In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the...In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.展开更多
The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online accep...The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online acceptability judgment task.The subject pool of this research included 60 English majors studying at a university in China;30 were selected as a higher-proficiency group and 30 as a lower-proficiency group according to their Vocabulary Levels Test(Schmitt et al.,2001)scores and their self-reported proficiency in English.The experimental materials were programmed to E-prime 2.0 and included six types of collocations:(1)15 high-frequency congruent collocations,(2)15 low-frequency congruent collocations,(3)15 high-frequency incongruent collocations,(4)15 low-frequency incongruent collocations,(5)15 Chinese-only items,and(6)75 unrelated items for baseline data.The collected response times(RTs)and accuracy rates data were statistically analyzed by the use of an ANOVA test and pairwise comparisons through SPSS 16.0 software.The results revealed that:(1)the adjective-noun collocational processing of Chinese English learners is influenced by collocational frequency,congruency and L2 proficiency;(2)the processing time is affected by the interaction of congruency and frequency;and(3)the interactive effect of L2 proficiency in conjunction with congruency and frequency also influences the processing quality.展开更多
Let 2m>2, m∈ℤ, be the given even number of the Strong Goldbach Conjecture Problem. Then, m can be called the median of the problem. So, all Goldbach partitions (p,q)exist a relationship, p=m−dand q=m+d, where p≤q...Let 2m>2, m∈ℤ, be the given even number of the Strong Goldbach Conjecture Problem. Then, m can be called the median of the problem. So, all Goldbach partitions (p,q)exist a relationship, p=m−dand q=m+d, where p≤qand d is the distance from m to either p or q. Now we denote the finite feasible solutions of the problem as S(2m)={ (2,2m−2),(3,2m−3),⋅⋅⋅,(m,m) }. If we utilize the Eratosthenes sieve principle to efface those false objects from set S(2m)in pistages, where pi∈P, pi≤2m, then all optimal solutions should be found. The Strong Goldbach Conjecture is true since we proved that at least one optimal solution must exist to the problem. The Weak Goldbach Conjecture is true since it is a special case of the Strong Goldbach Conjecture. Therefore, the Goldbach Conjecture is true.展开更多
The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infini...The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.展开更多
文摘In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.
文摘The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online acceptability judgment task.The subject pool of this research included 60 English majors studying at a university in China;30 were selected as a higher-proficiency group and 30 as a lower-proficiency group according to their Vocabulary Levels Test(Schmitt et al.,2001)scores and their self-reported proficiency in English.The experimental materials were programmed to E-prime 2.0 and included six types of collocations:(1)15 high-frequency congruent collocations,(2)15 low-frequency congruent collocations,(3)15 high-frequency incongruent collocations,(4)15 low-frequency incongruent collocations,(5)15 Chinese-only items,and(6)75 unrelated items for baseline data.The collected response times(RTs)and accuracy rates data were statistically analyzed by the use of an ANOVA test and pairwise comparisons through SPSS 16.0 software.The results revealed that:(1)the adjective-noun collocational processing of Chinese English learners is influenced by collocational frequency,congruency and L2 proficiency;(2)the processing time is affected by the interaction of congruency and frequency;and(3)the interactive effect of L2 proficiency in conjunction with congruency and frequency also influences the processing quality.
文摘Let 2m>2, m∈ℤ, be the given even number of the Strong Goldbach Conjecture Problem. Then, m can be called the median of the problem. So, all Goldbach partitions (p,q)exist a relationship, p=m−dand q=m+d, where p≤qand d is the distance from m to either p or q. Now we denote the finite feasible solutions of the problem as S(2m)={ (2,2m−2),(3,2m−3),⋅⋅⋅,(m,m) }. If we utilize the Eratosthenes sieve principle to efface those false objects from set S(2m)in pistages, where pi∈P, pi≤2m, then all optimal solutions should be found. The Strong Goldbach Conjecture is true since we proved that at least one optimal solution must exist to the problem. The Weak Goldbach Conjecture is true since it is a special case of the Strong Goldbach Conjecture. Therefore, the Goldbach Conjecture is true.
文摘The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.
