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On Linear Equations with Three Prime Variables in Arithmetic Progressions
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作者 KONG Yafang 《数学进展》 北大核心 2025年第6期1233-1242,共10页
Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further ... Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25). 展开更多
关键词 ternary linear equation small prime solution arithmetic progression
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On the Distribution of Values of Euler's Function over Integers in Arithmetic Progressions 被引量:2
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作者 FENG Bin 《Chinese Quarterly Journal of Mathematics》 2017年第2期111-117,共7页
Let φ(n) denote the Euler-totient function, we study the distribution of solutions of φ(n) ≤ x in arithmetic progressions, where n ≡ l(mod q) and an asymptotic formula was obtained by Perron formula.
关键词 Perron formula Euler-totient function arithmetic progressions
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Primes in Arithmetic Progressions to Moduli with a Large Power Factor
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作者 Ruting Guo 《Advances in Pure Mathematics》 2013年第7期25-32,共8页
Recently Elliott studied the distribution of primes in arithmetic progressions whose moduli can be divisible by highpowers of a given integer and showed that for integer a≥2 and real number A>0. There is a B=B(A)&... Recently Elliott studied the distribution of primes in arithmetic progressions whose moduli can be divisible by highpowers of a given integer and showed that for integer a≥2 and real number A>0. There is a B=B(A)>0 such that , holds uniformly for moduli that are powers of a. In this paper we are able to improve his result. 展开更多
关键词 PRIMES ARITHMETIC progressions RIEMANN HYPOTHESIS
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A Study on the Learning Progressions of Understanding the Core Concepts of Kinetic Energy in High School
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作者 Xuemei Cui Yue Zheng Yu Chen 《Journal of Contemporary Educational Research》 2024年第11期46-55,共10页
Learning progressions divide the logical system of a subject into ordered and continuously developing levels that are suitable for the cognitive development level of students,which plays an important role in understan... Learning progressions divide the logical system of a subject into ordered and continuously developing levels that are suitable for the cognitive development level of students,which plays an important role in understanding students’learning process.This paper focuses on the theme of“kinetic energy”in high school physics as the research object.Firstly,the concept map was used to represent the relationship between knowledge,and then five core concepts were selected based on the opinions of high school teachers.Secondly,the test tools were compiled and tested based on the relevant test questions.Finally,the paper analyzed the results based on the Rasch model,clarified students’cognitive development level of“kinetic energy”and constructed the learning progressions of“kinetic energy”based on the logical order of subject knowledge.The research provides theoretical and methodological support for the study of other subjects and learning progressions,and provides a valuable reference for high school teachers to effectively carry out the instruction of“kinetic energy.” 展开更多
关键词 Core concepts High school Kinetic energy Learning progressions
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ON POINTS CONTAIN ARITHMETIC PROGRESSIONS IN THEIR LROTH EXPANSION 被引量:1
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作者 张振亮 曹春云 《Acta Mathematica Scientia》 SCIE CSCD 2016年第1期257-264,共8页
