In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expre...In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.展开更多
We introduce a simple recursive relation and give an explicit formula of the Kauffman bracket of two-strand braid link . Then, we give general formulas of the bracket of the sequence of links of three-strand braids . ...We introduce a simple recursive relation and give an explicit formula of the Kauffman bracket of two-strand braid link . Then, we give general formulas of the bracket of the sequence of links of three-strand braids . Finally, we give an interesting result that the Kauffman bracket of the three-strand braid link is actually the product of the brackets of the two-strand braid links and . Moreover, a recursive relation for is also given.展开更多
The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors ...The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors on X , we construct in this paper two different compactifications of the moduli space M0,2（X, d[P1/Zr], x＇）： Nonlinear Sigma Model Mx＇d and Linear Sigma Model Nx＇d . Relations between Mx＇d and Nx＇d are studied and a new gluing recursive relation on Nx＇d is derived from Mx＇d due to virtual localization formula.展开更多
Relative clauses in traditional grammars,which are sometimes called attributive clauses,are divided into two types:restrictive and non-restrictive.Building upon the discussion of recursion in Halliday’s Systemic Func...Relative clauses in traditional grammars,which are sometimes called attributive clauses,are divided into two types:restrictive and non-restrictive.Building upon the discussion of recursion in Halliday’s Systemic Functional Grammar(SFG),this paper conducts a functional syntactic analysis of such clauses,aimed at probing into their logical structures.展开更多
This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we ex- pose analytic proper...This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we ex- pose analytic properties of gauge-boson amplitudes, BCFW-deformations, the large z-behavior of amplitudes, and on-shell recursion relations of gluons. We discuss further developments of on-shell recursion relations, including generalization to other quantum field theories, supersymmetric theo- ties in particular, recursion relations for off-shell currents, recursion relation with nonzero boundary contributions, bonus relations, relations for rational parts of one-loop amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we present samples of applications, including solutions of split helicity amplitudes and of Af = 4 SYM theories, consequences of consistent conditions under re- cursion relation, Kleiss-Kuijf （KK） and Bern-Carrasco-Johansson （BCJ） relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye （KLT） relations.展开更多
We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher gen...We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.展开更多
In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-compone...In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.展开更多
In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton’s relations on the moduli space of curves.As an application,we prove that Pix...In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton’s relations on the moduli space of curves.As an application,we prove that Pixton’s relations imply a known topological recursion relation on Mg,1 for genus g≤4.展开更多
基金The first author,Mrs.Yan Hong,was partially supported by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007)by the Science Research Fund of Inner Mongolia University for Nationalities(Grant No.NMDBY15019)by the Foun-dation of the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZY19157 and NJZY20119)in China。
文摘In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.
文摘We introduce a simple recursive relation and give an explicit formula of the Kauffman bracket of two-strand braid link . Then, we give general formulas of the bracket of the sequence of links of three-strand braids . Finally, we give an interesting result that the Kauffman bracket of the three-strand braid link is actually the product of the brackets of the two-strand braid links and . Moreover, a recursive relation for is also given.
基金supported by Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100181110071)National Natural Science Foundation of China (Grant No. 11071176),supported by National Natural Science Foundation of China (Grant Nos. 11071173 and 11221101)Hundred Talents Program for Young Teachers (Grant No. SWJTU12BR028)
文摘The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors on X , we construct in this paper two different compactifications of the moduli space M0,2（X, d[P1/Zr], x＇）： Nonlinear Sigma Model Mx＇d and Linear Sigma Model Nx＇d . Relations between Mx＇d and Nx＇d are studied and a new gluing recursive relation on Nx＇d is derived from Mx＇d due to virtual localization formula.
文摘Relative clauses in traditional grammars,which are sometimes called attributive clauses,are divided into two types:restrictive and non-restrictive.Building upon the discussion of recursion in Halliday’s Systemic Functional Grammar(SFG),this paper conducts a functional syntactic analysis of such clauses,aimed at probing into their logical structures.
文摘This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we ex- pose analytic properties of gauge-boson amplitudes, BCFW-deformations, the large z-behavior of amplitudes, and on-shell recursion relations of gluons. We discuss further developments of on-shell recursion relations, including generalization to other quantum field theories, supersymmetric theo- ties in particular, recursion relations for off-shell currents, recursion relation with nonzero boundary contributions, bonus relations, relations for rational parts of one-loop amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we present samples of applications, including solutions of split helicity amplitudes and of Af = 4 SYM theories, consequences of consistent conditions under re- cursion relation, Kleiss-Kuijf （KK） and Bern-Carrasco-Johansson （BCJ） relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye （KLT） relations.
文摘We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571192,11671219)K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.
基金supported by National Natural Science Foundation of China(Grant No11601279)the Fundamental Research Funds of Shandong University
文摘In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton’s relations on the moduli space of curves.As an application,we prove that Pixton’s relations imply a known topological recursion relation on Mg,1 for genus g≤4.
