Synthesis,Structure, and Properties of Scandium Dysprosium Antimonide ScDySb

Scandium dysprosium antimonide ScDySb was synthesized from scandium metal and DySb in an all‐solid state reaction at 1770 K. According to X‐ray analysis of the crystal structure [P4/nmm, Z = 4, a = 430.78(1) pm, c = 816.43(4) pm, R₁ = 0.0238, wR(all) = 0.0688, 268 independent reflections], ScDySb adopts the anti‐PbFCl type of structure, but with pronounced deviations in structural details, which are related to specific bonding interactions between the atoms involved. ScDySb shows antiferromagnetic ordering below 35.4 K, which was verified by susceptibility, heat capacity, and resistivity measurements. X‐ray structure determination, performed at 30 K, showed no significant structural changes to occur during the magnetic phase transition. The band structure was calculated in the framework of Density Functional Theory. The bonding properties are comparable to those of Sc₂Sb. Pronounced basins of the Electron Localization Function (ELF) appear in the tetragonal pyramidal Sc₄Dy voids.     

Global Continuity of the Integrated Density of States for Random Landau Hamiltonians

Abstract

We prove that the integrated density of states (IDS) for the randomly perturbed Landau Hamiltonian is Hölder continuous at all energies with any Hölder exponent 0 < q < 1. The random Anderson-type potential is constructed with a nonnegative, compactly supported single-site potential u. The distribution of the iid random variables is required to be absolutely continuous with a bounded, compactly supported density. This extends a previous result Combes et al. [Combes, J. M., Hislop, P. D., Klopp, F. (2003a). Hölder continuity of the integrated density of states for some random operators at all energies. Int. Math. Res. Notices 2003: 179--209] that was restricted to constant magnetic fields having rational flux through the unit square. We also prove that the IDS is Hölder continuous as a function of the nonzero magnetic field strength.     

Localized Sliced Inverse Regression

We develop a supervised dimension reduction method that integrates the idea of localization from manifold learning with the sliced inverse regression framework. We call our method localized sliced inverse regression (LSIR) since it takes into account the local structure of the explanatory variables. The resulting projection from LSIR is a linear subspace of the explanatory variables that captures the nonlinear structure relevant to predicting the response. LSIR applies to both classification and regression problems and can be easily extended to incorporate the ancillary unlabeled data in semi-supervised learning. We illustrate the utility of LSIR on real and simulated data. Computer codes and datasets from simulations are available online.     

Recent advances in mitochondria-and lysosomes-targeted small-molecule two-photon fluorescent probes

This review summarized the recent advances in small-molecule two-photon fl uorescent probes for monitoring a wide variety of biomolecules and changes inside micro-environment in mitochondria and lysosomes, or served as mitotracker and lysotracker with the assistance of two-photon microscopy.     

相位失配弹性平板复合波导中的缺陷态*

为了在弹性波波导中实现缺陷态的调控,该文基于相位失配原理设计了一种周期性平板波导结构。以正弦边界弹性波导为例,通过连接具有不同相位的两段波导结构,形成了弹性板中不同程度的缺陷,并分析了其谱带特性和能量局域化特征。结果表明,禁带中存在两个不同模式的缺陷态,其以透射峰形式出现并随着相位的改变产生频移。与此同时,两个缺陷态在空间上对应的应力场和位移场分布也具有不同的模态特征。该文提出的复合弹性波导缺陷态调控方法,不仅为研究弹性波与结构之间的内在联系提供了关键的理论支持,也为实际弹性波探测器件的设计提供重要参考。     

Phase Stability and Elastic Properties of Chromium Borides with Various Stoichiometries

Phase stability is important to the application of materials. By first‐principles calculations, we establish the phase stability of chromium borides with various stoichiometries. Moreover, the phases of CrB₃ and CrB₄ have been predicted by using a newly developed particle swarm optimization (PSO) algorithm. Formation enthalpy–pressure diagrams reveal that the MoB‐type structure is more energetically favorable than the TiI‐type structure for CrB. For CrB₂, the WB₂‐type structure is preferred at zero pressure. The predicted new phase of CrB₃ belongs to the hexagonal P‐6m2 space group and it transforms into an orthorhombic phase as the pressure exceeds 93 GPa. The predicted CrB₄ (space group: Pnnm) phase is more energetically favorable than the previously proposed Immm structure. The mechanical and thermodynamic stabilities of predicted CrB₃ and CrB₄ are verified by the calculated elastic constants and formation enthalpies. The full phonon dispersion calculations confirm the dynamic stability of WB₂‐type CrB₂ and predicted CrB₃. The large shear moduli, large Young’s moduli, low Poisson ratios, and low bulk and shear modulus ratios of CrB₄? PS_C and CrB₄? PS_D indicate that they are potential hard materials. Analyses of Debye temperature, electronic localization function, and electronic structure provide further understanding of the chemical and physical properties of these borides.     

Annihilating sets for the short time Fourier transform

We obtain a class of subsets of R2d such that the support of the short time Fourier transform (STFT) of a signal f∈L²(Rd) with respect to a window g∈L²(Rd) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L²-norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces.     

Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t→∞ of the L¹-norm of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established.     

Riemannian Superspaces,Exact Solutions and the Geometrical Meaning of the Field Localization

The geometrical origin of a special type of non-degenerate supermetric is elucidated and the connection with processes of topological origin in high energy physics is explained. The new mechanism of the localization of the fields in a particular sector of the supermanifold is explained and the similarity and differences with a 5-dimensional warped model are shown. The relation with gauge theories of supergravity based in the super SL(2,C) group is explicitly given and the possible original action is presented. From the point of view of the vacuum solutions, the simplest Riemannian superspaces are described.