This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber...This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber architecture.The Qing′s grand style timber structure, which is ready for prefabrication and assembly, is extremely hierarchical oriented and significantly standardized. The general procedure in designing a grand style timber structure is to start with the grade that defines the basic module (dou kou); next comes with the number of bracket set (cuan), the number of longitudinal bays and the number of purlins which affect its plan and cross section; thirdly choose a roof type that determines its longitudinal section and the facade as well. A series of formulae are conducted to help depict the layout, cross sectional roof curvature and special longitudinal treatments in 4 sloped and 9 spined roofs respectively.展开更多
The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su（1,2） algebraic structure： the Hamiltonian can be written as a linear function of the su（1,2） algebra generators. Based o...The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su（1,2） algebraic structure： the Hamiltonian can be written as a linear function of the su（1,2） algebra generators. Based on it, the energy eigenvalues are obta/ned by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.展开更多
With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collabo...With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collaborative mechanism for the purpose of service selection. The participation usually brings unnecessary burdens for users, such as giving opinions, storing service information. Extra communication overhead hinders the performance of the network. Thus, the community administrators are facing a problem of how to obtain an overall service selection result for the whole community readily and effectively. To address this problem, we present a k-median facility location agent model. The model analyzes the procedure of service selection through five entities and six types of messages. Two algorithms are elaborated in pursuit of a global optimization concerning connection costs between users and facilities where services are deployed. To evaluate our model, we conduct extensive simulations and present a detailed analysis of the simulation results.展开更多
To solve the problems of the AMR-WB+(Extended Adaptive Multi-Rate-WideBand) semi-open-loop coding mode selection algorithm,features for ACELP(Algebraic Code Excited Linear Prediction) and TCX(Transform Coded eXcitatio...To solve the problems of the AMR-WB+(Extended Adaptive Multi-Rate-WideBand) semi-open-loop coding mode selection algorithm,features for ACELP(Algebraic Code Excited Linear Prediction) and TCX(Transform Coded eXcitation) classification are investigated.11 classifying features in the AMR-WB+ codec are selected and 2 novel classifying features,i.e.,EFM(Energy Flatness Measurement) and stdEFM(standard deviation of EFM),are proposed.Consequently,a novel semi-open-loop mode selection algorithm based on EFM and selected AMR-WB+ features is proposed.The results of classifying test and listening test show that the performance of the novel algorithm is much better than that of the AMR-WB+ semi-open-loop coding mode selection algorithm.展开更多
In the digital age, people＇ s lifestyles and ways of thinking are in a series of changes, this change also makes it a big shift in consumer attitudes. It gives consumers a broader perspective, while also improving th...In the digital age, people＇ s lifestyles and ways of thinking are in a series of changes, this change also makes it a big shift in consumer attitudes. It gives consumers a broader perspective, while also improving the self-consciousness of consumers. These effects will no longer fully believe in traditional consumer marketing ＂bombing＂ the dissemination and indoctrination, they are more inclined to be questioned brands and products, and they can express their views on the basis that affects other people. In this era of environment, if businesses and vendors for their view is indifferent attitude, they will lose a lot of attention to the crowd, and also it makes the influence of the traditional marketing model spread greatly reduced.展开更多
In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex alg...In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).展开更多
We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and gener...We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.展开更多
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
Given a suitable ordering of the positive root system associated with a semisimple Lie algebra,there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra ac...Given a suitable ordering of the positive root system associated with a semisimple Lie algebra,there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module can be interpreted as a differential operator action on polynomials, and thus on the corresponding truncated formal power series. We prove that the space of truncated formal power series gives a differential-operator representation of the Weyl group W. We also introduce a system of partial differential equations to investigate singular vectors in the Verma module. It is shown that the solution space of the system in the space of truncated formal power series is the span of {w(1) | w ∈ W }. Those w(1) that are polynomials correspond to singular vectors in the Verma module. This elementary approach by partial differential equations also gives a new proof of the well-known BGG-Verma theorem.展开更多
This research work based on the development of 6σ capability indices in the Modern Quality Management Practices in the world level companies is briefly introduced. The process performance index （when a process indic...This research work based on the development of 6σ capability indices in the Modern Quality Management Practices in the world level companies is briefly introduced. The process performance index （when a process indicated by control charts is under control） and the percentage of defective products are calculated and compared with kσ. Finally, compared 6σ with 3σ, when process is on nominal （nominal - mean）, the process has 1.5σ shift from nominal.展开更多
文摘This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber architecture.The Qing′s grand style timber structure, which is ready for prefabrication and assembly, is extremely hierarchical oriented and significantly standardized. The general procedure in designing a grand style timber structure is to start with the grade that defines the basic module (dou kou); next comes with the number of bracket set (cuan), the number of longitudinal bays and the number of purlins which affect its plan and cross section; thirdly choose a roof type that determines its longitudinal section and the facade as well. A series of formulae are conducted to help depict the layout, cross sectional roof curvature and special longitudinal treatments in 4 sloped and 9 spined roofs respectively.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10447103 and 90305026the Natural Science Foundation of Beijing under Grant No.1072010the Foundation of Education Department of Beijing under Grant No.KM200610772007
文摘The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su（1,2） algebraic structure： the Hamiltonian can be written as a linear function of the su（1,2） algebra generators. Based on it, the energy eigenvalues are obta/ned by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.
基金This work is supported by Program for the Key Program of NSFC-Guangdong Union Foundation （U1135002）, Major national S＆T program （2011ZX03005-002）, National Natural Science Foundation of China （60872041, 61072066）, the Fundamental Research Funds for the Central Universities （JY10000903001, JY10000901034, K5051203010） and the GAD Pre-Research Foundation （9140A 15040210HK61 ）.
文摘With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collaborative mechanism for the purpose of service selection. The participation usually brings unnecessary burdens for users, such as giving opinions, storing service information. Extra communication overhead hinders the performance of the network. Thus, the community administrators are facing a problem of how to obtain an overall service selection result for the whole community readily and effectively. To address this problem, we present a k-median facility location agent model. The model analyzes the procedure of service selection through five entities and six types of messages. Two algorithms are elaborated in pursuit of a global optimization concerning connection costs between users and facilities where services are deployed. To evaluate our model, we conduct extensive simulations and present a detailed analysis of the simulation results.
文摘To solve the problems of the AMR-WB+(Extended Adaptive Multi-Rate-WideBand) semi-open-loop coding mode selection algorithm,features for ACELP(Algebraic Code Excited Linear Prediction) and TCX(Transform Coded eXcitation) classification are investigated.11 classifying features in the AMR-WB+ codec are selected and 2 novel classifying features,i.e.,EFM(Energy Flatness Measurement) and stdEFM(standard deviation of EFM),are proposed.Consequently,a novel semi-open-loop mode selection algorithm based on EFM and selected AMR-WB+ features is proposed.The results of classifying test and listening test show that the performance of the novel algorithm is much better than that of the AMR-WB+ semi-open-loop coding mode selection algorithm.
文摘In the digital age, people＇ s lifestyles and ways of thinking are in a series of changes, this change also makes it a big shift in consumer attitudes. It gives consumers a broader perspective, while also improving the self-consciousness of consumers. These effects will no longer fully believe in traditional consumer marketing ＂bombing＂ the dissemination and indoctrination, they are more inclined to be questioned brands and products, and they can express their views on the basis that affects other people. In this era of environment, if businesses and vendors for their view is indifferent attitude, they will lose a lot of attention to the crowd, and also it makes the influence of the traditional marketing model spread greatly reduced.
基金supported by National Natural Science Foundation of China (Grant Nos. 11271056, 11671056 and 11101030)National Science Foundation of Jiangsu (Grant No. BK20160403)+3 种基金National Science Foundation of Zhejiang (Grant Nos. LQ12A01005 and LZ14A010001)National Science Foundation of Shanghai (Grant No. 16ZR1425000)Beijing Higher Education Young Elite Teacher ProjectMorningside Center of Mathematics
文摘In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).
基金supported by National Natural Science Foundation of China(Grant Nos.11101436 and 11101151)the Fundamental Research Funds for the Central Universities
文摘We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金supported by National Natural Science Foundation of China(Grant No.11326059)
文摘Given a suitable ordering of the positive root system associated with a semisimple Lie algebra,there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module can be interpreted as a differential operator action on polynomials, and thus on the corresponding truncated formal power series. We prove that the space of truncated formal power series gives a differential-operator representation of the Weyl group W. We also introduce a system of partial differential equations to investigate singular vectors in the Verma module. It is shown that the solution space of the system in the space of truncated formal power series is the span of {w(1) | w ∈ W }. Those w(1) that are polynomials correspond to singular vectors in the Verma module. This elementary approach by partial differential equations also gives a new proof of the well-known BGG-Verma theorem.
文摘This research work based on the development of 6σ capability indices in the Modern Quality Management Practices in the world level companies is briefly introduced. The process performance index （when a process indicated by control charts is under control） and the percentage of defective products are calculated and compared with kσ. Finally, compared 6σ with 3σ, when process is on nominal （nominal - mean）, the process has 1.5σ shift from nominal.
