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一类特殊双射函数及在数据转换方面的应用 被引量:1
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作者 闫林 孙印杰 《计算机应用与软件》 CSCD 北大核心 2005年第3期100-102,共3页
为了实现多维数据到一维数据的转换 ,本文首先考虑两个集合 :自然数集N和笛卡尔积N×N。由于它们都是可数集 ,所以本文给出了一个从N×N到N的双射函数f(m ,n) ,进而将其扩展 ,得到了从任意个N的笛卡尔积N×N×…×N... 为了实现多维数据到一维数据的转换 ,本文首先考虑两个集合 :自然数集N和笛卡尔积N×N。由于它们都是可数集 ,所以本文给出了一个从N×N到N的双射函数f(m ,n) ,进而将其扩展 ,得到了从任意个N的笛卡尔积N×N×…×N到N的双射函数———排序函数。然后着重讨论了这些函数的应用 ,它们具有从多维数据到一维数据的转换功能 ,使得多维数据的处理转换为一维数据的比较 。 展开更多
关键词 数据转换 数据处理 双射函数 排序函数
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关于双射函数f:N×N×N→N的研究 被引量:1
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作者 许精明 《微机发展》 2003年第10期102-103,106,共3页
讨论了可数无穷个可数无穷集合的并的计算问题。通过对自然数集合N的二次笛卡尔积运算———N×N和三次笛卡尔积运算———N×N×N的详细分析,得出了它们与自然数集合N之间都存在双射关系结论,即集合N×N和集合N×N... 讨论了可数无穷个可数无穷集合的并的计算问题。通过对自然数集合N的二次笛卡尔积运算———N×N和三次笛卡尔积运算———N×N×N的详细分析,得出了它们与自然数集合N之间都存在双射关系结论,即集合N×N和集合N×N×N都是可数无穷的。文中推导出了自然数集合N的三次笛卡尔积运算———N×N×N与自然数集合N之间的双射函数运算公式,对可数无穷集合的复杂计算作了进一步研究。得出结论:任意可数无穷个可数无穷集合的并(如N×N×N×…,即Nn)也是可数无穷的。 展开更多
关键词 集合论 自然数集合 可数无穷集合 双射函数 笛卡尔积 三次笛卡尔积运算
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基于双射函数f∶N^4→N的可计算性研究
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作者 许精明 《计算机技术与发展》 2009年第1期100-102,共3页
对四重笛卡尔积双射函数f:N4→N计算过程进行了研究,分析了其内在启发式构造规律,导出了f:N4→N的显式计算式。运用的启发规则是,将N4集合中前三个元素和相等的四元组划归为同一类,并按顺序将各类连续排列,再用交替枚举访问的方式对N4... 对四重笛卡尔积双射函数f:N4→N计算过程进行了研究,分析了其内在启发式构造规律,导出了f:N4→N的显式计算式。运用的启发规则是,将N4集合中前三个元素和相等的四元组划归为同一类,并按顺序将各类连续排列,再用交替枚举访问的方式对N4中的各四元组进行访问,逐级构造出f:N4→N的显式计算式。并将该式整理为只含有加法和乘法的运算形式。进一步分析得:n重函数f∶Nn→N的时间复杂度是指数增长的,即O(cn),c∈N。对函数f∶Nn→N的计算属NP难问题。 展开更多
关键词 计算理论 双射函数 高重笛卡尔积 可数无穷集合 NP难
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满足k阶PC(l)的密码函数的新构造
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作者 韦永壮 高军涛 胡子濮 《电子与信息学报》 EI CSCD 北大核心 2005年第5期699-702,共4页
该文基于线性分组码和双射函数,给出了满足七阶PC(l)的均衡相关免疫布尔函数新的构造方法。并据此进一步给出满足七阶PC(l)的(n,m,t)弹性函数的一般构造方法。此外,该文还揭示了这些函数的其它良好的密码学性质,如较高的非线性度、良好... 该文基于线性分组码和双射函数,给出了满足七阶PC(l)的均衡相关免疫布尔函数新的构造方法。并据此进一步给出满足七阶PC(l)的(n,m,t)弹性函数的一般构造方法。此外,该文还揭示了这些函数的其它良好的密码学性质,如较高的非线性度、良好的代数次数、良好的构造计数等。 展开更多
关键词 弹性函数 扩散性 线性码 双射函数
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论函数的构造与分析
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作者 姚俊萍 李新社 封富君 《赤峰学院学报(自然科学版)》 2014年第12期1-3,共3页
本文系统地论述了几种特殊条件下的函数构造问题,对有限集合间满射、单射、双射函数的构造问题进行了重点讨论分析,并特别针对有限集合间满射函数个数的计算问题给出了自己的思考方法和证明过程,最后举例说明了进行函数良定性证明的必要性.
