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最大度至多为5的平面图的Injective边染色
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作者 郭瑜倩 《应用数学进展》 2025年第11期22-29,共8页
图的injective边染色是指图中的任意两条距离为2的边或在同一个三角形的边不能染相同的颜色。称使得图具有injective边染色的最小正整数为图的injective边色数。本文运用权转移方法证明了以下结论:对于最大度小于等于5且无4-圈的平面图,... 图的injective边染色是指图中的任意两条距离为2的边或在同一个三角形的边不能染相同的颜色。称使得图具有injective边染色的最小正整数为图的injective边色数。本文运用权转移方法证明了以下结论:对于最大度小于等于5且无4-圈的平面图,其injective边色数小于等于21。 展开更多
关键词 injective边染色 平面图 最大度
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Study on Hyaluronic Acid-g-Lipoic Acid Microsphere-based Injectable Hydrogel for Treating Early Knee Osteoarthritis
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作者 Mu-Zhi Zhang Jia-Tian Qian +6 位作者 Da-Wei Niu Yan-Cheng Chen Shi-Ao Li Jiu-Jiang Zeng Kun-Xi Zhang Yan-Li Song Pei-Liang Fu 《Chinese Journal of Polymer Science》 2026年第2期450-464,I0013,共16页
Early knee osteoarthritis(KOA)is characterized by progressive degeneration of the articular cartilage,synovial inflammation,and excessive accumulation of reactive oxygen species(ROS).At present,intra-articular injecti... Early knee osteoarthritis(KOA)is characterized by progressive degeneration of the articular cartilage,synovial inflammation,and excessive accumulation of reactive oxygen species(ROS).At present,intra-articular injection of hyaluronic acid(HA)is widely used to alleviate symptoms;however,its lubrication persistence,antioxidant,and anti-inflammatory abilities are limited,and it is difficult to effectively delay the early process of cartilage degeneration.Based on this,hyaluronic acid-g-lipoic acid(HA-LA)was synthesized by esterification reaction,and HA-LA microspheres were prepared by a reversed-phase emulsion method,which was combined with a macromolecular HA-LA solution to form injectable hydrogels.The objective of this study was to evaluate the efficacy of an injectable hydrogel based on hyaluronic acid-g-lipoic acid microspheres(HA-LA MS)for the treatment of KOA and to verify its injectability,lubricity,reactive oxygen species(ROS)scavenging ability,and anti-inflammatory effects.The results show that the HA-LA MS hydrogel has excellent shear thinning characteristics and continuous injectability,and its microsphere structure significantly reduces the interfacial friction coefficient through the rolling effect.In vitro experiments have shown that the hydrogel can efficiently scavenge ROS,reduce the expression of inflammatory factors,and is non-cytotoxic.The HA-LA MS injectable hydrogel has excellent lubricity,ROS scavenging ability,and anti-inflammatory effects in vivo,which can effectively delay the degeneration of early KOA cartilage,and its efficacy is significantly better than that of traditional hyaluronic acid,making it a promising intra-articular injection preparation. 展开更多
关键词 Knee osteoarthritis Hyaluronic acid Microsphere hydrogel injectABLE Antioxidant LUBRICITY
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Prompt Injection Attacks on Large Language Models:A Survey of Attack Methods,Root Causes,and Defense Strategies
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作者 Tongcheng Geng Zhiyuan Xu +1 位作者 Yubin Qu W.Eric Wong 《Computers, Materials & Continua》 2026年第4期134-185,共52页
Large language models(LLMs)have revolutionized AI applications across diverse domains.However,their widespread deployment has introduced critical security vulnerabilities,particularly prompt injection attacks that man... Large language models(LLMs)have revolutionized AI applications across diverse domains.However,their widespread deployment has introduced critical security vulnerabilities,particularly prompt injection attacks that manipulate model behavior through malicious instructions.Following Kitchenham’s guidelines,this systematic review synthesizes 128 peer-reviewed studies from 2022 to 2025 to provide a unified understanding of this rapidly evolving threat landscape.Our findings reveal a swift progression from simple direct injections to sophisticated multimodal attacks,achieving over 90%success rates against unprotected systems.In response,defense mechanisms show varying effectiveness:input preprocessing achieves 60%–80%detection rates and advanced architectural defenses demonstrate up to 95%protection against known patterns,though significant gaps persist against novel attack vectors.We identified 37 distinct defense approaches across three categories,but standardized evaluation frameworks remain limited.Our analysis attributes these vulnerabilities to fundamental LLM architectural limitations,such as the inability to distinguish instructions from data and attention mechanism vulnerabilities.This highlights critical research directions such as formal verification methods,standardized evaluation protocols,and architectural innovations for inherently secure LLM designs. 展开更多
