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A CONVERSE OF THE BANACH CONTRACTION PRINCIPLE FOR PARTIAL METRIC SPACES AND THE CONTINUUM HYPOTHESIS

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arXiv 2021年

作者： Maćkowiak, Piotr Faculty of Mathematics and Computer Science Department of Nonlinear Analysis and Applied Topology Adam Mickiewicz University in Poznań ul. Uniwersytetu Poznańskiego 4 Poznań61-614 Poland

A version of the Bessaga inverse of the Banach contraction principle for partial metric spaces is presented. Equivalence of that version and the continuum hypothesis is shown as *** Codes 47H09, 47H10, 54E50 © 20... 详细信息

关键词： Set theory

Labor advantages drive the greater productivity of faculty at elite universities

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arXiv 2022年

作者： Zhang, Sam Wapman, K. Hunter Larremore, Daniel B. Clauset, Aaron Department of Applied Mathematics University of Colorado BoulderCO80309 United States Department of Computer Science University of Colorado BoulderCO80309 United States BioFrontiers Institute University of Colorado BoulderCO80309 United States Santa Fe Institute Santa FeNM87501 United States

Faculty at prestigious institutions dominate scientific discourse, with the small proportion of researchers at elite universities producing a disproportionate share of all research publications. Environmental prestige is known to drive such epistemic disparity, but the mechanisms by which it causes increased faculty productivity remain unknown. Here we combine employment, publication, and federal survey data for 78,802 tenure-track faculty at 262 PhD-granting institutions in the American university system between 2008-2017 to show through multiple lines of evidence that the greater availability of funded graduate and postdoctoral labor at more prestigious institutions drives the environmental effect of prestige on productivity. In particular, we show that greater environmental prestige leads to larger faculty-led research groups, which drive higher faculty productivity, primarily in disciplines with research group collaboration norms. In contrast, we show that productivity does not increase substantially with prestige for either faculty papers published without group members, nor group members themselves. The disproportionate scientific productivity of elite researchers is thus largely explained by their substantial labor advantage, indicating a more limited role for prestige itself in predicting scientific contributions. © 2022, CC BY-NC-ND.

关键词： Productivity

Multicomponent coagulation systems: Existence and non-existence of stationary non-equilibrium solutions

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arXiv 2021年

作者： Ferreira, Marina A. Lukkarinen, Jani Nota, Alessia Velázquez, Juan J.L. Department of Mathematics and Statistics University of Helsinki P.O. Box 68 Helsingin YliopistoFI-00014 Finland Department of Information Engineering Computer Science and Mathematics University of L'Aquila L'Aquila67100 Italy Institute for Applied Mathematics University of Bonn Endenicher Allee 60 BonnD-53115 Germany

We study multicomponent coagulation via the Smoluchowski coagulation equation under non-equilibrium stationary conditions induced by a source of small clusters. The coagulation kernel can be very general, merely satisfying certain power law asymptotic bounds in terms of the total number of monomers in a cluster. The bounds are characterized by two parameters and we extend previous results for one-component systems to classify the parameter values for which the above stationary solutions do or do not exist. Moreover, we also obtain criteria for the existence or non-existence of solutions which yield a constant flux of mass towards large clusters. Copyright © 2021, The Authors. All rights reserved.

关键词： Coagulation

Thermal comparison of mono-facial and bi-facial photovoltaic cells considering the effect of TPT layer absorptivity

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International Journal of Thermofluids 2023年 18卷

作者： Radwan, Ali Mahmoud, Montaser Olabi, Abdul-Ghani Rezk, Ahmed Maghrabie, Hussein M Abdelkareem, Mohammad Ali Sustainable Energy & Power Systems Research Centre RISE University of Sharjah Sharjah P.O. Box 27272 United Arab Emirates Mechanical Power Engineering Department Faculty of Engineering Mansoura University Mansoura35516 Egypt Department of Engineering School of Mathematics Computer Science and Engineering City University of London London United Kingdom Mechanical Engineering and Design Aston University School of Engineering and Applied Science Birmingham Aston TriangleB4 7ET United Kingdom College of Engineering and Physical Science Aston University Birmingham B4 7ET United Kingdom Department of Mechanical Engineering Faculty of Engineering South Valley University Qena83521 Egypt Chemical Engineering Department Minia University Elminia Egypt

