The convexity package for Hamiltonian actions on conformal symplectic manifolds

Consider a Hamiltonian action of a compact connected Lie group on a conformal symplectic manifold. We prove a convexity theorem for the moment map under the assumption that the action is of Lee type, which establishes an analog of Kirwan's convexity theorem in conformal symplectic geometry.Comment: 31 pages, 1 figure. Appendix on conformal presymplectic manifolds added. Minor mistakes correcte

Synthesis, crystal structure, luminescent, and photocatalytic properties of a uranyl(VI)-organic framework based on tripodal flexible zwitterionic ligand

The uranyl-organic framework based tripodal flexible zwitterion ligand 1,1',1''-[benzene-1,3,5-triyltris(methylene)] tris(pyridine-4-carboxylic acid) tribromine (H3LBr3), [(UO2)2(μ3-O)(μ2-OH)L]NO3·nH2O (n ≈ 5) (1) has been synthesized under hydrothermal condition and characterized by elemental analysis, IR spectroscopy, single-crystal X-ray diffraction, powder X-ray diffraction, thermogravimetric analysis, and UV-visible spectroscopy. Compound 1 contains a tetra-uranyl oxo-cluster, which displays a microporous 3D structure. The fluorescence measurement shows that 1 exhibits strong luminescence. Furthermore, 1 shows good photocatalytic activity for the degradation of methylene blue

DIP: Differentiable Interreflection-aware Physics-based Inverse Rendering

We present a physics-based inverse rendering method that learns the illumination, geometry, and materials of a scene from posed multi-view RGB images. To model the illumination of a scene, existing inverse rendering works either completely ignore the indirect illumination or model it by coarse approximations, leading to sub-optimal illumination, geometry, and material prediction of the scene. In this work, we propose a physics-based illumination model that explicitly traces the incoming indirect lights at each surface point based on interreflection, followed by estimating each identified indirect light through an efficient neural network. Furthermore, we utilize the Leibniz's integral rule to resolve non-differentiability in the proposed illumination model caused by one type of environment light -- the tangent lights. As a result, the proposed interreflection-aware illumination model can be learned end-to-end together with geometry and materials estimation. As a side product, our physics-based inverse rendering model also facilitates flexible and realistic material editing as well as relighting. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed method performs favorably against existing inverse rendering methods on novel view synthesis and inverse rendering

Can Outward Foreign Direct Investment in Producer Services Alleviate Premature Deindustrialization?

Deindustrialization is considered as a necessary path for industrial transformation in developed countries. In recent years, deindustrialization has also occurred in developing countries in the process of industrial transformation. However, many developing countries have started deindustrialization prematurely by transitioning to a service economy without experiencing full industrialization, which can negatively affect economic growth and even fall into a middle-income trap. Firstly, this paper analyzes whether there is premature deindustrialization in China. Secondly, it is argued that producer services outward foreign direct investment can promote the productivity improvement of manufacturing through reverse technology spillover effect and market competition effect. Finally, through the transmission path that producer services outward foreign direct investment leads to the increase of labor productivity of industry, and the increase of labor productivity of industry can alleviate the premature deindustrialization, this paper demonstrates the view that producer services outward foreign direct investment can alleviate the premature deindustrialization in China

And\^o dilations for a pair of commuting contractions: two explicit constructions and functional models

One of the most important results in operator theory is And\^o's \cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on a Hilbert space. While there are two explicit constructions (Sch\"affer \cite{sfr} and Douglas \cite{Doug-Dilation}) of the minimal isometric dilation of a single contraction, there was no such explicit construction of an And\^o dilation for a commuting pair $(T_1,T_2)$ of contractions, except in some special cases \cite{A-M-Dist-Var, D-S, D-S-S}. In this paper, we give two new proofs of And\^o's dilation theorem by giving both Sch\"affer-type and Douglas-type explicit constructions of an And\^o dilation with function-theoretic interpretation, for the general case. The results, in particular, give a complete description of all possible factorizations of a given contraction $T$ into the product of two commuting contractions. Unlike the one-variable case, two minimal And\^o dilations need not be unitarily equivalent. However, we show that the compressions of the two And\^o dilations constructed in this paper to the minimal dilation spaces of the contraction $T_1T_2$, are unitarily equivalent. In the special case when the product $T=T_1T_2$ is pure, i.e., if $T^{* n}\to 0$ strongly, an And\^o dilation was constructed recently in \cite{D-S-S}, which, as this paper will show, is a corollary to the Douglas-type construction. We define a notion of characteristic triple for a pair of commuting contractions and a notion of coincidence for such triples. We prove that two pairs of commuting contractions with their products being pure contractions are unitarily equivalent if and only if their characteristic triples coincide. We also characterize triples which qualify as the characteristic triple for some pair $(T_1,T_2)$ of commuting contractions such that $T_1T_2$ is a pure contraction.Comment: 24 page