Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Survivors of COVID-19 exhibit altered amplitudes of low frequency fluctuation in the brain: a resting-state functional magnetic resonance imaging study at 1-year follow-up

Although some short-term follow-up studies have found that individuals recovering from coronavirus disease 2019(COVID-19)exhibit anxiety,depression,and altered brain microstructure,their long-term physical problems,neuropsychiatric sequelae,and changes in brain function remain unknown.This observational cohort study collected 1-year follow-up data from 22 patients who had been hospitalized with COVID-19(8 males and 11 females,aged 54.2±8.7 years).Fatigue and myalgia were persistent symptoms at the 1-year follow-up.The resting state functional magnetic resonance imaging revealed that compared with 29 healthy controls(7 males and 18 females,aged 50.5±11.6 years),COVID-19 survivors had greatly increased amplitude of low-frequency fluctuation(ALFF)values in the left precentral gyrus,middle frontal gyrus,inferior frontal gyrus of operculum,inferior frontal gyrus of triangle,insula,hippocampus,parahippocampal gyrus,fusiform gyrus,postcentral gyrus,inferior parietal angular gyrus,supramarginal gyrus,angular gyrus,thalamus,middle temporal gyrus,inferior temporal gyrus,caudate,and putamen.ALFF values in the left caudate of the COVID-19 survivors were positively correlated with their Athens Insomnia Scale scores,and those in the left precentral gyrus were positively correlated with neutrophil count during hospitalization.The long-term follow-up results suggest that the ALFF in brain regions related to mood and sleep regulation were altered in COVID-19 survivors.This can help us understand the neurobiological mechanisms of COVID-19-related neuropsychiatric sequelae.This study was approved by the Ethics Committee of the Second Xiangya Hospital of Central South University(approval No.2020 S004)on March 19,2020.

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

THE AUTOMATIC GENERATION OF LIMIT STATE FUNCTION OF HINGED STRUCTURE

In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.

The vital point of the Parameters of Morpho-functional State of Gymnasts for the Assessment of Physical Development at the Stage of Sports Perfection

The article presents the data of the assessment of the physical development and functional state of highly qualifiedgymnasts engaged in rhythmic gymnastics. It was found that high-skilled gymnasts have heterogeneity ofsomatotypes determined according to the B. Heath-J. Carter scheme and heterogeneity of types of autonomousnervous regulation of heart rate variability, systolic, diastolic blood pressure and respiration, determined on thespiroarteriorhythmocardiograph device. Highly qualified gymnasts have vago- and normotonic types of regulationof heart rate variability;normal-sympathetic-and hypersympathicotonic types of regulation of the variability ofsystolic blood pressure and diastolic blood pressure, vagotonic type of regulation of the variability of the respiratoryrhythm. Statistically significant differences gymnasts, successful in the medal standings at the internationalcompetitions and gymnasts participating, but not in high prizes in competitions, consist in the ability to resistfatigue while performing strenuous mental work (differences were revealed in 10-letter “Mental performance” at aconstant speed (p > 0.0001), and 3-letter test (p > 0.001)), data stabilometric test “Target” indicator “Time stabilityon the left foot” (R > 0.039) with the advantage of a high performing gymnasts artists. Fleshed out the possibility ofusing the parameters of the morphofunctional state of gymnasts in training for the qualitative evaluation of thephysical development of gymnasts, evaluation set their sports uniforms indicated the possibility of developing thereference parameters of the morphofunctional status of gymnasts and recommendations on the frequency of thesurvey of morphological and functional status of gymnasts involved in rhythmic gymnastics.

Local density of states of dc-biased superlattices with time-dependent imperfection

The single-particle Green＇s function for a dc-biased superlattices with single impurity potential varying harmonically with time has been obtained in the framework of U（t,t＇） method and Floquet-Green＇s function. The calculation of the local density of states shows that new states will emerge between the resonant Wannier-Stark states as a result of the intervention of time-dependent impurity potential, and the increase in electric field strength of impurity will result in the growing of the number of new states between the gaps of neighbouring Stark ladders.