For any x ∈ (0, 1] (except at most countably many points), there exists a unique sequence {dn(x)}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1(x)(d1(x)-1)……dj-1(x)(dj-1... For any x ∈ (0, 1] (except at most countably many points), there exists a unique sequence {dn(x)}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1(x)(d1(x)-1)……dj-1(x)(dj-1(x)-1)dj(x). The dexter infinite series expansion is called the Liiroth expansion of x. This paper is con- cerned with the size of the set of points x whose digit sequence in its Liiroth expansion is strictly increasing and contains arbitrarily long arithmetic progressions with arbitrary com- mon difference. More precisely, we determine the Hausdorff dimension of the above set. 展开更多
关键词 Luroth expansion arithmetic progression Hausdorff dimension
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Modulating active targeting nanoparticle design according to tumor progressions
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作者 Huifang Nie Rong Huang +7 位作者 Guangwei Jiang Wenshuai Li Lan Yang Meng Zhang Min Qian Wei Guo Tao Ye Rongqin Huang 《Acta Pharmaceutica Sinica B》 2025年第2期1143-1158,共16页
Targeting drug delivery systems mediated by nanoparticles has shown great potential in the diagnosis and treatment of cancer.However,influences of different tumor progressions on the accumulation of nanoparticles,espe... Targeting drug delivery systems mediated by nanoparticles has shown great potential in the diagnosis and treatment of cancer.However,influences of different tumor progressions on the accumulation of nanoparticles,especially the ligand-modified active targeting nanoparticles are seldom exploited.In this work,the accumulation and penetration of RGD-modified gold nanoparticles(active AuNPs)with different sizes were investigated in orthotopic breast cancer with different tumor progressions.The results showed that the smallest active AuNPs had better accumulation and permeation effects in early tumor tissues with the relatively looser extracellular matrix,larger gaps,lower interstitial fluid pressure,and less receptor expression,which was due to size effects.However,the larger active AuNPs had better accumulation and penetration effects in late tumor tissues with highly expressed target receptors integrinαvβ3 because of the multivalent interactions between larger active nanoparticles and integrinαvβ3.In the midterm,tumor accumulation of active AuNPs was equally influenced by size effects and multivalent interactions.Therefore,RGD-modified nanoparticles with sizes of 7 and 90 nm accumulated more in tumors.This study will guide a rational design of active targeting nanoparticles for enhancing the diagnosis and treatment of tumors based on their progressions. 展开更多
关键词 Tumor progression Active targeting Particle size Tumor accumulation Receptor expression Pathophysiological characteristics
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On infinite arithmetic progressions in sumsets 被引量:1
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作者 Yong-Gao Chen Quan-Hui Yang Lilu Zhao 《Science China Mathematics》 SCIE CSCD 2023年第12期2669-2682,共14页
Let k be a positive integer.Denote by D_(1/k)the least integer d such that for every set A of nonnegative integers with the lower density 1/k,the set(k+1)A contains an infinite arithmetic progression with difference a... Let k be a positive integer.Denote by D_(1/k)the least integer d such that for every set A of nonnegative integers with the lower density 1/k,the set(k+1)A contains an infinite arithmetic progression with difference at most d,where(k+1)A is the set of all sums of k+1 elements(not necessarily distinct)of A.Chen and Li(2019)conjectured that D_(1/k)=k~2+o(k~2).The purpose of this paper is to confirm the above conjecture.We also prove that D_(1/k)is a prime for all sufficiently large integers k. 展开更多
关键词 infinite arithmetic progressions SUMSETS PRIMES circle method
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Prime in Quadratic Progressions on Average 被引量:1
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作者 Guang Shi LU Hai Wei SUN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第6期1187-1194,共8页
In this paper we study the distribution of primes in quadratic progressions on average. Our result improves a previous result of Baier and Zhao in some aspects.
