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Structure Polynomials and Subgraphs of Rooted Regular Trees

Algebra Colloquium 2018年第1期25卷 45-70页

作者： Daniele D'Angeli Alfredo donno Institut ffir Diskrete Mathematik Technische Universitat Graz Steyrergasse 30 8010 Graz Austria universitg degli studi niccolo cusano - via don carlo gnocchi 300166 Roma Italia

We introduce an algebraic structure allowing us to describe subgraphs of a regular rooted tree. Its elements are called structure polynomials, and they are in a one- to-one correspondence with the set of all subgraphs of the tree. We define two operations, the sum and the product of structure polynomials, giving a graph interpretation of them. Then we introduce an equivalence relation between polynomials, using the action of the full automorphism group of the tree, and we count equivalence classes of subgraphs modulo this equivalence. We also prove that this action gives rise to symmetric Gelfand pairs. Finally, when the regularity degree of the tree is a prime p, we regard each level of the tree as a finite dimensional vector space over the finite field Fp, and we are able to completely characterize structure polynomials corresponding to subgraphs whose leaf set is a vector subspace.

关键词： rooted tree structure polynomial rooted subtree automorphism group of a tree Gelfand pair

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Metal-Halide Perovskite Submicrometer-Thick Films for Ultra-Stable Self-Powered Direct X-Ray Detectors

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Nano-Micro Letters 2024年第9期16卷 410-431页

作者： Marco Girolami Fabio Matteocci Sara Pettinato Valerio Serpente Eleonora Bolli Barbara Paci Amanda Generosi Stefano Salvatori Aldo Di carlo Daniele M.Trucchi CNR‑ISM Consiglio Nazionale delle RicercheIstituto di Struttura della MateriaSede Secondaria di MontelibrettiDiaTHEMA LabStrada Provinciale 35D900010 MontelibrettiRomeItaly CHOSE–Centre for Hybrid and Organic Solar Energy Department of Electronic EngineeringUniversity of Rome“Tor Vergata”Via del Politecnico 100133 RomeItaly Faculty of Engineering Universita degli Studi Niccolo CusanoVia don Carlo Gnocchi 300166 RomeItaly SpecXLab CNR‑ISMConsiglio Nazionale Delle RicercheIstituto di Struttura Della MateriaArea della Ricerca di Tor VergataVia del Fosso del Cavaliere 10000133 RomeItaly

Metal-halide perovskites are revolutionizing the world of X-ray detectors,due to the development of sensitive,fast,and cost-effective ***-powered operation,ensuring portability and low power consumption,has also been recently demonstrated in both bulk materials and thin ***,the signal stability and repeatability under continuous X-ray exposure has only been tested up to a few hours,often reporting degradation of the detection *** it is shown that self-powered direct X-ray detectors,fabricated starting from a FAPbBr_(3)submicrometer-thick film deposition onto a mesoporous TiO_(2)scaffold,can withstand a 26-day uninterrupted X-ray exposure with negligible signal loss,demonstrating ultra-high operational stability and excellent *** structural modification is observed after irradiation with a total ionizing dose of almost 200 Gy,revealing an unexpectedly high radiation hardness for a metal-halide perovskite thin *** addition,trap-assisted photoconductive gain enabled the device to achieve a record bulk sensitivity of 7.28 C Gy^(−1)cm^(−3)at 0 V,an unprecedented value in the field of thin-film-based photoconductors and photodiodes for“hard”***,prototypal validation under the X-ray beam produced by a medical linear accelerator for cancer treatment is also introduced.

关键词： Metal-halide perovskite thin films Direct X-ray detectors Self-powered devices Operational stability Medical linear accelerator

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