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图像的分形几何维数和系数模拟
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作者 祝清赫 《中国科技信息》 2016年第20期70-71,共2页
欧几里德几何学难以描述自然界物体的几何结构,而分形几何却可以对自然界物体广泛具备的自相似性、形状不规则性和结构复杂性加以描述。本文通过对欧几里得几何学里几个病态图形的分析研究,对物体的的自相似维数进行了分析,并依据分形... 欧几里德几何学难以描述自然界物体的几何结构,而分形几何却可以对自然界物体广泛具备的自相似性、形状不规则性和结构复杂性加以描述。本文通过对欧几里得几何学里几个病态图形的分析研究,对物体的的自相似维数进行了分析,并依据分形物体的自相似特征编写了分形图像仿真算法,实现了对分形物体的细节分析。 展开更多
关键词 分形几何 分形图像 几何维数 欧几里德几何 欧几里得几何 模拟 结构复杂性 自相似
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免疫荧光图像中神经突起的分维研究 被引量:2
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作者 汤敏 王惠南 《生物医学工程学杂志》 EI CAS CSCD 北大核心 2008年第6期1438-1441,共4页
分形维数已经广泛应用于医学图像处理分析中。我们介绍一种基于三棱形表面积(Triangular prismsurface area,TPSA)的分形维数测定方法,并将它创造性地应用于免疫荧光图像中,定量分析不同浓度神经再生素对大鼠背根神经节神经突起生长的... 分形维数已经广泛应用于医学图像处理分析中。我们介绍一种基于三棱形表面积(Triangular prismsurface area,TPSA)的分形维数测定方法,并将它创造性地应用于免疫荧光图像中,定量分析不同浓度神经再生素对大鼠背根神经节神经突起生长的影响。实验表明:基于分维的神经突起生长状况的研究易于理解,便于操作,与显微镜观测结果一致,其定量结果对实验的分析和判断具有很好的指导作用。 展开更多
关键词 分形几何分形图像特征 图像测量
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3维地理信息系统:现状与展望
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作者 朱国宾 《武测译文》 1997年第4期13-19,共7页
关键词 GIS 空间 几何维数 据模型 3建模
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四维直觉
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作者 P.J.Davis R.Hersh 王前 《世界科学》 1989年第1期18-19,17,共3页
直线是一维的,平面是二维的,立体是三维的,那么什么东西是四维的? 有时人们说时间是第四维。在爱因斯坦的相对论物理学中,使用的四维几何是由三维空间和一维时间组成的一个四维连续统。但我们不想谈论相对论和时空。我们只想知道在几何... 直线是一维的,平面是二维的,立体是三维的,那么什么东西是四维的? 有时人们说时间是第四维。在爱因斯坦的相对论物理学中,使用的四维几何是由三维空间和一维时间组成的一个四维连续统。但我们不想谈论相对论和时空。我们只想知道在几何维数表上一步一步走下去是否有意义。例如,在二维中,我们有熟悉的图形圆和正方形,它们的三维类似物是球和立方体。我们能谈论四维超球和超立方体,并使其有意义吗? 我们可以从一个点出发,用三步得到一个立方体。第一步。 展开更多
关键词 直觉 几何维数 几何
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Fractal character of lenticles and its influence on sediment state in tailings dam 被引量:3
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作者 蒋卫东 《Journal of Central South University of Technology》 EI 2005年第6期753-756,共4页
The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 g... The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 geological cross-sections, including 7 cross-sections of tailings dam constructed by the upstream method and 5 cross-sections by the middle line method, were analyzed with box dimension method. The results show that the distribution of tailings lenticles has better fractal character with box dimension from 1.290 7 to 1.513 6. The box dimension of the tailings dam constructed by upstream method is nearly 1.50 and that by middle line method is 1.30. Thereby the values of lenticles dimension have obvious relation to the method of constructing dam, and reflect the sediment state of tailings dam with the rule that smaller value means better state. 展开更多
关键词 tailings dam box dimension FRACTAL tailings lenticles
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Experimental Study on 3D Geometrical and Fractal Characteristics of Fracture Surface of Rock-Like Materials Based on GIS Technique
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作者 李尤嘉 黄醒春 +1 位作者 邓建华 陈翔 《Journal of Donghua University(English Edition)》 EI CAS 2010年第4期477-485,共9页
In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and me... In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and measured by means of a new-type 3D laser scanning system.Based on geographic information system(GIS)technique,the fracture surfaces were 3D visualized and reestablished.According to GIS 3D statistics,the geometrical characteristics of fracture surfaces under different breakage conditions were analyzed,and then based on fractal theory,the change laws of fractal dimension of fracture surfaces were discussed under the conditions of different cell pressures and initial water contents of rock.Furthermore,the relationships between characteristics of fracture surface and mechanical properties of rock were discussed.The results indicate that cell pressure,initial water content,and mechanical parameters of rock are the important factors to influence on the geometrical characteristics of fracture surface.The research provides a new experimental method for quantitative study on the fracture characteristics of various materials under different breakage conditions. 展开更多
关键词 FRACTURE geometrical characteristic FRACTAL cell pressure water content geographic information system(GIS)
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Using texture synthesis in fractal pattern design
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作者 魏宝刚 李建平 庞向斌 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第3期289-295,共7页
Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometr... Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique. 展开更多
关键词 Fractal geometry Texture synthesis Two-dimensional autocorrelation function Pattern design Image render
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Effect of Fiber Properties on Nonwovens' Pore Structures with Fractal Geometry Analysis
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作者 杨旭红 李栋高 《Journal of Donghua University(English Edition)》 EI CAS 2005年第4期103-108,共6页
