On the basis of other researchers' achievements and the authors' understanding of flow units, a proposal on classification and denomination of flow units for clastic reservoirs of continental deposit is put fo...On the basis of other researchers' achievements and the authors' understanding of flow units, a proposal on classification and denomination of flow units for clastic reservoirs of continental deposit is put forward according to the practical need of oilfield development and relevant theories. The specific implications of development and geology are given to each type of flow units, which has provided a scientific basis for oil development.展开更多
This paper begins with the overthrow of the concept of combining ability in crossbreeding by the concept of heritability.The reason is that general combining ability changes with the number and kind of pure strains in...This paper begins with the overthrow of the concept of combining ability in crossbreeding by the concept of heritability.The reason is that general combining ability changes with the number and kind of pure strains in the foundation stock and hence special combining ability changes also,so that work with different kinds of pure strains in the foundation stock cannot be compared.Hence combining ability is useless as a parameter to predict the amount of heterosis expected in the next generation.On the other hand,since each cross has a separate heritability,it can be applied to a cross population just as successfully as in purebreeding.Since the same concept holds in both cases,resort to any other concept would be superfluous.That's why combining ability must be rejected.Another reason(not given in the full text)is,an infinite number of pure strains would be required in the foundation stock for its results to be comparable with those of the heritability theory,which disposes of its utility altogether.The main content of the thesis is then the centennial enigma of heterosis can be resolved by Descarte's theoretic method of deduction.Accordingly we start from the definition of heterosis.H=F¡-MP,where H is heterosis,F,is the first generation offspring,MP is the mean of the parents or midparent,and from the use of a binomial random variable and its extention to the multinomial case derive the basic relations of heterosis with its components.Starting with second degree statistics,we obtain Vn=Vr,-2cov(F,,MP)+Vup,where V and cov stand for variance and covariance.The equations of heterosis are v„=(1/2)Na²+(1/4)Nd’+Vr(F,)=additive dominance F,epistasis Vup=(1/2)Na’+(1/2)V1,additive parental epistasis V„=(1/4)Nd’+V(F)+(1/2)V1,dominance F,epistasis parental epistasis.where N is number of genes controlling a trait,a=(P1-P,)12,d is deviation from midparent,while the variance components are all indicated by their names under the repective terms.It turns out that all these can be easily computed from the data so that the problem becomes a simple one which any college student may solve.In other words,the right answers are found when the right questions are asked.Who had ever shown that the heritability principle is inapplicable in crossbreeding,e.g.,in a crossing of two pure strains?From this cue arose the realization that the F,of a cross of two pure strains must also be a Mendelian population,with p and q both equal to 1/2 which simplifies the algebra outright.This Heritability Theory of Heterosis,or HTH in capital letters,re-sts on 2 initial anguments:1)Since 0.5+0.5=1,crossing two pure strains gives a population which is only a special case of pure-breeding,thereforea heritability coefficient must exist for the F1;2)Our problem reduces to that of finding that coefficient;the an-swer is given by the additive component divided by Ve.,i.e.,(1/2)No'1 Vp..which is readily found from the solution of the het-erosis equations.Thus the elemnal enigma of heterosis is resolved!This happened at the end of the 20th century.We now come to the second point of the discovery,the new genetic parameter crossheritability which will rise in size with the increase of the number of times it's used and form the link between breeding and evolution.The advent of the Age of Evolution Engineering in the 21st century marks a totally new era,showing that artificial will ultimately supercede natural selection,with the long span of time element eliminated.For agriculture at least,it means there is no limit to the increase of food supply by the new method,with the concentra-tion of desirable genes by hybridization in place of the old theory of their fixation.Genetic gain is achieved through artificial selec-tion,with an 80%saving of time,labor and cost by adoption of the new method.Applied to a further increase in all kinds of agri-cultural products including hybrd rice,it means that a huge eacalation,in fact a New Green Revolution,on a much langer scale than that of any such before,is in view,provided it is adopted in our research and educational institutions as early as possible,ere its spread elsewhere.The possibilities from the evolution point of view can only be pictured by science fiction.展开更多
The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of ...The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.展开更多
In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster de...In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.展开更多
By using Frobenius maps and F-stable representations,we count the number of isomor- phism classes of indecomposable representations with the fixed dimension vector of a species of type _n over a finite field,first,and...By using Frobenius maps and F-stable representations,we count the number of isomor- phism classes of indecomposable representations with the fixed dimension vector of a species of type _n over a finite field,first,and then,as an application,give a q-analogue of the Weyl-Kac denominator identity of type _n.展开更多
The so-called“small denominator problem”was a fundamental problem of dynamics,as pointed out by Poincar´e.Small denominators appear most commonly in perturbative theory.The Duffing equation is the simplest exam...The so-called“small denominator problem”was a fundamental problem of dynamics,as pointed out by Poincar´e.Small denominators appear most commonly in perturbative theory.The Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small denominators.In this paper,using the forced Duffing equation as an example,we illustrate that the famous“small denominator problems”never appear if a non-perturbative approach based on the homotopy analysis method(HAM),namely“the method of directly defining inverse mapping”(MDDiM),is used.The HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully obtained.So,from the viewpoint of the HAM,the famous“small denominator problems”are only artifacts of perturbation methods.Therefore,completely abandoning perturbation methods but using the HAM-based MDDiM,one would be never troubled by“small denominators”.The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called“small denominators”.展开更多
We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and gener...We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.展开更多
文摘On the basis of other researchers' achievements and the authors' understanding of flow units, a proposal on classification and denomination of flow units for clastic reservoirs of continental deposit is put forward according to the practical need of oilfield development and relevant theories. The specific implications of development and geology are given to each type of flow units, which has provided a scientific basis for oil development.
