Complex monge-ampère operators - Open Access .click

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SARS‐CoV‐2 infection and venous thromboembolism after surgery: an international prospective cohort study

Anaesthesia, Volume 77, Issue 1, Page 28-39, January 2022., 2022
Summary SARS‐CoV‐2 has been associated with an increased rate of venous thromboembolism in critically ill patients. Since surgical patients are already at higher risk of venous thromboembolism than general populations, this study aimed to determine if patients with peri‐operative or prior SARS‐CoV‐2 were at further increased risk of venous ...
COVIDSurg Collaborative +16163 more
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Lp‐Curvature Measures and Lp,q‐Mixed Volumes

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
Motivated by Lutwak et al.’s Lp‐dual curvature measures, we introduce the concept of Lp‐curvature measures. This new Lp‐curvature measure is an extension of the classical surface area measure, Lp‐surface area measure, and curvature measure. In this paper, we first prove some properties of the Lp‐curvature measure.
Tongyi Ma, Raúl E. Curto
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Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions

International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022
Elliptic grid generation equations based on the Laplacian operator have the well‐known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue.
Pat Piperni, Maahi M. Talukder, Nawab Hussain +2 more
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Integrability Ex Machina

Fortschritte der Physik, Volume 69, Issue 7, July 2021., 2021
Abstract Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of relevant structures, the Lax pair and Lax connection respectively.
Sven Krippendorf, Dieter Lüst, Marc Syvaeri +2 more
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Three ways to solve partial differential equations with neural networks — A review

GAMM-Mitteilungen, Volume 44, Issue 2, June 2021., 2021
Abstract Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high‐dimensional problems: physics‐informed neural networks, methods based on the ...
Jan Blechschmidt, Oliver G. Ernst
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Timing of surgery following SARS‐CoV‐2 infection: an international prospective cohort study

Anaesthesia, Volume 76, Issue 6, Page 748-758, June 2021., 2021
Summary Peri‐operative SARS‐CoV‐2 infection increases postoperative mortality. The aim of this study was to determine the optimal duration of planned delay before surgery in patients who have had SARS‐CoV‐2 infection. This international, multicentre, prospective cohort study included patients undergoing elective or emergency surgery during October 2020.
COVIDSurg Collaborative +16155 more
wiley +1 more source

A Partial Differential Equation‐Based Image Restoration Method in Environmental Art Design

Advances in Mathematical Physics, Volume 2021, Issue 1, 2021., 2021
With the rapid development of networks and the emergence of various devices, images have become the main form of information transmission in real life. Image restoration, as an important branch of image processing, can be applied to real‐life situations such as pixel loss in image transmission or network prone to packet loss.
Chen Li, Miaochao Chen
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Canonical complex extensions of Kähler manifolds

Journal of the London Mathematical Society, Volume 101, Issue 2, Page 786-827, April 2020., 2020
Abstract Given a complex manifold X, any Kähler class defines an affine bundle over X, and any Kähler form in the given class defines a totally real embedding of X into this affine bundle. We formulate conditions under which the affine bundles arising this way are Stein and relate this question to other natural positivity conditions on the tangent ...
Daniel Greb, Michael Lennox Wong
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On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation

Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020
This paper considers some multiscale radial basis function collocation methods for solving the two‐dimensional Monge–Ampère equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods. The first method is the cascadic meshfree method, which was proposed by Liu and He (2013).
Zhiyong Liu, Qiuyan Xu, Mohammad D. Aliyu +2 more
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On uniqueness of solutions to complex Monge–Ampère mean field equations

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3163-3180, October 2025.
Abstract We establish the uniqueness of solutions to complex Monge–Ampère mean field equations when (minus) the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Chinh H. Lu, Trong‐Thuc Phung
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