We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi sa...We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor展开更多
Surveying and early detection of invasive weeds are essential for strategic management and monitoring. Accordingly, a weed mapping was conducted during July 2011, against native （Orobanche ramosa, Cuscuta spp., Sorgh...Surveying and early detection of invasive weeds are essential for strategic management and monitoring. Accordingly, a weed mapping was conducted during July 2011, against native （Orobanche ramosa, Cuscuta spp., Sorghum halepense and Xanthium strumarium） and non native （Abutilon theophrasti, Datura stramonium, Solanum elaeagnifolium and Verbesina encelioide） weeds of Lebanon. A global positioning system （Garmin 2006） was used for precise waypoint, elevation, navigation and distance. The result of interviewing and interacting with the residents in 95 villages distributed between the Beq＇aa and the North governorates of Lebanon, along with the observations made on the route, yielded the first detection of Abutilon theophrasti in both governorates. Solanum elaeagnifolium and Verbesina encelioide were not found in the agro-ecosystems of either governorates. This is the first report of the introduction ofAbutilon theophrasti in Lebanon and the establishment of a baseline data on weeds of Lebanon. The adoption of an integrated weed management program with a quarantine and control techniques and methods is needed to manage the spreading of weeds and to lessen their ability to adapt to a constantly changing system which uses several control practices.展开更多
Bit-plane decomposition makes images obtain a number of layers. According to the amount of data information, images are encrypted, and the paper proposes image encryption method with Chaotic Mapping based on multi-lay...Bit-plane decomposition makes images obtain a number of layers. According to the amount of data information, images are encrypted, and the paper proposes image encryption method with Chaotic Mapping based on multi-layer parameter disturbance. The advantage of multi-layer parameter disturbance is that it not only scrambles pixel location of images, but also changes pixel values of images. Bit-plane decomposition can increase the space of key. And using chaotic sequence generated by chaotic system with different complexities to encrypt layers with different information content can save operation time. The simulation experiments show that using chaotic mapping in image encryption method based on multi-layer parameter disturbance can cover plaintext effectively and safely, which makes it achieve ideal encryption effect.展开更多
The classical Schwarz-Pick lemma and Julia lemma for holomorphic mappings on the unit disk D are generalized to real harmonic mappings of the unit disk, and the results are precise. It is proved that for a harmonic ma...The classical Schwarz-Pick lemma and Julia lemma for holomorphic mappings on the unit disk D are generalized to real harmonic mappings of the unit disk, and the results are precise. It is proved that for a harmonic mapping U of D into the open interval I = （-1, 1）, AU（z）/cosU（z）π/2≤4/π 1/1-｜z｜^2 holds for z E D, where Au（z） is the maximum dilation of U at z. The inequality is sharp for any z E D and any value of U（z）, and the equality occurs for some point in D if and only if U（z） = 4Re {arctan ~a（z）}, z E D, with a M＆bius transformation φa of D onto itself.展开更多
In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous e...In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.展开更多
The classical Schwarz-Pick lemma for holomorphic mappings is generalized to planar harmonic mappings of the unit disk D completely. (I) For any 0 < r < 1 and 0 ρ < 1, the author constructs a closed convex do...The classical Schwarz-Pick lemma for holomorphic mappings is generalized to planar harmonic mappings of the unit disk D completely. (I) For any 0 < r < 1 and 0 ρ < 1, the author constructs a closed convex domain Er,ρ such that F((z,r)) eiαEr,ρ = {eiαz : z ∈ Er,ρ} holds for every z ∈ D, w = ρeiα and harmonic mapping F with F(D)D and F(z) = w, where △(z,r) is the pseudo-disk of center z and pseudo-radius r; conversely, for every z ∈ D, w = ρeiα and w ∈ eiαEr,ρ, there exists a harmonic mapping F such that F(D) D, F(z) = w and F(z ) = w for some z ∈ △(z,r). (II) The author establishes a Finsler metric Hz(u) on the unit disk D such that HF(z)(eiθFz(z) + e-iθFz(z)) ≤1 /(1- |z|2)holds for any z ∈ D, 0 θ 2π and harmonic mapping F with F(D)D; furthermore, this result is precise and the equality may be attained for any values of z, θ, F(z) and arg(eiθFz(z) + e-iθFz(z)).展开更多
Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some ...Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.展开更多
Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linear...Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linearly isometrically extended to the whole space for p 〉 2; if T is injective and the inverse mapping T^-1 is a 1-Lipschitz mapping, then T can be extended to be a linear isometry from l^p（Г） into l^p（△） for 1 〈 p ≤ 2.展开更多
基金the Talent Introduction Project of Xianyang Normal University under Grant No.07XSYK217
文摘We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor
文摘Surveying and early detection of invasive weeds are essential for strategic management and monitoring. Accordingly, a weed mapping was conducted during July 2011, against native （Orobanche ramosa, Cuscuta spp., Sorghum halepense and Xanthium strumarium） and non native （Abutilon theophrasti, Datura stramonium, Solanum elaeagnifolium and Verbesina encelioide） weeds of Lebanon. A global positioning system （Garmin 2006） was used for precise waypoint, elevation, navigation and distance. The result of interviewing and interacting with the residents in 95 villages distributed between the Beq＇aa and the North governorates of Lebanon, along with the observations made on the route, yielded the first detection of Abutilon theophrasti in both governorates. Solanum elaeagnifolium and Verbesina encelioide were not found in the agro-ecosystems of either governorates. This is the first report of the introduction ofAbutilon theophrasti in Lebanon and the establishment of a baseline data on weeds of Lebanon. The adoption of an integrated weed management program with a quarantine and control techniques and methods is needed to manage the spreading of weeds and to lessen their ability to adapt to a constantly changing system which uses several control practices.
文摘Bit-plane decomposition makes images obtain a number of layers. According to the amount of data information, images are encrypted, and the paper proposes image encryption method with Chaotic Mapping based on multi-layer parameter disturbance. The advantage of multi-layer parameter disturbance is that it not only scrambles pixel location of images, but also changes pixel values of images. Bit-plane decomposition can increase the space of key. And using chaotic sequence generated by chaotic system with different complexities to encrypt layers with different information content can save operation time. The simulation experiments show that using chaotic mapping in image encryption method based on multi-layer parameter disturbance can cover plaintext effectively and safely, which makes it achieve ideal encryption effect.
基金supported by National Natural Science Foundation of China(Grant No.11071083)
文摘The classical Schwarz-Pick lemma and Julia lemma for holomorphic mappings on the unit disk D are generalized to real harmonic mappings of the unit disk, and the results are precise. It is proved that for a harmonic mapping U of D into the open interval I = （-1, 1）, AU（z）/cosU（z）π/2≤4/π 1/1-｜z｜^2 holds for z E D, where Au（z） is the maximum dilation of U at z. The inequality is sharp for any z E D and any value of U（z）, and the equality occurs for some point in D if and only if U（z） = 4Re {arctan ~a（z）}, z E D, with a M＆bius transformation φa of D onto itself.
基金supported by Key Program of National Natural Science Foundation of China(Grant No.11031008)National Natural Science Foundation of China(Grant No.11061015)
文摘In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.
基金supported by National Natural Science Foundation of China (Grant No.10671093)
文摘The classical Schwarz-Pick lemma for holomorphic mappings is generalized to planar harmonic mappings of the unit disk D completely. (I) For any 0 < r < 1 and 0 ρ < 1, the author constructs a closed convex domain Er,ρ such that F((z,r)) eiαEr,ρ = {eiαz : z ∈ Er,ρ} holds for every z ∈ D, w = ρeiα and harmonic mapping F with F(D)D and F(z) = w, where △(z,r) is the pseudo-disk of center z and pseudo-radius r; conversely, for every z ∈ D, w = ρeiα and w ∈ eiαEr,ρ, there exists a harmonic mapping F such that F(D) D, F(z) = w and F(z ) = w for some z ∈ △(z,r). (II) The author establishes a Finsler metric Hz(u) on the unit disk D such that HF(z)(eiθFz(z) + e-iθFz(z)) ≤1 /(1- |z|2)holds for any z ∈ D, 0 θ 2π and harmonic mapping F with F(D)D; furthermore, this result is precise and the equality may be attained for any values of z, θ, F(z) and arg(eiθFz(z) + e-iθFz(z)).
基金supported by National Natural Science Foundation of China (Grant No.10871101)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060055010)
文摘Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.
基金the Natural Science Foundation of the Education Department of Jiangsu Province (No.06KJD110092)
文摘Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linearly isometrically extended to the whole space for p 〉 2; if T is injective and the inverse mapping T^-1 is a 1-Lipschitz mapping, then T can be extended to be a linear isometry from l^p（Г） into l^p（△） for 1 〈 p ≤ 2.
