Self-Similar Tilings of Fractal Blow-Ups

New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produces a usually infinite family of tilings that satisfy the following properties: (1) the prototile set is finite; (2) the tilings are repetitive (quasiperiodic); (3) each family contains self-similartilings, usually infinitely many; and (4) when the IFS is rigid in an appropriate sense, the tiling has no non-trivial symmetry; in particular the tiling is non-periodic

Cross-Power Spectrum and Its Application on Window Functions in the WMAP data

Cross-power spectrum is a quadratic estimator between two maps that can provide unbiased estimate of the underlying power spectrum of the correlated signals, which is therefore used for extracting the power spectrum in the WMAP data. In this paper we discuss the limit of cross-power spectrum and derive the residual from uncorrelated signal, which is the source of error in power spectrum extraction. We employ the estimator to extract window functions by crossing pairs of extragalactic point sources. We desmonstrate its usefulness in WMAP Difference Assembly maps where the window functions are measured via Jupiter and then extract the window functions of the 5 WMAP frequency band maps.Comment: added the part of applying cross power spectrum on WMAP DA maps and frequency band maps and submitted to Ap

Radio Regulation Development and Radio Spectrum Analysis of Earth Station in Motion Service

Although Earth Station in Motion (ESIM) services are widely used and there is a huge market demand around the world, International Telecommunication Union (ITU) does not have unified conclusion for the use of ESIM yet. ESIM are Mobile Satellite Services (MSS) due to its mobile-based attributes, while multiple administrations want to use ESIM in Fixed Satellite Service (FSS). However, Radio Regulations (RR) have strict distinction between MSS and FSS. In this case, ITU has been very controversial because this kind of application will violate the RR Article and the conflict will bring risks to the global deployment. Thus, this paper illustrates the development of rules, regulations, standards concerning ESIM and the radio spectrum usage of ESIM in different regions around the world. Firstly, the basic rules, standard and definition of ITU’s Radiocommunication Sector (ITU-R) is introduced. Secondly, the World Radiocommunication Conference (WRC) agenda item on radio spectrum allocation for ESIM, e.g. in C/Ku/Ka band, is introduced and multi-view on the radio spectrum allocation is elaborated, especially on 19.7-20.2 GHz & 29.5-30.0 GHz. Then, some ITU-R Recommendations and Reports are analyzed on the specific technique to enable these ESIM to communicate with Geostationary Earth Orbit Satellite (GSO) space stations in the FSS without causing interference at levels in excess of that caused by conventional FSS earth stations. Meanwhile, the opposite opinion on not allocating EISM service in FSS frequency band is also elaborated. Finally, based on the ESIM’s future application, the ITU-R standards development trend is forecasted. In conclusion, using radio spectrum resource in an equitable, rational and efficient manner is the basic guideline of ITU. Although it is not a good approach to obstruct the revise of RR when there is a large demand for radio spectrum resource in satellite industry, still the propulsion and global demand of the whole industry may face difficulties on the unclear application in modify rules of RR

Self-evolving ghost imaging

Ghost imaging can capture 2D images with a point detector instead of an array sensor. It therefore offers a solution to the challenge of building area format sensors in wavebands where such sensors are difficult and expensive to produce and opens up new imaging modalities due to high-performance single-pixel detectors. Traditionally, ghost imaging retrieves the image of an object offline, by correlating measured light intensities and applied illuminating patterns. Here we present a feedback-based approach for online updating of the imaging result that can bypass post-processing, termed self-evolving ghost imaging (SEGI). We introduce a genetic algorithm to optimize the illumination patterns in real-time to match the objects shape according to the measured total light intensity. We theoretically and experimentally demonstrate this concept for static and dynamic imaging. This method opens new perspectives for real-time ghost imaging in applications such as remote sensing (e.g. machine vision, LiDAR systems in autonomous vehicles) and biological imaging

Self-evolving ghost imaging

Funding Australian Research Council (DE200100074, DP190101058); China Scholarship Council (201607950009, 201706020170); University of Technology Sydney. Acknowledgment We thank Prof. Fengli Gao from Jilin University for the helpful discussion about PGPeer reviewedPublisher PD

Path-integral quantization of tensionless (super) string

In this work, we study the tensionless (super)string in the formalism of path-integral quantization. We introduce BMS $bc$ and $\beta\gamma$ ghosts intrinsically by accounting for the Faddeev-Popov determinants appeared in fixing the gauges. We then do canonical quantization and obtain the critical dimensions for different tensionless strings. We find that among four kinds of tensionless superstrings, the $\mathcal{N}=2$ homogeneous and inhomogeneous doublet tensionless superstrings have the same critical dimension as the usual superstrings. Taking the BMS $bc$ and $\beta\gamma$ ghosts as new types of BMS free field theories, we find that their enhanced underlying symmetries are generated by BMS-Kac-Moody algebras, with the Kac-Moody subalgebras being built from a three-dimensional non-abelian and non-semi-simple Lie algebra.Comment: 46 pages, 1 table; v2: typos correcte

(5,5′-Dicarboxy­biphenyl-2,2′-dicarboxyl­ato-κ2 O 2,O 2′)bis­(1,10-phenanthroline-κ2 N,N′)zinc(II) dihydrate

In the title compound, [Zn(C16H8O8)(C12H8N2)2]·2H2O, the ZnII atom is located on a twofold rotation axis and is six-coordinated by two O atoms from a 5,5′-dicarboxy­biphenyl-2,2′-dicarboxyl­ate ligand and four N atoms from two 1,10-phenanthroline mol­ecules in a distorted octa­hedral geometry. The crystal structure involves O—H⋯O hydrogen bonds