Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties. The theory of real algebraic numbers and more generally of semi-algebraic varieties is at the core of a number of effective methods in real analysis, including decision procedures for non linear arithmetic or optimization methods for real valued functions. After defining an abstract structure of discrete real closed field and the elementary theory of real roots of polynomials, we describe the formalization of an algebraic proof of quantifier elimination based on pseudo-remainder sequences following the standard computer algebra literature on the topic. This formalization covers a large part of the theory which underlies the efficient algorithms implemented in practice in computer algebra. The success of this work paves the way for formal certification of these efficient methods.Comment: 40 pages, 4 figure

Implied Open‐circuit Voltage Imaging via a Single Bandpass Filter Method—Its First Application in Perovskite Solar Cells

A direct, camera-based implied open-circuit voltage (iVOC) imaging method via the novel use of a single bandpass filter (s-BPF) is developed for large-area photovoltaic solar cells and solar cell precursors. This method images the photoluminescence (PL) emission using a narrow BPF with centre energy in the high-energy tail of the PL emission taking advantage of the close-to-unity absorptivity of typical photovoltaic devices with low variability in this energy range. As a result, the exact value of the sample\u27s absorptivity within the BPF transmission band is not required. The use of a s-BPF enables the adaptation of a fully contactless approach to calibrate the absolute PL photon flux for camera-based spectrally-integrated imaging tools. The method eliminates the need for knowledge of the imaging system spectral response and the use of the emission and excitation spectral shapes. Through an appropriate choice of the BPF centre energy, a range of absorber compositions or a single absorber with different surface morphologies (e.g., planar vs textured) can be imaged, all without the need for additional detection optics. The feasibility of this s-BPF method is first assessed using a high-quality Cs$_{0.05}$FA$_{0.79}$MA$_{0.16}$Pb(I$_{0.83}$Br$_{0.17}$)$_3$ perovskite neat film. The error in iVOC is determined to be less than 1.5%. The efficacy of the method is then demonstrated on device stacks with two different perovskite compositions commonly used in single-junction and monolithic tandem solar cells

Implied Open‐circuit Voltage Imaging via a Single Bandpass Filter Method—Its First Application in Perovskite Solar Cells

A novel, camera-based method for direct implied open-circuit voltage (iV$_{OC}$) imaging via the use of a single bandpass filter (s-BPF) is developed for large-area photovoltaic solar cells and precursors. The photoluminescence (PL) emission is imaged using a narrow BPF with centre energy inside the high-energy tail of the PL emission, utilising the close-to-unity and nearly constant absorptivity of typical photovoltaic devices in this energy range. As a result, the exact value of the sample\u27s absorptivity within the BPF transmission band is not required. The use of an s-BPF enables a fully contactless approach to calibrate the absolute PL photon flux for spectrally integrated detectors, including cameras. The method eliminates the need for knowledge of the imaging system spectral response. Through an appropriate choice of the BPF centre energy, a range of absorber compositions or a single absorber with different surface morphologies, such as planar and textured, can be imaged, all without the need for additional detection optics. The feasibility of this s-BPF method is first validated. The relative error in iV$_{OC}$ is determined to be ≤1.5%. The method is then demonstrated on device stacks with two different perovskite compositions commonly used in single-junction and monolithic tandem solar cells

Cohort profile: The Golestan Cohort Study-a prospective study of oesophageal cancer in Northern Iran

[No abstract available

Enabling Technologies for Silicon Microstrip Tracking Detectors at the HL-LHC

While the tracking detectors of the ATLAS and CMS experiments have shown excellent performance in Run 1 of LHC data taking, and are expected to continue to do so during LHC operation at design luminosity, both experiments will have to exchange their tracking systems when the LHC is upgraded to the high-luminosity LHC (HL-LHC) around the year 2024. The new tracking systems need to operate in an environment in which both the hit densities and the radiation damage will be about an order of magnitude higher than today. In addition, the new trackers need to contribute to the first level trigger in order to maintain a high data-taking efficiency for the interesting processes. Novel detector technologies have to be developed to meet these very challenging goals. The German groups active in the upgrades of the ATLAS and CMS tracking systems have formed a collaborative "Project on Enabling Technologies for Silicon Microstrip Tracking Detectors at the HL-LHC" (PETTL), which was supported by the Helmholtz Alliance "Physics at the Terascale" during the years 2013 and 2014. The aim of the project was to share experience and to work together on key areas of mutual interest during the R&D phase of these upgrades. The project concentrated on five areas, namely exchange of experience, radiation hardness of silicon sensors, low mass system design, automated precision assembly procedures, and irradiations. This report summarizes the main achievements

Diophantine Approximation and applications in Interference Alignment

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1]

A double-sided, shield-less stave prototype for the ATLAS upgrade strip tracker for the high luminosity LHC

A detailed description of the integration structures for the barrel region of the silicon strips tracker of the ATLAS Phase-II upgrade for the upgrade of the Large Hadron Collider, the so-called High Luminosity LHC (HL-LHC), is presented. This paper focuses on one of the latest demonstrator prototypes recently assembled, with numerous unique features. It consists of a shortened, shield-less, and double sided stave, with two candidate power distributions implemented. Thermal and electrical performances of the prototype are presented, as well as a description of the assembly procedures and tools