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
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 (<strong>g, h</strong>) can multiplicatively generate an n-dimensional overlap function <em><strong>O</strong></em><sub><strong>g,h</strong></sub><strong>.</strong> 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
Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods ...Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.展开更多
Cuboid fractures due to the particular bone anatomy and its protected location in the midfoot are rare, and they are usually associated with complex injuries of the foot. Clinical examination to diagnose these fractur...Cuboid fractures due to the particular bone anatomy and its protected location in the midfoot are rare, and they are usually associated with complex injuries of the foot. Clinical examination to diagnose these fractures should be detailed and the differential diagnosis, especially in the case of vague symptoms, should include the exclusion of all lateral foot pain causes. Conventional radiographs do not always reveal occult fractures, which can be under diagnosed especially in children. In this case, further investigation including magnetic resonance imaging or scintigraphy may be required. The treatment of these injuries depends on the particular fracture characteristics. Non-displaced isolated fractures of the cuboid bone can be effectively treated conservatively by immobilization and by avoiding weight bearing on the injured leg. In the case of shortening of the lateral column> 3 mm or articular displacement > 1 mm, surgical management of the fracture is mandatory in order to avoid negative biomechanical and functional consequences for the foot and adverse effects such as arthritis and stiffness as well as painful gait. In this review, an update on diagnosis and management of cuboid fractures is presented.展开更多
A simplified method is proposed for analyzing the overpressure history of an optional point on the walls of a closed cuboid due to its internal optional point-explosion. Firstly, the overpressure histories of all node...A simplified method is proposed for analyzing the overpressure history of an optional point on the walls of a closed cuboid due to its internal optional point-explosion. Firstly, the overpressure histories of all nodes on the walls of a cube with a side-length of 2 m are computed under a reference-charge explosion at each node of its inner space using the LS-DYNA software, and then are collected to form a reference database. Next, with the thought of the isoparametric finite element, an interpolating algori...展开更多
Two novel Co-based clusters with the 2-(hydroxylmethyl)pyridine(hmpH)ligand,formulated as[Co3(hmp)6(hmpH)]×2NO3×3H2O(ZTU-3)and[Co4(hmp)4(CH3CO2)2(H2O)4]×2NO3(ZTU-4),have been successfully synthesized an...Two novel Co-based clusters with the 2-(hydroxylmethyl)pyridine(hmpH)ligand,formulated as[Co3(hmp)6(hmpH)]×2NO3×3H2O(ZTU-3)and[Co4(hmp)4(CH3CO2)2(H2O)4]×2NO3(ZTU-4),have been successfully synthesized and structurally characterized.ZTU-3 features a triangular core geometry,while ZTU-4 exhibits a cuboidal core geometry.In addition,the magnetic properties of ZTU-3 and ZTU-4 are also all investigated.展开更多
Traveling Salesman Problem (TSP) is one of the most widely studied real world problems of finding the shortest (minimum cost) possible route that visits each node in a given set of nodes (cities) once and then returns...Traveling Salesman Problem (TSP) is one of the most widely studied real world problems of finding the shortest (minimum cost) possible route that visits each node in a given set of nodes (cities) once and then returns to origin city. The optimization of cuboid areas has potential samples that can be adapted to real world. Cuboid surfaces of buildings, rooms, furniture etc. can be given as examples. Many optimization algorithms have been used in solution of optimization problems at present. Among them, meta-heuristic algorithms come first. In this study, ant colony optimization, one of meta-heuristic methods, is applied to solve Euclidian TSP consisting of nine different sized sets of nodes randomly placed on a cuboid surface. The performance of this method is shown in tests.展开更多
Vertical orthogonal joints are a common feature in shallow crustal rocks.There are several competing theories for their formation despite the ubiquity.We examined the exceptional exposures of orthogonal joints in flat...Vertical orthogonal joints are a common feature in shallow crustal rocks.There are several competing theories for their formation despite the ubiquity.We examined the exceptional exposures of orthogonal joints in flat-lying Ordovician limestone beds from the Havre-Saint-Pierre Region in Quebec,Canada(north shore of Saint-Lawrence River)to test conceptual models of joint formation in a natural setting.In the region,the spacing of cross-joints is consistently larger than the spacing of systematic joints by a factor of 1.5 approximately.The joint-spacing-to-bed-thickness ratios(s/t)are much larger in these beds(s/t=4.3 for systematic joints,and 6.4 for cross-joints)than those in higher strained strata along the south shore of the Saint-Lawrence River(s/t=1),highlighting the effect of tectonic strain in decreasing fracture spacing and block size.The high values of s/t indicate that cross-joint formation was unlikely caused by a switch from compression to tension once a critical s/t ratio for systematic joints was reached(as hypothesized in previous studies).We proposed a new model for the formation of orthogonal joint systems where the principal stress axes locally switch during the formation of systematic fractures.The presence of ladder-shaped orthogonal joints suggests a state of effective stress withσ_(1)^(∗)≫0>σ_(2)^(∗)>σ_(3)^(∗)and whereσ_(2)^(∗)-σ_(3)^(∗)is within the range of fracture strength variability at the time of fracture.This research provides a new mechanical model for the formation of orthogonal joint systems and cuboidal blocks.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.
