In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where...In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.展开更多
As potential alternative power sources used in portable electric generators, opposite axial piston engines in small-scale were investigated to show their advantages in power density. A novel cylinder charge system was...As potential alternative power sources used in portable electric generators, opposite axial piston engines in small-scale were investigated to show their advantages in power density. A novel cylinder charge system was introduced, based on which a quasi-dimension model and a CFD(computational fluid dynamics) model were established. Comparison of those two models was carried out to validate the quasi-dimension model. Furthermore, optimal diameter of charge cylinder and speed were determined after evaluating the quasi-dimension model based on different parameters. High agreement between the quasi-dimension model and the CFD model validates the quasi-dimension model. Further studies show that the power of engine increases with the diameter of charge cylinder. However, a too big charge cylinder lowers the fuel efficiency instead. Taking economic influence into consideration the charge cylinder should be 1.4 times power cylinder, which could ensure the power density, volumetric efficiency and fuel economic at the same time. Axial piston engine running at 1.0×104 r/min could achieve a better overall performance. The maximal power of engine with optimal parameters is 0.82 k W, which fits the power need of the portable electric generators completely.展开更多
This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the ...This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor with finite fractal dimension. Result on exponential attractors of the system is also proved.展开更多
A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces S...A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.展开更多
The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional proje...The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional projective H-module P such that dimu P is invertible.展开更多
Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the cla...Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.展开更多
Considering a family of rational maps Tnλconcerning renormalization transform ation,we give a perfect description about the dynamical properties of Tnλand the topological properties of the Fatou components F(Tnλ).F...Considering a family of rational maps Tnλconcerning renormalization transform ation,we give a perfect description about the dynamical properties of Tnλand the topological properties of the Fatou components F(Tnλ).Furthermore,we discuss the continuity of the Hausdorff dimension HD(J(Tnλ))about real param eter A.展开更多
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\...By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite展开更多
Few-layer Tellurium, an elementary semiconductor, succeeds most of striking physical properties that black phosphorus(BP) offers and could be feasibly synthesized by simple solution-based methods. It is comprised of n...Few-layer Tellurium, an elementary semiconductor, succeeds most of striking physical properties that black phosphorus(BP) offers and could be feasibly synthesized by simple solution-based methods. It is comprised of non-covalently bound parallel Te chains, among which covalent-like feature appears.This feature is, we believe, another demonstration of the previously found covalent-like quasi-bonding(CLQB) where wavefunction hybridization does occur. The strength of this inter-chain CLQB is comparable with that of intra-chain covalent bonding, leading to closed stability of several Te allotropes. It also introduces a tunable bandgap varying from nearly direct 0.31 eV(bulk) to indirect 1.17 eV(2L) and four(two) complex, highly anisotropic and layer-dependent hole(electron) pockets in the first Brillouin zone.It also exhibits an extraordinarily high hole mobility(~10~5 cm^2/Vs) and strong optical absorption along the non-covalently bound direction, nearly isotropic and layer-dependent optical properties, large ideal strength over 20%, better environmental stability than BP and unusual crossover of force constants for interlayer shear and breathing modes. All these results manifest that the few-layer Te is an extraordinary-high-mobility, high optical absorption, intrinsic-anisotropy, low-cost-fabrication, tunable bandgap, better environmental stability and nearly direct bandgap semiconductor. This ‘‘one-dimen sion-like" few-layer Te, together with other geometrically similar layered materials, may promote the emergence of a new family of layered materials.展开更多
文摘In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.
基金Projects(51475464,51175500) supported by the National Natural Science Foundation of China
文摘As potential alternative power sources used in portable electric generators, opposite axial piston engines in small-scale were investigated to show their advantages in power density. A novel cylinder charge system was introduced, based on which a quasi-dimension model and a CFD(computational fluid dynamics) model were established. Comparison of those two models was carried out to validate the quasi-dimension model. Furthermore, optimal diameter of charge cylinder and speed were determined after evaluating the quasi-dimension model based on different parameters. High agreement between the quasi-dimension model and the CFD model validates the quasi-dimension model. Further studies show that the power of engine increases with the diameter of charge cylinder. However, a too big charge cylinder lowers the fuel efficiency instead. Taking economic influence into consideration the charge cylinder should be 1.4 times power cylinder, which could ensure the power density, volumetric efficiency and fuel economic at the same time. Axial piston engine running at 1.0×104 r/min could achieve a better overall performance. The maximal power of engine with optimal parameters is 0.82 k W, which fits the power need of the portable electric generators completely.
文摘This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor with finite fractal dimension. Result on exponential attractors of the system is also proved.
基金the National Natural Science Foundation of China (Nos.60533060 10726067)+1 种基金the Natural Science Foundation for Doctoral Career of Liaoning Province (No.20061060)the Science Foundation of Dalian University of Technology (No.SFDUT07001)
文摘A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.
文摘The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional projective H-module P such that dimu P is invertible.
文摘Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11571049)the Special Basic Scientific Research Funds of Central Universities in China.
文摘Considering a family of rational maps Tnλconcerning renormalization transform ation,we give a perfect description about the dynamical properties of Tnλand the topological properties of the Fatou components F(Tnλ).Furthermore,we discuss the continuity of the Hausdorff dimension HD(J(Tnλ))about real param eter A.
基金the National Natural Science Foundation of China (Grnat No. 19971068) .
文摘By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite
基金supported by the National Natural Science Foundation of China(11274380,91433103,11622437,61674171,and 61761166009)the Fundamental Research Funds for the Central Universities of China and the Research Funds of Renmin University of China(16XNLQ01)+1 种基金The Hong Kong Polytechnic University(G-SB53)J.Q. and C.W. were supported by the Outstanding Innovative Talents Cultivation Funded Programs 2016 and 2017 of Renmin University of China,respectively
文摘Few-layer Tellurium, an elementary semiconductor, succeeds most of striking physical properties that black phosphorus(BP) offers and could be feasibly synthesized by simple solution-based methods. It is comprised of non-covalently bound parallel Te chains, among which covalent-like feature appears.This feature is, we believe, another demonstration of the previously found covalent-like quasi-bonding(CLQB) where wavefunction hybridization does occur. The strength of this inter-chain CLQB is comparable with that of intra-chain covalent bonding, leading to closed stability of several Te allotropes. It also introduces a tunable bandgap varying from nearly direct 0.31 eV(bulk) to indirect 1.17 eV(2L) and four(two) complex, highly anisotropic and layer-dependent hole(electron) pockets in the first Brillouin zone.It also exhibits an extraordinarily high hole mobility(~10~5 cm^2/Vs) and strong optical absorption along the non-covalently bound direction, nearly isotropic and layer-dependent optical properties, large ideal strength over 20%, better environmental stability than BP and unusual crossover of force constants for interlayer shear and breathing modes. All these results manifest that the few-layer Te is an extraordinary-high-mobility, high optical absorption, intrinsic-anisotropy, low-cost-fabrication, tunable bandgap, better environmental stability and nearly direct bandgap semiconductor. This ‘‘one-dimen sion-like" few-layer Te, together with other geometrically similar layered materials, may promote the emergence of a new family of layered materials.
