The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

Comparative study on phase transition behaviors of fractional molecular field theory and random-site Ising model

Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.

Durable hierarchical phosphorus‐doped biphase MoS_(2)electrocatalysts with enhanced H^(*)adsorption

Phase engineering is an efficient strategy for enhancing the kinetics of electrocatalytic reactions.Herein,phase engineering was employed to prepare high‐performance phosphorous‐doped biphase(1T/2H)MoS_(2)(P‐BMS)nanoflakes for hydrogen evolution reaction(HER).The doping of MoS_(2)with P atoms modifies its electronic structure and optimizes its electrocatalytic reaction kinetics,which significantly enhances its electrical conductivity and structural stability,which are verified by various characterization tools,including X‐ray photoelectron spectroscopy,high‐resolution transmission electron microscopy,X‐ray absorption near‐edge spectroscopy,and extended X‐ray absorption fine structure.Moreover,the hierarchically formed flakes of P‐BMS provide numerous catalytic surface‐active sites,which remarkably enhance its HER activity.The optimized P‐BMS electrocatalysts exhibit low overpotentials(60 and 72 mV at 10 mA cm^(−2))in H_(2)SO_(4)(0.5 M)and KOH(1.0 M),respectively.The mechanism of improving the HER activity of the material was systematically studied using density functional theory calculations and various electrochemical characterization techniques.This study has shown that phase engineering is a promising strategy for enhancing the H*adsorption of metal sulfides.

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide （GAP） from zinc-blende （ZB） to a rocksalt （RS） structure is investigated by the plane-wave pseudopotential density functional theory （DFT）. Lattice constant a0, elastic constants cij, bulk modulus B0 and the pressure derivative of bulk modulus B0 are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/Vo, the Debye temperature 8, the heat capacity Cv and the thermal expansion coefficient a are also discussed in a pressure range from 0 CPa to 40 GPa and a temperature range from 0 K to 1500 K.

OSCILLATION FREQUENCY THEORY OF A PIEZOELECTRIC SENSOR INLIQUID PHASE WITH TWO SEPARATED－ELECTRODES

In this paper, an oscillation frequency equation for a pizoelectric sensor with two separated-electrodes is theoretically derived and experimentally verified. The correlatione of the oscillation frequency and the liquid properties are investigated.

Quantitative feedback theory and zero phase error tracking control combined robust control for radar truck leveling simulator

Radar leveling system is the key equipment for improving the radar mobility and survival capability. A combined quantitative feedback theory (QFT) controller is designed for the radar truck leveling simulator in this paper, which suffers from strong nonlinearities and system parameter uncertainties. QFT can reduce the plant uncertainties and stabilize the system, but it fails to obtain high-precision tracking. This drawback can be solved by a robust QFT control scheme based on zero phase error tracking control (ZPETC) compensation. The combined controller not only possesses high robustness, but greatly improves the system performance. To verify the effiectiveness and the potential of the proposed controller, a series of experiments have been carried out. Experimental results have demonstrated its robustness against a large range of parameters variation and high tracking precision performance, as well as its capability of restraining the load coupling among channels. The combined QFT controller can drive the radar truck leveling platform accurately, quickly and stably.

Nonlinear Kinetic Theory and Pulse Interactions in Phase Transition

The kinetics of nucleation of phase transition is a phenomenal theory.Some new technologies of preparation of nanomaterials,for example,by shock wave and by electropulsing,are pulse interactions.Based on the known nonlinear theories of phase transition,the nonlinear kinetics of phase transition is discussed,and a soliton-like model is proposed. This mathematical method can not only explain the basic characteristics of pulse interactions and suddenness of phase transition, and possesses a consistency of mechanism for nucleation and growth.

