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算子型Hilbert零点定理及构造弹性力学方程组一般解的符号算法 被引量:3
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作者 张鸿庆 朝鲁 《大连理工大学学报》 CAS CSCD 北大核心 1996年第4期373-379,共7页
基于Hilbert零点定理,在统一理论框架中考虑了弹性力学方程组一般解的机械化构造问题.给出:①A·C=B·D,C:KerD→KerA满射与C·KerD=KerA的等价性;②常系数线性算子型Hilbert... 基于Hilbert零点定理,在统一理论框架中考虑了弹性力学方程组一般解的机械化构造问题.给出:①A·C=B·D,C:KerD→KerA满射与C·KerD=KerA的等价性;②常系数线性算子型Hilbert零点定理及其简单构造性证明.简化了以往文献中对所考虑算子的限制;对构造弹性力学方程组一般解,给出了一种简单易行的机械化算法。 展开更多
关键词 弹性力学 符号法 零点定理 微分方程
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关于Hilbert符号的讨论 被引量:1
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作者 吴茂全 裴晓雯 《沈阳化工学院学报》 2007年第3期235-237,共3页
在乘群k*中,希尔伯特定义了一种两个元素a,b之间的运算(a,b),称为希尔伯特符号,在此我们利用已经推得的(a,b)简单运算公式及性质,采用指数α,β,仅由它们的模2的剩余类决定这一特性,将α,β分成3种情形,根据乘群k*的性质、Legendre符号... 在乘群k*中,希尔伯特定义了一种两个元素a,b之间的运算(a,b),称为希尔伯特符号,在此我们利用已经推得的(a,b)简单运算公式及性质,采用指数α,β,仅由它们的模2的剩余类决定这一特性,将α,β分成3种情形,根据乘群k*的性质、Legendre符号性质及p进方程的理论,对它的计算进行讨论. 展开更多
关键词 希尔伯特符号 乘群 非平凡解 P进单位元素群
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关于Hilbert符号的进一步讨论
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作者 吴茂全 裴晓雯 鲁亚男 《沈阳化工大学学报》 CAS 2010年第4期370-371,379,共3页
根据Hilbert定理及p进域的理论,推导出对于给定的Hilbert符号(a,b)有理数存在的充分必要条件,即对于Q*的一个有限元的簇(ai)i∈I和元素的值等于±1的簇(εi,v)i∈I,v∈V,存在有理数x∈Q*,对所有i∈I和v∈V,使(ai,x)v=εi,v成立的充... 根据Hilbert定理及p进域的理论,推导出对于给定的Hilbert符号(a,b)有理数存在的充分必要条件,即对于Q*的一个有限元的簇(ai)i∈I和元素的值等于±1的簇(εi,v)i∈I,v∈V,存在有理数x∈Q*,对所有i∈I和v∈V,使(ai,x)v=εi,v成立的充分必要条件是满足以下3个条件:(1)对于几乎所有的εi,v都等于1;(2)对所有i∈I,有∏v∈Vεi,v=1;(3)对所有的v∈V,存在xv∈Qv*,使(ai,xv)v=εi,v成立(对所有的i∈I). 展开更多
关键词 hilbert符号 二次乘幂 稠密
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基于小波变换的码元速率估计优化算法
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作者 谭晓衡 张雪静 《自动化学报》 EI CSCD 北大核心 2020年第8期1748-1752,共5页
针对低信噪比下MPSK(M-ary phase shift keying)信号的码元速率估计问题,提出一种优化算法.该算法无需先验知识,通过Hilbert变换提取瞬时相位基带序列,经多尺度小波变换,对每个尺度下的小波系数的模值的平方进行叠加,对叠加后的结果再... 针对低信噪比下MPSK(M-ary phase shift keying)信号的码元速率估计问题,提出一种优化算法.该算法无需先验知识,通过Hilbert变换提取瞬时相位基带序列,经多尺度小波变换,对每个尺度下的小波系数的模值的平方进行叠加,对叠加后的结果再进行功率谱计算,在码元速率整数倍处有离散谱线,估计正确率在信噪比大于1 dB时大于90%. 展开更多
关键词 MPSK信号 码元速率估计 hilbert变换 小波变换
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Noise Reduction for Digital Communications—The Masterpiece, a Modified Costas Loop
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作者 János Ladvánszky 《Circuits and Systems》 2020年第6期57-64,共8页
An efficient way of noise reduction has been presented: A modified Costas loop called as Masterpiece. The basic version of the Costas loop has been developed for SSB SC demodulation, but the same circuit can be applie... An efficient way of noise reduction has been presented: A modified Costas loop called as Masterpiece. The basic version of the Costas loop has been developed for SSB SC demodulation, but the same circuit can be applied for QAM (quadrature amplitude modulation) demodulation as well. Noise sensitivity of the basic version has been decreased. One trick is the transformation of the real channel input into complex signal, the other one is the application of our folding algorithm. The result is that the Masterpiece provides a 4QAM symbol error rate (SER) of 6 × 10<sup><span style="white-space:nowrap;">&#8722;</span>4</sup> for input signal to noise ratio (SNR) of <span style="white-space:nowrap;">&#8722;</span>1 dB. In this paper, an improved version of the original Masterpiece is introduced. The complex channel input signal is normalized, and rotational average is applied. The 4QAM result is SER of 3 × 10<sup><span style="white-space:nowrap;">&#8722;</span>4</sup> for SNR of <span style="white-space:nowrap;">&#8722;</span>1 dB. At SNR of 0 dB, the improved version produces 100 times better SER than that the original Costas loop does. In our times, this topic has a special importance because by application of our Masterpiece, all dangerous field strengths from 5G and WiFi, could be decreased by orders of magnitude. The Masterpiece can break the Shannon formula. 展开更多
关键词 Noise symbol Error Rate QAM Costas Loop hilbert Filter Folding Algorithm
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Hilbert genus fields of biquadratic fields 被引量:1
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作者 OUYANG Yi ZHANG Zhe 《Science China Mathematics》 SCIE 2014年第10期2111-2122,共12页
The Hilbert genus field of the real biquadratic field K=Q(√δ,√d)is described by Yue(2010)and Bae and Yue(2011)explicitly in the case&=2 or p with p=1 mod 4 a prime and d a squarefree positive integer.In this... The Hilbert genus field of the real biquadratic field K=Q(√δ,√d)is described by Yue(2010)and Bae and Yue(2011)explicitly in the case&=2 or p with p=1 mod 4 a prime and d a squarefree positive integer.In this article,we describe explicitly the Hilbert genus field of the imaginary biquadratic field K=Q(√δ,√d),whereδ=-1,-2 or-p with p=3 mod 4 a prime and d any squarefree integer.This completes the explicit construction of the Hilbert genus field of any biquadratic field which contains an imaginary quadratic subfield of odd class number. 展开更多