关键词 PRIMES quadratic progressions circle method
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Rankin-Selberg coefficients in large arithmetic progressions 被引量:1
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作者 Emmanuel Kowalski Yongxiao Lin Philippe Michel 《Science China Mathematics》 SCIE CSCD 2023年第12期2767-2778,共12页
Let(λ_f(n))_(n≥1)be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f.We prove that,for any fixedη>0,under the Ramanujan-Petersson conjecture for GL_(2)Maass forms,th... Let(λ_f(n))_(n≥1)be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f.We prove that,for any fixedη>0,under the Ramanujan-Petersson conjecture for GL_(2)Maass forms,the Rankin-Selberg coefficients(λ_f(n)^(2))_(n≥1)admit a level of distributionθ=2/5+1/260-ηin arithmetic progressions. 展开更多
关键词 arithmetic progressions Rankin-Selberg L-functions δ-method
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Arithmetic Progressions,Different Regularity Lemmas and Removal Lemmas
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作者 Endre Szemerédi 《Communications in Mathematics and Statistics》 SCIE 2015年第3期315-328,共14页
This lecture note is mainly about arithmetic progressions,different regularity lemmas and removal lemmas.We will be very brief most of the time,trying to avoid technical details,even definitions.For most technical det... This lecture note is mainly about arithmetic progressions,different regularity lemmas and removal lemmas.We will be very brief most of the time,trying to avoid technical details,even definitions.For most technical details,we refer the reader to references.Apart from arithmetic progressions,we also discuss property testing and extremal graph theory. 展开更多
关键词 Arithmetic progressions Regularity lemmas Removal lemmas
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ZFJ wins the First Prize for Technological Progress from the China National Textile and Apparel Council
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作者 Niu Fang Qiu Shuchen 《China Textile》 2026年第1期10-10,共1页
On November 28th,the 2025 China National Textile and Apparel Council Science and Technology Awards Ceremony was held in Beijing.The project"Key Technologies and Systems for Green and Intelligent Production of Lyo... On November 28th,the 2025 China National Textile and Apparel Council Science and Technology Awards Ceremony was held in Beijing.The project"Key Technologies and Systems for Green and Intelligent Production of Lyocell Fibers,"in which Zhengzhou Textile Machinery Co.,Ltd.(ZFJ)participated,won the first prize for scientific and technological progress. 展开更多
关键词 science technology awards technologies systems intelligent production lyocell fibers scientific technological progress lyocell fibersin green production technological progress
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An Inspiring Path--There is nothing like travelling to China that can help to appreciate the country’s progress and learn lessons from it
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作者 LE PRINCE ELIDAD MODE ELENGA 《ChinAfrica》 2026年第1期36-38,共3页
Far from being mere rhetoric or abstract theory,Chinese-style modernisation is a concrete reality best grasped through direct experience.Before arriving in China,my knowledge of Chinese modernisation was based mainly ... Far from being mere rhetoric or abstract theory,Chinese-style modernisation is a concrete reality best grasped through direct experience.Before arriving in China,my knowledge of Chinese modernisation was based mainly on reading,classroom education,and accounts from colleagues who had already travelled around the country. 展开更多
关键词 MODERNIZATION education China PROGRESS travel experience
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Illusion of inactivity:Revisiting progressive multiple sclerosis treatment paradigms
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作者 Tal Ganz Tamir Ben-Hur 《Neural Regeneration Research》 2026年第3期1134-1135,共2页
Active inflammation in“inactive”progressive multiple sclerosis:Traditionally,the distinction between relapsing-remitting multiple sclerosis and progressive multiple sclerosis(PMS)has been framed as an inflammatory v... Active inflammation in“inactive”progressive multiple sclerosis:Traditionally,the distinction between relapsing-remitting multiple sclerosis and progressive multiple sclerosis(PMS)has been framed as an inflammatory versus degenerative dichotomy.This was based on a broad misconception regarding essentially all neurodegenerative conditions,depicting the degenerative process as passive and immune-independent occurring as a late byproduct of active inflammation in the central nervous system(CNS),which is(solely)systemically driven. 展开更多
