The static drill rooted nodular pile is a new type of pile foundation consisting of precast nodular pile and the surrounding cemented soil.This composite pile has a relatively high bearing capacity and the mud polluti...The static drill rooted nodular pile is a new type of pile foundation consisting of precast nodular pile and the surrounding cemented soil.This composite pile has a relatively high bearing capacity and the mud pollution will be largely reduced during the construction process by using this type of pile.In order to investigate the bearing capacity and load transfer mechanism of this pile,a group of experiments were conducted to provide a comparison between this new pile and the bored pile.The axial force of a precast nodular pile was also measured by the strain gauges installed on the pile to analyze the distribution of the axial force of the nodular pile and the skin friction supported by the surrounding soil,then 3D models were built by using the ABAQUS finite element program to investigate the load transfer mechanism of this composite pile in detail.By combining the results of field tests and the finite element method,the outcome showed that the bearing capacity of a static drill rooted nodular pile is higher than the bored pile,and that this composite pile will form a double stress dispersion system which will not only confirm the strength of the pile,but also make the skin friction to be fully mobilized.The settlement of this composite pile is mainly controlled by the precast nodular pile;meanwhile,the nodular pile and the surrounding cemented soil can be considered as deformation compatibility during the loading process.The nodes on the nodular pile play an important role during the load transfer process,the shear strength of the interface between the cemented soil and the soil of the static drill rooted pile is larger than that of the bored pile.展开更多
Vertical occurrence of soil urease activity along with ammonia content from three distinct regions viz. Deep forest region (No tidal action and wave attack occurs as it is furthest from river shore and it contains max...Vertical occurrence of soil urease activity along with ammonia content from three distinct regions viz. Deep forest region (No tidal action and wave attack occurs as it is furthest from river shore and it contains maximum content of organic carbon and minimum soil salinity and silicate concentration. In this zone plenty of pneumatophores, below ground root and dense vegetation are found), Rooted region (It is situated in between Deep forest region and Un-rooted region. This region contains only pneumatophores but it is devoid of long roots and vegetations. It faces wave attack and tidal action less than that of Un-rooted region) and Un-rooted region (It is closest to river shore and faces maximum wave attack and tidal action;it contains minimum organic carbon but maximum soil salinity and silicate concentration. This zone is totally devoid of any roots, pneumatophores and vegetations) of Sundarban mangrove forest ecosystem, India revealed an interesting explanation. Soil urease activity showed a decreasing pattern with increase in depth from the deep forest region of the Sundarban forest ecosystem. Soil urease activity was found to be more sensitive to soil temperature and pH rather than soil salinity. This ensured that soil urease along with the microbes present in the Sundarban forest ecosystem are more tolerant to fluctuation in salinity than that of temperature. Soil ammonia concentration was found to be directly governed by the soil urease activity [The regression equation is Ammonia in soil = -1.64 + 0.0402 Urease Activity (R-Sq = 62.9%, P < 0.001, n = 41)].展开更多
In order to improve our knowledge of the mechanical effect of the roots of mixed-plantings on soil reinforcement and slope protection,the influence of roots of a mixed-planting with four herb species(Medicago sativa L...In order to improve our knowledge of the mechanical effect of the roots of mixed-plantings on soil reinforcement and slope protection,the influence of roots of a mixed-planting with four herb species(Medicago sativa L.,Elymus nutans Griseb.,Puccinellia distanx(L.),and Poa pratensis L.)and one shrub species(Caragana korshinskii Kom.)were investigated on the shear strength characteristics of saline loess soil.The root distribution characteristics were assessed via a survey when the plants grew for one year.The effects of the root biomass density,the root mass ratio(RMR)of the fine roots to the coarse roots,the moisture content,and the salt content on the shear strength index of the rooted soil were analyzed via a triaxial compression test,and the mechanism of these effects was discussed.The results indicate that the biomass density decreased linearly with increasing depth.The RMR initially decreased with depth and then increased,exhibiting in a quadratic relationship.The cohesion of the rooted soil increased linearly as the biomass density increased.The cohesion of the rooted soil initially increased with increasing RMR and salt content,and then it decreased.The turning point of the cohesion occurred when the RMR was 0.6 and the salt content was 1.18%.The internal friction angle of the rooted soil initially increased with biomass density and then decreased,and the turning point of the internal friction angle occurred when the biomass density was 0.015 g/cm3.The relationships between the internal friction angle of the rooted soil and the RMR and salt content were exponential incremental and linear subtractive relationship,respectively.Both the cohesion and the internal friction angle of the rooted soil linearly decreased with increasing moisture content.展开更多
Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorph...Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.展开更多
A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and fo...A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Mo- tivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD （RBTD） operator, an operator combining the Rota-Baxter operator and TD oper- ator, and coming from a recent study of Rota＇s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.展开更多
All maps we deal with in this note are rooted planar ones, which, in brief, are called maps. Most of terminologies here come from Refs. [1—3]. The purpose of this note is to determine the asymptotic enumerations base...All maps we deal with in this note are rooted planar ones, which, in brief, are called maps. Most of terminologies here come from Refs. [1—3]. The purpose of this note is to determine the asymptotic enumerations based on the enumerations in [1, 2]. Bender and Richmond gave a survey of the asymptotic enumeration. New asymptotic enumerations here can be considered as a complement and improvement of the survey.展开更多
The proposal of the strategy of developing the country through science education has clarified China’s demand for the development of the science and education industry and the cultivation of science and education tal...The proposal of the strategy of developing the country through science education has clarified China’s demand for the development of the science and education industry and the cultivation of science and education talents,and the birth of Science Education majors is an important link in the cultivation of scientific literacy.Based on the grounded theory,we interviewed three Science Education graduates from a university and coded the interview data by using NVivo 12.0 to find eight important factors affecting their professional training and employment choices.The factors are“social factors,”“individual career choice factors,”“campus resources,”“employment advantages,”“professional self-development,”“teacher factors,”“planning for further education and employment,”and“student motivation.”This study analyzes the interaction between the influencing factors,constructs a theoretical model of the influencing factors of the quality of Science Education professional training,explores the problems of the training process of Science Education majors and employment dilemmas,and puts forward corresponding suggestions.展开更多
Artificial vegetation restoration is the main measure for vegetation restoration and soil and water conservation in alpine mine dumps on the Qinghai-Tibet Plateau,China.However,there are few reports on the dynamic cha...Artificial vegetation restoration is the main measure for vegetation restoration and soil and water conservation in alpine mine dumps on the Qinghai-Tibet Plateau,China.However,there are few reports on the dynamic changes and the influencing factors of the soil reinforcement effect of plant species after artificial vegetation restoration under different recovery periods.We selected dump areas of the Delni Copper Mine in Qinghai Province,China to study the relationship between the shear strength and the peak displacement of the root-soil composite on the slope during the recovery period,and the influence of the root traits and soil physical properties on the shear resistance characteristics of the root-soil composite via in situ direct shear tests.The results indicate that the shear strength and peak displacement of the rooted soil initially decreased and then increased with the increase of the recovery period.The shear strength of the rooted soil and the recovery period exhibited a quadratic function relationship.There is no significant function relationship between the peak displacement and the recovery period.Significant positive correlations(P<0.05)exists between the shear strength of the root-soil composite and the root biomass density,root volume density,and root area ratio,and they show significant linear correlations(P<0.05).There are no significant correlations(P>0.05)between the shear strength of the root-soil composite and the root length density,and the root volume ratio of the coarse roots to the fine roots.A significant negative linear correlation(P<0.05)exists between the peak displacement of the rooted soil and the coarse-grain content,but no significant correlations(P>0.05)with the root traits,other soil physical property indices(the moisture content and dry density of the soil),and slope gradient.The coarse-grain content is the main factor controlling the peak displacement of the rooted soil.展开更多
This paper focuses on a question raised by Holm and Jorgensen,who asked if the induced cotorsion pairs(Φ(X),Φ(X)^(⊥))and(^(⊥)Ψ(Y),Ψ(Y))in Rep(Q,A)—the category of all A-valued representations of a quiver Q—are...This paper focuses on a question raised by Holm and Jorgensen,who asked if the induced cotorsion pairs(Φ(X),Φ(X)^(⊥))and(^(⊥)Ψ(Y),Ψ(Y))in Rep(Q,A)—the category of all A-valued representations of a quiver Q—are complete whenever(X,Y)is a complete cotorsion pair in an abelian category A satisfying some mild conditions.We give an affirmative answer if the quiver Q is rooted.As an application,we show under certain mild conditions that if a subcategory L,which is not necessarily closed under direct summands,of A is special precovering(resp.,preenveloping),thenΦ(L)(resp.,Ψ(L))is special precovering(resp.,preenveloping)in Rep(Q,A).展开更多