关键词 有限集合 无限集合 满射函数 单射函数 双射函数
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面向大数据处理的高精度多维计数布鲁姆过滤器 被引量:11
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作者 李玮 张大方 +1 位作者 黄昆 谢鲲 《电子学报》 EI CAS CSCD 北大核心 2015年第4期652-657,共6页
分析了现有多维布鲁姆过滤器查询算法的工作原理和特点,针对大数据处理特点提出了一种基于双射函数的高精度多维计数布鲁姆过滤器(AMD-CBF)查询算法.AMD-CBF中元素表示和查找分两步进行,第1步将元素各属性哈希映射到各自对应的高精度计... 分析了现有多维布鲁姆过滤器查询算法的工作原理和特点,针对大数据处理特点提出了一种基于双射函数的高精度多维计数布鲁姆过滤器(AMD-CBF)查询算法.AMD-CBF中元素表示和查找分两步进行,第1步将元素各属性哈希映射到各自对应的高精度计数布鲁姆过滤器(A-CBF)中;第2步将元素的所有属性通过双射函数转换为一个值来表示元素整体信息,然后将这个值哈希映射到联合计数布鲁姆过滤器中(C-CBF),完成元素整体的表示和查询确认.理论分析和仿真实验结果表明,AMD-CBF能够支持多维集合元素的高效表示和查询及删除,相比同类研究查询假阳性降低明显,查询精度大幅度提高. 展开更多
关键词 大数据处理 多维布鲁姆过滤器 双射函数 高精度计数布鲁姆过滤器 假阳性
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仪器调节的零点判别法
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作者 贾亚民 《高校实验室工作研究》 2002年第2期52-53,共2页
以测量仪器的快速调校为研究对象,提出了仪器调节的零点判别法则,旨在为仪器校准、检验、故障诊断、调试维修等提供一种便捷可靠的方法。
关键词 机械构件 调节系统 判别法 同构 双射函数
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A Real-Time Photo-Realistic Rendering Algorithm of Ocean Color Based on Bio-Optical Model 被引量:4
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作者 MA Chunyong XU Shu +2 位作者 WANG Hongsong TIAN Fenglin CHEN Ge 《Journal of Ocean University of China》 SCIE CAS 2016年第6期996-1006,共11页
Abstract A real-time photo-realistic rendering algorithm of ocean color is introduced in the paper, which considers the impact of ocean bio-optical model. The ocean bio-optical model mainly involves the phytoplankton,... Abstract A real-time photo-realistic rendering algorithm of ocean color is introduced in the paper, which considers the impact of ocean bio-optical model. The ocean bio-optical model mainly involves the phytoplankton, colored dissolved organic material (CDOM), inorganic suspended particle, etc., which have different contributionsto absorption and scattering of light. We decompose the emergent light of the ocean surface into the reflected light from the sun and the sky, and the subsurface scattering light. We estab- lish an ocean surface transmission model based on ocean bidirectional reflectance distribution function (BRDF) and the Fresnel law, and this model's outputs would be the incident light parameters of subsurface scattering. Using ocean subsurface scattering algorithm combined with bio-optical model, we compute the scattering light emergent radiation in different directions. Then, we blend the re- flection of sunlight and sky light to implement the real-time ocean color rendering in graphics processing unit (GPU). Finally, we use two kinds of radiance reflectance calculated by Hydrolight radiative transfer model and our algorithm to validate the physical reality of our method, and the results show that our algorithm can achieve real-time highly realistic ocean color scenes. 展开更多
关键词 ocean color BRDF subsurface scattering bio-optical model
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Modeling of radiative properties of metallic microscale rough surface 被引量:1
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作者 王爱华 蔡九菊 《Journal of Central South University》 SCIE EI CAS 2012年第6期1482-1487,共6页
The radiative properties of a gold surface with one-dimensional Gaussian random roughness distribution were obtained with the finite-difference time-domain (FDTD) method and the recursive convolution treatment of th... The radiative properties of a gold surface with one-dimensional Gaussian random roughness distribution were obtained with the finite-difference time-domain (FDTD) method and the recursive convolution treatment of the Drude Model. The bi-directional reflection distribution function (BRDF) for both TM mode and TE mode were obtained and compared with the highly accurate experimental data from the earlier work. The incident wavelength varies from 1.152 μm to 3.392 μm and incident angle is at 300-70°, respectively. The results show that, the predicted values and experimental results are in good agreement. The highly specular peak in the BRDF is reproduced in the numerical simulations, and the increase of the TM mode BRDF is found to be attributed to the effect of a variation in the optical constant at the incident wavelength period. 展开更多
关键词 bi-directional reflection distribution function Gaussian random roughness distribution gold surface finite-differencetime-domain method
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Modeling bidirectional reflection distribution function of microscale random rough surfaces
