A Survey on L 2 Extension Problem

Zhou, Xiangyu

doi:10.1007/978-3-319-20337-9_13

Cited by 23 publications

(8 citation statements)

References 62 publications

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“…Taken together, the Gel/BP/ZnO + NIR hydrogel could promote infected wound healing with the fastest closure rate (64%) due to the immunoregulation effect of ZnO in combination with mild heat stimulation which could ablate inflammation and induce angiogenesis resulting in shortening bacteria infected wound healing time. [ 121 ] Further to increase the antibacterial killing efficacy of broad spectrum‐bacteria by photothermal therapy, Liu et al. provided a poly(N‐acryloyl glycinamide) (PNAGA) polymer mixing with PDA‐coated gold nanorods (Au@PDA NRs) and coated with E.coli or S. aureus ‐activated macrophage membrane (called E/SMM‐PNAGAAu@PDA hydrogel) which could target specific bacteria due to the expression of a specific bacterial receptor on macrophage membrane ( Figure A).…”

Section: Emerging Immunomodulatory Trends In Dfus Treatmentsmentioning

confidence: 99%

Immunomodulatory Hydrogels: Advanced Regenerative Tools for Diabetic Foot Ulcer

Xiong

Qian

Lü

et al. 2023

Adv Funct Materials

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Diabetic foot ulcer (DFU) is one of the most common complications of diabetes, bringing physical and mental challenges for patients due to the lack of efficient curative therapy. Despite considerable advances in pharmacological and surgical approaches, clinical trials for DFU patients remain disappointing due to the local overactive and excessive inflammation. Immunomodulatory hydrogels has significant advantages to overcome the clinical challenge of DFUs therapy. Here, recent fabrication and regenerative advances in the utilization of functional hydrogels for altering the immune microenvironment of DFUs are comprehensively reviewed. The pathological features and the healing processes of DFUs, followed by summarizing the physicochemical properties essential for the design of regenerative hydrogels for immunomodulation in DFUs, are briefly introduced. Then, the potential immuno-therapeutic modalities of hydrogels and emerging trends used to treat DFUs via multitherapeutic approaches and enhanced efficacy and safety are discussed. Taken together, by linking the structural properties of hydrogels to their functions in DFU therapy with a particular focus on immunomodulatory stimuli, this review can promote further advances in designing advanced hydrogels for DFUs, resulting in improved diabetic wound repair through translation into clinical setting in the near future.

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Section: Emerging Immunomodulatory Trends In Dfus Treatmentsmentioning

confidence: 99%

Immunomodulatory Hydrogels: Advanced Regenerative Tools for Diabetic Foot Ulcer

Xiong

Qian

Lü

et al. 2023

Adv Funct Materials

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“…Bacterial infection would attack the wound and aggravate inflammation. [ 57 ] To determine the inflammatory response quantitatively, the levels of three inflammatory indicators, C‐reactive protein (CRP), interleukin 6 (IL‐6), and tumor necrosis factor α (TNF‐ α ), were tested (Figure 6c). IL‐6 can reflect the intensity of infection directly.…”

Section: Resultsmentioning

confidence: 99%

BODIPY‐Functionalized Natural Polymer Coatings for Multimodal Therapy of Drug‐Resistant Bacterial Infection

Zhang

Sun

et al. 2023

Advanced Science

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The fact that multidrug resistance (MDR) could induce medical device‐related infections, along with the invalidation of traditional antibiotics has become an intractable global medical issue. Therefore, there is a pressing need for innovative strategies of antibacterial functionalization of medical devices. For this purpose, a multimodal antibacterial coating that combines photothermal and photodynamic therapies (PTT/PDT) is developed here based on novel heavy atom‐free photosensitizer compound, BDP‐6 (a kind of boron‐dipyrromethene). The photothermal conversion efficiency of BDP‐6 is of 55.9%, which could improve biocompatibility during PTT/PDT process by reducing the exciting light power density. Furthermore, BDP‐6, together with oxidized hyaluronic acid, is crosslinked with a natural polymer, gelatin, to fabricate a uniform coating (denoted as polyurethane (PU)‐GHB) on the surface of polyurethane. PU‐GHB has excellent synergistic in vitro PTT/PDT antibacterial performance against both susceptible bacteria and MDR bacteria. The antibacterial mechanisms are revealed as that hyperthermia could reduce the bacterial activity and enhance the permeability of inner membrane to reactive oxygen species by disturbing cell membrane. Meanwhile, in an infected abdominal wall hernia model, the notable anti‐infection performance, good in vivo compatibility, and photoacoustic imaging property of PU‐GHB are verified. A promising strategy of developing multifunctional antibacterial coatings on implanted medical devices is provided here.

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“…We will also use the techniques to study the Arveson–Douglas Conjecture in connection with the

L^{2}

‐extension problem . The covering constructed in Section can be useful in constructing a holomorphic extension.…”

Section: Discussionmentioning

confidence: 99%

Essential normality — a unified approach in terms of local decompositions

2019

Proc. London Math. Soc.

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In this paper, we define the asymptotic stable division property for submodules of La2false(Bnfalse). We show that under a mild condition, a submodule with the asymptotic stable division property is p‐essentially normal for all p>n. A new technique is developed to show that certain submodules have the asymptotic stable division property. This leads to a unified proof of most known results on essential normality of submodules as well as new results. In particular, we show that an ideal defines a p‐essentially normal submodule of La2false(Bnfalse), ∀p>n, if its associated primary ideals are powers of prime ideals whose zero loci satisfy standard regularity conditions near the sphere.

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A Survey on L 2 Extension Problem

Cited by 23 publications

References 62 publications

Immunomodulatory Hydrogels: Advanced Regenerative Tools for Diabetic Foot Ulcer

Immunomodulatory Hydrogels: Advanced Regenerative Tools for Diabetic Foot Ulcer

BODIPY‐Functionalized Natural Polymer Coatings for Multimodal Therapy of Drug‐Resistant Bacterial Infection

Essential normality — a unified approach in terms of local decompositions

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