Establishment, maintenance, and re-establishment of the safe and efficient steady-following state

We present an integrated mathematical model of vehicle-following control for the establishment, maintenance, and re-establishment of the previous or new safe and efficient steady-following state. The hyperbolic functions are introduced to establish the corresponding mathematical models, which can describe the behavioral adjustment of the following vehicle steered by a well-experienced driver under complex vehicle following situations. According to the proposed mathematical models, the control laws of the following vehicle adjusting its own behavior can be calculated for its moving in safety,efficiency, and smoothness(comfort). Simulation results show that the safe and efficient steady-following state can be well established, maintained, and re-established by its own smooth(comfortable) behavioral adjustment with the synchronous control of the following vehicle’s velocity, acceleration, and the actual following distance.

Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment

In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.

Application Research of Music Therapy in Mental Health of Special Children

A healthy psychological state is the premise for children to carry out various activities.Previous surveys have shown that children with special needs are affected by their own obstacles and are more prone to psychological problems such as sensitivity,low self-esteem,and impulsiveness.Therefore,it is necessary to provide more sys-tematic mental health education support for special children.Mental health education programs are an efficient form of maintaining children’s mental health.However,in thefield of special education,the number of mental health education courses developed according to the physical and mental characteristics and developmental needs of special children is relatively small,and there are many difficulties in the implementation process.Autism dis-order(ASD)is a kind of pervasive developmental dysfunction that is relatively common and representative in clinical practice.In recent years,the number of autistic children has continued to surge,and has gradually expanded from a family problem to a serious social problem.At present,the evaluation of the effect of autism intervention mainly relies on various behavioral scales,which are subjective to a certain extent.At the same time,due to the unclear pathogenesis of autism,the treatment of autism cannot be predicated on the right medicine,and can only be intervened in various ways.The purpose of this paper is to explore the difference between the EEG signals of autistic children and typically developing control(TD)children through the analysis method of EEG signals,and based on the analysis of EEG signals from an objective point of view,to study whether the music therapy method of Chinese Zither playing training can effectively Improving the brain functional status of chil-dren with autism yields positive therapeutic outcomes.The experimental results show that the complexity of brain electrical signals of ASD children is much lower than that of TD children,and there is a significant difference in the brain functional state between the two.The music therapy method based on Chinese zither playing training can improve the brain function of autistic patients,and there is a positive therapeutic effect.And with the exten-sion of the training period,the effect may be more significant.Chinese zither playing training can provide a new direction for the intervention of autism.

DAMAGE THEORY OF MATERIALS WITH MICROSTRUCTURE

A new form of damage theory of materials is proposed,that is valid for the case of nonconservative stresses.The partial entropy,strain and microstructure parameters are taken as the state variables.Without assuming the free energy to be a state function,the basic governing equations are derived.According to the balance of released and dissipated energy,the general form of damage evolution equation is obtained.Further,assuming the existence of independent damage mechanisms, the normality of damage evolution equation is proven.The generalized damage variables are dis- cussed.Finally,some examples are given to show the applications of the theory.

Theoretical and Experimental Studies on the Reaction Mechanism of Cl_2 + I_2 = 2ICl

The gas phase reaction mechanism of Cl2 ＋ I2 = 2ICl has been theoretically investigated by DFF method at the B3LYP/3-21 G＊ level. Transition states of three reaction channels were consequently given. The results indicate that in the title reaction the least activation energy of bi-molecular reaction was smaller than the dissociation energies of I2 and Cl2, and thus the reaction mechanism was the course of molecule-molecule interaction at low reaction rate. If other factors such as illumination were taken into account, I2 could dissociate into I atoms and then react with Cl2, or Cl2 dissociates into CI atoms and reacts with I2. These were photochemical reactions with high reaction speed. The theoretical results were further validated with absorbance measurement at 516 nm.

The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

An Explicit Iteration Algorithm for Structural Reliability and its Realization by MATLAB

Based on the improved first order second moment method of the structural reliability, an explicit iteration algorithm is proposed, which can avoid solving structural performance function to obtain reliability index β and have simple calculation forms. Finally, the validity of the explicit iteration algorithm is illustrated through two examples by MATLAB programming.

