The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by apply...The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.展开更多
Schubert's method for solving systems of sparse equations has achieved a great deal of computational success. In this paper, Schubert's method was extended to multiple version, and the compact representation o...Schubert's method for solving systems of sparse equations has achieved a great deal of computational success. In this paper, Schubert's method was extended to multiple version, and the compact representation of multple Schubert's updating matrix was derived. The compact representation could be used to efficiently implement limited memory methods for large problems.展开更多
A set of methods for interprocedural analysis is proposed. First, an ap-proach for interprocedural constant propagation is given. Then the concept of constant propagation is extended so as to meet the needs of data de...A set of methods for interprocedural analysis is proposed. First, an ap-proach for interprocedural constant propagation is given. Then the concept of constant propagation is extended so as to meet the needs of data dependence analysis. Besides certain constant, constant range can also be propagated. The related propagating rules are introduced, and an idea for computing Return function is given. This approach can solve almost all interprocedural constant propagation problems with non-recursive calls. Second, a muItiple-version par-allelizing technique is also proposed for alias problem. The work related to this paper has been implemented on a shared-memory parallel computer.展开更多
Let f(n)be a multiplicative function satisfying |f(n)|≤1,q(≤N^2)be a positive integer and a be an integer with(a,q)= 1.In this paper,we shall prove that ∑n≤N(n,q)=1f(n)e(an/q)■(1/2)(τ(q)/q)N loglog(6N)+ q^(1/4+...Let f(n)be a multiplicative function satisfying |f(n)|≤1,q(≤N^2)be a positive integer and a be an integer with(a,q)= 1.In this paper,we shall prove that ∑n≤N(n,q)=1f(n)e(an/q)■(1/2)(τ(q)/q)N loglog(6N)+ q^(1/4+ε/2)N^(2/1)(log(6N))^(1/2)+N/(1/2)(loglog(6N)),where n is the multiplicative inverse of n such that nn ≡ 1(mod q),e(x)= exp(2πix),and τ(·)is the divisor function.展开更多
基金This research was supported by Thailand ScienceResearch and Innovation(TSRI)and Rajamangala University of Technology Thanyaburi(RMUTT)under National Science,Research and Innovation Fund(NSRF)BasicResearch Fund:Fiscal year 2022(ContractNo.FRB650070/0168 and under Project number FRB65E0634 M.3).
文摘The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.
文摘Schubert's method for solving systems of sparse equations has achieved a great deal of computational success. In this paper, Schubert's method was extended to multiple version, and the compact representation of multple Schubert's updating matrix was derived. The compact representation could be used to efficiently implement limited memory methods for large problems.
文摘A set of methods for interprocedural analysis is proposed. First, an ap-proach for interprocedural constant propagation is given. Then the concept of constant propagation is extended so as to meet the needs of data dependence analysis. Besides certain constant, constant range can also be propagated. The related propagating rules are introduced, and an idea for computing Return function is given. This approach can solve almost all interprocedural constant propagation problems with non-recursive calls. Second, a muItiple-version par-allelizing technique is also proposed for alias problem. The work related to this paper has been implemented on a shared-memory parallel computer.
基金supported by National Natural Science Foundation of China(Grant Nos.11201117 and 11126150),supported by National Natural Science Foundation of China(Grant Nos.11371344 and 11321101)National Key Basic Research Program of China(Grant No.2013CB834202)
文摘Let f(n)be a multiplicative function satisfying |f(n)|≤1,q(≤N^2)be a positive integer and a be an integer with(a,q)= 1.In this paper,we shall prove that ∑n≤N(n,q)=1f(n)e(an/q)■(1/2)(τ(q)/q)N loglog(6N)+ q^(1/4+ε/2)N^(2/1)(log(6N))^(1/2)+N/(1/2)(loglog(6N)),where n is the multiplicative inverse of n such that nn ≡ 1(mod q),e(x)= exp(2πix),and τ(·)is the divisor function.