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作者 王爱华 HSU P.F. 蔡九菊 《Journal of Central South University》 SCIE EI CAS 2010年第2期228-234,共7页
The radiative properties of three different materials surfaces with one-dimensional microscale random roughness were obtained with the finite difference time domain method(FDTD) and near-to-far-field transformation.Th... The radiative properties of three different materials surfaces with one-dimensional microscale random roughness were obtained with the finite difference time domain method(FDTD) and near-to-far-field transformation.The surface height conforms to the Gaussian probability density function distribution.Various computational modeling issues that affect the accuracy of the predicted properties were discussed.The results show that,for perfect electric conductor(PEC) surfaces,as the surface roughness increases,the magnitude of the spike reduces and eventually the spike disappears,and also as the ratio of root mean square roughness to the surface correlation distance increases,the retroreflection becomes evident.The predicted values of FDTD solutions are in good agreement with the ray tracing and integral equation solutions.The overall trend of bidirectional reflection distribution function(BRDF) of PEC surfaces and silicon surfaces is the same,but the silicon's is much less than the former's.The BRDF difference from two polarization modes for the gold surfaces is little for smaller wavelength,but it is much larger for the longer wavelength and the FDTD simulation results agree well with the measured data.In terms of PEC surfaces,as the incident angle increases,the reflectivity becomes more specular. 展开更多
关键词 bidirectional reflection distribution fimction random rough surfaces Maxwell equations finite difference time domain method
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A Study on Radiative Dileptonic Decays B^0(Bs)→γe^+e^-
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作者 CHEN Jun-Xiao HOU Zhao-Yu LUE Cai-Dian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2期299-302,共4页
We study the rare radiative dileptonlc decays B^0(Bs)→γe^+e^- (e = e, μ) in the standard model By using the B meson wave function constrained by non-leptonic decays, the branching ratios turn out to be of the ... We study the rare radiative dileptonlc decays B^0(Bs)→γe^+e^- (e = e, μ) in the standard model By using the B meson wave function constrained by non-leptonic decays, the branching ratios turn out to be of the order of 10^-9 for Bs→γe^+e^-, γe^+e^-, and 10^-10 for Bs→γe^+e^-, γe^+e^-. Based on the study, these decays are accessible at the near future LHC-b experiment, which are useful to determine the B(B,) wave function. 展开更多
关键词 radiative decay B meson wave function
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关系与函数的举例说明
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作者 张锦文 廖祖纬 《中国远程教育》 1985年第3期9-12,共4页
关系虽是一个司空见惯的“名词”,却又具有重要的数学意义,而函数则是数学中既普遍又广泛应用的一个概念。两者之间有着密切的联系。下面就从集合的角度,通过一些具体例子,对关系与函数作一些说明。
关键词 函数 举例说明 函数 双射函数 单射 具体例子 数学意义 矩阵表示 有序对 列集
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A unified canopy bidirectional reflectance (BRDF) model for row ceops 被引量:3
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作者 YAN BinYan XU XiRu FAN WenJie 《Science China Earth Sciences》 SCIE EI CAS 2012年第5期824-836,共13页
Row sowing is a basic crop sowing method in China,and thus an accurate Bidirectional Reflectance Distribution Function (BRDF) model of row crops is the foundation for describing the canopy bidirectional reflectance ch... Row sowing is a basic crop sowing method in China,and thus an accurate Bidirectional Reflectance Distribution Function (BRDF) model of row crops is the foundation for describing the canopy bidirectional reflectance characteristics and estimating crop ecological parameters.Because of the macroscopically geometric difference,the row crop is usually regarded as a transition between continuous and discrete vegetation in previous studies.Were row treated as the unit for calculating the four components in the Geometric Optical model (GO model),the formula would be too complex and difficult to retrieve.This study focuses on the microscopic structure of row crops.Regarding the row crop as a result of leaves clumped at canopy scale,we apply clumping index to link continuous vegetation and row crops.Meanwhile,the formula of clumping index is deduced theoretically.Then