In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface...In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.展开更多
In this paper, the source localization by utilizing the measurements of a single electromagnetic （EM） vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describ...In this paper, the source localization by utilizing the measurements of a single electromagnetic （EM） vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describe the orthogonality among the electric and magnetic measurements, two multivectors of the geometric algebra of Euclidean 3-space （G3） are used to model the outputs of a spatially collocated EM vector-sensor. Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3. Since the information used by the two estimators is different, a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error （MMSE）. Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart. The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.展开更多
We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkow...We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.展开更多
In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establis...In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.展开更多
Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian struct...Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P+ 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13.展开更多
In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularit...In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularities and the geometric invariants of curves which are deeply related to its order of contact with helices.展开更多
文章采用有机分子焊接方法,将苝-3,4,9,10-四羧酸二酐(PTCDA)分子通过酰胺键焊接于Ti_(3)CN层间,制备了PTCDA分子焊接插层的Ti_(3)CN(Ti_(3)CN-PTCDA)。PTCDA分子焊接不仅扩大了Ti_(3)CN层状结构的层间距,而且提升了其层结构稳定性,从...文章采用有机分子焊接方法,将苝-3,4,9,10-四羧酸二酐(PTCDA)分子通过酰胺键焊接于Ti_(3)CN层间,制备了PTCDA分子焊接插层的Ti_(3)CN(Ti_(3)CN-PTCDA)。PTCDA分子焊接不仅扩大了Ti_(3)CN层状结构的层间距,而且提升了其层结构稳定性,从而显著提高了储钠倍率性能和循环稳定性。在0.1Ag^(-1)电流密度下,Ti_(3)CN-PTCDA材料的比容量经过895次循环后可达127.9 mAh g^(-1),当电流密度提升至5.0Ag^(-1)时仍可保持51.8 mAh g^(-1)。本研究证明,二维储钠材料的层结构对其储钠倍率和循环稳定性有重要影响,该结论为设计高倍率二维储钠材料提供了新思路。展开更多
采用熔盐法制备α-Al_(2)O_(3),采用硅烷偶联剂γ-氨丙基三乙氧基硅烷(KH550)对α-Al_(2)O_(3)进行表面改性,得到KH-α-Al_(2)O_(3)。以低密度聚乙烯(LDPE)为基体、不同的α-Al_(2)O_(3)为添加剂,制备α-Al_(2)O_(3)/XLPE和KH-α-Al_(2)...采用熔盐法制备α-Al_(2)O_(3),采用硅烷偶联剂γ-氨丙基三乙氧基硅烷(KH550)对α-Al_(2)O_(3)进行表面改性,得到KH-α-Al_(2)O_(3)。以低密度聚乙烯(LDPE)为基体、不同的α-Al_(2)O_(3)为添加剂,制备α-Al_(2)O_(3)/XLPE和KH-α-Al_(2)O_(3)/XLPE接地线绝缘材料。对α-Al_(2)O_(3)和KH-α-Al_(2)O_(3)的晶体结构、微观结构以及基团进行分析,考察不同α-Al_(2)O_(3)含量对α-Al_(2)O_(3)/XLPE接地线绝缘材料电学性能和热学性能的影响。结果表明:熔盐法制备的α-Al_(2)O_(3)是具有六方结构、结晶度高、直径5~10μm的不规则圆片,KH550的改性不会造成α-Al_(2)O_(3)结晶度的变化。KH-α-Al_(2)O_(3)在KH-α-Al_(2)O_(3)/XLPE接地线绝缘材料中沿材料厚度方向排列,且分散更为均匀,有利于抑制电荷在基体中的传输。KH-α-Al_(2)O_(3)有利于提高XLPE的直流击穿场强和直流电导率。当KH-α-Al_(2)O_(3)的添加质量分数为1.5%时,KH-α-Al_(2)O_(3)/XLPE的直流击穿场强达到320 k V/mm,电导率为1.043×10^(-13)S/m。KH-α-Al_(2)O_(3)的引入使XLPE基体和KH-α-Al_(2)O_(3)之间的界面产生一定数量的陷阱,有效实现了对注入电荷的抑制。KH-α-Al_(2)O_(3)可以明显降低XLPE的热失重速率,提高KH-α-Al_(2)O_(3)/XLPE接地线绝缘材料热稳定性。当KH-α-Al_(2)O_(3)的质量分数达到1.5%时,分解温度升高至475.44℃,90℃条件下的导热系数从0.390 W/(m·K)增加到0.545 W/(m·K)。展开更多
目的探讨1.5T磁共振三维快速自旋回波成像(3D sampling perfection with application optimized contrasts by using different flip angle evolutions,3D-SPACE)与多回波融合成像(multiple echo data image combination,3D-MEDIC)序列...目的探讨1.5T磁共振三维快速自旋回波成像(3D sampling perfection with application optimized contrasts by using different flip angle evolutions,3D-SPACE)与多回波融合成像(multiple echo data image combination,3D-MEDIC)序列对正常人腰骶丛神经的显示。方法 31例无症状正常志愿者行MRI检查,包括常规腰椎MRI、3D-SPACE及MEDIC序列扫描,原始图像传入后处理工作站行多平面图像重组。结合原始及重组图像,比较3D-SPACE及MEDIC序列图像腰骶丛神经根的信噪比及对神经的显示评分。结果 3D-MEDIC序列显示神经根的信噪比高于3D-SPACE序列(分别为70.15±24.03及28.78±7.12,P=0.000)。3D-MEDIC序列对腰骶丛的显示评分高于3D-SPACE序列(P=0.000)。结论1.5T磁共振腰骶丛神经显像中,3D-MEDIC序列优于3D-SPACE序列,可清晰显示神经根走行,是常规腰椎MRI的重要补充。展开更多
文摘In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.