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 (<strong>g, h</strong>) can multiplicatively generate an n-dimensional overlap function <em><strong>O</strong></em><sub><strong>g,h</strong></sub><strong>.</strong> 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 China Geological Survey Northeastern Tarim Aeromagnetic and Aerogravity comprehensive survey project(No.12120115039401)
文摘Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.
文摘Cuboid fractures due to the particular bone anatomy and its protected location in the midfoot are rare, and they are usually associated with complex injuries of the foot. Clinical examination to diagnose these fractures should be detailed and the differential diagnosis, especially in the case of vague symptoms, should include the exclusion of all lateral foot pain causes. Conventional radiographs do not always reveal occult fractures, which can be under diagnosed especially in children. In this case, further investigation including magnetic resonance imaging or scintigraphy may be required. The treatment of these injuries depends on the particular fracture characteristics. Non-displaced isolated fractures of the cuboid bone can be effectively treated conservatively by immobilization and by avoiding weight bearing on the injured leg. In the case of shortening of the lateral column> 3 mm or articular displacement > 1 mm, surgical management of the fracture is mandatory in order to avoid negative biomechanical and functional consequences for the foot and adverse effects such as arthritis and stiffness as well as painful gait. In this review, an update on diagnosis and management of cuboid fractures is presented.
基金Supported by National Natural Science Foundation of China (No. 50678116)National Key Technology R&D Program of China (No. 2006BAJ13B02)Tianjin Municipal Major Project of Application Foundation and Frontal Technology Research (No. 08JCZDJC19500)
文摘A simplified method is proposed for analyzing the overpressure history of an optional point on the walls of a closed cuboid due to its internal optional point-explosion. Firstly, the overpressure histories of all nodes on the walls of a cube with a side-length of 2 m are computed under a reference-charge explosion at each node of its inner space using the LS-DYNA software, and then are collected to form a reference database. Next, with the thought of the isoparametric finite element, an interpolating algori...
基金Supported by the National Natural Science Foundation of China(21861044 and 21601137)the Project funded by China Postdoctoral Science Foundation(2018M633426)the Project funded by Yunnan Province Postdoctoral Science Foundation
文摘Two novel Co-based clusters with the 2-(hydroxylmethyl)pyridine(hmpH)ligand,formulated as[Co3(hmp)6(hmpH)]×2NO3×3H2O(ZTU-3)and[Co4(hmp)4(CH3CO2)2(H2O)4]×2NO3(ZTU-4),have been successfully synthesized and structurally characterized.ZTU-3 features a triangular core geometry,while ZTU-4 exhibits a cuboidal core geometry.In addition,the magnetic properties of ZTU-3 and ZTU-4 are also all investigated.
文摘Traveling Salesman Problem (TSP) is one of the most widely studied real world problems of finding the shortest (minimum cost) possible route that visits each node in a given set of nodes (cities) once and then returns to origin city. The optimization of cuboid areas has potential samples that can be adapted to real world. Cuboid surfaces of buildings, rooms, furniture etc. can be given as examples. Many optimization algorithms have been used in solution of optimization problems at present. Among them, meta-heuristic algorithms come first. In this study, ant colony optimization, one of meta-heuristic methods, is applied to solve Euclidian TSP consisting of nine different sized sets of nodes randomly placed on a cuboid surface. The performance of this method is shown in tests.
基金The authors express their gratitude to the Natural Sciences and Engineering Research Council of Canada for financial support through a Discovery Grant(Grant No.06408).
文摘Vertical orthogonal joints are a common feature in shallow crustal rocks.There are several competing theories for their formation despite the ubiquity.We examined the exceptional exposures of orthogonal joints in flat-lying Ordovician limestone beds from the Havre-Saint-Pierre Region in Quebec,Canada(north shore of Saint-Lawrence River)to test conceptual models of joint formation in a natural setting.In the region,the spacing of cross-joints is consistently larger than the spacing of systematic joints by a factor of 1.5 approximately.The joint-spacing-to-bed-thickness ratios(s/t)are much larger in these beds(s/t=4.3 for systematic joints,and 6.4 for cross-joints)than those in higher strained strata along the south shore of the Saint-Lawrence River(s/t=1),highlighting the effect of tectonic strain in decreasing fracture spacing and block size.The high values of s/t indicate that cross-joint formation was unlikely caused by a switch from compression to tension once a critical s/t ratio for systematic joints was reached(as hypothesized in previous studies).We proposed a new model for the formation of orthogonal joint systems where the principal stress axes locally switch during the formation of systematic fractures.The presence of ladder-shaped orthogonal joints suggests a state of effective stress withσ_(1)^(∗)≫0>σ_(2)^(∗)>σ_(3)^(∗)and whereσ_(2)^(∗)-σ_(3)^(∗)is within the range of fracture strength variability at the time of fracture.This research provides a new mechanical model for the formation of orthogonal joint systems and cuboidal blocks.
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.
