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MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRDINGER SYSTEMS 被引量:1
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作者 万优艳 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1199-1218,共20页
We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of... We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function. 展开更多
关键词 Elliptic system Schrdinger equation variational methods Nehari manifold relative category CONCENTRATION
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NIH funding for disease categories related to neurodegenerative diseases
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《Neural Regeneration Research》 SCIE CAS CSCD 2011年第23期1818-1840,共23页
Introduction The National Institutes of Health (NIH), a part of the U.S. Department of Health and Human Services is the nation's medical research agency-making important discoveries that improve health and save liv... Introduction The National Institutes of Health (NIH), a part of the U.S. Department of Health and Human Services is the nation's medical research agency-making important discoveries that improve health and save lives.Thanks in large part to NIH-funded medical research, Americans today are living longer and healthier. The NIH invests over $31.2* billion annually in medical research for the American people. More than 80% of the NIH's funding is awarded through almost 50 000 competitive grants to more than 325 000 researchers at over 3 000 universities, medical schools, and other research institutions in every state and around the world. 展开更多
关键词 NIH funding for disease categories related to neurodegenerative diseases over NEI AG NS INC Portfolio CTR MRI LISA OD
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National Institutes of Health Funding for disease categories related to Neural Regeneration Research
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《Neural Regeneration Research》 SCIE CAS CSCD 2011年第26期2053-2080,共28页
The National Institutes of Health (NIH), a part of the U.S. Department of Health and Human Services, is the nation's medical research agency-making important discoveries that improve health and save lives.Thanks in... The National Institutes of Health (NIH), a part of the U.S. Department of Health and Human Services, is the nation's medical research agency-making important discoveries that improve health and save lives.Thanks in large part to NIH-funded medical research, Americans today are living longer and healthier. Life expectancy in the United States has jumped from 47 years in 1900 to 78 years as reported in 2009, and disability in people over age 65 has dropped dramatically in the past 3 decades. In recent years, nationwide rates of new diagnoses and deaths from all cancers combined have fallen significantly. 展开更多
关键词 NS NEI National Institutes of Health Funding for disease categories related to Neural Regeneration Research CTR HD NCI DC NIH ATP DE
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NIH Funding for Disease Categories related to Neural Regeneration Research
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《Neural Regeneration Research》 SCIE CAS CSCD 2011年第14期1108-1120,共13页
The National Institutes of Health (NIH),a part of the U.S. Department of Health and Human Services,is the nation's medical research agency-making important discoveries that improve health and save lives.Thanks in l... The National Institutes of Health (NIH),a part of the U.S. Department of Health and Human Services,is the nation's medical research agency-making important discoveries that improve health and save lives.Thanks in large part to NIH-funded medical research,Americans today are living longer and healthier. Life expectancy in the United States has jumped from 47 years in 1900 to 78 years as reported in 2009,and disability in people over age 65 has dropped dramatically in the past 3 decades. In recent years,nationwide rates of new diagnoses and deaths from all cancers combined have fallen significantly. 展开更多
关键词 NIH Funding for Disease Categories related to Neural Regeneration Research
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Applications of balanced pairs 被引量:3
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作者 LI HuanHuan WANG JunFu HUANG ZhaoYong 《Science China Mathematics》 SCIE CSCD 2016年第5期861-874,共14页
Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or ... Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y(resp. Y-coresolution dimension of X)is finite, then the bounded homotopy category of Y(resp. X) is contained in that of X(resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite. 展开更多
关键词 balanced pairs relative cotorsion pairs relative derived categories relative singularity categories relative(co)resolution dimension
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Resolving Subcategories of Triangulated Categories and Relative Homological Dimension 被引量:2
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作者 Xin MA Ti Wei ZHAO Zhao Yong HUANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2017年第11期1513-1535,共23页
We introduce and study (pre)resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.
关键词 (Pre)resolving subcategories triangulated categories relative homological dimension Gorenstein categories
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Relative Quotient Triangulated Categories 被引量:1
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作者 Shengyong Pan 《Algebra Colloquium》 SCIE CSCD 2014年第2期195-206,共12页
Let A be a finite dimensional algebra over a field k. We consider a subfunc- tor F of Ext1A(-, -), which has enough projectives and injectives such that P(F) is of finite type, where P(F) denotes the set of F-pr... Let A be a finite dimensional algebra over a field k. We consider a subfunc- tor F of Ext1A(-, -), which has enough projectives and injectives such that P(F) is of finite type, where P(F) denotes the set of F-projectives. One can get the relative derived category Db(A) of A-rood. For an F-self-orthogonal module TF, we discuss the relation between the relative quotient triangulated category Db(A)/Kb(addTF) and the relative stable category of the Frobenius category of TF-Cohen-Macaulay modules. In particular, for an F-Gorenstein algebra A and an F-tilting A-module TF, we get a triangle equiva- lence between DbF(A)/Kb(add TF) and the relative stable category of TF-Cohen-Macaulay modules. This gives the relative version of a result of Chen and Zhang. 展开更多
关键词 F-tilting module relative quotient triangulated category F-Gorenstein alge-bra
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Categorical resolutions of a class of derived categories 被引量:4
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作者 Pu Zhang 《Science China Mathematics》 SCIE CSCD 2018年第2期391-402,共12页
We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough p... We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough projective objects such that D_(hf)~b(A) = K^b(P), and finding an example such that D_(hf)~b(A)≠K^b(P). We realize the bounded derived category D^b(A) as a Verdier quotient of the relative derived category D_C^b(A), where C is an arbitrary resolving contravariantly finite subcategory of A. Using this relative derived categories, we get categorical resolutions of a class of bounded derived categories of module categories of infinite global dimension.We prove that if an Artin algebra A of infinite global dimension has a module T with inj.dimT <∞ such that ~⊥T is finite, then D^b(modA) admits a categorical resolution; and that for a CM(Cohen-Macaulay)-finite Gorenstein algebra, such a categorical resolution is weakly crepant. 展开更多
关键词 homologically finite object perfect complex smooth triangulated category (weakly crepant)categorical resolution (relative) derived category CM-finite Gorenstein algebra
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Relative Derived Equivalences and Relative Homological Dimensions
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作者 Sheng Yong PAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第4期439-456,共18页
Let A be a small abelian category.For a closed subbifunctor F of Ext_A^1(-,-),Buan has generalized the construction of Verdier’s quotient category to get a relative derived category,where he localized with respect ... Let A be a small abelian category.For a closed subbifunctor F of Ext_A^1(-,-),Buan has generalized the construction of Verdier’s quotient category to get a relative derived category,where he localized with respect to F-acyclic complexes.In this paper,the homological properties of relative derived categories are discussed,and the relation with derived categories is given.For Artin algebras,using relative derived categories,we give a relative version on derived equivalences induced by F-tilting complexes.We discuss the relationships between relative homological dimensions and relative derived equivalences. 展开更多
关键词 Relative derived category F-tilting complex relative derived equivalence relative homological dimension
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