Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distribu...Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.展开更多
In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wa...In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wave method. The results show that the birefringence of the fibre is induced by asymmetries of both the cladding and the core. Moreover, by adjusting the non-symmetrical ratio factor of cladding η from 0.4 to 1 in step 0.1, we find the optimized design parameters of the fibre with high birefringence and limited polarization mode dispersion, operating in a single mode regime at an appropriate wavelength range. The range of wavelength approaches the visible and near-infrared which is consistent with the communication windows of polymer optical fibres.展开更多
This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the ...This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.展开更多
Consider the following Neumann problem d△u- u ＋ k（x）u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k（x） = k（｜x｜） ≠ 0 is nonnegative and in C（-↑B1）, 1 〈 p 〈 N＋2/N...Consider the following Neumann problem d△u- u ＋ k（x）u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k（x） = k（｜x｜） ≠ 0 is nonnegative and in C（-↑B1）, 1 〈 p 〈 N＋2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem （＊） has no nonconstant radially symmetric least energy solution if k（x） ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that （＊） has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k（x） ≡ 1 and nonconstant if k（x） ≠ 1. In particular, for k（x） ≡ 1, do can be expressed explicitly.展开更多
First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric soluti...First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.展开更多
Let R（x） be a smooth function on the 2-sphere S2. A question in differential geometry may be raised: Can R（x） be the scalar curvature of a metric g on S2 which is pointwise conformal to the standard metric go （i....Let R（x） be a smooth function on the 2-sphere S2. A question in differential geometry may be raised: Can R（x） be the scalar curvature of a metric g on S2 which is pointwise conformal to the standard metric go （i. e. g= eug0）? This problem can be reduced to solving the following elliptic展开更多
In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at in...In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.展开更多
We discuss the properties of solutions for the following elliptic partial differential equations system in Rn,where 0 〈α〈 n, pi and qi （i = 1, 2） satisfy some suitable assumptions. Due to equivalence between the ...We discuss the properties of solutions for the following elliptic partial differential equations system in Rn,where 0 〈α〈 n, pi and qi （i = 1, 2） satisfy some suitable assumptions. Due to equivalence between the PDEs system and a given integral system, we prove the radial symmetry and regularity of positive solutions to the PDEs system via the method of moving plane in integral forms and Regularity Lifting Lemma. For the special case, when p1 ＋ p2= q1 ＋ q2 = n＋α/n-α, we classify the solutions of the PDEs system.展开更多
文摘Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.
基金Project supported by National Nature Science Foundation of China （Grant No 60437020） and the Science and Technology Plan Project of Shannxi Province （Grant No 2004K05-G47）.
文摘In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wave method. The results show that the birefringence of the fibre is induced by asymmetries of both the cladding and the core. Moreover, by adjusting the non-symmetrical ratio factor of cladding η from 0.4 to 1 in step 0.1, we find the optimized design parameters of the fibre with high birefringence and limited polarization mode dispersion, operating in a single mode regime at an appropriate wavelength range. The range of wavelength approaches the visible and near-infrared which is consistent with the communication windows of polymer optical fibres.
基金The project supported by National Natural Science Foundation of China under Grant No. 10447007 and the Natural Science Foundation of Shaanxi Province of China under Grant No. 2005A13
文摘This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.
基金the National Natural Science Foundation of China(No.10571174,10631030)Chinese Academy oF Sciences grant KJCX3-SYW-S03.
文摘Consider the following Neumann problem d△u- u ＋ k（x）u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k（x） = k（｜x｜） ≠ 0 is nonnegative and in C（-↑B1）, 1 〈 p 〈 N＋2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem （＊） has no nonconstant radially symmetric least energy solution if k（x） ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that （＊） has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k（x） ≡ 1 and nonconstant if k（x） ≠ 1. In particular, for k（x） ≡ 1, do can be expressed explicitly.
基金Supported by Natural Science Foundation of China (10631020, 10871061)the Grant for Ph.D Program of Ministry of Education of Chinasupported by Innovation Propject for the Development of Science and Technology (IHLB) (201098)
文摘First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.
文摘Let R（x） be a smooth function on the 2-sphere S2. A question in differential geometry may be raised: Can R（x） be the scalar curvature of a metric g on S2 which is pointwise conformal to the standard metric go （i. e. g= eug0）? This problem can be reduced to solving the following elliptic
基金carried out in the framework of the Labex Archimède(ANR-11-LABX-0033)the A*MIDEX project(ANR-11-IDEX-0001-02)+6 种基金funded by the "Investissements d’Avenir" French Government program managed by the French National Research Agency(ANR)funding from the European Research Council under the European Union’s Seventh Framework Programme(FP/2007-2013)ERC Grant Agreement n.321186-ReaDiReaction-Diffusion Equations,Propagation and Modelling and from the ANR NONLOCAL project(ANR-14-CE25-0013)supported by INRIA-Team MEPHYSTOMIS F.4508.14(FNRS)PDR T.1110.14F(FNRS)ARC AUWB-2012-12/17-ULB1-IAPAS
文摘In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.
基金Supported by National Natural Science Foundation of China(Grant No.11571268)the foundation of Xi’an University of Finance and Economics(Grant No.12XCK07)
文摘We discuss the properties of solutions for the following elliptic partial differential equations system in Rn,where 0 〈α〈 n, pi and qi （i = 1, 2） satisfy some suitable assumptions. Due to equivalence between the PDEs system and a given integral system, we prove the radial symmetry and regularity of positive solutions to the PDEs system via the method of moving plane in integral forms and Regularity Lifting Lemma. For the special case, when p1 ＋ p2= q1 ＋ q2 = n＋α/n-α, we classify the solutions of the PDEs system.
基金supported by NSFC-Tian Yuan Special Foundation(11226116)Natural Science Foundation of Jiangsu Province of China for Young Scholar(BK2012109)+3 种基金the China Scholarship Council(201208320435)the Fundamental Research Funds for the Central Universities(JUSRP11118)supported by NSFC(10871096)supported by Graduate Education Innovation of Jiangsu Province(CXZZ13-0389)
