In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 ...In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 and any 0【ε【14,E k(x+H)-E k(x)≤H(log x) -Aholds for x 12-14k+ε≤H≤x, here the implies constant depends at most on A and ε.展开更多
The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of...The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.展开更多
We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on the co-multiplication map and requiring that these isomorphisms satisfy certairl law of their own, which is called the...We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on the co-multiplication map and requiring that these isomorphisms satisfy certairl law of their own, which is called the copentagon identity. We also set up a 2-category of 2-coalgebras. The purpose of this study is from the idea of reconsidering the quasi-Hopf algebras by the categorification process, so that we can study the theory of quasi-Hopf algebras and their representations in some new framework of higher category theory in natural ways.展开更多
As grammatical words, conjunction and relative pronoun play a similar role. They join clauses, phrases, and even words. The terms independent and dependent clauses have become popular for quite a long time. When the c...As grammatical words, conjunction and relative pronoun play a similar role. They join clauses, phrases, and even words. The terms independent and dependent clauses have become popular for quite a long time. When the concept of clause and sentence meets at the presence of NP （Noun Phrase） and VP （Verb Phrase）, there is a right to consider construction as an S or a sentence leaving the conjunction and relative pronoun as means of uniting device and leaving every NP-VP construction as equal units. By employing an embedding theory, we can see hidden parts of a sentence and their roles in other sentences. This article tries to see if it is still necessary to distinguish between dependent and independent clauses.展开更多
The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,...The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,in all the deliverability equation,the additional pressure drop caused by the threshold pressure gradient is viewed as constant,but this method has big error in the practical application. Based on the non-Darcy steady flow equation,the limited integral of the additional pressure drop is solved in this paper and it is realized that the additional pressure drop is not a constant but has something to do with production data,and a new deliverability equation is derived,with the relevant processing method for modified isochronal test data. The new deliverability equation turns out to be practical through onsite application.展开更多
CR theory focuses on the study of academic or professional writing across different cultural settings. One recurring question of CR theory in the Chinese ESL context is whether the rhetorical differences in organizati...CR theory focuses on the study of academic or professional writing across different cultural settings. One recurring question of CR theory in the Chinese ESL context is whether the rhetorical differences in organization, modeling, and syntax between Chinese and English writing indeed exist, and if so how they affect ESL writing. Through examining the controversies surrounding these rhetorical differences along with a brief review of the development of CR theory and pedagogical implications, this paper contends that the study of CR theory has exerted beneficial influences on L2 writing.展开更多
From two aspects of intellectual property management, namely the subject and the object,this article discusses the development and im-provement of intellectual property system in China and the gap and problems existed...From two aspects of intellectual property management, namely the subject and the object,this article discusses the development and im-provement of intellectual property system in China and the gap and problems existed compared with developed countries. Based on this, the issue ofhow to improve the coordinated management of intellectual property is studied and the relevant proposals are put forward.展开更多
We give new proofs of many injectivity results in analysis that make more careful use of the duality between abelian C*-algebras and topological spaces. We then extend many of these ideas to incorporate the case of a ...We give new proofs of many injectivity results in analysis that make more careful use of the duality between abelian C*-algebras and topological spaces. We then extend many of these ideas to incorporate the case of a group action. This approach gives new insight into Hamana's theory of G-injective operator spaces and G-injective envelopes. Our new proofs of these classic results, use only topological methods and eliminate the need for results from the theory of Boolean algebras and AW*-algebras.展开更多
文摘In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 and any 0【ε【14,E k(x+H)-E k(x)≤H(log x) -Aholds for x 12-14k+ε≤H≤x, here the implies constant depends at most on A and ε.
基金financial support of the Natural Science Foundation of China (NSFC,No.50974094)
文摘The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 11031005 10871135, 10871227, and PHR201007107
文摘We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on the co-multiplication map and requiring that these isomorphisms satisfy certairl law of their own, which is called the copentagon identity. We also set up a 2-category of 2-coalgebras. The purpose of this study is from the idea of reconsidering the quasi-Hopf algebras by the categorification process, so that we can study the theory of quasi-Hopf algebras and their representations in some new framework of higher category theory in natural ways.
文摘As grammatical words, conjunction and relative pronoun play a similar role. They join clauses, phrases, and even words. The terms independent and dependent clauses have become popular for quite a long time. When the concept of clause and sentence meets at the presence of NP （Noun Phrase） and VP （Verb Phrase）, there is a right to consider construction as an S or a sentence leaving the conjunction and relative pronoun as means of uniting device and leaving every NP-VP construction as equal units. By employing an embedding theory, we can see hidden parts of a sentence and their roles in other sentences. This article tries to see if it is still necessary to distinguish between dependent and independent clauses.
基金National Basic Research Program of China(2007CB209506)
文摘The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,in all the deliverability equation,the additional pressure drop caused by the threshold pressure gradient is viewed as constant,but this method has big error in the practical application. Based on the non-Darcy steady flow equation,the limited integral of the additional pressure drop is solved in this paper and it is realized that the additional pressure drop is not a constant but has something to do with production data,and a new deliverability equation is derived,with the relevant processing method for modified isochronal test data. The new deliverability equation turns out to be practical through onsite application.
文摘CR theory focuses on the study of academic or professional writing across different cultural settings. One recurring question of CR theory in the Chinese ESL context is whether the rhetorical differences in organization, modeling, and syntax between Chinese and English writing indeed exist, and if so how they affect ESL writing. Through examining the controversies surrounding these rhetorical differences along with a brief review of the development of CR theory and pedagogical implications, this paper contends that the study of CR theory has exerted beneficial influences on L2 writing.
文摘From two aspects of intellectual property management, namely the subject and the object,this article discusses the development and im-provement of intellectual property system in China and the gap and problems existed compared with developed countries. Based on this, the issue ofhow to improve the coordinated management of intellectual property is studied and the relevant proposals are put forward.
基金supported in part by National Science Foundation of USA (Grant No. DMS-0600191)
文摘We give new proofs of many injectivity results in analysis that make more careful use of the duality between abelian C*-algebras and topological spaces. We then extend many of these ideas to incorporate the case of a group action. This approach gives new insight into Hamana's theory of G-injective operator spaces and G-injective envelopes. Our new proofs of these classic results, use only topological methods and eliminate the need for results from the theory of Boolean algebras and AW*-algebras.