We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expecte...We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.展开更多
As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a nume...As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.展开更多
Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we giv...Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.展开更多
In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical ...In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical solution of initial value problems (IVPs). The methods are derived through the application of order and stability conditions normally associated with Runge-Kutta methods;the derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme;they are shown to satisfy the criteria for both consistency and stability;hence their convergence is guaranteed. Numerical experiments carried out further justified the efficiency of the methods.展开更多
A summation free formula for enumerating rooted nonseparable outerplanar maps with a face partition given is herein presented. As its corollaries, some summation free formulae for the bipartite and the simple cases ar...A summation free formula for enumerating rooted nonseparable outerplanar maps with a face partition given is herein presented. As its corollaries, some summation free formulae for the bipartite and the simple cases are also derived. Moreover, the formula for planted plane trees according to a given vertex partition is demonstrated in a new way.展开更多
This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit ...This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.展开更多
In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two ...In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.展开更多
In this paper, using the Strong Rooted Theorem of complex polynomial systems we prove the existence of global general solutions of a class of complex polynomial systems, discuss the qualitative structure of global gen...In this paper, using the Strong Rooted Theorem of complex polynomial systems we prove the existence of global general solutions of a class of complex polynomial systems, discuss the qualitative structure of global general solutions of normal polynomial systems, and obtain their representation theorem. Finally, we give some applications of the theorem.展开更多
文摘The static drill rooted nodular pile is a new type of pile foundation consisting of precast nodular pile and the surrounding cemented soil.This composite pile has a relatively high bearing capacity and the mud pollution will be largely reduced during the construction process by using this type of pile.In order to investigate the bearing capacity and load transfer mechanism of this pile,a group of experiments were conducted to provide a comparison between this new pile and the bored pile.The axial force of a precast nodular pile was also measured by the strain gauges installed on the pile to analyze the distribution of the axial force of the nodular pile and the skin friction supported by the surrounding soil,then 3D models were built by using the ABAQUS finite element program to investigate the load transfer mechanism of this composite pile in detail.By combining the results of field tests and the finite element method,the outcome showed that the bearing capacity of a static drill rooted nodular pile is higher than the bored pile,and that this composite pile will form a double stress dispersion system which will not only confirm the strength of the pile,but also make the skin friction to be fully mobilized.The settlement of this composite pile is mainly controlled by the precast nodular pile;meanwhile,the nodular pile and the surrounding cemented soil can be considered as deformation compatibility during the loading process.The nodes on the nodular pile play an important role during the load transfer process,the shear strength of the interface between the cemented soil and the soil of the static drill rooted pile is larger than that of the bored pile.
文摘Vertical occurrence of soil urease activity along with ammonia content from three distinct regions viz. Deep forest region (No tidal action and wave attack occurs as it is furthest from river shore and it contains maximum content of organic carbon and minimum soil salinity and silicate concentration. In this zone plenty of pneumatophores, below ground root and dense vegetation are found), Rooted region (It is situated in between Deep forest region and Un-rooted region. This region contains only pneumatophores but it is devoid of long roots and vegetations. It faces wave attack and tidal action less than that of Un-rooted region) and Un-rooted region (It is closest to river shore and faces maximum wave attack and tidal action;it contains minimum organic carbon but maximum soil salinity and silicate concentration. This zone is totally devoid of any roots, pneumatophores and vegetations) of Sundarban mangrove forest ecosystem, India revealed an interesting explanation. Soil urease activity showed a decreasing pattern with increase in depth from the deep forest region of the Sundarban forest ecosystem. Soil urease activity was found to be more sensitive to soil temperature and pH rather than soil salinity. This ensured that soil urease along with the microbes present in the Sundarban forest ecosystem are more tolerant to fluctuation in salinity than that of temperature. Soil ammonia concentration was found to be directly governed by the soil urease activity [The regression equation is Ammonia in soil = -1.64 + 0.0402 Urease Activity (R-Sq = 62.9%, P < 0.001, n = 41)].