With the widespread utilization of solar photovoltaics (PV), it is becoming increasingly important to understand its performance using various configurations to harvest solar energy at the most suitable efficiency, specifically in hot climates. Therefore, this paper compares mono-facial and bi-facial PV cells under the high-temperature desert climate of Sharjah (United Arab Emirates). The optimally tilted and vertical east-west configurations were compared to evaluate the annual energy production for these scenarios. In addition, new parameter, the effect of the rear side layer absorptivity of the mono-facial PV cell, was investigated. The comparative study considered solar radiation, ambient temperature, wind speed, and albedo. The results showed that considering the effect of absorptivity achieves better performance predictions. However, the effect of the absorptivity did not exhibit a significant influence compared to the case with neglected backsheet absorptivity. As such, the PV cell temperature increased by 0.4 °C and 1.4 °C at an albedo of 0.2 and 0.7, considering the actual absorptivity value of 0.2. On the other hand, it is worth mentioning that improper designs result in considerable temperature rises as the absorptivity value increases. Under the investigated conditions and based on the yearlong comparison, the tilted bi-facial performed better than the vertical bi-facial;as the albedo increased from 0.2 to 0.7, the power gain ratio of the tilted bi-facial increased from 7.18% to 20.88% and that of vertical bi-facial from -19.4% to 12.65%. © 2023 The Author(s)

关键词： Solar energy

A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives

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arXiv 2022年

作者： Domfeh, Dixon Chatterjee, Arpita Dixon, Matthew Department of Computer Science Georgia Institute of Technology 266 Ferst Dr AtlantaGA30313 United States Department of Mathematical Sciences Georgia Southern University StatesboroGA30458 United States Department of Applied Mathematics Illinois Institute of Technology 10 S Wabash Ave ChicagoIL60616 United States

Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing. As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe occurrences and interest rates in a sufficiently flexible and statistically reliable way within a unifying asset pricing framework. Consequently, little is known empirically about the expected risk-premia of CAT bonds. The primary contribution of this paper is to present a unified Bayesian CAT bond pricing framework based on uncertainty quantification of catastrophes and interest rates. Our framework allows for complex beliefs about catastrophe risks to capture the distinct and common patterns in catastrophe occurrences, and when combined with stochastic interest rates, yields a unified asset pricing approach with informative expected risk premia. Specifically, using a modified collective risk model - Dirichlet Prior-Hierarchical Bayesian Collective Risk Model (DP-HBCRM) framework - we model catastrophe risk via a model-based clustering approach. Interest rate risk is modeled as a CIR process under the Bayesian approach. As a consequence of casting CAT pricing models into our framework, we evaluate the price and expected risk premia of various CAT bond contracts corresponding to clustering of catastrophe risk profiles. Numerical experiments show how these clusters reveal how CAT bond prices and expected risk premia relate to claim frequency and loss *** Codes 91G05, 91G70, 91G30 Copyright © 2022, The Authors. All rights reserved.

关键词： Risk assessment

GPU-Accelerated DNS of Compressible Turbulent Flows

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arXiv 2022年

作者： Kim, Youngdae Ghosh, Debojyoti Constantinescu, Emil M. Balakrishnan, Ramesh Computational Science Division Argonne National Laboratory 9700 S. Cass Ave. LemontIL60439 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory 7000 East Ave. LivermoreCA94550 United States Mathematics and Computer Science Division Argonne National Laboratory 9700 S. Cass Ave. LemontIL60439 United States

This paper explores strategies to transform an existing CPU-based high-performance computational fluid dynamics solver, HyPar, for compressible flow simulations on emerging exascale heterogeneous (CPU+GPU) computing platforms. The scientific motivation for developing a GPU-enhanced version of HyPar is to simulate canonical turbulent flows at the highest res-MSC Codes 76F65, 65Y05, 76F05, 35Q30, 65M06 Copyright © 2022, The Authors. All rights reserved.

