Koll\'ar's Package for Twisted Saito's S-sheaves

We generalize Koll\'ar's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$-sheaves twisted by a $\mathbb{Q}$-divisor. This gives a uniform treatment for various kinds of Koll\'ar's package in different topics in complex geometry. As a consequence we prove Koll\'ar's package of pluricanonical bundles twisted by a certain multiplier ideal sheaf. The method of the present paper is $L^2$-theoretic.Comment: Comments are welcom

L2L^2-Dolbeault resolution of the lowest Hodge piece of a Hodge module

Let $X$ be a complex space and $M$ a pure Hodge module with strict support $X$. The purpose of this paper is to introduce a coherent subsheaf $S(M,\varphi)$ of M. Saito's $S(M)$ which is a combination of $S(M)$ and the multiplier ideal sheaf $\mathscr{I}(\varphi)$ while constructing a resolution of $S(M,\varphi)$ by differential forms with certain $L^2$-boundary conditions. This could be viewed as a wide generalization of MacPherson's conjecture on the $L^2$-representation of the Grauert-Riemenschneider sheaf. As applications, various vanishing theorems for $S(M)$ (Saito's vanishing, Kawamata-Viehweg vanishing and some new ones like Nadel vanishing, partial vanishing) are proved via standard differential geometrical arguments.Comment: 25 pages. Comments are welcome

Hyperbolicity of the base of an admissible family of log canonical stable minimal models

We investigate the stratified hyperbolicity properties of Birkar's moduli stack of log canonical (lc) stable minimal models. The main technical result is a construction of Viehweg-Zuo's system of Higgs sheaves associated with an admissible family of lc stable minimal models, using the theory of degenerations of Hodge structure and non-abelian Hodge theory.Comment: 34 pages. Some typos are fixed. Comments are welcom

An Improved NMS-Based Adaptive Edge Detection Method and Its FPGA Implementation

For improving the processing speed and accuracy of edge detection, an adaptive edge detection method based on improved NMS (nonmaximum suppression) was proposed in this paper. In the method, the gradient image was computed by four directional Sobel operators. Then, the gradient image was processed by using NMS method. By defining a power map function, the elements values of gradient image histogram were mapped into a wider value range. By calculating the maximal between-class variance according to the mapped histogram, the corresponding threshold was obtained as adaptive threshold value in edge detection. Finally, to be convenient for engineering application, the proposed method was realized in FPGA (Field Programmable Gate Array). The experiment results demonstrated that the proposed method was effective in edge detection and suitable for real-time application

Earth Shielding and Daily Modulation from Electrophilic Boosted Dark Particles

Boosted dark particles of astrophysical origin can lead to nonstandard nuclear or electron recoil signals in direct detection experiments. %It has been shown that this interpretation successfully explains the excess of keV electron recoil events recently observed by the XENON1T experiment, and that a daily modulation of the signal in the detector is expected. We conduct an investigation of the daily modulation feature of a potential future signal of this type. In particular, we perform simulations of the dark particle interactions with electrons in atoms building up the Earth on its path to the detector, and provide in-depth predictions for the expected daily changes in the signal for various direct detection experiments, including XENONnT, PandaX, and LUX-ZEPLIN.Comment: 15 pages, 12 figures, published version in PRD. For the code to calculate the atomic ionization form factor, see https://github.com/XueXiao-Physics/AtomIonCalc (AtomIonCalc) . For the Monte Carlo simulation of the electrophilic dark particles traveling inside the earth, see https://github.com/XueXiao-Physics/realEarthScatterDM (realEarthScatterDM

Temperature-dependent structure of an intermetallic ErPd2_2Si2_2 single crystal: A combined synchrotron and in-house X-ray diffraction study

We have grown intermetallic ErPd$_2$Si$_2$ single crystals employing laser-diodes with the floating-zone method. The temperature-dependent crystallography was determined using synchrotron and in-house X-ray powder diffraction measurements from 20 to 500 K. The diffraction patterns fit well with the tetragonal $I$4/$mmm$ space group (No. 139) with two chemical formulas within one unit cell. Our synchrotron X-ray powder diffraction study shows that the refined lattice constants are $a$ = 4.10320(2) {\AA}, $c$ = 9.88393(5) {\AA} at 298 K and $a$ = 4.11737(2) {\AA}, $c$ = 9.88143(5) {\AA} at 500 K, resulting in the unit-cell volume $V$ = 166.408(1) {\AA}$^3$ (298 K) and 167.517(2) {\AA}$^3$ (500 K). In the whole studied temperature range, we did not find any structural phase transition. Upon cooling, the lattice constants a and c are shortened and elongated, respectively.Comment: 5 Figures, 4 Table