幂计数算子的表示

讨论平方可积Bernoulli泛函空间L^(2)(M)上幂计数算子a^(N)的表示问题,a是任意非负实数.得到4种表示方法:a^(N)的谱表示,a^(N)以{an;n≥0}为其特征值,a^(N)的特征向量全体构成L^(2)(M)的一组标准正交基,当a=2时,2^(N)可用■-QNBs的异型等时混合积算子级数表示;关于L^(2)(M)的标准正交基的表示;利用真空态Zϕ以及■-QNBs,给出a^(N)的■-QNBs-真空态表示;利用一列特殊的■-QNBs,给出a^(N)的极限表示.考虑a^(N)与■-QNBs等时混合积复合后特征根与特征子空间均会随复合顺序发生变化.

属性构造原则与时序计数算子的研究

包括计数算子在内的属性构造技术往往能够提高数据挖掘模型的预测精度,但不加条件地使用会导致属性关系不一致问题.为解决此问题,在提出了属性关系一致等3个属性构造原则后,给出了在时序相关模型下避免属性关系不一致问题的新算法——时序计数算子.时序增量计数算子在满足其假设条件下,可以较小的代价显著地降低时序计数算子的高计算成本.实验结果验证了上述结论.

广义计数算子的Skorohod积分-随机梯度表示

对N上不同类型的非负函数h,讨论了离散时间正规鞅平方可积泛函空间L^(2)(M)中广义计数算子N_(h)关于广义Skorohod积分δ_(h)和广义随机梯度▽_(h)的表示问题.若h是N上的常值函数,则N_(h)与计数算子N有相同的定义域,并且对任意指数α∈R,N_(h)是▽h_(1-α)和δ_(hα)在DomN上的复合;若h是N上非负可和函数,则对α∈(-∞,1/2]和α∈(1/2,+∞],N_(h)可以表示为▽h_(1-α)和δ_(hα)在L_(2)(M)的不同稠子空间上的表示;若h是N上有正下界的非负实函数,则对α∈(-∞,0)和[0,+∞),N_(h)关于δ_(h),▽_(h)的复合表示在L_(2)(M)的不同稠子空间上成立;N_(h)关于交换代数P_(+)(N)上函数逐点乘积对广义Skorohod积分δ_(h)和广义随机梯度▽_(h)的表示是可交换的.

Bernoulli 泛函空间中广义计数算子的表示

得到离散时间正规鞅平方可积泛函空间L2(M)中广义计数算子N_(h)的5种表示:(1)量子Bernoulli噪声(quantum Bernoulli noises,QBN){∂_(k),∂_(k)^(*);k≥0}的加权表示;(2)N_(h)的谱表示,广义计数算子N_(h)以h-计数测度#h的值域为其点谱;(3)N_(h)的“对角化”表示,N_(h)可表示为L^(2)(M)的标准正交基{Zσ;σ∈Γ}所生成的一维对角化正交投影算子的加权极限;(4)广义Skorohod积分-广义随机梯度表示,N_(h)可表示为互共轭算子δ_(h)和■_(h)的复合算子;(5)对N上的任意非负函数h,可构造一列有界广义计数算子,N_(h)恰为该有界广义计数算子的强极限,当h可和时,N_(h)为该有界广义计数算子的一致极限。

离散时间正规鞅泛函空间中的广义计数算子

在离散时间正规鞅平方可积泛函空间L^(2)(M)中引入了一族线性算子{N_(h);h∈P+(N)}.N_(h)是L^(2)(M)中正的、稠定、自伴闭线性算子,一般未必有界.给出N_(h)有界的充分必要条件;讨论了N_(h)对h的依赖性,即N_(h)是关于h严格单调递增的算子值映射;证明了N上非负可和函数空间l^(1)_(+)(N)与有界广义计数算子族所成子空间是等距的;讨论了广义计数算子列强收敛和一致收敛的条件;对单调收敛函数列,讨论了其定义域收敛的条件和相应广义计数算子列收敛的条件;最后证明了{N_(h);h∈P+(N)}是S_(0)(M)中的一族可交换观测.

Bernoulli泛函空间中截断计数算子的时间算子

本文利用自伴算子的时间算子理论,初步构造了Bernoulli 泛函空间中与量子Bernoulli 噪声有密切联系的计数算子其截断算子的时间算子,且证明该时间算子并不唯一。

Bernoulli泛函空间计数算子的谱

谱是泛函分析的重要概念之一.用初等方法得出了计数算子的谱,并且讨论了它的点谱和谱之间的关系.