Nonwovens' pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geom... Nonwovens' pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geometry, in combination with computer image anaysis, is used to express the irregularity of pore size distribution in nonwovens, and the effect of fiber properties on fractal dimension of pore size distribution is discussed by using simulated images which are composed of nonlinear staple fibers. The results show that the fiber properties, such as crimp, diameter, angular distribution, and especially the number of fibers prominently influence the pore structure. 展开更多
关键词 NONWOVENS fiber properties fractal dimension of pore size distribution simulated images.
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Structural Mechanics Analysis Using an FE-Mesh Adaption to Real, 3D Surface Detected Geometry Data
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作者 Sebastian Katona Michael Koch +1 位作者 Tobias C. Spruegel Sandro Wartzack 《Journal of Mechanics Engineering and Automation》 2015年第7期387-394,共8页
Within today's product development process, various FE-simulations (finite element) for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simul... Within today's product development process, various FE-simulations (finite element) for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simulations are performed with great effort for discretization, use of simulations conditions, like taking different non-linearities (i.e., material behavior, etc.) into account, to create meaningful results. Despite knowing the effects of deformations occurring during the production processes, always the non-deformed design model of a CAD-system (computer aided design) is used for the FE-simulations. It seems rather doubtful that further refinement of simulation methods makes sense, if the real manufactured geometry of the component is not considered for in the simulation. For an efficient exploit of the potential of simulation methods, an approach has been developed which offers a geometry model for simulation based on the existing CAD-model but with integrated production deviations as soon as a first prototype is at hand by adapting the FE-mesh to the real, 3D surface detected geometry. 展开更多
关键词 FEA (finite element analysis) PREPROCESSING simulation 3D surface detection RE (reverse engineering)
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A 3D GIS spatial data model based on conformal geometric algebra 被引量:26
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作者 YUAN LinWang YU ZhaoYuan +2 位作者 LUO Wen ZHOU LiangChen LU GuoNia 《Science China Earth Sciences》 SCIE EI CAS 2011年第1期101-112,共12页
We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresp... We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis. 展开更多
关键词 conformal geometric algebra 3D data model 3D measurement 3D spatial relation
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GEOMETRY AND DIMENSION OF SELF-SIMILAR SET 被引量:2
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作者 YIN YONGCHENG JIANG HAIYI SUN YESHUN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第1期57-64,共8页
The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case tha... The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given. 展开更多
关键词 Self-similar set Uniformly perfect set Hausdorff dimension
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The plate contact geometry investigation based on earthquake source parameters at the Burma arc subduction zone 被引量:8
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作者 ZHANG LangPing SHAO ZhiGang +2 位作者 MA HongSheng WANG XingZhou LI ZhiHai 《Science China Earth Sciences》 SCIE EI CAS 2013年第5期806-817,共12页
Accurately characterizing the threedimensional geometric contacts between the crust of the Chinese mainland and adjacent regions is important for understanding the dynamics of this part of Asia from the viewpoint of g... Accurately characterizing the threedimensional geometric contacts between the crust of the Chinese mainland and adjacent regions is important for understanding the dynamics of this part of Asia from the viewpoint of global plate systems. In this pa per, a method is introduced to investigate the geometric contacts between the Eurasian and Indian plates at the Burma arc sub duction zone using earthquake source parameters based on the Slabl.0 model of Hayes et al. (2009, 2010). The distribution of earthquake focus depths positioned in 166 sections along the Burma Arc subduction zone boundary has been investigated. Linear plane fitting and curved surface fitting has been performed on each section. Threedimensional geometric contacts and the extent of subduction are defined quantitatively. Finally, the focal depth distribution is outlined for six typical sections along the Burma arc subduction zone, combining focal mechanisms with background knowledge of geologic structure. Possible dy namic interaction patterns are presented and discussed. This paper provides an elementary method for studying the geometric contact of the Chinese mainland crust with adjacent plates and serves as a global reference for dynamic interactions between plates and related geodynamic investigations. 展开更多
关键词 Burma arc subduction zone earthquake source parameters plate boundary geometric contact Slab1.0 model
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The Gelfand-Kirillov dimension of a unitary highest weight module 被引量:1
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作者 BAI ZhanQiang HUNZIKER Markus 《Science China Mathematics》 SCIE CSCD 2015年第12期2489-2498,共10页