taking leaf as the basic unit,we calculate the four components of the GO model and develop a BRDF model for continuous vegetation,which is gradually extended to the unified BRDF model for row crops.It is of great importance to introduce clumping index into BRDF model.In order to evaluate the performance of the unified BRDF model,the canopy BRDF data collected in field experiment,"Watershed Allied Telemetry Experiment Research (WATER)",from May 30th to July 1st,2008 are used as the validation dataset for the simulated values.The results show that the unified model proposed in this paper is able to accurately describe the non-isotropic characteristics of canopy reflectance for row crops.In addition,the model is simple and easy to retrieve.In general,there is no irreconcilable conflict between continuous and discrete vegetation,so understanding their common and individual characteristics is advantageous for simulating canopy BRDF.It is proven that the four components of the GO model is the basic motivational factor for bidirectional reflectance of all vegetation types. 展开更多
关键词 row crop BRDF CLUMPING clumping index
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Visible characteristics of space-based targets based on bidirectional reflection distribution function 被引量:3
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作者 WANG HongYuan ZHANG Wei WANG FuGang 《Science China(Technological Sciences)》 SCIE EI CAS 2012年第4期982-989,共8页
A precise modeling method of visible characteristics of the space-based target was presented based on bidirectional reflection distribution function (BRDF). The background characteristics of the space-based target wer... A precise modeling method of visible characteristics of the space-based target was presented based on bidirectional reflection distribution function (BRDF). The background characteristics of the space-based target were represented to build models of direct solar radiation and reflected radiation of the Earth based on blackbody radiation theory. The geometry characteristics of the target were analyzed to establish a surface equation of each surface based on its body coordinate system. The material characteristics of the target surface were described by introducing a BRDF model which considers the character of surface Gauss statistics and self-shadow and is obtained by measurement and modeling in advance. The relative positions of the space-based target, the background radiation sources and the observation platform were determined based on coordinate con- version to judge contributing surface of the target to observation system. Then a mathematical model on visible characteristics of the space target for the given optical system was built by summing reflection components of all the surfaces. Simulation of visible characteristics of the space-based target in orbit was achieved according to its given geometrical dimensions, physical parameters and orbital parameters. The results show that the method is effective for analysis on visible characteristics of the space-based target when single reflection is considered and its surface is regularly described in a surface equation, which provides a way to real-time calculation of visible characteristics of the space-based target. 展开更多
关键词 space optics space-based target visible characteristics bidirectional reflection distribution function (BRDF)
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On the Gracefulness of the Digraphs n·Cm*
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作者 Jirimutu Jun Wang Xu Xirong 《Journal of Systems Science and Information》 2009年第3期281-288,共8页
A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) →{0, 1,... , |E|} such that the induced function f' : E(G) --~ {1, 2,… , |E|} which is defined by f' (u, v) = [f(v) - ... A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) →{0, 1,... , |E|} such that the induced function f' : E(G) --~ {1, 2,… , |E|} which is defined by f' (u, v) = [f(v) - f(u)] (rood |E|+ 1) for every directed edge (u, v) is a bijection. Here, f is called a graceful labeling (graceful numbering) of D(V, E), while f' is called the induced edge's graceful labeling of D. In this paper we discuss the gracefulness of the digraph n- Cm and prove that n. Cm is a graceful digraph for m = 15, 17 and even 展开更多
关键词 DIGRAPH directed cycles graceful graph graceful labeling
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