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Very weak solutions to the two-dimensional Monge-Ampére equation Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

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Science China Mathematics 2019年第6期62卷 1041-1056页

作者： Wentao Cao László Székelyhidi Jr. institut für mathematik Universit?t Leipzig

In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with H?lder-continuous ?rst derivatives of exponent β < 1/5. Our approach is based on combining the approach of Lewicka and Pakzad(2017) with a new diagonalization procedure which avoids the use of conformal coordinates, which was introduced by De Lellis et al.(2018) for the isometric immersion problem.

关键词： Monge-Ampére equation convex integration weak solutions

Many faces of neuronal activity manipulation in Drosophila

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Neural Regeneration Research 2025年第9期20卷 2574-2576页

作者： Amber Krebs Steffen Kautzmann Christian Klämbt institut für Neuro-und Verhaltensbiologie MünsterGermany

Animals exhibit complex responses to external and internal *** information is computed by interconnected neurons that express numerous ion channels,which modulate the neuronal membrane *** can neuronal activity orchestrate complex motor patterns or allow learning from previous experience?To answer such questions,we need the ability not only to record,but also to modulate neuronal activity in both space(e.g.,neuronal subsets)and time.

关键词： manipulation potential. neuronal

BACKWARD ERROR ANALYSIS OF SYMPLECTIC INTEGRATORS FOR LINEAR SEPARABLE HAMILTONIAN SYSTEMS

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Journal of Computational Mathematics 2002年第5期20卷 449-460页

作者： PeterGrtz institut fur Praktische mathematik Universitat Karlsruhe Englerstrabe 德国 Karlsruhe 276128

Presents a study that analyzed the symplecticness, stability and asymptotic of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystr ? m methods applied to linear Hamiltonian systems. Numerical representation of the problem; Results in connection to P-stability; Details of the application of backward error analysis in the study.

关键词： Hamiltonian systems Backward error analysis Symplectic integrators.

On the Estimation of Solutions for Some Linear Systems of Differential Equations

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Acta Mathematica Sinica,English Series 1998年第1期14卷 41-46页

作者： L. R. Awad E. M. El-Kholy Sh. El-Bendary Universitat Hamburg institut fur Angewandte mathematik Bundesstraβe 55 20146 Hamburg Germany

In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear... 详细信息

关键词： Homogeneous linear Unbounded coefficient

A characterization of finite simple groups by the orders of solvable subgroups

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Science China Mathematics 2007年第5期50卷 715-726页

作者： Klaus DENECKE institut für mathematik Universitt PotsdamGermany

Let G be a finite group and S be a finite simple group. In this paper, we prove that if G and S have the same sets of all orders of solvable subgroups, then G is isomorphic to S, or G and S are isomorphic to Bn(q), Cn... 详细信息

关键词： finite simple groups solvable subgroup order characterization 20D08 20D05

MULTIGRID METHODS FOR OBSTACLE PROBLEMS

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Journal of Computational Mathematics 2009年第1期27卷 1-44页

作者： Carsten Grser Ralf Kornhuber freie Universitt Berlin Institut für Mathematik

In this review, we intend to clarify the underlying ideas and the relations between various multigrid methods ranging from subset decomposition, to projected subspace decomposition and truncated multigrid. In addition, we present a novel globally convergent inexact active set method which is closely related to truncated multigrid. The numerical properties of algorithms are carefully assessed by means of a degenerate problem and a problem with a complicated coincidence set.

关键词： Multigrid methods Variational inequalities.

Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles

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Algebra Colloquium 2016年第1期23卷 15-22页

作者： Huan Xiong institut fur mathematik Universitat Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland

Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs （associated with degrees） have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.

关键词： finite group character graph codegree

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

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Journal of Computational Mathematics 2003年第4期21卷 401-410页

作者： Torsten Linfi (institut fur Numerische mathematik, Technische Universitdt Dresden, D-01062 Dresden, Germany) institut für Numerische mathematik Technische Universit?t Dresden D-01062 Dresden Germany

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposition is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.

关键词： Convection-diffusion Singular perturbation Solution decomposition Shishkin mesh.

Like a G6-nal:transcriptional control of G-protein coupled receptors during oligodendroglial development

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Neural Regeneration Research 2025年第7期20卷 2001-2002页

作者： Tim Aberle Michael Wegner institut für Biochemie Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

Multilayered control of myelination:Quick,saltatory conduction of action potentials along nerve fibers requires the electrical insulation of axons by myelinating *** the central nervous system,this role is taken up by *** are marked by the expression of the lineage determinants Sox10 and Olig2 and arise from oligodendrocyte precursor cells(OPCs)during embryonal *** the majority of OPCs differentiate into mature oligodendrocytes when nearby axonal segments require myelination,a small subpopulation of OPCs persist as a progenitor ***,the timing of myelination and maintenance of the OPC pool both need to be precisely *** transcription factors either positively or negatively affect oligodendrocyte differentiation and maintenance of the OPC pool as components of a complex gene regulatory network(reviewed in Sock and Wegner,2021).Network activity is additionally influenced by extracellular signaling molecules that bind to receptors on the oligodendroglial cell surface and activate intracellular signaling *** the receptors are linked to the network is poorly understood so far,but pivotal to understanding the overall regulation of central nervous system(CNS)myelination in response to environmental *** insights were recently gained for Gpr37(Schmidt et al.,2024),a G-protein coupled receptor(GPCR)with known relevance in differentiating oligodendrocytes(Yang et al,2016).

关键词： gained insulation conduction