基金the Second Tibetan Plateau Scientific Expedition and Research(STEP)program(Grant No.2019QZKK0905)the National Natural Science Foundation of China(Grant Nos.42002283,41572306,42041006 and 42062019)+2 种基金the Project of the Qinghai Science&Technology Department(Grant Nos.2020-ZJ-906 and 2014-ZJ-906)the Key Discipline Construction Project for Geological Resources and Geological Engineering of Qinghai University(Grant No.41250103)the Ministry of Education’s‘Innovative Team Development Scheme’(IRT17R62)。
文摘In order to improve our knowledge of the mechanical effect of the roots of mixed-plantings on soil reinforcement and slope protection,the influence of roots of a mixed-planting with four herb species(Medicago sativa L.,Elymus nutans Griseb.,Puccinellia distanx(L.),and Poa pratensis L.)and one shrub species(Caragana korshinskii Kom.)were investigated on the shear strength characteristics of saline loess soil.The root distribution characteristics were assessed via a survey when the plants grew for one year.The effects of the root biomass density,the root mass ratio(RMR)of the fine roots to the coarse roots,the moisture content,and the salt content on the shear strength index of the rooted soil were analyzed via a triaxial compression test,and the mechanism of these effects was discussed.The results indicate that the biomass density decreased linearly with increasing depth.The RMR initially decreased with depth and then increased,exhibiting in a quadratic relationship.The cohesion of the rooted soil increased linearly as the biomass density increased.The cohesion of the rooted soil initially increased with increasing RMR and salt content,and then it decreased.The turning point of the cohesion occurred when the RMR was 0.6 and the salt content was 1.18%.The internal friction angle of the rooted soil initially increased with biomass density and then decreased,and the turning point of the internal friction angle occurred when the biomass density was 0.015 g/cm3.The relationships between the internal friction angle of the rooted soil and the RMR and salt content were exponential incremental and linear subtractive relationship,respectively.Both the cohesion and the internal friction angle of the rooted soil linearly decreased with increasing moisture content.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671350 and 11571173)
文摘Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.
基金This work is supported by the National Natural Science Foundation of China （Grant No. 11371178） and the National Science Foundation of US （Grant No. DMS 1001855）. Shuyun Zhou thanks the hospitality of Rutgers University at Newark during her visit in 2012-2013.
文摘A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Mo- tivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD （RBTD） operator, an operator combining the Rota-Baxter operator and TD oper- ator, and coming from a recent study of Rota＇s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.
基金Project supported by the National Natural Science Foundation of China.
文摘All maps we deal with in this note are rooted planar ones, which, in brief, are called maps. Most of terminologies here come from Refs. [1—3]. The purpose of this note is to determine the asymptotic enumerations based on the enumerations in [1, 2]. Bender and Richmond gave a survey of the asymptotic enumeration. New asymptotic enumerations here can be considered as a complement and improvement of the survey.
文摘The proposal of the strategy of developing the country through science education has clarified China’s demand for the development of the science and education industry and the cultivation of science and education talents,and the birth of Science Education majors is an important link in the cultivation of scientific literacy.Based on the grounded theory,we interviewed three Science Education graduates from a university and coded the interview data by using NVivo 12.0 to find eight important factors affecting their professional training and employment choices.The factors are“social factors,”“individual career choice factors,”“campus resources,”“employment advantages,”“professional self-development,”“teacher factors,”“planning for further education and employment,”and“student motivation.”This study analyzes the interaction between the influencing factors,constructs a theoretical model of the influencing factors of the quality of Science Education professional training,explores the problems of the training process of Science Education majors and employment dilemmas,and puts forward corresponding suggestions.
基金supported by the Project of Qinghai Science&Technology Department(Grant No.2021-ZJ-956Q).
