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UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N(C) WITH TRUNCATED MULTIPLICITIES 被引量:4
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作者 涂振汉 王中华 《Acta Mathematica Scientia》 SCIE CSCD 2013年第1期122-130,共9页
This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N(C) with truncated multiplicities, and our results improve some earlier work.
关键词 meromorphic mappings truncated multiplicities uniqueness theorems value distribution theory
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Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue 被引量:1
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作者 Shouzhong Fu Zhong Wang 《Applied Mathematics》 2014年第15期2185-2194,共10页
In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the l... In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the linear differential operator are given, and a fundamental fact that the algebraic, geometric and analytic multiplicities for any eigenvalue of self-adjoint differential operators are equal is proven. 展开更多
关键词 Differential OPERATORS EIGENVALUE ALGEBRAIC multiplicities Geometric multiplicities ANALYTIC multiplicities
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TWO MEROMORPHIC FUNCTIONS SHARE SOME PAIRS OF SMALL FUNCTIONS WITH TRUNCATED MULTIPLICITIES
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作者 曹红哲 曹廷彬 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1854-1864,共11页
Using the techniques proposed in [3], we prove that two nonconstant meromorphic functions f and g on C must be linked by a quasi-Mbius transformation if they share some pairs of small functions with more precise trunc... Using the techniques proposed in [3], we prove that two nonconstant meromorphic functions f and g on C must be linked by a quasi-Mbius transformation if they share some pairs of small functions with more precise truncated multiplicities, which improve and extend the results of Duc Quang Si. 展开更多
关键词 meromorphic function small function truncated multiplicities quasi-Mbius transformation
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COMPARISON OF CHARGED PARTICLE MULTIPLICITIES IN THREE-JET AND TWO-JET EVENTS FROM e^(+)e^(-) ANNIHILATION AT HIGH ENERGIES
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作者 LIU Ximing 《Chinese Physics Letters》 SCIE CAS CSCD 1989年第5期193-196,共4页
The charged particle multiplicity(n3j) in the three-jet events in e^(+)e^(-) annihilation is considered.The comparison of(n3j) with (n2j) is presented.The prediction of the multiplicity agrees well with experiments.Mo... The charged particle multiplicity(n3j) in the three-jet events in e^(+)e^(-) annihilation is considered.The comparison of(n3j) with (n2j) is presented.The prediction of the multiplicity agrees well with experiments.Moreover,some predictions for high energy range are made. 展开更多
关键词 MULTIPLICITY ANNIHILATION
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Existence and Multiplicities of Solutions for Asymptotically Linear Ordinary Differential Equations Satisfying Sturm-Liouville BVPs with Resonance
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作者 Keqiang Li Ronghua Tong 《Journal of Applied Mathematics and Physics》 2019年第5期1197-1211,共15页
In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 tha... In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H3 that is similar to (LL) in Theorem 1.1, by index theory and Morse theory, we obtain more nontrivial solutions. 展开更多
关键词 Asymptotically Linear Ordinary Differential Equations with RESONANCE Multiple SOLUTIONS STURM-LIOUVILLE Boundary Value Problem Index THEORY Morse THEORY
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Multiplicities of fixed points of holomorphic maps in several complex variables 被引量:1
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作者 张广远 《Science China Mathematics》 SCIE 2001年第3期330-337,共8页
Let Δυ be the unit ball in ?υ with center 0 (the origin of υ) and let F:Δυ→?υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF i =F°... Let Δυ be the unit ball in ?υ with center 0 (the origin of υ) and let F:Δυ→?υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF i =F°?°F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally. 展开更多
关键词 holomorphic maps complex dynamical systems multiplicities of fixed points
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Counting Multiplicities in a Hypersurface over Number Fields
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作者 Hao Wen Chunhui Liu 《Algebra Colloquium》 SCIE CSCD 2018年第3期437-458,共22页
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the ... We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition. 展开更多
关键词 algebraic point counting multiplicities height function over projective space intersection tree rational point
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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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Changing Tracks--The new CR450 train, currently in the testing phase, reaches speeds of 450 km/h thanks to technological advances
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作者 GE LIJUN 《ChinAfrica》 2026年第1期51-51,共1页
