Search Results (3)

We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane ${\mathbb{CP}}^2$. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in ${\mathbb{CP}}^n$ for $n>2$ is well known, the case $n=2$ remains open. By combining techniques from the classification of homogeneous CR-manifolds with projective foliation geometry, we prove that no homogeneous Levi-flat hypersurfaces exist in ${\mathbb{CP}}^2$, thus partially resolving the problem under natural symmetry assumptions. Full article

The T2K experiment is a long baseline neutrino oscillation experiment conducted in Japan. It aims to precisely measure the neutrino oscillation parameters by measuring the muon neutrino beam produced at the J-PARC accelerator complex at both near and far detectors. The magnetized T2K near detector complex ND280 plays an important role in measuring the neutrino interactions before the oscillations and constraining the systematic uncertainties in the measurements of neutrino oscillation parameters. The physics goals of T2K are to test Charge-Parity (CP) symmetry in the lepton sector, to precisely measure the neutrino oscillation parameters ${\theta }_{23}$ and $\Delta m_{32}^2$, and to determine the neutrino mass ordering and the octant of ${\theta }_{23}$. T2K has disfavored CP conservation with a significance level of $2\sigma$, and the higher significance level can be achieved by increasing the statistics and reducing the systematic uncertainties. Thus, the T2K collaboration proposed upgrading ND280 by replacing the P0D detector with a new fine-grained scintillator detector SuperFGD and two Time-Projection Chambers (TPCs). In addition, these new detectors will be covered by six Time Of Flight (TOF) planes. The performances of these upgrade detectors have been tested and confirmed to satisfy the requirements of the ND280 upgrade program. The physics performances of the upgraded ND280 have also been studied and they show promising improvements in neutrino interaction measurements by introducing transverse kinematics variables. Full article

The cocrystallization of trans-[PtI₂(NCN(CH₂)₅)₂] and iodoform (CHI₃) yields crystalline adduct trans-[PtI₂(NCN(CH₂)₅)₂]∙2CHI₃, the structure of which was studied via single-crystal X-ray diffractometry (XRD). In the XRD structure of trans-[PtI₂(NCN(CH₂)₅)₂]∙2CHI₃, apart from rather predictable C–H∙∙∙I hydrogen bonds (HBs) and C−I∙∙∙I halogen bonds (XBs) with the iodide ligands, we identified C–I∙∙∙Pt metal-involving XBs, where the platinum center functions as an XB acceptor (that includes a metal d_z²-orbital) toward the σ-holes of I atoms of CHI₃. DFT calculations (PBE-D3/jorge-TZP-DKH with plane waves in the GAPW method) were carried out in the CP2K program for isolated molecules, complex–iodoform clusters, and crystal models with periodic boundary conditions, where the noncovalent nature and the existence of the interactions were confirmed using charge analysis, Wiberg bond indexes, and QTAIM topology analysis of electron density, whereas the philicities of the noncovalent partners were proved using charge analysis, electron localization function, electron density deformation, and one-electron potential projections, as well as electron density/electrostatic potential profiles for cluster models and electrostatic potential surfaces (ρ = 0.001 a.u.) for isolated molecules. Full article