An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations

Zhang, Shuo

doi:10.1007/s11425-020-1882-6

Cited by 6 publications

(3 citation statements)

References 55 publications

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“…the R package based on differential expression analysis of negative binomial distribution, and the analysis of differentially expressed genes with biological repetition. Three database tools: targetscan, miRanda, and PITA were used to analyze the genetic sequence information of the subjects with known miRNAs and newly predicted, differentially expressed miRNAs (Wang et al 2021 ; Zhang 2021 ). Finally, Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis were performed on the set of miRNA target genes (Ashburner et al 2000 ; Minoru et al 2004 ).…”

Section: Methodsmentioning

confidence: 99%

Fatiguing freestyle swimming modifies miRNA profiles of circulating extracellular vesicles in athletes

Lai,

Lin,

Yan

et al. 2023

Eur J Appl Physiol

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Extracellular vesicles (EVs) are secreted by various tissues and cells under normal physiological or pathological conditions. Exercise-induced EVs may be involved in the adaptation of exercise-induced fatigue. The 1500-m freestyle is the longest pool-based swimming event in the Olympic Games, and there is a paucity of information regarding changes in the miRNA profiles of circulating EVs after a single session of fatiguing swimming. In this study, 13 male freestyle swimmers conducted a fatiguing 1500-m freestyle swimming session at the speed of their best previously recorded swimming performance. Fasting venous blood was collected before and after the swimming session for analysis. 70 miRNAs from the circulating EVs were found to be differentially expressed after the fatiguing 1500-m freestyle swimming session, among which 45 and 25 miRNAs were up-regulated and down-regulated, respectively. As for the target genes of five miRNAs (miR-144-3p, miR-145-3p, miR-509-5p, miR-891b, and miR-890) with the largest expression-fold variation, their functional enrichment analysis demonstrated that the target genes were involved in the regulation of long-term potentiation (LTP), vascular endothelial growth factor (VEGF), glutathione metabolism pathway, dopaminergic synapse, signal transmission, and other biological processes. In summary, these findings reveal that a single session of fatiguing swimming modifies the miRNAs profiles of the circulating EVs, especially miR-144-3p, miR-145-3p, miR-509-5p, miR-891b, and miR-890, which clarifies new mechanisms for the adaptation to a single session of fatiguing exercise from the perspective of EV-miRNAs.

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Section: Methodsmentioning

confidence: 99%

Fatiguing freestyle swimming modifies miRNA profiles of circulating extracellular vesicles in athletes

Lai,

Lin,

Yan

et al. 2023

Eur J Appl Physiol

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“…Examples of ABCDs are given. The construction of ABCFES is similar to some nonconforming spline functions ( [25,38,45,46]) and with a new way to impose continuities: different from most existing finite element methods, the ABCFES uses a dual way to impose proper continuities. Though, it can be interesting to clarify, these are not mixed element methods.…”

Section: Andmentioning

confidence: 99%

Partially adjoint discretizations of adjoint operators

Zhang¹

2022

Preprint

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This paper concerns the discretizations in pair of adjoint operators between Hilbert spaces so that the adjoint properties can be preserved. Due to the finite-dimensional essence of discretized operators, a new framework, theory of partially adjoint operators, is motivated and presented in this paper, so that adjoint properties can be figured out for finite-dimensional operators which can not be non-trivially densely defined in other background spaces. A formal methodology is presented under the framework to construct partially adjoint discretizations by a conforming discretization (CD) and an accompanied-by-conforming discretization (ABCD) for each of the operators. Moreover, the methodology leads to an asymptotic uniformity of an infinite family of finite-dimensional operators. The validities of the theoretical framework and the formal construction of discretizations are illustrated by a systematic family of in-pair discretizations of the adjoint exterior differential operators.The adjoint properties concerned in the paper are the closed range theorem and the strong dualities, whose preservations have not been well studied yet. Quantified versions of the closed range theorem are established for both adjoint operators and partially adjoint discretizations. The notion Poincaré-Alexander-Lefschetz (P-A-L for short) type duality is borrowed for operator theory, and horizontal and vertical P-A-L dualities are figured out for adjoint operators and their analogues are established for partially adjoint discretizations. Particularly by partially adjoint discretizations of exterior differential operators, the Poincaré-Lefschetz duality is preserved as an identity, which was not yet obtained before. The ABCD, a new kind of discretization method, is motivated by and plays a crucial role in the construction of partially adjoint discretizations. Besides, it can be used for the discretization of single operators; for example, in this paper, de Rham complexes that start with the Crouzeix-Raviart finite element spaces are constructed by series of ABCDs, including both the discretized operators and the domain spaces; commutative diagrams with appropriate regularities are constructed thereon. Equivalences are established between primal and dual discretizations for the elliptic source and eigenvalue problems and the primal and dual mixed discretizations of the Hodge Laplacian problems of exterior differential operators based on the partially adjoint discretizations of adjoint operators. This shows how structure-preserving schemes for equations with linear operators can be lead to by partially adjoint discretizations under the new theoretical framework. SHUO ZHANG 1.3. Organization of the paper 7 1.4. Notations and conventions 8 2. Theory of partially adjoint operators 8 2.1. Basics of adjoint operators revisited 8 2.2. Theory of partially adjoint operators 10 2.3. Some technical proofs 19 3. Partially adjoint discretizations of adjoint operators 23 3.1. Partially adjoint discretizations by CD and ABCD 24 3.2. Characteristics of lo...

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“…Besides, a precise set of basis functions can be presented, the supports of which are each contained in a vertex patch, and the programming of the scheme can be done in a standard routine as for the standard "finite element" method. Indeed, locally supported basis functions have been also found and implemented for many specific non-Ciarlet type finite element spaces [16,22,[25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

A primal finite element scheme of the $\mathbf{H}(\mathbf{d})\cap \mathbf{H}(\boldsymbolδ)$ elliptic problem

Zhang¹

2022

Preprint

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In this paper, a unified family, for n 2 and 1 k n − 1, of finite element schemes are presented for the primal weak formulation of the n-dimensional H(d k ) ∩ H(δ k ) elliptic problem. 2010 Mathematics Subject Classification. Primary 47N40, 65N30. Key words and phrases. H(d) ∩ H(δ), primal formulation, nonconforming finite element method, non-Ciarlet type. The research is partially supported by NSFC (11871465) and CAS (XDB 41000000).

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An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations

Cited by 6 publications

References 55 publications

Fatiguing freestyle swimming modifies miRNA profiles of circulating extracellular vesicles in athletes

Fatiguing freestyle swimming modifies miRNA profiles of circulating extracellular vesicles in athletes

Partially adjoint discretizations of adjoint operators

A primal finite element scheme of the $\mathbf{H}(\mathbf{d})\cap \mathbf{H}(\boldsymbolδ)$ elliptic problem

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