文摘Artificial vegetation restoration is the main measure for vegetation restoration and soil and water conservation in alpine mine dumps on the Qinghai-Tibet Plateau,China.However,there are few reports on the dynamic changes and the influencing factors of the soil reinforcement effect of plant species after artificial vegetation restoration under different recovery periods.We selected dump areas of the Delni Copper Mine in Qinghai Province,China to study the relationship between the shear strength and the peak displacement of the root-soil composite on the slope during the recovery period,and the influence of the root traits and soil physical properties on the shear resistance characteristics of the root-soil composite via in situ direct shear tests.The results indicate that the shear strength and peak displacement of the rooted soil initially decreased and then increased with the increase of the recovery period.The shear strength of the rooted soil and the recovery period exhibited a quadratic function relationship.There is no significant function relationship between the peak displacement and the recovery period.Significant positive correlations(P<0.05)exists between the shear strength of the root-soil composite and the root biomass density,root volume density,and root area ratio,and they show significant linear correlations(P<0.05).There are no significant correlations(P>0.05)between the shear strength of the root-soil composite and the root length density,and the root volume ratio of the coarse roots to the fine roots.A significant negative linear correlation(P<0.05)exists between the peak displacement of the rooted soil and the coarse-grain content,but no significant correlations(P>0.05)with the root traits,other soil physical property indices(the moisture content and dry density of the soil),and slope gradient.The coarse-grain content is the main factor controlling the peak displacement of the rooted soil.
基金partly supported by NSF of China(Grant No.11971388)partly supported by NSF of China(Grant No.12171146)+4 种基金partly supported by NSF of China(Grant No.12271230)partly supported by NSF of China(Grant No.12171297)the Scientific Research Funds of Huaqiao University(Grant No.605-50Y22050)the Fujian Alliance Of Mathematics(Grant No.2024SXLMMS04)the Foundation for Innovative Fundamental Research Group Project of Gansu Province(Grant No.23JRRA684)。
文摘This paper focuses on a question raised by Holm and Jorgensen,who asked if the induced cotorsion pairs(Φ(X),Φ(X)^(⊥))and(^(⊥)Ψ(Y),Ψ(Y))in Rep(Q,A)—the category of all A-valued representations of a quiver Q—are complete whenever(X,Y)is a complete cotorsion pair in an abelian category A satisfying some mild conditions.We give an affirmative answer if the quiver Q is rooted.As an application,we show under certain mild conditions that if a subcategory L,which is not necessarily closed under direct summands,of A is special precovering(resp.,preenveloping),thenΦ(L)(resp.,Ψ(L))is special precovering(resp.,preenveloping)in Rep(Q,A).
基金Supported by the National Natural Science Foundation of China(No:6087206011071158)+1 种基金the Science Foundation of Shanghai Education Committee(No:12ZZ193)the Natural Science Foundation of Shanghai city(No:12ZR1421000)
文摘We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.
文摘As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.
基金Acknowledgements The authors thank the Kavli Institute for Theoretical Physics China and the Morningside Center for Mathematics in Beijing for their hospitality and support. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11201201, 11371178）, the Fundamental Research Funds for the Central Universities （lzujbky-2013-8）, and the National Science Foundation of US （Grant No. DMS 1001855）.
文摘Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.
文摘In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical solution of initial value problems (IVPs). The methods are derived through the application of order and stability conditions normally associated with Runge-Kutta methods;the derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme;they are shown to satisfy the criteria for both consistency and stability;hence their convergence is guaranteed. Numerical experiments carried out further justified the efficiency of the methods.
基金Project supported by the National Natural Science Foundation of China.
文摘A summation free formula for enumerating rooted nonseparable outerplanar maps with a face partition given is herein presented. As its corollaries, some summation free formulae for the bipartite and the simple cases are also derived. Moreover, the formula for planted plane trees according to a given vertex partition is demonstrated in a new way.
基金NNSFC under Grant No.60373030 and Grant No.10571031
文摘This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.
文摘In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, using the Strong Rooted Theorem of complex polynomial systems we prove the existence of global general solutions of a class of complex polynomial systems, discuss the qualitative structure of global general solutions of normal polynomial systems, and obtain their representation theorem. Finally, we give some applications of the theorem.
