, new techniques have to be implemented to gain the required sensitivity for on-line enzyme assays. For stable analytes, high temperature LC offers a solution to the organic modifier problem. When enzymes are highly expensive, like those used in the screening for Cytochrome P450 inhibitors, miniaturisation to chip format may offer a way out. Microreactors (chips) are not only useful for miniaturising larger assays but also offer completely new prospects in phytochemical analysis. One such application is in the sample clean-up of acids and bases like alkaloids. In a lay-out of three parallel channels of 100 ¿m width with the middle one containing organic phase and the two outer ones water of high pH (feed phase) and low pH (trapping phase) such a chip replaces two classical LLE steps but is much faster and requires less solvents and less manpower input