关键词 inflammatory versus degenerative dichotomythis treatment paradigms illusion inactivity multiple sclerosis traditionallythe central nervous system cns which progressive multiple sclerosis active inflammation progressive multiple sclerosis pms
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Research on the Cultivation Technology of Yam(Dioscorea opposita)in Northern China
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作者 Jintong LIU Wenjia ZENG +3 位作者 Qiangtian LONG Jiayi WANG Yufei LI Huiqin LIU 《Agricultural Biotechnology》 2026年第1期9-12,共4页
Yam(Dioscorea opposita)is an important economic crop,and the development of its the cultivation tecchnology is of great significance for increasing yield,improving quality,and reducing the occurrence of pests and dise... Yam(Dioscorea opposita)is an important economic crop,and the development of its the cultivation tecchnology is of great significance for increasing yield,improving quality,and reducing the occurrence of pests and diseases.With the progression of agricultural technology and changes in market demands,the cultivation tecchnology of yam is constantly innovating and improving.This paper reviewed recent research advances in yam cultivation tecchnology,covering aspects such as soil improvement,variety selection,technological innovations,green pest control,and harvesting and storage.The goal is to provide references for the sustainable development of the yam industry. 展开更多
关键词 YAM CULTIVATION MANAGEMENT Research progress
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Tear proteomics reveals biomarkers for visual field progression in normal-tension glaucoma
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作者 Le-Wei Tang Hui-Yan Mao +5 位作者 Mei-Min Lin Si Zhu Qiang-Jie Huang De-Fu Chen Wei-He Zhou Yuan-Bo Liang 《International Journal of Ophthalmology(English edition)》 2026年第1期1-10,共10页
AIM:To identify early biomarkers associated with glaucomatous visual field(VF)progression in patients with normal-tension glaucoma(NTG).METHODS:This study included patients were divided into two groups based on diseas... AIM:To identify early biomarkers associated with glaucomatous visual field(VF)progression in patients with normal-tension glaucoma(NTG).METHODS:This study included patients were divided into two groups based on disease progression status.Tear samples were collected for proteomic analysis.Dataindependent acquisition(DIA)mass spectrometry combined with bioinformatic analyses was performed to identify and validate potential protein biomarkers for NTG progression.Additionally,differentially expressed proteins(DEPs)were evaluated using mediating effect models and receiver operating characteristic(ROC)curve analysis.RESULTS:A total of 19 patients(20 eyes)with NTG participated in this study,including 10 patients(4 males and 6 females;10 eyes)in the progression group with mean age of 67.70±9.03y and 10 patients(4 males and 6 females;10 eyes)in the non-progression group with mean age of 68.60±7.58y.A total of 158 significantly differentially expressed proteins were detected.UniProt database annotation identified 3 upregulated proteins and 12 downregulated proteins.Kyoto Encyclopedia of Genes and Genomes(KEGG)pathway analysis showed that these DEPs were mainly enriched in pathways such as oocyte meiosis.Gene Ontology(GO)enrichment analysis revealed functional clusters related to cellular processes.Weighted gene coexpression network analysis(WGCNA)indicated that the core proteins were primarily involved in the neurodegenerationmultiple diseases pathway and cellular processes.Mediating effect analysis identified PRDX4(L)as a potential protein biomarker.ROC curve analysis showed that GNAI1 had the largest area under the curve(AUC=0.889).CONCLUSION:This study identifies 15 differentially expressed proteins in the tear fluid of NTG patients,including PRDX4(L).PRDX4(L)plays a key role in oxidative stress. 展开更多
关键词 normal-tension glaucoma TEARS PROTEOMICS biomarkers visual field progression
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Multibipolar radiofrequency vs single needle microwave ablation for the treatment of newly diagnosed hepatocellular carcinoma
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作者 Cécilia Bahloul Agnès Rode +6 位作者 Pierre Pradat Laurent Milot Jérôme Dumortier Philippe Merle Jean-Yves Mabrut Loïc Boussel Angelo Della Corte 《World Journal of Gastroenterology》 2026年第2期104-113,共10页