During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform... During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform formulas remain elusive—even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring(in the dual pair setting) and is inspired by Wang's formula for the dimension of a minimal nilpotent orbit. 展开更多
关键词 unitary highest weight module associated variety Gelfand-Kirillov dimension nilpotent orbit
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Mbius geometry of three-dimensional Wintgen ideal submanifolds in S^5 被引量:1
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作者 XIE ZhenXiao LI TongZhu +1 位作者 MA Xiang WANG ChangPing 《Science China Mathematics》 SCIE 2014年第6期1203-1220,共18页
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This pro... Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms). 展开更多
关键词 Wintgen ideal submanifolds DDVV inequality MSbius geometry austere submanifolds complexcurves
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A New Fractal Model of Elastic,Elastoplastic and Plastic Normal Contact Stiffness for Slow Sliding Interface Considering Dynamic Friction and Strain Hardening 被引量:2
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作者 田红亮 陈保家 +4 位作者 何孔德 董元发 钟先友 王骁鹏 郤能 《Journal of Shanghai Jiaotong university(Science)》 EI 2017年第5期589-601,共13页
The deflection properties of elastic stage, elastoplastic stage and plastic stage of elastomer were analyzed. Taking account of the kinetic friction force in friction interface and strain hardening in slow sliding int... The deflection properties of elastic stage, elastoplastic stage and plastic stage of elastomer were analyzed. Taking account of the kinetic friction force in friction interface and strain hardening in slow sliding interface, the elastic, elastoplastic and plastic normal contact stiffness model for harsh surface was established, which revised the Majumdar-Bhushan fractal model and made it more perfect. In the combination of macro and micro perspective, the effects of coarse surface fractal variables, kinetic friction force in the friction interface, material characters of the friction couples on the contact status and contact property were discussed by the study of digital analysis. Results imply that the normal contact stiffness improves with the increasing real contact area and normal contact load, and reduces with the augment of kinetic friction coefficient. When the kinetic friction coefficient is smaller than 0.3, the normal contact stiffness comprises a linear decrease with the increment of kinetic friction coefficient. When the kinetic friction coefficient is bigger than 0.3, the normal contact stiffness has an exponential decrease with the increasing kinetic friction coefficient. © 2017, Shanghai Jiaotong University and Springer-Verlag GmbH Germany. 展开更多
关键词 Elastoplasticity Fractals HARDENING Interfaces (materials) Kinetics STIFFNESS Strain hardening TRIBOLOGY
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Global existence of solutions of the critical semilinear wave equations with variable coefficients outside obstacles
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作者 LAI NingAn ZHOU Yi 《Science China Mathematics》 SCIE 2011年第2期205-220,共16页
In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coef... In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence. 展开更多
关键词 exterior problem variable coefficients wave equations critical nonlinearity
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Method for extracting geometrical characteristics of joint probability density based on contour lines 被引量:1
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作者 Shengli Chen Zhiqiang Wu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第2期130-140,I0004,共12页
This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and po... This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems. 展开更多
关键词 Joint probability density function PEAK CRATER Contour lines Stochastic P-bifurcation
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Transformation Between Eigenfunctions of Three Components of Geometric Momentum on Two-Dimensional Sphere
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作者 孙浩然 寻大毛 +1 位作者 唐良辉 刘全慧 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第7期31-33,共3页
A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimens... A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate. 展开更多
关键词 quantum mechanics differential geometry partial differential equations
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Lower bounds on the minimum distance in Hermitian one-point differential codes
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作者 KORCHMROS Gábor NAGY Gábor Pétery 《Science China Mathematics》 SCIE 2013年第7期1449-1455,共7页
Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2 (H) at a... Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2 (H) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ(D, mP) where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2 (H) and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ(D, mP). Further improvements from G(P) were obtained by Korchmaros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject. 展开更多
关键词 AG code Weierstrass gap Hermitian curve
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