文摘This paper begins with the overthrow of the concept of combining ability in crossbreeding by the concept of heritability.The reason is that general combining ability changes with the number and kind of pure strains in the foundation stock and hence special combining ability changes also,so that work with different kinds of pure strains in the foundation stock cannot be compared.Hence combining ability is useless as a parameter to predict the amount of heterosis expected in the next generation.On the other hand,since each cross has a separate heritability,it can be applied to a cross population just as successfully as in purebreeding.Since the same concept holds in both cases,resort to any other concept would be superfluous.That's why combining ability must be rejected.Another reason(not given in the full text)is,an infinite number of pure strains would be required in the foundation stock for its results to be comparable with those of the heritability theory,which disposes of its utility altogether.The main content of the thesis is then the centennial enigma of heterosis can be resolved by Descarte's theoretic method of deduction.Accordingly we start from the definition of heterosis.H=F¡-MP,where H is heterosis,F,is the first generation offspring,MP is the mean of the parents or midparent,and from the use of a binomial random variable and its extention to the multinomial case derive the basic relations of heterosis with its components.Starting with second degree statistics,we obtain Vn=Vr,-2cov(F,,MP)+Vup,where V and cov stand for variance and covariance.The equations of heterosis are v„=(1/2)Na²+(1/4)Nd’+Vr(F,)=additive dominance F,epistasis Vup=(1/2)Na’+(1/2)V1,additive parental epistasis V„=(1/4)Nd’+V(F)+(1/2)V1,dominance F,epistasis parental epistasis.where N is number of genes controlling a trait,a=(P1-P,)12,d is deviation from midparent,while the variance components are all indicated by their names under the repective terms.It turns out that all these can be easily computed from the data so that the problem becomes a simple one which any college student may solve.In other words,the right answers are found when the right questions are asked.Who had ever shown that the heritability principle is inapplicable in crossbreeding,e.g.,in a crossing of two pure strains?From this cue arose the realization that the F,of a cross of two pure strains must also be a Mendelian population,with p and q both equal to 1/2 which simplifies the algebra outright.This Heritability Theory of Heterosis,or HTH in capital letters,re-sts on 2 initial anguments:1)Since 0.5+0.5=1,crossing two pure strains gives a population which is only a special case of pure-breeding,thereforea heritability coefficient must exist for the F1;2)Our problem reduces to that of finding that coefficient;the an-swer is given by the additive component divided by Ve.,i.e.,(1/2)No'1 Vp..which is readily found from the solution of the het-erosis equations.Thus the elemnal enigma of heterosis is resolved!This happened at the end of the 20th century.We now come to the second point of the discovery,the new genetic parameter crossheritability which will rise in size with the increase of the number of times it's used and form the link between breeding and evolution.The advent of the Age of Evolution Engineering in the 21st century marks a totally new era,showing that artificial will ultimately supercede natural selection,with the long span of time element eliminated.For agriculture at least,it means there is no limit to the increase of food supply by the new method,with the concentra-tion of desirable genes by hybridization in place of the old theory of their fixation.Genetic gain is achieved through artificial selec-tion,with an 80%saving of time,labor and cost by adoption of the new method.Applied to a further increase in all kinds of agri-cultural products including hybrd rice,it means that a huge eacalation,in fact a New Green Revolution,on a much langer scale than that of any such before,is in view,provided it is adopted in our research and educational institutions as early as possible,ere its spread elsewhere.The possibilities from the evolution point of view can only be pictured by science fiction.
基金Supported partially by the National 973 Programs (Grant No. 2006CB805905)
文摘The main result of this paper is that any two non-isomorphic indecomposable modules of a cluster-tilted algebra of finite representation type have different dimension vectors. As an application to cluster algebras of Types A, D, E, we give a proof of the Fomin Zelevinsky denominators conjecture for cluster variables, namely, different cluster variables have different denominators with respect to any given cluster.
基金supported by National Natural Science Foundation of China(Grant No.11901586)the Natural Science Foundation of Guangdong Province(Grant No.2019A1515011323)the Sun Yat-sen University Research Grant for Youth Scholars(Grant No.19lgpy244)。
文摘In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.
基金the Doctoral Program of Higher Education(Grant No.20030027002)
文摘By using Frobenius maps and F-stable representations,we count the number of isomor- phism classes of indecomposable representations with the fixed dimension vector of a species of type _n over a finite field,first,and then,as an application,give a q-analogue of the Weyl-Kac denominator identity of type _n.
基金This work is partly supported by National Natural Science Foundation of China(Approval No.12272230)Shanghai Pilot Program for Basic Research–Shanghai Jiao Tong University(No.21TQ1400202).
文摘The so-called“small denominator problem”was a fundamental problem of dynamics,as pointed out by Poincar´e.Small denominators appear most commonly in perturbative theory.The Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small denominators.In this paper,using the forced Duffing equation as an example,we illustrate that the famous“small denominator problems”never appear if a non-perturbative approach based on the homotopy analysis method(HAM),namely“the method of directly defining inverse mapping”(MDDiM),is used.The HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully obtained.So,from the viewpoint of the HAM,the famous“small denominator problems”are only artifacts of perturbation methods.Therefore,completely abandoning perturbation methods but using the HAM-based MDDiM,one would be never troubled by“small denominators”.The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called“small denominators”.
基金supported by National Natural Science Foundation of China(Grant Nos.11101436 and 11101151)the Fundamental Research Funds for the Central Universities
文摘We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.
