费米子数的时空性质

将4维 Minkowski 时空推广到5维时空,并将“基本”粒子静质量和时空自由度 x₅相联系,m=—i（（?）/（?）x₅）,我们讨论了5维非线性变换共形群 C（M₅）.对于C（M₅）交换,保持有 dx₁²+dx₂²+dx₃²-dx₀²+dx₅²=0不变.C（M₅）群和线性变换群 SO（5,2）同构.在此基础上我们分析了费米子数的时空性质,并给出了自旋为半整数（整数）的粒子费米子数为奇数（偶数）的这一实验规律.     

弱电统一理论——SU(3)×U(1)模型

本文提出了一个对称性破缺前不仅左、右对称, 而且中微子(或反中微子)与荷电轻子、反轻子的弱作用也相同的SU(3)×U(1)模型. 这一模型无三角反常; 导出了sin²θ_w≤1/4; 在低能范围内与标准模型一致. 我们反轻子数推广为轻子荷. 证明了只有轻子荷才是严格守恒的, 各代轻子数分别守恒只能近似成立. 夸克不仅带有重子数、电荷, 而且也带有轻子荷. 本模型预言有μ_R→e_R+ν_eL+ν_μR, e^－+e^－→μ^－+μ^－等现象.     

d-玻色子体系波函数的SU2⊙SU2基、物理基与无迹玻色子算符(Ⅱ)

为了完满地解决求现有几类物理基矢在SU₂⊙SU₂表象的表示问题, 文中从第一类|PPO₃>基矢的无迹玻色子算符形式出发, 直接求出内积A_εx|PP⊙LL>的明显表达式. 同时用这种基矢的迭加表示出第二类基矢A_εx|PP(x)LL>的相应的迭加表示出A_εx|PP(y)LL}. 在结语部分还把本文的方法与前文(Ⅰ)的方法作了简单的对比.     

复杂粒子出射几率中聚合几率γβ的能量依赖

复杂粒子出射几率中聚合几率γ_β是一个复杂的函数. 我们假设γ_β=γ_β(A, E)[ε_β/MeV]^χ     

高温高压下CeTbO3合成过程中电阻的动态测试研究

 在0.5 GPa、4.0 GPa的压力下，从室温到800 ℃的温度范围内测量了氧化物CeTbO₃、单稀土氧化物Tb₄O₇、CeO₂和摩尔比维4∶1配比的混合物CeO₂+Tb₄O₇等的电阻随温度变化关系。对这四种物质均反映出电阻随温度增加而减小的半导体特征。在压力维0.5 GPa，温度高于600 ℃时发现了混合物CeO₂+Tb₄O₇、氧化物Tb₄O₇中电阻变化的起伏。X射线衍射谱表明，对应这一电阻变化，在结构上出现了变化。结果分析表明，这一变化与Tb⁴⁺→Tb³⁺的价态变化密切相联。     

SU(2)×U(1)×S3模型及类K0-K0系统的混合和CP破坏效应

本文内容包括:(ⅰ)进一步给出SU(2)×U(1)×S₃模型的结果S₂≈S₃≈(m_s²)/(m_b²);sin δ≤(m_um_d)/(m_cm_s),并预言b夸克的主要衰变道是b→u+W,b夸克的寿命可能长到10^-9秒.(ⅱ)给出类K⁰-K⁰系统混合时的精确表达式ρ=错号事例数/对号事例数=(1/2)(|p/q|²+|q/p|²)([Γ²+(Δm)²]²-(γ1γ2)²)/([Γ²+(Δm)²]²+(γ1γ2)²);并给出CP破坏的精确表达式:A=(1-ρ')/(1+ρ')=(I_M12Γ₁₂^*)/(|M₁₂|²+1/4|Γ₁₂|²),这里ρ′=(负电错号事例数)/(正电错号事例数)。     