Safer,smarter,faster...In China,people prefer high-speed trains to flights if the journey time is under five hours.High-speed train travel is set to become even more attractive with the addition of a new member to the... Safer,smarter,faster...In China,people prefer high-speed trains to flights if the journey time is under five hours.High-speed train travel is set to become even more attractive with the addition of a new member to the high-speed train family:the CR450,the world’s fastest electric multiple unit(EMU). 展开更多
关键词 journey time electric multiple unit CR high speed trains FLIGHTS electric multiple unit emu
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Predicting lymph node metastasis in colorectal cancer using caselevel multiple instance learning
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作者 Ling-Feng Zou Xuan-Bing Wang +4 位作者 Jing-Wen Li Xin Ouyang Yi-Ying Luo Yan Luo Cheng-Long Wang 《World Journal of Gastroenterology》 2026年第1期110-125,共16页
BACKGROUND The accurate prediction of lymph node metastasis(LNM)is crucial for managing locally advanced(T3/T4)colorectal cancer(CRC).However,both traditional histopathology and standard slide-level deep learning ofte... BACKGROUND The accurate prediction of lymph node metastasis(LNM)is crucial for managing locally advanced(T3/T4)colorectal cancer(CRC).However,both traditional histopathology and standard slide-level deep learning often fail to capture the sparse and diagnostically critical features of metastatic potential.AIM To develop and validate a case-level multiple-instance learning(MIL)framework mimicking a pathologist's comprehensive review and improve T3/T4 CRC LNM prediction.METHODS The whole-slide images of 130 patients with T3/T4 CRC were retrospectively collected.A case-level MIL framework utilising the CONCH v1.5 and UNI2-h deep learning models was trained on features from all haematoxylin and eosinstained primary tumour slides for each patient.These pathological features were subsequently integrated with clinical data,and model performance was evaluated using the area under the curve(AUC).RESULTS The case-level framework demonstrated superior LNM prediction over slide-level training,with the CONCH v1.5 model achieving a mean AUC(±SD)of 0.899±0.033 vs 0.814±0.083,respectively.Integrating pathology features with clinical data further enhanced performance,yielding a top model with a mean AUC of 0.904±0.047,in sharp contrast to a clinical-only model(mean AUC 0.584±0.084).Crucially,a pathologist’s review confirmed that the model-identified high-attention regions correspond to known high-risk histopathological features.CONCLUSION A case-level MIL framework provides a superior approach for predicting LNM in advanced CRC.This method shows promise for risk stratification and therapy decisions,requiring further validation. 展开更多
关键词 Colorectal cancer Lymph node metastasis Deep learning Multiple instance learning HISTOPATHOLOGY
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Role of peroxisome proliferator-activated receptor alpha in neurodegenerative diseases and other neurological disorders:Clinical application prospects
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作者 Zijun Wu Yuying Zhao +3 位作者 Shujing Hao Mengyao An Chengcheng Song Jing Li 《Neural Regeneration Research》 2026年第4期1468-1482,共15页
Peroxisome proliferator-activated receptor alpha is a member of the nuclear hormone receptor superfamily and functions as a transcription factor involved in regulating cellular metabolism.Previous studies have shown t... Peroxisome proliferator-activated receptor alpha is a member of the nuclear hormone receptor superfamily and functions as a transcription factor involved in regulating cellular metabolism.Previous studies have shown that PPARαplays a key role in the onset and progression of neurodegenerative diseases.Consequently,peroxisome proliferator-activated receptor alpha agonists have garnered increasing attention as potential treatments for neurological disorders.This review aims to clarify the research progress regarding peroxisome proliferator-activated receptor alpha in nervous system diseases.Peroxisome proliferator-activated receptor alpha is present in all cell types within adult mouse and adult neural tissues.Although it is conventionally believed to be primarily localized in the nucleus,its function may be regulated by a dynamic balance between cytoplasmic and nuclear shuttling.Both endogenous and exogenous peroxisome proliferator-activated receptor alpha agonists bind to the peroxisome proliferator-activated response element to exert their biological effects.Peroxisome proliferator-activated receptor alpha plays a significant therapeutic role in neurodegenerative diseases.For instance,peroxisome proliferator-activated receptor alpha agonist gemfibrozil has been shown to reduce levels of soluble and insoluble amyloid-beta in the hippocampus of Alzheimer's disease mouse models through the autophagy-lysosomal pathway.Additionally,peroxisome proliferator-activated receptor alpha is essential for the normal development and functional maintenance of the substantia nigra,and it can mitigate motor dysfunction in Parkinson's disease mouse models.Furthermore,peroxisome proliferator-activated receptor alpha has been found to reduce neuroinflammation and oxidative stress in various neurological diseases.In summary,peroxisome proliferator-activated receptor alpha plays a crucial role in the onset and progression of multiple nervous system diseases,and peroxisome proliferator-activated receptor alpha agonists hold promise as new therapeutic agents for the treatment of neurodegenerative diseases,providing new options for patient care. 展开更多