关键词 Prompt injection attacks large language models defense mechanisms security evaluation
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Candidate injector design for the Southern Advanced Photon Source based on linac and booster
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作者 Liang-Sheng Huang Yan-Liang Han +5 位作者 Wei-Hang Liu Jian-Liang Chen Sheng Wang Yi Jiao Xiao Li Jia-Xin Chen 《Nuclear Science and Techniques》 2026年第2期67-78,共12页
The Southern Advanced Photon Source(SAPS)is a diffraction-limited synchrotron light source under design,which employs longitudinal injection as its primary injection scheme.This kind of injection scheme requires that ... The Southern Advanced Photon Source(SAPS)is a diffraction-limited synchrotron light source under design,which employs longitudinal injection as its primary injection scheme.This kind of injection scheme requires that the injected beam has a short bunch length and low emittance,and the preferred injector should offer high stability and low cost.Therefore,an injector based on a booster synchrotron was developed.The proposed injector includes a 250 MeV linac,a booster synchrotron that ramps the beam energy to 3.5 GeV,and two beam transport lines to ensure efficient beam delivery and beam quality preservation.The linac utilizes a thermionic high-voltage DC gun for reliable operation and features a bunching system with an advanced focusing system to preserve the emittance.To meet the injection requirements of the SAPS,a comprehensive design for the booster has been conducted.The booster synchrotron employs a threefold lattice structure,incorporating modified theoretical minimum emittance cells with a small momentum compaction factor and a high voltage to achieve an emittance of 3.98 nm rad and a bunch length of 4.8 mm.The injector has the potential to deliver a high charge,reducing the injection period of the storage ring to less than 1 min.Simulations demonstrated the expected performance,with a transmission efficiency of 90%,confirming its capability to meet the injection requirement of the SAPS storage ring.This design offers a stable and efficient solution for the SAPS. 展开更多
关键词 Southern Advanced Photon Source Longitudinal injection Booster synchrotron EMITTANCE Bunch length
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Penile shaft reconstruction after cream self-injection:a case report
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作者 Léa Bollen Stéphane Rysselinck +1 位作者 Jean-Philippe Salmin Gilles Dosin 《The Canadian Journal of Urology》 2026年第1期221-225,共5页
Background:Penile augmentation through injectable substances is becoming increasingly common.A growing number of aesthetic clinics are developing penile enlargement procedures using various injectable materials.Althou... Background:Penile augmentation through injectable substances is becoming increasingly common.A growing number of aesthetic clinics are developing penile enlargement procedures using various injectable materials.Although these procedures are now performed in more controlled and medically supervised environments,their long-term outcomes remain poorly understood.The promotion of such medical treatments contributes to an increasing interest among adult males in self-injection as a method to alleviate psychological distress associated with penile size concerns.At the same time,access to injectable substances through unofficial or unregulated sources has become increasingly easy.Tor our knowledge,we report the first documented case of self-injection with Garamycin®(gentamicin)cream,contributing to the literature on the often multidisciplinary management of penile enlargement injections,a field still lacking well-established guidelines.Case Description:This case report describes a young patient who self-injected Garamycin®into the penis for the purpose of enlargement.He presented to our urology department with worsening symptoms,including severe and poorly tolerated pain.His primary request was prompt relief of pain while preserving,as much as possible,the aesthetic appearance and functional integrity of his penis.This case required a multi-stage surgical approach to salvage the penis and preserve both its structural integrity and functional outcome.Conclusions:To our knowledge,this case report documents the first reported instance of Garamycin®injection performed for the purpose of penile enlargement.It provides insight into the clinical course of such penile cream injections,demonstrates that a two-stage scrotal flap can achieve both functional and aesthetic outcomes,and highlights the importance of comprehensive management particularly addressing the traumatic impact of penile deformity secondary to inflammation and/or infection,as well as the body dysmorphic concerns often associated with these cases. 展开更多
