An improved recursive doubling algorithm for solving linear recurrence R <n,1>is given,whose parallel time complexity is (τ++τ.) logn when n processors are available,achieving the lower bound in array processo...An improved recursive doubling algorithm for solving linear recurrence R <n,1>is given,whose parallel time complexity is (τ++τ.) logn when n processors are available,achieving the lower bound in array processor type computation.展开更多
Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the...Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.展开更多
It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of ...It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.展开更多
The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The ...The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The recursion formula is factorized completely.展开更多
Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function ...Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid(X.Z. Wang, Phys. Rev. E66(2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.展开更多
文摘An improved recursive doubling algorithm for solving linear recurrence R <n,1>is given,whose parallel time complexity is (τ++τ.) logn when n processors are available,achieving the lower bound in array processor type computation.
文摘Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11271210 and 11201451Anhui Province Natural Science Foundation under Grant No.1608085MA04
文摘It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.
基金Supported by Program "Frontier Topics in Mathematical Physics"(KJCX3-SYW-S03)National Natural Science Foundation of China under Grant No.11035008
文摘The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The recursion formula is factorized completely.
文摘Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid(X.Z. Wang, Phys. Rev. E66(2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.