关键词 AGONISTS Alzheimer's disease gut microbiota multiple sclerosis nervous system disease NEURODEGENERATION neurodegenerative disease NEUROINFLAMMATION Parkinson's disease peroxisome proliferator-activated receptor alpha
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Effects and mechanisms of adipose tissue-derived extracellular vesicles in vascular inflammation and dysfunction
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作者 Daphne Lintsen Bieke Broux 《Neural Regeneration Research》 2026年第5期2005-2006,共2页
Neuroinflammation is a key process in the pathogenesis of various neurodegenerative diseases,such as multiple sclerosis(MS),Alzheimer's disease,and traumatic brain injury.Even for disorders historically unrelated ... Neuroinflammation is a key process in the pathogenesis of various neurodegenerative diseases,such as multiple sclerosis(MS),Alzheimer's disease,and traumatic brain injury.Even for disorders historically unrelated to neuroinflammation,such as Alzheimer's disease,it is now shown to precede pathological protein aggregations. 展开更多
关键词 pathological protein aggregations vascular inflammation NEUROINFLAMMATION neurodegenerative diseasessuch multiple sclerosis Alzheimers disease adipose tissue derived extracellular vesicles alzheimers diseaseit
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Is age-related myelinodegenerative change an initial risk factor of neurodegenerative diseases?
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作者 Shuangchan Wu Jun Chen 《Neural Regeneration Research》 2026年第2期648-658,共11页
Myelination,the continuous ensheathment of neuronal axons,is a lifelong process in the nervous system that is essential for the precise,temporospatial conduction of action potentials between neurons.Myelin also provid... Myelination,the continuous ensheathment of neuronal axons,is a lifelong process in the nervous system that is essential for the precise,temporospatial conduction of action potentials between neurons.Myelin also provides intercellular metabolic support to axons.Even minor disruptions in the integrity of myelin can impair neural performance and increase susceptibility to neurological diseases.In fact,myelin degeneration is a well-known neuropathological condition that is associated with normal aging and several neurodegenerative diseases,including multiple sclerosis and Alzheimer’s disease.In the central nervous system,compact myelin sheaths are formed by fully mature oligodendrocytes.However,the entire oligodendrocyte lineage is susceptible to changes in the biological microenvironment and other risk factors that arise as the brain ages.In addition to their well-known role in action potential propagation,oligodendrocytes also provide intercellular metabolic support to axons by transferring energy metabolites and delivering exosomes.Therefore,myelin degeneration in the aging central nervous system is a significant contributor to the development of neurodegenerative diseases.Interventions that mitigate age-related myelin degeneration can improve neurological function in aging individuals.In this review,we investigate the changes in myelin that are associated with aging and their underlying mechanisms.We also discuss recent advances in understanding how myelin degeneration in the aging brain contributes to neurodegenerative diseases and explore the factors that can prevent,slow down,or even reverse age-related myelin degeneration.Future research will enhance our understanding of how reducing age-related myelin degeneration can be used as a therapeutic target for delaying or preventing neurodegenerative diseases. 展开更多
关键词 aging Alzheimer’s disease multiple sclerosis MYELIN myelin-axon metabolite crosstalk myelinodegeneration neurodegenerative disease OLIGODENDROCYTE Parkinson’s disease white matter
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Determinants of alpha-synuclein pathogenesis in Parkinson's disease
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作者 Oriol Barcenas Marc Estivill-Alonso Salvador Ventura 《Neural Regeneration Research》 2026年第4期1568-1569,共2页
Alpha-synuclein and Parkinson's disease:Neuronal damage and inflammation caused by the aggregation of alpha-synuclein(α-syn)are central to a group of disorders known as synucleopathies,which includes Parkinson... Alpha-synuclein and Parkinson's disease:Neuronal damage and inflammation caused by the aggregation of alpha-synuclein(α-syn)are central to a group of disorders known as synucleopathies,which includes Parkinson's disease(PD),dementia with Lewy bodies,and multiple system atrophy,among others.PD,the most common synucleinopathy,is the second most prevalent neurodegenerative disease after Alzheimer's disease,and it is the fastest growing.Its primary hallmark is the degeneration of dopaminergic neurons in the substantia nigra pars compacta,disrupting the communication with the striatum. 展开更多
