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竞赛中复数列递推问题的解法
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作者 陈君君 《数理天地(高中版)》 2022年第21期33-35,共3页
在数学竞赛试题中,常出现复数列问题,这类问题以递推数列为背景,求解既用到复数的概念、性质及运算法则等,又要考虑递推数列的结构特点和运用数列的有关知识,是情形较为复杂、综合性较强的一类竞赛题.
关键词 竞赛 复数列 解法
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中学数学教学中应涉及复数列吗?
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作者 于小平 《数学通报》 2000年第6期27-27,20,共2页
关键词 中学 数学教学 复数列 延拓数
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基于共轭对称列率复数哈达玛变换的水印算法 被引量:1
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作者 张悦 舒华忠 《东南大学学报(自然科学版)》 EI CAS CSCD 北大核心 2011年第2期312-316,共5页
为了提高水印的鲁棒性和计算效率,提出了一种基于共轭对称列率复数哈达玛变换的图像水印算法.该算法首先对载体图像分块并进行筛选,找到适合嵌入水印的块;在嵌入之前,根据方差将这些块分成纹理简单和纹理复杂2类,不同类的块使用不同的... 为了提高水印的鲁棒性和计算效率,提出了一种基于共轭对称列率复数哈达玛变换的图像水印算法.该算法首先对载体图像分块并进行筛选,找到适合嵌入水印的块;在嵌入之前,根据方差将这些块分成纹理简单和纹理复杂2类,不同类的块使用不同的量化步长,以此来增强水印的鲁棒性;然后,利用量化的方法将经过置乱和扩频的二值水印嵌入到上述块的系数相位中.为了抵抗图像的去同步攻击,提出了一种根据图像变换前后几何矩之间的关系来判断仿射变换的策略,并在此基础上计算变换参数,恢复图像的同步信息.实验结果表明,在满足不可见性的前提下,经历各种攻击之后所提取出的水印仍然清晰可辨,说明该算法具有较好的鲁棒性.同时,所提出的判断策略也能准确地判定载体图像是否经历了去同步攻击以及何种方式攻击. 展开更多
关键词 共轭对称复数哈达玛变换 共轭对称 去同步攻击 仿射变换 检测阈值
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复数域无穷级数相关问题的研究与探讨
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作者 赵伟舟 张辉 景慧丽 《贵阳学院学报(自然科学版)》 2015年第2期4-6,共3页
本文基于无穷级数主要讨论了复数列极限的求法、复数项级数敛散性的判别流程以及特殊级数的收敛半径。
关键词 无穷级数 复数列极限 复数项级数敛散性 收敛半径
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复级数列N次方倒数和的收敛性与部分复级数求和
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作者 易善峰 《科技视界》 2014年第21期114-114,128,共2页
求解自然数平方倒数和这个无穷级数的和是历史上有名的难题,欧拉创造性的应用函数的级数展开式与多项式根与系数的关系的类比方法解决了这个难题,后来这个人们发现这个问题也可以利用傅里叶来求解,本文通过对历史上这类倒数N次方求和问... 求解自然数平方倒数和这个无穷级数的和是历史上有名的难题,欧拉创造性的应用函数的级数展开式与多项式根与系数的关系的类比方法解决了这个难题,后来这个人们发现这个问题也可以利用傅里叶来求解,本文通过对历史上这类倒数N次方求和问题的解答得出来在复平面上复数列N次方倒数收敛性的判断条件与部分级数的求解。 展开更多
关键词 无穷级数 自然数平方倒数和院辐角 复数列 复平面
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一种基于新的正交复数变换的鲁棒水印算法 被引量:3
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作者 张悦 舒华忠 +1 位作者 伍家松 罗立民 《电子学报》 EI CAS CSCD 北大核心 2013年第8期1574-1579,共6页
本文提出了一种基于共轭对称列率复数哈达码变换(CS-SCHT)的鲁棒水印算法.在水印嵌入时,选择图像的CS-SCHT系数幅度作为水印载体,同时设计一种新的人眼视觉系统改善含水印图像的不可见性.检测时,运用Kolmogorov-Smirno方法估计系数幅度... 本文提出了一种基于共轭对称列率复数哈达码变换(CS-SCHT)的鲁棒水印算法.在水印嵌入时,选择图像的CS-SCHT系数幅度作为水印载体,同时设计一种新的人眼视觉系统改善含水印图像的不可见性.检测时,运用Kolmogorov-Smirno方法估计系数幅度的近似分布.然后根据该分布构造局部最优检测器.实验表明该变换适合于水印领域,新检测器具有良好的鲁棒性,且人眼视觉系统能够改善含水印图像的视觉质量. 展开更多
关键词 共轭对称复数哈达码变换 人眼视觉系统 检测 近似分布 局部最优检测器
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乘积型常系数递推关系的若干研究 被引量:1
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作者 张上伟 吴康 《河南教育学院学报(自然科学版)》 2012年第4期14-17,共4页