BACKGROUND Data comparing the outcomes of hepatocellular carcinoma(HCC)ablation by multibipolar radiofrequency ablation(mbp-RFA)and microwave ablation(MWA)are lacking.This study compares safety and efficacy of the two... BACKGROUND Data comparing the outcomes of hepatocellular carcinoma(HCC)ablation by multibipolar radiofrequency ablation(mbp-RFA)and microwave ablation(MWA)are lacking.This study compares safety and efficacy of the two techniques in treatment-naive HCC.AIM To compare the risk of local tumor progression(LTP)according to the technique;secondary endpoints included technique efficacy rate at one-month,overall survival and major complication rate.METHODS A bi-institutional retrospective analysis of patients undergoing treatment-naive HCC ablation by either technique was performed.Inverse probability of treatment weighting was used to compare the two groups.Mixed effects multivariate Cox regression was applied to identify risk factors for LTP.RESULTS A total of 362 patients(mean age,66.1±6.2 years,308 men)were included,of which 242(323 tumors)treated by mbp-RFA and 120(168 tumors)by MWA.After a median follow-up of 27 months,cumulative LTP was 11.4%after mbp-RFA and 25.2%after MWA.Independent risk factors for LTP at multivariate analysis were MWA(hazard ratio=2.85,P<0.001)and tumor size(hazard ratio=1.08,P<0.001).Two-year LTP-free survival was higher after mbp-RFA than MWA regardless of size(<3 cm:96%vs 87.1%,P<0.01;≥3 cm:87.5%vs 74%,P=0.04).Technique efficacy rate was higher after mbp-RFA(94.1%vs 87.5%,P=0.01).No difference was observed in major complication rate(9.5%vs 7.5%,P=0.59),nor 5-year overall survival(63.6%vs 58.3%,P=0.33).CONCLUSION Mbp-RFA leads to better local tumor control of treatment-naïve HCC than MWA regardless of tumor size and has better primary efficacy,while maintaining a comparable safety profile. 展开更多
关键词 Local tumor progression Ablation MICROWAVE RADIOFREQUENCY Hepatocellular carcinoma
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Tumor microenvironment-driven microRNA dysregulation:Key interactions in colorectal cancer progression
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作者 Adriana G Quiroz-Reyes Paulina Delgado-Gonzalez +6 位作者 Jose Francisco Islas Veronica L Loaiza-Gutierrez Michelle G Santoyo-Suarez Juan A Garcia-Loredo Carlos A Gonzalez-Villarreal Fernanda Ramirez-Fernandez Elsa N Garza-Treviño 《World Journal of Gastrointestinal Oncology》 2026年第1期28-46,共19页
Colorectal cancer remains one of the leading causes of morbidity and mortality worldwide.Despite notable advances in early detection and therapeutic strategies,the molecular mechanisms underlying tumor survival,chemot... Colorectal cancer remains one of the leading causes of morbidity and mortality worldwide.Despite notable advances in early detection and therapeutic strategies,the molecular mechanisms underlying tumor survival,chemotherapy resistance,and metastasis are not yet fully understood.MicroRNAs(miRNAs)have emerged as pivotal regulators of cancer development,as they modulate gene expression and orchestrate key signaling pathways.However,the epigenetic mechanisms that control miRNA expression and their downstream gene targets remain largely unclear.In this review,we highlight the critical role of the colorectal cancer microenvironment in influencing miRNA expression and discuss how this regulation contributes to tumorigenesis.A better understanding of these processes may lead to the identification of novel therapeutic targets and strategies to prevent recurrence. 展开更多
关键词 Cancer progression MICRORNAS Colorectal cancer Tumor microenvironment Therapeutic response
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Therapeutic Potential of Fingolimod and Dimethyl Fumarate in Preclinical Pancreatic Cancer Models
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作者 Pauline Gousseau Laurie Genest +1 位作者 Guillaume Froget Tristan Rupp 《Oncology Research》 2026年第3期387-405,共19页
Objectives:The five-year survival rate for pancreatic cancer is notably low,posing a significant challenge to patient health.The primary treatments are radiotherapy and chemotherapy,sometimes combined with targeted th... Objectives:The five-year survival rate for pancreatic cancer is notably low,posing a significant challenge to patient health.The primary treatments are radiotherapy and chemotherapy,sometimes combined with targeted therapy;however,their clinical benefits are limited.Therefore,developing new models to evaluate the therapeutic potential of novel molecules is essential.Fingolimod and Dimethyl Fumarate(DMF),currently used to treat multiple sclerosis,have recently been shown to have anti-cancer effects in several preclinical tumor models.This study aims to evaluate the therapeutic potential of Fingolimod and DMF in pancreatic cancer