关键词 class group hilbert symbol hilbert genus field
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Hilbert Genus Fields of Imaginary Biquadratic Fields
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作者 Zhe Zhang Qin Yue 《Communications in Mathematics and Statistics》 SCIE 2017年第2期175-197,共23页
Let K_(0)=Q(√δ)beaquadraticfield.Forthose K_(0) withoddclassnumber,much work has been done on the explicit construction of the Hilbert genus field of a biquadratic extension K=Q(√δ,√d)over Q.Whenδ=2 or p with p... Let K_(0)=Q(√δ)beaquadraticfield.Forthose K_(0) withoddclassnumber,much work has been done on the explicit construction of the Hilbert genus field of a biquadratic extension K=Q(√δ,√d)over Q.Whenδ=2 or p with p≡1 mod 4 a prime and K is real,it was described in Yue(Ramanujan J 21:17–25,2010)and Bae and Yue(Ramanujan J 24:161–181,2011).In this paper,we describe the Hilbert genus field of K explicitly when K_(0) is real and K is imaginary.In fact,we give the explicit construction of the Hilbert genus field of any imaginary biquadratic field which contains a real quadratic subfield of odd class number. 展开更多
关键词 Class group hilbert symbol hilbert genus fields
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A conjecture on a class of elements of finite order in K_2F_■ 被引量:3
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作者 徐克舰 秦厚荣 《Science China Mathematics》 SCIE 2001年第4期484-490,共7页
For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a... For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin. 展开更多
关键词 K2 group local field tame symbol hilbert symbol
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The Structure of Certain K_2O_F
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作者 岳勤 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2001年第1期1-6,共6页
In this paper, we investigate tile structure of K2OF for F = -3 mod 9 and d ≠ -3. We find the element of order 3 of K2OF for F = and generated elements of K2OF /(2) /(8) /(3) for F = . We get the property of 2F, ... In this paper, we investigate tile structure of K2OF for F = -3 mod 9 and d ≠ -3. We find the element of order 3 of K2OF for F = and generated elements of K2OF /(2) /(8) /(3) for F = . We get the property of 2F, which develops a Tate and Bass's theorem, and give the structure of K2OF for F = and the presentation relations of SLn(OF)(n ≥ 3) 展开更多
关键词 K2-group hilbert symbol Dennis-Stein symbol.
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A note on Weil index
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作者 Jing-song CHAI Xu-ri CONG 《Science China Mathematics》 SCIE 2007年第7期951-956,共6页
Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(... Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(?))γ(1,(?))(a,b)andγ(a,(?))~4 =(-1,-1),where(a,b)is the Hilbert symbol for F.The Weil index plays an important role in the theory of theta series and in the general representation theory.In this paper,we establish an identity relating the Weil indexγ(a,(?))and the Gauss sum. 展开更多
关键词 Weil index hilbert symbol local fields Gauss sum 11S15 11F27
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A class of torsion elements in K2 of a local field 被引量:2
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作者 徐克舰 秦厚荣 《Science China Mathematics》 SCIE 2003年第1期24-32,共9页
For some local fields F, a description of torsion subgroups of K2 (F) via the elements of a specific form is given.
关键词 K2 group local field hilbert symbol.
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Some results for operators on a model space
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作者 Mehmet GURDAL Ulas YAMANCI Mubariz GARAYEV 《Frontiers of Mathematics in China》 SCIE CSCD 2018年第2期287-300,共14页
We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H^2θθH^2 is studied. We... We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H^2θθH^2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated Toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic Toeplitz operators and hypercyclicity of model operators. 展开更多
关键词 Reproducing kernel hilbert space (RKHS) reproducing kernel Berezin symbol Berezin number truncated Toeplitz operator modeloperator Toeplitz operator
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