研究乘积型常系数递推关系的相关性质.分别在{a_n}为正实数列,p_1,p_2,…,P_k为实数以及{a_n}为复数列,p_1,p_2,…,p_k为整数这两种情况下研究乘积型常系数齐次递推关系的相关性质及数列{a_n}通项公式的求法.定义乘积型斐波那契数列,得... 研究乘积型常系数递推关系的相关性质.分别在{a_n}为正实数列,p_1,p_2,…,P_k为实数以及{a_n}为复数列,p_1,p_2,…,p_k为整数这两种情况下研究乘积型常系数齐次递推关系的相关性质及数列{a_n}通项公式的求法.定义乘积型斐波那契数列,得到相应的性质和定理. 展开更多
关键词 乘积型常系数递推关系 正实数 复数列 乘积型斐波那契数
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基于CS-SCHT域的相幅结合水印算法 被引量:1
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作者 杜荔 高利平 温馨 《东北大学学报(自然科学版)》 EI CAS CSCD 北大核心 2018年第4期492-496,共5页
针对目前一些水印算法鲁棒性有待提高的问题,提出一种将相位和幅度相结合的CS-SCHT域水印算法.由于相位的抗干扰能力比幅度的强,而幅度对旋转、剪切和缩放具有不变性,故若先将水印均分,然后再分别嵌入到同一系数的相位和幅度中,将可兼... 针对目前一些水印算法鲁棒性有待提高的问题,提出一种将相位和幅度相结合的CS-SCHT域水印算法.由于相位的抗干扰能力比幅度的强,而幅度对旋转、剪切和缩放具有不变性,故若先将水印均分,然后再分别嵌入到同一系数的相位和幅度中,将可兼得相位算法和幅度算法的优势,进而达到提高鲁棒性的目的.仿真结果表明:新算法在未受到攻击时峰值信噪比达到47.451 7 d B,在经过各种攻击后归一化相关系数也都在0.9以上.新算法的不可感知性好,并且对增亮攻击、旋转攻击、剪切攻击、高斯噪声攻击、高斯低通滤波攻击,以及JPEG压缩攻击都有很强的鲁棒性. 展开更多
关键词 数字图像 版权保护 数字水印 哈达玛变换 共轭对称复数
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Taxonomic Status of Daduhe Loquat (Eriobotrya prinoides var. dadunensis) 被引量:1
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作者 Wang Yongqing Yan Juan Yang Qin Fu Yan Luo Nan Lv Xiulan 《Journal of Agricultural Science and Technology(B)》 2012年第6期659-664,共6页
The taxonomic status of Daduhe loquat (E. prinoides var. dadunensis) was studied through analyzing genetic relationships among Oakleaf loquat (E. prinoides), Daduhe loquat and Common loquat (E. japonica) using i... The taxonomic status of Daduhe loquat (E. prinoides var. dadunensis) was studied through analyzing genetic relationships among Oakleaf loquat (E. prinoides), Daduhe loquat and Common loquat (E. japonica) using inter simple sequence repeats (ISSR) molecular marker and morphologic marker in this paper. Based on ISSR marker research, the similarity coefficient between Oakleaf loquat and Common loquat was lower than the similarity coefficient between Oakleaf loquat and Daduhe loquat while the similarity coefficient between Daduhe loquat and Common loquat was intermediate. The highest additivity was obtained when Daduhe loquat was regarded as the undetermined hybrid (45.8%). The specific bands of Oakleaf loquat and Common loquat were present in Daduhe loquat. Based on morphologic traits research, Daduhe loquat was also between Oakleaf loquat and Common loquat but a little leaning to Oakleaf loquat. All the results support that Daduhe loquat was hybrid of Oakleaf loquat and Common loquat. 展开更多
关键词 Common loquat Daduhe loquat genetic relationship ISSR marker morphologic traits Oakleaf loquat taxonomic status.