关键词 penile augmentation foreign body injection penile reconstruction scrotal flap complications case report
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The Impact of Double-puncture Tympanic Membrane Puncture and Tympanic Cavity Drug Injection on the Complication Rate of Acute Secretory Otitis Media
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作者 Wei Zheng 《Proceedings of Anticancer Research》 2026年第1期54-60,共7页
Objective:To explore the therapeutic effect of double-puncture tympanic membrane puncture and tympanic cavity drug injection in patients with acute secretory otitis media.Methods:A total of 84 patients with acute secr... Objective:To explore the therapeutic effect of double-puncture tympanic membrane puncture and tympanic cavity drug injection in patients with acute secretory otitis media.Methods:A total of 84 patients with acute secretory otitis media admitted to our hospital from June 2024 to June 2025 were selected and randomly divided into two groups by drawing lots.The control group(42 cases)was treated with the traditional single-puncture tympanic membrane puncture and tympanic cavity drug injection method,while the observation group(42 cases)was treated with the double-puncture tympanic membrane puncture and tympanic cavity drug injection method.The therapeutic effects of the two groups were compared.Results:The overall treatment response rate,overall complication rate,time to symptom relief,and improvement in hearing threshold in the observation group were all superior to those in the control group,with statistically significant differences(P<0.05).Conclusion:For acute secretory otitis media,the treatment method of double-puncture tympanic membrane puncture and tympanic cavity drug injection demonstrates definite efficacy,significantly reducing the incidence of complications,accelerating symptom relief,and improving hearing function,making it worthy of promotion. 展开更多
关键词 Acute secretory otitis media Double puncture Tympanic membrane puncture and tympanic cavity drug injection COMPLICATIONS
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围长至少为5的平面图的injective-染色 被引量:3
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作者 卜月华 叶飘飘 《数学进展》 CSCD 北大核心 2018年第3期363-372,共10页
图G的injective k-染色是指映射c:V(G)→{1,2,…,k},使有公共邻点的两个顶点u,v满足c(u)≠c(v),用X_i(G)表示使G有一个injective k-染色的最小正整数k.对g(G)≥5的平面图G,若△(G)≥20,证明了X_i(G)≤△+3.
关键词 平面图 围长 injective染色
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围长至少为5的平面图的injective染色 被引量:1
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作者 卜月华 叶飘飘 《浙江师范大学学报(自然科学版)》 CAS 2017年第1期1-8,共8页
通过构造一个(Δ+3)-临界图G,运用权转移的方法证明了该图G不存在.同时,用反证法证明了:对于围长至少为5的平面图G,若Δ(G)≥30,则χi(G)≤Δ+3.这个结论改进了现有的一个结果.
关键词 平面图 围长 injective染色
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围长至少为5的平面图的injective列表染色 被引量:1
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作者 卜月华 王超 《浙江师范大学学报(自然科学版)》 CAS 2016年第1期6-12,共7页
研究了围长至少为5的平面图的injective列表染色问题.通过分析极小反例的结构性质并利用权转移方法,证明了围长至少为5且最大度至少为12的平面图G的injective列表色数不超过Δ(G)+4.此结果进一步拓展了平面图关于injective色数的Luar... 研究了围长至少为5的平面图的injective列表染色问题.通过分析极小反例的结构性质并利用权转移方法,证明了围长至少为5且最大度至少为12的平面图G的injective列表色数不超过Δ(G)+4.此结果进一步拓展了平面图关于injective色数的Luar猜想成立的充分条件. 展开更多
关键词 平面图 围长 injective列表染色
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Injective Envelopes of a Hilbert C~*Module
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作者 许天周 蔡涛 李炳照 《Journal of Beijing Institute of Technology》 EI CAS 2001年第2期119-124,共6页
As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelope... As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H . 展开更多
关键词 C * algebra Hilbert C * module injective envelope
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On minimal quasi-injective modules and strong Kasch modules 被引量:2
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作者 朱占敏 张小向 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2009年第3期243-248,253,共7页
设R为一个环,M为一个右R-模.若每个从M的单子模到M的同态都可以开拓为M的自同态,则称M为一个极小拟内射模.若每个单的右R-模都可以嵌入M,则称M为一个强Kasch模.本文研究了这两类模的一些刻画和性质.
关键词 极小拟内射模 强Kasch模 半完全环 半局部环
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围长至少为6平面图的injective-染色
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作者 卜月华 杨强 《浙江师范大学学报(自然科学版)》 CAS 2023年第2期121-131,共11页
为了进一步探究平面图的injective-染色,通过分析临界图的结构性质并利用权转移方法,证明了围长至少为6,Δ(G)≥9且6-圈与6-圈不交的平面图G,有χ_(i)(G)≤Δ(G)+1.所得结果推广了平面图injective-染色的已知结果.