APPLICATION OF MOLECULAR ORBITAL THEORY TO ANALYSIS OF PHASE STABILITY FOR ALLOYS

The critical _d vahues ( _ ) of the γ/(γ+σ).γ/(γ+μ) and γ/(γ+γ') phase boundaries in some ternar alloy phase diagrams at various temperatures are calculated by averaging the _d values of sererai selected characteristic points at the phase boundaries.Approxmate equations for the temperature dependence of the critical _d of γ/(γ+σ).γ/(γ+μ) and γ/(γ+γ') phase boundaries are established.The accuracy of the analysis is discussed in detail. It is found for the first time that the average value of the bond order _ at the phase boundaries ts also approximatelr a constant and therefore a critical average bond order _ like - can be introduced for the analysts of phase stability

A Back Look on the Binary Phase Diagrams of Metals from the Mass Action Law and the Coexistence Theory of Metallic Melts

According to the mass action law and the coexistence theory of metallic melts, the mass action concentrations of Cu-Mg, Bi-Tl and Ni-Al melts involving compound formation have been calculated. The calculated results show that, except the ultimate case of pure element, when two elements are present in the melts, all structural units (atoms and molecules) without exception will be present in the melts, i.e., their concentrations may change from great to small, but they will not vanish into nothing, and only under such conditions, the calculated results both agree with practice and obey the law of mass action. In view of that over considerable wide composition range, the activities of both elements of the three solid binary alloys mentioned above have been measured, this seems in contradiction with the present relevant phase diagrams, in which the structural units are determined by composition range, so the latter needs further investigation and consideration.

Orbital Phase Theory and the Diastereoselectivity of Some Organic Reactions

The orbital phase refers to the relationship between orbitals that originates from their wave character. We show here that the orbital phase essentially determines the diastereoselectivity of the following three organic reactions. 1) Torquoselectivity of the electrocyclicring-opening reaction of 3-substituted cyclobutenes;2) Contradictory torquoselectivity of the retro-Nazarov reaction;3) Diastereoselectivity in electrophilic addition to substituted ethylenes.

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive （ferromagnetic interaction） and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative （ferromagnetic or antiferromagnetic interaction）. The temperature dependence of the layer magnetizations of the system is examined to characterize the nature （continuous or discontinuous） of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point （TP）, critical end point （E）, multicritical point （A）, isolated critical point （C） and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.

Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase

In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.

Study on the Phase Equilibria of Hard Core Asakura-Oosawa Fluids with Renormalization-group Theory

An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard sphere fluid.The phase equilibria are studied by using the renormalization-group (RG) theory. The obtained results agree well with the simulation data. Investigation shows that the attractive range parameter plays an important role in the phase equilibria for AO fluid.

Bayesian Decision Theory and its Applications in Early Phase Clinical Trails

Bayes'theorem is named after the Reverend Thomas Bayes who proposed the idea in the 18th century[1].It has been adapted by scientists for many different applications.One of the applications is clinical trials,where decisions are guided by clinical expertise as well as by data,especially in early phases.This paper reviews Bayes' theorem,decision theory and their applications in clinical trials.

Phase-Space Areas of the Body Motion in the Solar System Deduced from the Bohr-Sommerfeld Atomic Theory and Approximate Invariance of Their Ratios for the Pairs of Planets and Satellites

Energy-time and momentum-position phase spaces defined by the electron orbits in the hydrogen-like atom exhibit special properties of equivalence. It is demonstrated that equivalence of the same kind can be obtained for the phase-space areas defined by the orbit pairs of planets, or satellites, which compose the solar system. In the choice of the examined areas it is useful to be guided by the Bohr-Sommerfeld atomic theory.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

行为分阶段转变理论的个案管理模式在慢性阻塞性肺疾病稳定期患者中的应用

目的探讨行为分阶段转变理论的个案管理模式在慢性阻塞性肺疾病(以下简称“慢阻肺”)稳定期患者中的应用效果。方法纳入南京市第一医院2021年6月至2022年6月门诊访视的112例慢阻肺稳定期患者进行前瞻性研究,通过随机数字表法将其分为对照组和观察组,各56例。对照组给予个案管理模式干预,观察组给予行为分阶段转变理论的个案管理模式。两组均连续干预6个月。比较干预前、干预6个月后呼吸功能[圣乔治呼吸问卷(SGRQ)、改良版英国医院研究委员会呼吸困难量表(m MRC)]、自我管理能力[健康行为能力自评量表(SRAHP)]。结果干预后,两组SGRQ、m MRC评分均低于干预前,且观察组低于对照组,差异有统计学意义(P<0.05)。干预后,两组SRAHP评分高于干预前,且观察组高于对照组,差异有统计学意义(P<0.05)。结论行为分阶段转变理论的个案管理模式提高慢阻肺稳定期患者的自我管理能力,改善呼吸功能,具有较好应用效果。

