53 research outputs found

    On the \alpha-Invariants of Cubic Surfaces with Eckardt Points

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    In this paper, we show that the \alpha_{m,2}-invariant of a smooth cubic surface with Eckardt points is strictly bigger than 2/3. This can be used to simplify Tian's original proof of the existence of Kaehler-Einstein metrics on such manifolds. We also sketch the computations on cubic surfaces with one ordinary double points, and outline the analytic difficulties to prove the existence of orbifold Kaehler-Einstein metrics.Comment: 22 pages. We add a new section discussing singular stable cubic surface

    A Rapid Method for Detection of Salmonella in Milk Based on Extraction of mRNA Using Magnetic Capture Probes and RT-qPCR

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    Magnetic separation is an efficient method for target enrichment and elimination of inhibitors in the molecular detection systems for foodborne pathogens. In this study, we prepared magnetic capture probes by modifying oligonucleotides complementary to target sequences on the surface of amino-modified silica-coated magnetic nanoparticles and optimized the conditions and parameters of probe synthesis and hybridization. We innovatively put the complexes of magnetic capture probes and target sequences into qPCR without any need for denaturation and purification steps. This strategy can reduce manual steps and save time. We used the magnetic capture probes to separate invA mRNA from Salmonella in artificially contaminated milk samples. The detection sensitivity was 104 CFU/ml, which could be increased to 10 CFU/ml after a 12 h enrichment step. The developed method is robust enough to detect live bacteria in a complex environmental matrix

    Observation of first-order quantum phase transitions and ferromagnetism in twisted double bilayer graphene

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    Twisted graphene multilayers are highly tunable flatband systems for developing new phases of matter. Thus far, while orbital ferromagnetism has been observed in valley polarized phases, the long-range orders of other correlated phases as well as the quantum phase transitions between different orders mostly remain unknown. Here, we report an observation of Coulomb interaction driven first-order quantum phase transitions and ferromagnetism in twisted double bilayer graphene (TDBG). At zero magnetic field, the transitions are revealed in a series of step-like abrupt resistance jumps with prominent hysteresis loop when either the displacement field (D) or the carrier density (n) is tuned across symmetry-breaking boundary near half filling, indicating a formation of ordered domains. It is worth noting that the good turnability and switching of these states gives a rise to a memory performance with a large on/off ratio. Moreover, when both spin and valley play the roles at finite magnetic field, we observe abundant first-order quantum phase transitions among normal metallic states from charge neutral point, orbital ferromagnetic states from quarter filling, and spin-polarized states from half filling. We interpret these first-order phase transitions in the picture of phase separations and spin domain percolations driven by multi-field tunable Coulomb interactions, in agreement with Lifshitz transition from Hartree-Fock calculations. The observed multi-filed tunable domain structure and its hysteresis resembles the characteristics of multiferroics, revealing intriguing magnetoelectric properties. Our result enriches the correlated phase diagram in TDBG for discovering novel exotic phases and quantum phase transitions, and it would benefit other twisted moir\'e systems as well