关键词 injective-染色 平面图 围长 最大度
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Absolutely Clean N-Complexes
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作者 HAN Xia WANG Xin LU Bo 《Wuhan University Journal of Natural Sciences》 2025年第2期133-138,共6页
The notion of absolutely clean N-complexes is studied.We show that an N-complex X is absolutely clean if and only if X is Nexact and Z,(X)is an absolutely clean module for each n e Z and i=1,2,..,N.In particular,we pr... The notion of absolutely clean N-complexes is studied.We show that an N-complex X is absolutely clean if and only if X is Nexact and Z,(X)is an absolutely clean module for each n e Z and i=1,2,..,N.In particular,we prove that a bounded above N-complex X is absolutely clean if and only if X,is an absolutely clean module for each n e Z.We also show that under certain hypotheses,an Ncomplex X is Gorenstein AC-injective if and only if Z;(X)is a Gorenstein AC-injective module for each n e Z and t=1,2,.,N. 展开更多
关键词 absolutely clean module absolutely clean n-complex Gorenstein AC-injective n-complex
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n-strongly Gorenstein Projective and Injective and Flat Modules 被引量:3
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作者 YANG Xiao-yan 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第4期553-564,共12页
In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applicati... In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given. 展开更多
关键词 n-strongly Gorenstein projective module n-strongly Gorenstein injective module n-strongly Gorenstein flat module
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Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules 被引量:1
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作者 SHANG Wen-liang 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第3期389-396,共8页
In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, poly... In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations. 展开更多
关键词 excellent extensions strongly n-Gorenstein projective modules strongly nGorenstein injective modules strongly n-Gorenstein flat modules
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EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES
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作者 M.R.Pournaki M.Tousi 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期511-514,共4页
Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module... Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p. 展开更多
关键词 Noetherian ring injective module indecomposable injective module injective envelope weakly locally principal prime ideal
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围长至少是6的平面图的injective-边染色 被引量:2
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作者 卜月华 陈雯雯 《浙江师范大学学报(自然科学版)》 CAS 2020年第1期19-25,共7页
为了进一步探究平面图的性质,运用极小反例和权转移的方法,研究了围长至少为6且6-圈与7^--圈不相交的平面图G的injective-边染色数,并证明该染色数的上界至多为3Δ(G)-3.研究成果改进了现有injective-边染色数的一个结论.
关键词 injective-边染色 平面图 最大度 围长
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5^——圈和5^——圈不交的平面图的injective-列表染色 被引量:1
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作者 卜月华 黄超媛 《浙江师范大学学报(自然科学版)》 CAS 2020年第3期241-250,共10页
通过构造一个(Δ+6)-临界图,运用权转移的方法证明了:对于5^--圈和5^--圈不交且Δ(G)≥18的平面图G,有χi^l(G)≤Δ(G)+6.所得结果研究了平面图G在短圈不交的限制条件下的injective-列表染色的问题.
关键词 平面图 围长 injective-染色 列表染色
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Some Studies on Quasi AP-injective Modules 被引量:6
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作者 赵玉娥 杜先能 《Northeastern Mathematical Journal》 CSCD 2006年第1期73-80,共8页
Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr(a) = Ra+Xa. We extend this notion to modules. A right R-module M with S = End(MR) is called quasi AP-... Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr(a) = Ra+Xa. We extend this notion to modules. A right R-module M with S = End(MR) is called quasi AP-injective if, for any s∈S, there exists a left ideal Xs of S such that ls(Ker(s)) = Ss+Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou. 展开更多
关键词 quasi AP-injective module AP-injective ring self-generator ANNIHILATOR
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Generalizations of Nil-Injective Rings 被引量:1
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作者 Yu-e ZHAO Xianneng DU 《Journal of Mathematical Research with Applications》 CSCD 2014年第3期278-288,共11页
The definition of AP-injectivity wnil-injectivity and almost nil n-injectivity motivates us to generalize the injectivity to almost The aim of this paper is to investigate characterizations and properties of almost w... The definition of AP-injectivity wnil-injectivity and almost nil n-injectivity motivates us to generalize the injectivity to almost The aim of this paper is to investigate characterizations and properties of almost wnil-injective rings and almost nil n-injective rings. Various results are developed, and many conclusions extend known results. 展开更多
关键词 almost wnil-injective rings almost nil-injective rings almost nil n-injective rings nil-injective rings nil n-injective rings.
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