by investigating their respective in vitro cytotoxicity and in vivo antitumor effects.Methods:In this study,we evaluated for the first time these two drugs in pancreatic preclinical models in vitro using 3D spheroid tumor models and in vivo,which are compared to two standard-of-care consisting of Gemcitabine and Erlotinib.Results:In vitro,both Fingolimod and DMF induced cytotoxicity in spheroids from two pancreatic cell lines.Additionally,Fingolimod and DMF displayed anticancer effects in two subcutaneous xenograft models using PANC-1 and CFPAC-1 cells.Conclusions:Although the responses observed with Fingolimod and DMF were similar to those of Gemcitabine and Erlotinib,these findings indicate a potential emerging interest in Fingolimod and DMF for the treatment of pancreatic cancer.However,further work is still necessary to fully characterize how these drugs affect tumor progression. 展开更多
关键词 Pancreatic cancer preclinical models tumor progression FINGOLIMOD dimethyl Fumarate
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Analysis of Histochemical Localization and Content Influencing Factors of Saponins in Pseudostellaria heterophylla
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作者 Huiqing PAN Yanda ZHANG +3 位作者 Zhenhua WANG Qi ZHAO Zuyun YE Xin WANG 《Medicinal Plant》 2026年第1期5-9,19,共6页
This paper provides a systematic review of the histochemical localization,content characteristics,and influencing factors of saponins in Pseudostellaria heterophylla based on an extensive literature survey.It provides... This paper provides a systematic review of the histochemical localization,content characteristics,and influencing factors of saponins in Pseudostellaria heterophylla based on an extensive literature survey.It provides an in-depth analysis and summary of the effects of biological factors,environmental conditions,agronomic practices,processing methods,and continuous cropping obstacles on the synthesis of P.heterophylla saponins,as well as their underlying mechanisms.Based on identified gaps in the current literature,future research directions and prospects are proposed.The findings of this review offer valuable insights for advancing the understanding of the saponin biosynthesis mechanisms in P.heterophylla and for enhancing its quality. 展开更多
关键词 Pseudostellaria heterophylla SAPONIN Histochemical localization Content influencing factors Research progress
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MRFNet:A Progressive Residual Fusion Network for Blind Multiscale Image Deblurring
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作者 Wang Zhang Haozhuo Cao Qiangqiang Yao 《Computers, Materials & Continua》 2026年第3期1851-1866,共16页
Recent advances in deep learning have significantly improved image deblurring;however,existing approaches still suffer from limited global context modeling,inadequate detail restoration,and poor texture or edge percep... Recent advances in deep learning have significantly improved image deblurring;however,existing approaches still suffer from limited global context modeling,inadequate detail restoration,and poor texture or edge perception,especially under complex dynamic blur.To address these challenges,we propose the Multi-Resolution Fusion Network(MRFNet),a blind multi-scale deblurring framework that integrates progressive residual connectivity for hierarchical feature fusion.The network employs a three-stage design:(1)TransformerBlocks capture long-range dependencies and reconstruct coarse global structures;(2)Nonlinear Activation Free Blocks(NAFBlocks)enhance local detail representation and mid-level feature fusion;and(3)an optimized residual subnetwork based on gated feature modulation refines texture and edge details for high-fidelity restoration.Extensive experiments demonstrate that MRFNet achieves superior performance compared to state-of-the-art methods.On GoPro,it attains 32.52 dB Peak Signal-to-Noise Ratio(PSNR)and 0.071 Learned Perceptual Image Patch Similarity(LPIPS),outperforming MIMOWNet(32.50 dB,0.075).On HIDE,it achieves 30.25 dB PSNR and 0.945 Structural Similarity Index Measure(SSIM),representing gains of+0.26 dB and+0.015 SSIM over MIMO-UNet(29.99 dB,0.930).On RealBlur-J,it reaches 28.82 dB PSNR and 0.872 SSIM,surpassing MIMO-UNet by+1.19 dB and+0.035 SSIM(27.63 dB,0.837).These results validate the effectiveness of the proposed progressive residual fusion and hybrid attention mechanisms in balancing global context understanding and local detail recovery for blind image deblurring. 展开更多
关键词 Blind deblurring progressive network multi-scale features residual structure
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