关于单粒子位阱理论的一点注记

对应于（N±1）核的断续（d）与连续（c）能谱,单粒子格林函数的Lehmann表示G_αβ（ω）可以分为两部分之和: G_αβ（ω）=G_αβ^d（ω）+G_αβ^c（ω）。虽然G_αβ^d（ω）为半纯函数,但G_αβ^c（ω）却含有支点割线。在前几文关于非厄米单粒子位阱u_αβ=M_αβ（ε_β）[M_αβ（ω）为质量算符]的讨论中,我们只明显地考虑了G_αβ^d（ω）。这相当于引进了切断近似。本文进一步讨论了G_αβ^c（ω）的影响。文中证明了,由此除可多得少许新结论外,以前所得结果均依然正确。     

重离子深部非弹性碰撞中的一种动力学方法

为了解释重离子碰撞中的耗散与涨落问题, 发展了关联动力学方程和扩散方程的一种动力学方法. 考虑相对运动、碎片转动以及质量有对称自由度, 我们得到摩擦张量和扩散张量之间的关系. 根据这种关系, 在假定径向摩擦与切向摩擦擦具有相同形式因子, 即C_rr=KC_θθ情况下, 由数值求解动力学与扩散方程, 从而获知深部非弹性散射的有关知识. 对⁸⁶Kr(8.18MeV/A)+¹⁶⁶Er、⁸⁴Kr(8.5MeV)+¹⁶⁵Ho以及¹³⁶Xe(8.31MeV/A)+²⁰⁹Bi三个反应计算表明, 前两个反应具有旋转效应, 后一个反应显示出强聚焦效应. 由于核力及输运系数等的不确定因素, 仅对于大的l分波理论其计算结果与实验符合较好.     

SEVERAL PROBABLE QUESTIONS ON "A STUDY OF A SEMICLASSICAL APPROXIMATIONS FOR HEAVY ION TRANSFER REACTIONS"

The identity G(S,θ,π,0)=(－1)^{λ₁－λ₂}G(S,θ,0,0) is proved thus the transition amplitude's formula ((33), H-B,see[1]) stands good under the nonforward angular scattering conditions. The equation (ε₁-Δε₁-h²k₁²/2m_x⁾=(ε₂-Δε₂- h²k₂²/2m_x⁾ in Ref[1] may be questionable. The transfer amplitude's formula ((48), H-B) may be suitable only in post representation. The choice of different representations probablely influences the calculation results. The two symmetry properties of the transfer amplitude can simplify the numerical calculation.     

高压对以沸石分子筛基质的Eu（Ⅲ）稀土发光材料荧光光谱影响的研究

 本文研究了高压下无机微孔材料的相转变，并讨论了压力对离子交换的Eu（Ⅲ）NaA和Eu（Ⅲ）NaY两种以沸石分子筛为基质的稀土发光材料发光性质的影响。实验结果表明，对于不同基质材料，压力对Eu（Ⅲ）离子的光谱结构的影响，尤其是对⁵D₀→⁷F₁磁偶极跃迁与⁵D₀→⁷F₂电偶极跃迁强度比（I_m/I_e）的影响十分显著。对于Eu（Ⅲ）NaA样品来说，I_m/I_e值随压力的增加而增加，而对于Eu（Ⅲ）NaY样品，I_m/I_e值随压力的增加而减少。     

Entropy and Fractal Dimension Study of the TDP-43 Protein Low Complexity Domain Sequence in ALS Disease Severity and SARS-CoV-2 Gene Sequences in Virulence Variability

The low complexity domain (LCD) sequence has been defined in terms of entropy using a 12 amino acid sliding window along a protein sequence in the study of disease-related genes. The amyotrophic lateral sclerosis (ALS)-related TDP-43 protein sequence with intra-LCD structural information based on cryo-EM data was published recently. An application of entropy and Higuchi fractal dimension calculations was described using the Znf521 and HAR1 sequences. A computational analysis of the intra-LCD sequence entropy and Higuchi fractal dimension values at the amino acid level and at the ATCG nucleotide level were conducted without the sliding window requirement. The computational results were consistent in predicting the intermediate entropy/fractal dimension value produced when two subsequences at two different entropy/fractal dimension values were combined. The computational method without the application of a sliding-window was extended to an analysis of the recently reported virulent genes—Orf6, Nsp6, and Orf7a—in SARS-CoV-2. The relationship between the virulence functionality and entropy values was found to have correlation coefficients between 0.84 and 0.99, using a 5% uncertainty on the cell viability data. The analysis found that the most virulent Orf6 gene sequence had the lowest nucleotide entropy and the highest protein fractal dimension, in line with extreme value theory. The Orf6 codon usage bias in relation to vaccine design was discussed.     

Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties

We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation’s transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochastic) information dimension and gives a global characterization of the dynamics on the network. These general results are corroborated by examples of regular and of fractal networks.     

非晶铁中位形熵与信息维的压力响应

本文分析了非晶铁模型中原子能量分布的信息维和位形熵随压力的变化。计算了原子相互作用能的粒子数分布,将其分布的信息维作为非晶态位形熵的度量。计算结果表明,原子能量分布曲线和位形熵与统计时所取能量间隔有关;位形熵与能量间隔之间具有分形标度关系。用介于由能量间隔的下截止限和上截止限所确定的无标度区内的平均值表示各压力下的位形熵。模拟结果表明,原子能量分布的信息维是描述非晶系统无序状态的另一有效参量;压力对非晶金属结构无序及分维值的影响呈较复杂的波动变化趋势。 关键词：     

Percolation on infinitely ramified fractals

We present a family of exact fractals with a wide range of fractal and fracton dimensionalities. This includes the case of the fracton dimensionality of 2, which is critical for diffusion. This is achieved by adjusting the scaling factor as well as an internal geometrical parameter of the fractal. These fractals include the cases of finite and infinite ramification characterized by a ramification exponentp. The infinite ramification makes the problem of percolation on these lattices a nontrivial one. We give numerical evidence for a percolation transition on these fractals. This transition is tudied by a real-space renormalization group technique on lattices with fractal dimensionality ¯d between 1 and 2. The critical exponents for percolation depend strongly on the geometry of the fractals.     

信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系--兼论玻尔兹曼熵和克劳修斯熵是否等价

论述了信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系;由不涉及具体系统的方法从玻尔兹曼关系、信息熵推导出了克劳修斯熵的表达式;指出玻尔兹曼熵与克劳修斯熵不是等价关系,而是玻尔兹曼熵包含克劳修斯熵,信息熵又包含玻尔兹曼熵。     

The world according to Rényi: thermodynamics of multifractal systems

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs-Shannon entropy into more general framework—Rényi’s information entropy. We address the renormalization issue for Rényi’s entropy on (multi)fractal sets and consequently show how Rényi’s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Rényi’s information entropy and thermodynamics of multifractals. Important issues such as Rényi’s entropy versus Tsallis-Havrda-Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed.     

The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.     

一簇金刚石晶格上S~4模型的相变

采用重整化群和累积展开的方法,研究了一簇金刚石晶格上S~4模型的相变,求得了系统的临界点.结果表明:当分支数m=2和m 12时,该系统只存在一个Gauss不动点K~*=b_2/2, u_2~*=0;当分支数3≤m≤12时,该系统不仅有Gauss不动点,还存在一个Wilson-Fisher不动点,并且后一个不动点对系统的临界特性产生决定性的影响.     

Measurements of fractal dimensionality in 0.1Cs2O-0.9TeO2 glass-forming tellurite system by Raman spectroscopy

Low-frequency Raman spectroscopy was utilized in order to estimate the fractal dimensionality for tellurite 0.1Cs₂O-0.9TeO₂ binary glass-forming system in a temperature range, which includes the glassy and supercooled liquid state. A variation in fractal dimensionality was observed and calculated directly from the Raman spectroscopic data. This variation can be interpreted as an indication of structural alterations caused by temperature variation and correlated with existing structural models concerning tellurite network. Low-frequency Raman spectroscopy has proved to be a valuable tool for studying the fractal dimensionality and structural transformation in amorphous phases. The estimation of the localization degree of lattice vibration in disordered materials is important and discussed in the context of current phenomenological status of the field.     

The Spin-wave Fracton Excitations in Periodic Fractal Structure

The periodic fractal structure is introduced in this paper. The density of states of a ferromagnetic Heisenberg model on this structure is studied and the basic relation d_s = d_sr + 1 for the spin-fracton dimensionality is derived. Furthermore, the thermal properties on the periodic critical-bond-percolation network within effective-medium approximation (EMA) are discussed.