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Genetically identified complete hydatidiform mole coexisting with a normal fetus following IVF-ET 被引量:1
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作者 Sui Jianzhong Sun Xiaofang 《Journal of Medical Colleges of PLA(China)》 CAS 2009年第6期360-365,共6页
A complete hydatidiform mole coexisting with a fetus following in vitro fertilization and embryo transfer (IVF-ET) is a rare event. The diagnosis is often not easy because of the morphological similarity to a partial ... A complete hydatidiform mole coexisting with a fetus following in vitro fertilization and embryo transfer (IVF-ET) is a rare event. The diagnosis is often not easy because of the morphological similarity to a partial mole, but important to the treatment. We present a recent case in which STR polymorphism analysis clearly revealed a different genetic origin for the fetal and molar parts. STR polymorphisms on 15 variable number tandem repeat loci and a gender-determination locus, which were detected by polymerase chain reaction, indicating that the cord/placenta and molar tissue were parental and androgenous, respectively. During follow-up, the patient developed persistent gestational trophoblastic tumor (GTT) which was successfully treated with chemotherapy. In this case, STR polymorphism analysis exactly diagnosed a twin pregnancy consisting of a complete hydatidiform mole and a fetus. 展开更多
关键词 STR Complete hydatidiform mole In vitro fertilization Twin pregnancy
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Transcriptome of intraperitoneal organs of starry flounder Platichthys stellatus challenged by Edwardsiella ictaluri JCM1680 被引量:2
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作者 仝颜丽 孙修勤 +5 位作者 王波 王玲 李妍 田金虎 郑凤荣 郑明刚 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2015年第1期20-27,共8页
Platichthys stellatus is an economically important marine bony fish species that is cultured in China on a large scale.However,very little is known about its immune-related genes.In this study,the transcriptome of the... Platichthys stellatus is an economically important marine bony fish species that is cultured in China on a large scale.However,very little is known about its immune-related genes.In this study,the transcriptome of the immune organs ofP.stellatus that were intraperitoneally challenged with the pathogen Edwardsiella ictaluri JCM1680 is analyzed.Total RNA from four tissues(spleen,kidney,liver,and intestine) was mixed equally and then sequenced on an Illumina HiSeq 2000 platform.Overall,28 465 813 quality reads were generated and assembled into 43 061 unigenes.Similarity searches against public protein sequence databases were used to annotate 28 291 unigenes(65.7%of the total),368 of which were associated with immunoregulation,including 188 related to immunity response.Additionally,the transcript levels of immunity response unigenes annotated as related to tumor necrosis factor(TNF),TNF receptor,chemokine,major histocompatibility complex,and interleukin-6 were investigated in the different tissues of normal and infected P.stellatus by real-time quantitative PCR.The results confirmed that the unigenes identified in the transcriptome database were indeed expressed and up-regulated in infected P.stellatus.To our knowledge,this is the first report of the sequencing and analysis of the transcriptome of P.stellatus.These findings provide insights into the transcriptomics and immunogenetics of bony fish. 展开更多
关键词 Platichthys stellatus illumina sequencing TRANSCRIPTOME immunity gene real-time quantitativePCR
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DISTRIBUTION OF THE (0,∞) ACCUMULATIVE LINES OF MEROMORPHHIC FUNCTIONS 被引量:1
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作者 WU SHENGJIAN(Department of Mathematics, Beijing University,BeiJing 100871, China.) 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1994年第4期453-462,共10页
Suppose that f(z) is a meromorphic function of order and of lower order μin the plane. Let ρ be a positive number such that .(1) If f(l)(z) () has ρ() finite nonzero deficient values ai (i =1,…,p) with deficienci... Suppose that f(z) is a meromorphic function of order and of lower order μin the plane. Let ρ be a positive number such that .(1) If f(l)(z) () has ρ() finite nonzero deficient values ai (i =1,…,p) with deficiencies δ(ai, f(l)), then f(z) has a (0, ∝) accumulative line of order inany angular domain whose vertex is at the origin and whose magnitude is larger than(2) If f(z) has only p ()(0, ∝) accumulative lines of order : arg z = θk (θ1<θ2…<θp<2π, θp+1 = θ1 + 2π), then , where , providedthat has a finite noasero deficient value. 展开更多
关键词 Meromorphic function Accumulative line Order.
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Examples of entropy generating sequence 被引量:1
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作者 PARK Kyewon Koh 《Science China Mathematics》 SCIE 2011年第3期531-538,共8页
We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such th... We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate. 展开更多
关键词 entropy dimension entropy generating sequence COMPLEXITY
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Arbitrated quantum signature scheme based on reusable key 被引量:1
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作者 YU ChaoHua GUO GongDe LIN Song 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2014年第11期2079-2085,共7页
An arbitrated quantum signature scheme without using entangled states is proposed.In the scheme,by employing a classical hash function and random numbers,the secret keys of signer and receiver can be reused.It is show... An arbitrated quantum signature scheme without using entangled states is proposed.In the scheme,by employing a classical hash function and random numbers,the secret keys of signer and receiver can be reused.It is shown that the proposed scheme is secure against several well-known attacks.Specifically,it can stand against the receiver’s disavowal attack.Moreover,compared with previous relevant arbitrated quantum signature schemes,the scheme proposed has the advantage of less transmission complexity. 展开更多
关键词 signature signer receiver secret message cryptography encryption entangled reused resist
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DISTRIBUTION OF ONE-ERROR LINEAR COMPLEXITY OF BINARY SEQUENCES FOR ARBITRARY PRIME PERIOD
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作者 Lin TAN Wenfeng QI Hong XU 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2012年第6期1223-1233,共11页
Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of ... Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-error linear complexity. 展开更多
关键词 k-error linear complexity linear complexity periodic sequences stream ciphers.
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