First-Principles Study of the High-Temperature Behaviors of the Willemite-Ⅱ and Post-Phenacite Phases of Silicon Nitride

The structural and elastic properties of the recently-discovered wⅡ- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa,respectively.The α→wⅡ phase transition can be observed at 18.6 GPa and 300 K.The β→δ phase transformation occurs at pressures of 29.6,32.1,35.9,39.6,41.8,and 44.1 GPa when the temperatures are100,200,300,400,500,and 600 K,respectively.The results show that the interactions among the N-2s,Si-3s,3p bands（lower valence band） and the Si-3p,N-2p bands（upper valence band） play an important role in the stabilities of the wⅡ and S phases.Moreover,several thermodynamic parameters（thermal expansion,free energy,bulk modulus and heat capacity） of δ-Si3N4 are also obtained.Some interesting features are found in these properties.δ-Si3N4 is predicted to be a negative thermal expansion material.The adiabatic bulk modulus decreases with applied pressure,but a majority of materials show the opposite trend.Further experimental investigations with higher precisions may be required to determine the fundamental properties of wⅡ- andδ-Si3N4.

PRINCIPAL RESPONSE OF VAN DER POL-DUFFING OSCILLATOR UNDER COMBINED DETERMINISTIC AND RANDOM PARAMETRIC EXCITATION

The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.

Density Functional Theory Study of C_2H_x(x=4～6) Adsorption on the Fe(110) Surface

The density functional theory（DFT） and self-consistent periodic calculation were used to investigate the C2Hx（x = 4～6） species adsorption on the Fe（110） surface. The adsorption energy and equilibrium geometry of the species C2Hx（x = 4～6） on four possible sites（top,hcp,SB and LB） on the Fe（110） surface were predicted and compared. Mulliken charges and density of states analysis of the most stable site have been discussed. It is found that the species of C2H6 and C2H5 are adsorbed strongly on the Fe（110） surface with calculated adsorption energy of -80.24 and -178.89 kJ·mol^-1 at the Fe-LB（long-bridge） ,respectively. However,the C2H4 is adsorbed strongly on the Fe（110） surface with calculated adsorption energies of -114.96 kJ·mol^-1 at the top. The results indicate that the charge transferring process can be completed by chemisorption between Fe（110） surface and the species. Moreover,the chemical bands can be formed by chemisorptions between the Fe（110） surface and the species,too.

Theoretical Study on the C-H Activation in Decarbonylation of Acetaldehyde by NiL_2(L=SO_3CH_3) Using Density Functional Theory

Density functional theory calculations were carried out to explore the potential energy surface（PES） associated with the gas-phase reaction of Ni L2（L=SO3CH3） with acetone. The geometries and energies of the reactants, intermediates, products and transition states of the triplet ground potential energy surfaces of [Ni, O, C2, H4] were obtained at the B3LYP/6-311＋＋G（d,p） levels in C,H,O atoms and B3LYP/ Lanl2 dz in Ni atom. It was found through our calculations that the decabonylation of acetaldehyde contains four steps including encounter complexation, C-C activation, aldehyde H-shift and nonreactive dissociation. The results revealed that C-C activation induced by Ni L2（L=SO3CH3） led to the decarbonylation of acetaldehyde.

Orbital electronic heat capacity of hydrogenated monolayer and bilayer graphene

The tight-binding Harrison model and Green＇s function approach have been utilized in order to investigate the contribution of hybridized orbitals in the electronic density of states（DOS） and electronic heat capacity（EHC） for four hydrogenated structures, including monolayer chair-like, table-like, bilayer AA- and finally AB-stacked graphene. After hydrogenation, monolayer graphene and bilayer graphene are behave as semiconducting systems owning a wide direct band gap and this means that all orbitals have several states around the Fermi level. The energy gap in DOS and Schottky anomaly in EHC curves of these structures are compared together illustrating the maximum and minimum band gaps are appear for monolayer chair-like and bilayer AA-stacked graphane, respectively. In spite of these, our findings show that the maximum and minimum values of Schottky anomaly appear for hydrogenated bilayer AA-stacked and monolayer table-like configurations, respectively.