基金National Natural Science Foundation of China(61171127)National Basic Research Program of China(2011CB302903)
文摘In this paper, the source localization by utilizing the measurements of a single electromagnetic （EM） vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describe the orthogonality among the electric and magnetic measurements, two multivectors of the geometric algebra of Euclidean 3-space （G3） are used to model the outputs of a spatially collocated EM vector-sensor. Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3. Since the information used by the two estimators is different, a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error （MMSE）. Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart. The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.
文摘We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.
文摘In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.
基金supported by Research Foundation for Doctor Programme(Grant No.20040001034)National Natural Science Foundation of China(Grant No.10125105).
文摘Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P+ 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13.
基金the National Natural Science Foundation of China （No. 10471020） the Program for New Century Excellent Talents in University of China （No. 05-0319）.
文摘In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularities and the geometric invariants of curves which are deeply related to its order of contact with helices.
文摘文章采用有机分子焊接方法,将苝-3,4,9,10-四羧酸二酐(PTCDA)分子通过酰胺键焊接于Ti_(3)CN层间,制备了PTCDA分子焊接插层的Ti_(3)CN(Ti_(3)CN-PTCDA)。PTCDA分子焊接不仅扩大了Ti_(3)CN层状结构的层间距,而且提升了其层结构稳定性,从而显著提高了储钠倍率性能和循环稳定性。在0.1Ag^(-1)电流密度下,Ti_(3)CN-PTCDA材料的比容量经过895次循环后可达127.9 mAh g^(-1),当电流密度提升至5.0Ag^(-1)时仍可保持51.8 mAh g^(-1)。本研究证明,二维储钠材料的层结构对其储钠倍率和循环稳定性有重要影响,该结论为设计高倍率二维储钠材料提供了新思路。
文摘采用熔盐法制备α-Al_(2)O_(3),采用硅烷偶联剂γ-氨丙基三乙氧基硅烷(KH550)对α-Al_(2)O_(3)进行表面改性,得到KH-α-Al_(2)O_(3)。以低密度聚乙烯(LDPE)为基体、不同的α-Al_(2)O_(3)为添加剂,制备α-Al_(2)O_(3)/XLPE和KH-α-Al_(2)O_(3)/XLPE接地线绝缘材料。对α-Al_(2)O_(3)和KH-α-Al_(2)O_(3)的晶体结构、微观结构以及基团进行分析,考察不同α-Al_(2)O_(3)含量对α-Al_(2)O_(3)/XLPE接地线绝缘材料电学性能和热学性能的影响。结果表明:熔盐法制备的α-Al_(2)O_(3)是具有六方结构、结晶度高、直径5~10μm的不规则圆片,KH550的改性不会造成α-Al_(2)O_(3)结晶度的变化。KH-α-Al_(2)O_(3)在KH-α-Al_(2)O_(3)/XLPE接地线绝缘材料中沿材料厚度方向排列,且分散更为均匀,有利于抑制电荷在基体中的传输。KH-α-Al_(2)O_(3)有利于提高XLPE的直流击穿场强和直流电导率。当KH-α-Al_(2)O_(3)的添加质量分数为1.5%时,KH-α-Al_(2)O_(3)/XLPE的直流击穿场强达到320 k V/mm,电导率为1.043×10^(-13)S/m。KH-α-Al_(2)O_(3)的引入使XLPE基体和KH-α-Al_(2)O_(3)之间的界面产生一定数量的陷阱,有效实现了对注入电荷的抑制。KH-α-Al_(2)O_(3)可以明显降低XLPE的热失重速率,提高KH-α-Al_(2)O_(3)/XLPE接地线绝缘材料热稳定性。当KH-α-Al_(2)O_(3)的质量分数达到1.5%时,分解温度升高至475.44℃,90℃条件下的导热系数从0.390 W/(m·K)增加到0.545 W/(m·K)。
文摘目的探讨1.5T磁共振三维快速自旋回波成像(3D sampling perfection with application optimized contrasts by using different flip angle evolutions,3D-SPACE)与多回波融合成像(multiple echo data image combination,3D-MEDIC)序列对正常人腰骶丛神经的显示。方法 31例无症状正常志愿者行MRI检查,包括常规腰椎MRI、3D-SPACE及MEDIC序列扫描,原始图像传入后处理工作站行多平面图像重组。结合原始及重组图像,比较3D-SPACE及MEDIC序列图像腰骶丛神经根的信噪比及对神经的显示评分。结果 3D-MEDIC序列显示神经根的信噪比高于3D-SPACE序列(分别为70.15±24.03及28.78±7.12,P=0.000)。3D-MEDIC序列对腰骶丛的显示评分高于3D-SPACE序列(P=0.000)。结论1.5T磁共振腰骶丛神经显像中,3D-MEDIC序列优于3D-SPACE序列,可清晰显示神经根走行,是常规腰椎MRI的重要补充。