连续时间Guichardet-Fock空间中的计数算子的表示

考虑了连续时间Guichardet-Fock空间L2(Γ;η)中计数算子N的表示问题。利用修正随机梯度■及非适应性Skorohod积分δ,给出N的梯度-积分表示:N=δ°■;其次,应用L^2(Γ;η)中有界算子族{■S^*■s;s∈R+}的算子积分,证明在弱意义下,N有有界算子族的Bocher积分表示:N=∫R+■s^*■sds;同时,发现L^2(Γ;η)的一列相互正交闭子空间L^2(Γ(n);η)是N的特征子空间,从而给出N的谱表示:N=∞∑n=1nJn,其中Jn:L^2(Γ;η)→L^2(Γ(n);η)是正交投影。

广义计数算子的交换性质

讨论了Bernoulli泛函空间L2(M)中广义计数算子Nh与Γ-指标集量子Bernoulli噪声{■σ,■σ*:σ∈Γ}的Lie括号交换性、与■σ(■σ*)复合表达式以及与同指标σ-增生■σ*(σ-湮灭■σ)复合■σ■σ*(■σ*■σ)的交换性。L2(M)上{■σ,■σ*:σ∈Γ}是一族有界线性算子满足典则反交换关系、幂零性、指标交为空时的复合可交换性以及"吸收"交换性。接下来讨论Nh与{■σ,■σ*:σ∈Γ}的各种交换性问题。一般地,Nh与量子σ-增生■σ*(σ-湮灭■σ)的Lie括号恰是#h(σ)■σ*(#h(σ)■σ);对于支撑不是全空间N的h,Nh与一类特殊σ-增生■σ*(σ-湮灭■σ)可交换;而对于具有有限支撑的h,Nh与一类特殊■σ*(■σ)的复合仍保持其"增生(湮灭)"性质;Nh与{■σ■σ*,■σ*■σ:σ∈Γ}可交换。

连续时间Guichardet-Fock空间中的Dirichlet形式

首先,用有界算子的重积分研究连续时间Guichardet-Fock空间L^(2)(Γ;η)中的Dirichlet形式(ε,Domε),得到了(ε,Domε)与加权计数算子S_(ω)之间的关系:1)ε(f,g)=〈〈f,S_(ω)g〉〉,f∈Domε,g∈Dom S_(ω);2)ε(f,f)=‖S_(ω)f‖2,Domε=Dom S_(ω),f∈Domε.其次,考虑一类算子半群(C_(0)-半群)(T t)t≥0=(e-tS_(ω))t≥0,证明(ε,Domε)与算子半群之间的关系:ε(f,f)=lim t→0+W_(f):1 t(I-e-tS_(ω)),f∈Domε,其中W_(f):(x)=〈〈xf,f〉〉,x∈L^(2)(Γ;η),I为L^(2)(Γ;η)中的平凡表示.

Finite element solution based on fast numerical technique for large-scale electromagnetic computation

A numerical technique of the target-region locating （TRL） solver in conjunction with the wave-front method is presented for the application of the finite element method （FEM） for 3-D electromagnetic computation. First, the principle of TRL technique is described. Then, the availability of TRL solver for nonlinear application is particularly discussed demonstrating that this solver can be easily used while still remaining great efficiency. The implementation on how to apply this technique in FEM based on magnetic vector potential （MVP） is also introduced. Finally, a numerical example of 3-D magnetostatic modeling using the TRL solver and FEMLAB is given. It shows that a huge computer resource can be saved by employing the new solver.

基于改进时延神经网络的说话人识别方法

提出了一种改进的时延神经网络(Time Delay Neural Network,TDNN)的说话人识别方法以提高说话人识别准确率。首先通过TDNN网络训练音频的特征获取部分说话人的特征表达,然后由加入的量化和计数算子(Quantization and Counting Operators,QCO)同时处理,QCO能够充分利用音频的低层纹理特征,得到特征的细节信息。实验结果表明,改进的时延神经网络在相对较少的数据量中即可由网络训练获取更多信息的特征表达,在小数量训练集网络中体现出明显优势。当数据量进一步增多时效果更为明显,训练加入了纹理统计方法的结构提取的细节特征使说话人识别表现更好。

Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.