关键词 parkinsons disease pd dementia parkinsons disease neuronal neurodegenerative disease multiple system atrophyamong alzheimers diseaseand Parkinsons disease alpha synuclein degeneration dopaminergic neurons
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Intelligent integration and advancement of multi-organ-on-a-chip
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作者 Chen-Xi Song Lu Huang 《Biomedical Engineering Communications》 2026年第1期1-3,共3页
Multi-organ-on-a-chip(MOOC)technology represents a pivotal direction in the organ-on-a-chip field,seeking to emulate the complex interactions of multiple human organs in vitro through microfluidic systems.This technol... Multi-organ-on-a-chip(MOOC)technology represents a pivotal direction in the organ-on-a-chip field,seeking to emulate the complex interactions of multiple human organs in vitro through microfluidic systems.This technology overcomes the limitations of traditional single-organ models,providing a novel platform for investigating complex disease mechanisms and evaluating drug efficacy and toxicity.Although it demonstrates broad application prospects,its development still faces critical bottlenecks,including inadequate physiological coupling between organs,short functional maintenance durations,and limited real-time monitoring capabilities.Contemporary research is advancing along three key directions,including functional coupling,sensor integration,and full-process automation systems,to propel the technology toward enhanced levels of physiological relevance and predictive accuracy. 展开更多
关键词 investigating complex disease mechanisms emulate complex interactions multiple human organs vitro sensor integration intelligent integration predictive accuracy physiological coupling multi organ chip microfluidic systemsthis
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Chemical exchange saturation transfer MRI for neurodegenerative diseases:An update on clinical and preclinical studies
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作者 Ahelijiang Saiyisan Shihao Zeng +4 位作者 Huabin Zhang Ziyan Wang Jiawen Wang Pei Cai Jianpan Huang 《Neural Regeneration Research》 2026年第2期553-568,共16页
Chemical exchange saturation transfer magnetic resonance imaging is an advanced imaging technique that enables the detection of compounds at low concentrations with high sensitivity and spatial resolution and has been... Chemical exchange saturation transfer magnetic resonance imaging is an advanced imaging technique that enables the detection of compounds at low concentrations with high sensitivity and spatial resolution and has been extensively studied for diagnosing malignancy and stroke.In recent years,the emerging exploration of chemical exchange saturation transfer magnetic resonance imaging for detecting pathological changes in neurodegenerative diseases has opened up new possibilities for early detection and repetitive scans without ionizing radiation.This review serves as an overview of chemical exchange saturation transfer magnetic resonance imaging with detailed information on contrast mechanisms and processing methods and summarizes recent developments in both clinical and preclinical studies of chemical exchange saturation transfer magnetic resonance imaging for Alzheimer’s disease,Parkinson’s disease,multiple sclerosis,and Huntington’s disease.A comprehensive literature search was conducted using databases such as PubMed and Google Scholar,focusing on peer-reviewed articles from the past 15 years relevant to clinical and preclinical applications.The findings suggest that chemical exchange saturation transfer magnetic resonance imaging has the potential to detect molecular changes and altered metabolism,which may aid in early diagnosis and assessment of the severity of neurodegenerative diseases.Although promising results have been observed in selected clinical and preclinical trials,further validations are needed to evaluate their clinical value.When combined with other imaging modalities and advanced analytical methods,chemical exchange saturation transfer magnetic resonance imaging shows potential as an in vivo biomarker,enhancing the understanding of neuropathological mechanisms in neurodegenerative diseases. 展开更多
关键词 Alzheimer’s disease chemical exchange saturation transfer Huntington’s disease magnetic resonance imaging molecular imaging multiple sclerosis neurodegenerative disease Parkinson’s disease
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Neuroinflammation in neurodegenerative diseases:Focusing on the mediation of T lymphocytes
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作者 Ke Li Rongsha Chen +4 位作者 Ruohua Wang Wenhui Fan Ninghui Zhao Zhongshan Yang Jinyuan Yan 《Neural Regeneration Research》 2026年第5期1864-1889,共26页
