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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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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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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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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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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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Common Prosperity:A Goal for All Governments?
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作者 ROBERT WALKER 《China Today》 2026年第1期20-23,共4页
China’s“common prosperity”policy is a multidimensional pursuit of social and economic progress aimed at full realization by 2050.A CHIEVING common prosperity–prosperity that is universally shared–has been a longs... China’s“common prosperity”policy is a multidimensional pursuit of social and economic progress aimed at full realization by 2050.A CHIEVING common prosperity–prosperity that is universally shared–has been a longstanding aspiration of the Chinese government. 展开更多
关键词 multidimensional pursuit Chinese government chieving common prosperity prosperity social economic progress common prosperity universal sharing
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Neurodegenerative processes of aging: A perspective of restoration through insulin-like growth factor-1
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作者 Rosana Crespo Claudia Herenu 《Neural Regeneration Research》 2026年第4期1562-1563,共2页
The aging process is an inexorable fact throughout our lives and is considered a major factor in develo ping neurological dysfunctions associated with cognitive,emotional,and motor impairments.Aging-associated neurode... The aging process is an inexorable fact throughout our lives and is considered a major factor in develo ping neurological dysfunctions associated with cognitive,emotional,and motor impairments.Aging-associated neurodegenerative diseases are characterized by the progressive loss of neuronal structure and function. 展开更多
关键词 neurodegenerative diseases neurodegenerative processes cognitive impairments progressive loss neuronal structure function develo ping neurological dysfunctions insulin growth factor RESTORATION aging process
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Potential common pathogenesis of several neurodegenerative diseases
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作者 Ting Fan Jiaman Peng +3 位作者 Huiting Liang Wenzhi Chen Junlin Wang Renshi Xu 《Neural Regeneration Research》 2026年第3期972-988,共17页
With the gradual advancement of research methods and technologies,various biological processes have been identified as playing roles in the pathogenesis of neurodegenerative diseases.However,current descriptions of th... With the gradual advancement of research methods and technologies,various biological processes have been identified as playing roles in the pathogenesis of neurodegenerative diseases.However,current descriptions of these biological processes do not fully explain the onset,progression,and development of these conditions.Therefore,exploration of the pathogenesis of neurodegenerative diseases remains a valuable area of research.This review summarizes the potential common pathogeneses of Alzheimer’s disease,Parkinson’s disease,amyotrophic lateral sclerosis,Huntington’s disease,frontotemporal lobar dementia,and Lewy body disease.Research findings have indicated that several common biological processes,including aging,genetic factors,progressive neuronal dysfunction,neuronal death and apoptosis,protein misfolding and aggregation,neuroinflammation,mitochondrial dysfunction,axonal transport defects,and gut microbiota dysbiosis,are involved in the pathogenesis of these six neurodegenerative diseases.Based on current information derived from diverse areas of research,these biological processes may form complex pathogenic networks that lead to distinctive types of neuronal death in neurodegenerative diseases.Furthermore,promoting the regeneration of damaged neurons may be achievable through the repair of affected neural cells if the underlying pathogenesis can be prevented or reversed.Hence,these potential common biological processes may represent only very small,limited elements within numerous intricate pathogenic networks associated with neurodegenerative diseases.In clinical treatment,interfering with any single biological process has proven insufficient to completely halt the progression of neurodegenerative diseases.Therefore,future research on the pathogenesis of neurodegenerative diseases should focus on uncovering the complex pathogenic networks,rather than isolating individual biological processes.Based on this,therapies that aim to block or reverse various targets involved in the potential pathogenic mechanisms of neurodegenerative diseases may be promising directions,as current treatment methods that focus on halting a single pathogenic factor have not achieved satisfactory efficacy. 展开更多
关键词 aging Alzheimer’s disease amyotrophic lateral sclerosis frontotemporal lobar dementia genetics Huntington’s disease Lewy body disease Parkinson’s disease progressive neuron dysfunction and death protein misfolding
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The Ternary Goldbach Problem with Primes in Arithmetic Progressions 被引量:4
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作者 Zhen Feng ZHANG Tian Ze WANG State Key Laboratory of Information Security, Graduate School, Chinese Academy of Sciences, Beijing 100039, P. R. China Depariment of Mathematics, Henan University, Kaifeng 475001, P. R. China Department of Mathematics, Henan University, Kaifeng 475001, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第4期679-696,共18页
In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik const... In this paper, we give an explicit numerical upper bound for the moduli of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result implies a quantitative upper bound for the Linnik constant. 展开更多
关键词 Ternary Goldbach problem PRIME Arithmetic progression Circle method
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New Lower Bounds for the Least Common Multiples of Arithmetic Progressions 被引量:2
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作者 Rongjun WU Qianrong TAN Shaofang HONG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2013年第6期861-864,共4页
Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk := u0 + kr. Let Ln := 1cm(u0,u1,... ,un) and let a,l≥2 be any integers. In this paper, the authors show that, for integers... Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk := u0 + kr. Let Ln := 1cm(u0,u1,... ,un) and let a,l≥2 be any integers. In this paper, the authors show that, for integers α≥ a, r ≥max(a,l - 1) and n ≥lατ, the following inequality holds Ln≥u0r^(l-1)α+a-l(r+1)^n.Particularly, letting l = 3 yields an improvement on the best previous lower bound on Ln obtained by Hong and Kominers in 2010. 展开更多
关键词 Arithmetic progression Least common multiple Lower bound
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