关键词： Turbulent flow

Bivariate collocation for computing R0in epidemic models with two structures

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arXiv 2021年

作者： Breda, Dimitri De Reggi, Simone Scarabel, Francesca Vermiglio, Rossana Wu, Jianhong CDLab-Computational Dynamics Laboratory Department of Mathematics Computer Science and Physics University of Udine Via delle Scienze 206 33100 Italy LIAM-Laboratory for Industrial and Applied Mathematics Department of Mathematics and Statistics York University 4700 Keele Street TorontoONM3J 1P3 Canada Department of Mathematics The University of Manchester Oxford Rd ManchesterM13 9PL United Kingdom Joint UNIversities Pandemic and Epidemiological Research

Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the "spatial" variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate R0, which measures the transmissibility of an infectious disease and, rigorously, is defined as the dominant eigenvalue of a next-generation operator. Via bivariate collocation and cubature on tensor grids, the latter is approximated with a finite-dimensional matrix, so that its dominant eigenvalue can easily be computed with standard techniques. We use test examples to investigate experimentally the behavior of the approximation: the convergence order appears to be infinite when the corresponding eigenfunction is smooth, and finite for less regular eigenfunctions. To demonstrate the effectiveness of the technique for more realistic applications, we present a new epidemic model structured by demographic age and immunity, and study the approximation of R0in some particular cases of *** Codes 65J10, 65L15, 65M70, 37N25, 47A75, 92D30 © 2021, CC BY.

关键词： Matrix algebra

Performance of Superconducting Resonators Suspended on SiN Membranes

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arXiv 2024年

作者： Chistolini, Trevor Lee, Kyunghoon Banerjee, Archan Alghadeer, Mohammed Jünger, Christian Altoé, M.P. Virginia Song, Chengyu Chen, Sudi Wang, Feng Santiago, David I. Siddiqi, Irfan Department of Physics University of California BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Materials Science Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Molecular Foundry Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Kavli Energy NanoScience Institute The University of California Berkeley The Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Suspending devices on thin SiN membranes can limit their interaction with the bulk substrate and reduce parasitic capacitance to ground. While suspending devices on membranes is used in many fields including radiation detection using superconducting circuits, there has been less investigation into maximum membrane aspect ratios and achievable suspended device quality, metrics important to establish the applicable scope of the technique. Here, we investigate these metrics by fabricating superconducting coplanar waveguide resonators entirely atop thin (∼110 nm) SiN membranes, where the membrane’s shortest length to thickness yields an aspect ratio of approximately 7.4 × 103. We compare these membrane resonators to on-substrate resonators on the same chip, finding similar internal quality factors ∼105 at single photon levels. Furthermore, we confirm that these membranes do not adversely affect resonator thermalization and conduct further materials characterization. By achieving high quality superconducting circuit devices fully suspended on thin SiN membranes, our results help expand the technique’s scope to potential uses including incorporating higher aspect ratio membranes for device suspension and creating larger footprint, high impedance, and high quality devices. Copyright © 2024, The Authors. All rights reserved.

关键词： Aspect ratio

Machine Learning Approach to the Floquet-Lindbladian Problem

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arXiv 2022年

作者： Volokitin, V. Meyerov, I. Denisov, Sergey Department of Mathematical Software and Supercomputing Technologies Lobachevsky University Nizhny Novgorod603950 Russia Department of Computer Science Oslo Metropolitan University OsloN-0130 Norway NordSTAR – Nordic Center for Sustainable and Trustworthy AI Research OsloN-0166 Norway Department of Applied Mathematics Lobachevsky University Nizhny Novgorod603950 Russia

Similar to its classical version, quantum Markovian evolution can be either time-discrete or time-continuous. Discrete quantum Markovian evolution is usually modeled with completely-positive trace-preserving maps while time-continuous evolution is often specified with superoperators referred to as "Lindbladians". Here we address the following question: Being given a quantum map, can we find a Lindbladian which generates an evolution identical – when monitored at discrete instances of time – to the one induced by the map? It was demonstrated that the problem of getting the answer to this question can be reduced to an NP-complete (in the dimension N of the Hilbert space the evolution takes place in) problem. We approach this question from a different perspective by considering a variety of Machine Learning (ML) methods and trying to estimate their potential ability to give the correct answer. Complimentary, we use the performance of different ML methods as a tool to check the hypothesis that the answer to the question is encoded in spectral properties of the so-called Choi matrix, which can be constructed from the given quantum map. As a test bed, we use two single-qubit models for which the answer can be obtained by using the reduction procedure. The outcome of our experiment is that, for a given map, the property of being generated by a time-independent Lindbladian is encoded both in the eigenvalues and the eigenstates of the corresponding Choi matrix. Copyright © 2022, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions