In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q ...In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.展开更多
Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain d...Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain due to absent or insufficient data for failure probabilities or failure rates of components. The traditional fuzzy operation arithmetic based on extension principle or interval theory may lead to fuzzy accumulations. Moreover, the existing fuzzy dynamic fault tree analysis methods are restricted to the case that all system components follow exponential time-to-failure distributions. To overcome these problems, a new fuzzy dynamic fault tree analysis approach based on the weakest n-dimensional t-norm arithmetic and developed sequential binary decision diagrams method is proposed to evaluate system fuzzy reliability. Compared with the existing approach,the proposed method can effectively reduce fuzzy cumulative and be applicable to any time-tofailure distribution type for system components. Finally, a case study is presented to illustrate the application and advantages of the proposed approach.展开更多
Here an asymptotic study to the N-dimensional radial Schrdinger equation for the quark-antiquark interaction potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out. The comp...Here an asymptotic study to the N-dimensional radial Schrdinger equation for the quark-antiquark interaction potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out. The complete energy spectra of the consigned system is obtained by computing and adding energy eigenvalues for ground state, for large " r" and for small " r". From this analysis, the mass spectra of heavy quarkonia is derived in three dimensions. Our analytical and numerical results are in good correspondence with other experimental and theoretical studies.展开更多
In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix eleme...In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.展开更多
In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality...In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function O<sub>g,h</sub>. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.展开更多
The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.
It is proved that when solving SchrSdinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower-dimensi...It is proved that when solving SchrSdinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower-dimensional cases. This result is applied to giving solutions for several radially symmetric potentials in N dimensions.展开更多
Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations ...In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.展开更多
Functional diversity(FD)reflects within-and between-site variation of species traits(α-and β-FD,respectively).Understanding how much data types(occurrence-based vs.abundance-weighted)and spatial scales(sites vs.regi...Functional diversity(FD)reflects within-and between-site variation of species traits(α-and β-FD,respectively).Understanding how much data types(occurrence-based vs.abundance-weighted)and spatial scales(sites vs.regions)change FD and ultimately interfere with the detection of underlying geoclimatic filters is still debated.To contribute to this debate,we explored the occurrence of 1690 species in 690 sites,abundances of 1198 species in 343 sites,and seven functional traits of the Atlantic Forest woody flora in South America.All FD indices were sensitive and dependent on the data type at both scales,with occurrence particularly increasing a richness and dispersion(occurrence>abundance in 80%of the sites)while abundance increased β total,β replacement,and α evenness(abundance>occurrence in 60%of the sites).Furthermore,detecting the effect of geoclimatic filters depended on the data type and was scale-dependent.At the site scale,precipitation seasonality and soil depth had weak effects on α-and β-FD(max.R^(2)=0.11).However,regional-scale patterns of a richness,dispersion,and evenness strongly mirrored the variation in precipitation seasonality,soil depth,forest stability over the last 120 kyr,and cation exchange capacity(correlations>0.80),suggesting that geoclimatic filters manifest stronger effects at the regional scale.Also,the role of edaphic gradients expands the idea of biogeographical filters beyond climate.Our findings caution functional biogeographic studies to consider the effect of data type and spatial scale before designing and reaching ecological conclusions about the complex nature of FD.展开更多
基金The NSF (Q2008A01) of Shandong,Chinathe NSF (10871024) of China
文摘In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.
基金supported by the National Defense Basic Scientific Research program of China (No.61325102)
文摘Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain due to absent or insufficient data for failure probabilities or failure rates of components. The traditional fuzzy operation arithmetic based on extension principle or interval theory may lead to fuzzy accumulations. Moreover, the existing fuzzy dynamic fault tree analysis methods are restricted to the case that all system components follow exponential time-to-failure distributions. To overcome these problems, a new fuzzy dynamic fault tree analysis approach based on the weakest n-dimensional t-norm arithmetic and developed sequential binary decision diagrams method is proposed to evaluate system fuzzy reliability. Compared with the existing approach,the proposed method can effectively reduce fuzzy cumulative and be applicable to any time-tofailure distribution type for system components. Finally, a case study is presented to illustrate the application and advantages of the proposed approach.
基金University Grant Commission(UGC) INDIA for providing the financial assistance in terms of UGC-SRF
文摘Here an asymptotic study to the N-dimensional radial Schrdinger equation for the quark-antiquark interaction potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out. The complete energy spectra of the consigned system is obtained by computing and adding energy eigenvalues for ground state, for large " r" and for small " r". From this analysis, the mass spectra of heavy quarkonia is derived in three dimensions. Our analytical and numerical results are in good correspondence with other experimental and theoretical studies.
文摘In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.
文摘In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function O<sub>g,h</sub>. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.
基金Supported by the Nationa1 Natural Science Foundation of China under Grant No.10874018"the Fundamental Research Funds for the Central Universities"
文摘The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.
基金The project partly supported by National Natural Science Foundation of China under Grant No. 10247001.The author would like to thank Prof. T.D. Lee for his continuous guidance and instruction.
文摘It is proved that when solving SchrSdinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower-dimensional cases. This result is applied to giving solutions for several radially symmetric potentials in N dimensions.
文摘Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
文摘In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.
基金supported by FAPERJ-Fundação Carlos Chagas Filho de AmparoàPesquisa do Estado do Rio de Janeiro through a post-doctoral fellowship and scientific grant for JoséLuiz Alves Silva[E-26/204.257/2021]by CNPq-Conselho Nacional de Desenvolvimento Científico e Tecnológico through a grant for Angela Pierre Vitória[n°302325/2022-0].
文摘Functional diversity(FD)reflects within-and between-site variation of species traits(α-and β-FD,respectively).Understanding how much data types(occurrence-based vs.abundance-weighted)and spatial scales(sites vs.regions)change FD and ultimately interfere with the detection of underlying geoclimatic filters is still debated.To contribute to this debate,we explored the occurrence of 1690 species in 690 sites,abundances of 1198 species in 343 sites,and seven functional traits of the Atlantic Forest woody flora in South America.All FD indices were sensitive and dependent on the data type at both scales,with occurrence particularly increasing a richness and dispersion(occurrence>abundance in 80%of the sites)while abundance increased β total,β replacement,and α evenness(abundance>occurrence in 60%of the sites).Furthermore,detecting the effect of geoclimatic filters depended on the data type and was scale-dependent.At the site scale,precipitation seasonality and soil depth had weak effects on α-and β-FD(max.R^(2)=0.11).However,regional-scale patterns of a richness,dispersion,and evenness strongly mirrored the variation in precipitation seasonality,soil depth,forest stability over the last 120 kyr,and cation exchange capacity(correlations>0.80),suggesting that geoclimatic filters manifest stronger effects at the regional scale.Also,the role of edaphic gradients expands the idea of biogeographical filters beyond climate.Our findings caution functional biogeographic studies to consider the effect of data type and spatial scale before designing and reaching ecological conclusions about the complex nature of FD.