基于物种敏感度分布及相平衡理论的汾河流域磺胺类抗生素生态风险阈值研究

磺胺素类抗生素(SAs)广泛应用于医疗、畜禽养殖等领域。但过量的SAs通过多种方式最终进入流域水体和沉积物中,对流域生态系统带来潜在的风险。预测无效应浓度(PNEC)可以作为评估污染物潜在生态风险的阈值,因此确定水体和沉积物中SAs的PNEC是风险评估的关键。本研究以黄河支流——汾河流域为研究区,通过采集水体和沉积物的样品,发现水体中SAs的磺胺甲恶唑(SMX)含量最高,均值为73.6 ng·L^(-1),而磺胺醋酰(SAAM)检出率最高,高达100%。沉积物中仅检出了2种SAs类抗生素,为磺胺醋酰(SAAM)和磺胺喹恶啉(SQX),但检出频率却高达100%。基于物种敏感度分布(SSD)得到水体中SAs的生态风险阈值为3.40~440μg·L^(-1)。在此基础上,基于水-沉积物密度、体积比等参数,采用相平衡理论(EqP)进一步得到了沉积物中SAs的生态风险阈值为0.065~75.5 mg·kg^(-1)。基于确定的生态风险阈值,对汾河流域SAs现状进行风险评估,结果表明仅水体中的甲氧苄啶(TMP)的风险商(RQ)均值为0.014,存在一定的低风险,但超标概率仅为8%,而其他类别在水体和沉积物中RQ均低于0.01,均无显著风险。

基于分解集成及不确定理论的碳价格预测

准确的碳市场价格预测是碳排放交易市场相关政策制定和碳金融发展的基础.为消除碳市场价格原始序列存在的非线性、非平稳性、高噪声性和不确定性,准确预测碳市场价格,论文将不确定理论、集合经验模态分解(ensemble empirical mode decomposition,简称EEMD)和径向基神经网络(radial basis function,简称RBF)相结合,构建了碳市场价格预测模型,并将其应用于广东省碳市场价格预测.首先通过EEMD算法和fine-to-coarse方法对原始的碳市场价格数据进行分解和重构,得到具有不同变化规律的高频项和低频项,并将其代入RBF神经网络进行训练,然后采用不确定理论,对低频项的输出权重进行不确定性分析,对残差趋势项采用线性回归进行拟合,最后将3个子项的预测结果进行集成求和得到最终的碳市场价格预测值.实证结果表明无论是在均方根误差(root mean square error,简称RMSE)、平均绝对误差(mean absolute error,简称MAE)还是在平均绝对百分比误差(mean absolute percentage error,简称MAPE)指标方面,论文模型在碳市场价格预测方面都比其他预测模型更具优势,预测结果更准确.

运气学说指导下的乌梅丸临床应用体会

运气学说是中医学理论的基础,是中医学天人相应整体观的体现。学习五运六气,正确对待五运六气,对临床诊疗疾病具有积极的指导意义。乌梅丸为医圣张仲景所创,主治蛔厥、久利,经后世医家不断发挥,现已广泛应用于证见寒热错杂的内外妇儿诸多疾病。以运气学说指导乌梅丸应用时,要抓住厥阴枢机不利的病机,从辨天、辨人、辨病证三方面分析,当疾病在丑至卯时(厥阴病欲解时)发作或加重时,证属寒热错杂、阴阳不相顺接时,运气因素与“厥阴风木”相关时,乌梅丸常有良效。