Neurodegenerative diseases are a group of illnesses characterized by the gradual deterioration of the central nervous system,leading to a decline in patients'cognitive,motor,and emotional abilities.Neuroinflammati... Neurodegenerative diseases are a group of illnesses characterized by the gradual deterioration of the central nervous system,leading to a decline in patients'cognitive,motor,and emotional abilities.Neuroinflammation plays a significant role in the progression of these diseases.However,there is limited research on therapeutic approaches to specifically target neuroinflammation.The role of T lymphocytes,which are crucial mediators of the adaptive immune response,in neurodegenerative diseases has been increasingly recognized.This review focuses on the involvement of T lymphocytes in the neuroinflammation associated with neurodegenerative diseases.The pathogenesis of neurodegenerative diseases is complex,involving multiple mechanisms and pathways that contribute to the gradual degeneration of neurons,and T cells are a key component of these processes.One of the primary factors driving neuroinflammation in neurodegenerative diseases is the infiltration of T cells and other neuroimmune cells,including microglia,astrocytes,B cells,and natural killer cells.Different subsets of CD4~+T cells,such as Th1,Th2,Th17,and regulatory T cells,can differentiate into various cell types and perform distinct roles within the neuroinflammatory environment of neurodegenerative diseases.Additionally,CD8~+T cells,which can directly regulate immune responses and kill target cells,also play several important roles in neurodegenerative diseases.Clinical trials investigating targeted T cell therapies for neurodegenerative diseases have shown that,while some patients respond positively,others may not respond as well and may even experience adverse effects.Targeting T cells precisely is challenging due to the complexity of immune responses in the central nervous system,which can lead to undesirable side effects.However,with new insights into the pathophysiology of neurodegenerative diseases,there is hope for the establishment of a solid theoretical foundation upon which innovative treatment strategies that target T cells can be developed in the future. 展开更多
关键词 Alzheimer's disease amyotrophic lateral sclerosis CD4^(+)T cell CD8^(+)T cell helper T cell multiple sclerosis neurodegenerative diseases NEUROINFLAMMATION Parkinson's disease regulatory T cell
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Parametric“non-nested”discriminants for multiplicities of univariate polynomials
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作者 Hoon Hong Jing Yang 《Science China Mathematics》 SCIE CSCD 2024年第8期1911-1932,共22页
We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that suc... We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients.Those polynomials in the coefficients are called discriminants for multiplicities.It is also known that discriminants can be obtained using repeated parametric greatest common divisors.The resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so on.In this paper,we give a new type of discriminant that is not based on repeated greatest common divisors.The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees. 展开更多
关键词 parametric polynomial complex roots DISCRIMINANT MULTIPLICITY RESULTANT
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On Mixed Multiplicities of Good Filtrations
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作者 Duong Quoc Viet Le Van Dinh 《Algebra Colloquium》 SCIE CSCD 2015年第3期421-436,共16页
This paper interprets mixed multiplicities of good filtrations as Hilbert-Samuel multiplicities, and shows that (ε1,..., εm)-superficial sequences in [16] (2007) and superficial sequences in [15] (1973) are we... This paper interprets mixed multiplicities of good filtrations as Hilbert-Samuel multiplicities, and shows that (ε1,..., εm)-superficial sequences in [16] (2007) and superficial sequences in [15] (1973) are weak-(FC)-sequences in [19] (2000). As consequences, we not only obtain generalized results for mixed multiplicities of ideals in [15, 16, 19] but also get an improvement of [19, Theorem 3.4] that seems to account well for the essence of [16, Theorem 1.4]. 展开更多
关键词 mixed multiplicity filtration (FC)-sequence superficial sequence
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RATIO OF CHARGED PARTICLE MULTIPLICITIES OF GLUON JET AND QUARK JET
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作者 刘希明 王群 《Chinese Science Bulletin》 SCIE EI CAS 1991年第19期1610-1613,共4页
The primary quark and antiquark (e<sup>+</sup>e<sup>-</sup>→q<sub>0</sub>(?)<sub>0</sub>) produced through electromagnetic interaction in e<sup>+</sup>e... The primary quark and antiquark (e<sup>+</sup>e<sup>-</sup>→q<sub>0</sub>(?)<sub>0</sub>) produced through electromagnetic interaction in e<sup>+</sup>e<sup>-</sup> annihilation at high energy arc fragmented into various hadrons through strong interaction in hadronic events. According to the theory of quantum chromodynamics(QCD), both quark q<sub>0</sub> and antiquark (?)<sub>0</sub> have a certain probability of emitting a hard gluon (e<sup>+</sup>e<sup>-</sup>→q<sub>0</sub>(?)<sub>0</sub>g). In this ease, a three-jet event is formed by the fragmentation of q<sub>0</sub>, (?)<sub>0</sub> and g (all called partons). In Ref. [1], the number of partons evolved from 展开更多
关键词 PARTON multiplicity.
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