A Theoretical Study on the Dual-recognitions of Crown Tetraalanylpeptide with Small Ions

Under the method of density functional theory, the geometry structures, values of energy and population analysis of the combo of crown tetraalanylpeptide （C4-AIa） with ions （Xn） are calculated, based on the foundation of former studies. It was found that the coronary structure changed little whether in C4-Ala or C4-Ala-Xn, and the electrons transferred between C4-Ala and Xn at the mean time. There were coordinate bonds between Xn＋ and the nitrogen from -NH-, hydrogen bonds between Xa and the hydrogen from -NH-, and they became weaker when the radii of ions turned larger. Besides, the values of the single point bonding energy fluctuated gradually as a shape of saddle, but cations and anions located in opposite directions of the center of coronary structure when reach minimum, respectively.

Experimental and Theoretical Study of Deprotonation of DNA Adenine Cation Radical

Among all the DNA components, extremely redox-active guanine （G） and adenine （A） bases are subject to facile loss of an electron and form cation radicals （G＋＂ and A＋＇） when exposed to irradiation or radical oxidants. The subsequent deprotonation of G＋＇ and A＋＇ can invoke DNA damage or interrupt hole transfer in DNA. However, compared with intensive reports for G＋, studies on the deprotonation of A＋ are still limited at present. Herein, we investigate the deprotonation behavior of A＋. by time-resolved laser flash photolysis. The deprotonation product of A（N6-H）＇ is observed and the deprotonation rate constant, （2.0±0.1）×10 7 s-1, is obtained at room temperature. Further, the deprotonation rate con- stants of A＋. are measured at temperatures varying from 280 K to 300 K, from which the activation energy for the N6-H deprotonation is determined to be （17.1±1.0） kJ/mol by Arrhenius equation. In addition, by incorporating the aqueous solvent effect, we perform density functional theory calculations for A＋ deprotonation in free base and in duplex DNA. Together with experimental results, the deprotonation mechanisms of A＋ in free base and in duplex DNA are revealed, which are of fundamental importance for understanding the oxidative DNA damage and designing DNA-based electrochemical devices.

Using density functional calculations to elucidate atomic ordering of Pd-Rh nanoparticles at sizes relevant for catalytic applications

Pd-Rh nanoparticles are known to easily undergo surface restructuring in reactive environment. This study quantifies, with the help of density functional(DFT) calculations and a novel topological approach, atomic ordering and surface segregation effects in Pd-Rh particles with compositions 1:3, 1:1 and 3:1 containing up to 201 atoms(ca. 1.7 nm). The obtained data are used to reliably optimise energetically preferred atomic orderings in inaccessible by DFT Pd-Rh particles containing thousands of atoms and exhibiting sizes exceeding 5 nm, which are typical for catalytic metal particles. It is outlined, how segregation effects on the surface arrangement of Pd-Rh nanoalloy catalysts induced by adsorbates can be evaluated in a simple way within the present modelling setup.

Non-perturbative QCD Effect on K-Factor of Drell-Yan Process

By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative egect to K-factor of the Drell-Yan process is numerically investigated for 6^12C- 6^12C collision at the center-of-mass energy √s- 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.

Direct Approach to Construct the Periodic Wave Solutions for Two Nonlinear Evolution Equations

With symbolic computation, the Hirota method and Riemann theta function are employed to directly construct the periodic wave solutions for the Hirota-Satsuma equation for shallow water waves and Boiti-Leon-Manna- Pempinelli equation. Then, the corresponding figures of the periodic wave solutions are given. Fhrthermore, it is shown that the known soliton solutions can be reduced from the periodic wave solutions.

Cryptanalysis of Cryptosystems Based on General Linear Group

Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certain mathematical problems on non-commutative algebraic structures until now. In this background, Majid Khan et al.proposed two novel public-key encryption schemes based on large abelian subgroup of general linear group over a residue ring. In this paper we show that the two schemes are not secure. We present that they are vulnerable to a structural attack and that, it only requires polynomial time complexity to retrieve the message from associated public keys respectively. Then we conduct a detailed analysis on attack methods and show corresponding algorithmic description and efficiency analysis respectively. After that, we propose an improvement assisted to enhance Majid Khan's scheme. In addition, we discuss possible lines of future work.

Short-Time Decoherence of Solid-State Qubit at Optimal Operation Points

We investigate the short-time decoherence of a solid-state qubit under Ohmic noise at optimal operation points. The decoherence is analyzed by maximum norm of the deviation density operator. It is shown that at the temperature T = 3 mK, the loss of the fidelity due to decoherence is much smaller than the DiVincenzo low decoherence criterion, which means that the mode/may be an optimal candidate of qubit for quantum computation.