A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

Real-time embedded software testing method based on extended finite state machine

The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliability. Based on the analysis of the characteristics of real-time embedded software, the formal method is introduced into the real-time embedded software testing field and the real-time extended finite state machine （RT-EFSM） model is studied firstly. Then, the time zone division method of real-time embedded system is presented and the definition and description methods of time-constrained transition equivalence class （timeCTEC） are presented. Furthermore, the approaches of the testing sequence and test case generation are put forward. Finally, the proposed method is applied to a typical avionics real- time embedded software testing practice and the examples of the timeCTEC, testing sequences and test cases are given. With the analysis of the testing result, the application verification shows that the proposed method can effectively describe the real-time embedded software state transition characteristics and real-time requirements and play the advantages of the formal methods in accuracy, effectiveness and the automation supporting. Combined with the testing platform, the real-time, closed loop and automated simulation testing for real-time embedded software can be realized effectively.

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting （CZC） method is proposed in this paper, by combining the Duffing oscillator＇s phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high- efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent （MLE） method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

ONE-CELL-STATE METHOD FOR DETERMINATION OF ELECTRONIC STRUCTURE OF INTERMETALLIC COMPOUNDS

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Mixed H_2/H_∞ State Feedback Attitude Control of Microsatellite Based on Extended LMI Method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on singleoscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.

Present state,basic theories,methods and progresses of investigation and assessment on marine hazardous geology in China

The achievement progresses of investigation and studies on marine hazardous geology are summarized and presentsd in the late 20 century in China. The importance, research value and present-day studies of marine hazardous geology, a newly developing branch of geoscience, are well expatiated. Several often confused concepts and theories are explained and redefined here. The comment on the means of investigations, assessment of marine hazardous geology, as well as its evolution, innovation, existing questions and future tasks are also introduced and presented. The concepts of 'hazard geology', geohazard', 'map of marine hazard geology', 'integrated evaluaton on seafloor stablity' are respectively discussed, including their definition, research objects, methods and contents. The types and classification of marine hazardous geology, principles and methods of marine hazardous geology map compilation, the assessment methods and models of marine hazardous geology environment and seafloor stability and so on are also discussed.

An improved data space inversion method to predict reservoir state fields via observed production data

A data-space inversion(DSI)method has been recently proposed and successfully applied to the history matching and production prediction of reservoirs.Based on Bayesian theory,DSI can directly and effectively obtain good posterior flow predictions without inversion of geological parameters of reservoir model.This paper presents an improved DSI method to fast predict reservoir state fields(e.g.saturation and pressure profiles)via observed production data.Firstly,a large number of production curves and state data are generated by reservoir model simulation to expand the data space of original DSI.Then,efficient history matching only on the observed production data is carried out via the original DSI to obtain related parameters which reflects the weight of the real reservoir model relative to prior reservoir models.Finally,those parameters are used to predict the oil saturation and pressure profiles of the real reservoir model by combining large amounts of state data of prior reservoir models.Two examples including conventional heterogeneous and unconventional fractured reservoir are implemented to test the performances of predicting saturation and pressure profiles of this improved DSI method.Besides,this method is also tested in a real field and the obtained results show the high computational efficiency and high accuracy of the practical application of this method.

Power System State Estimation Solution With Zero Injection Constraints Using Modified Newton Method and Fast Decoupled Method in Polar Coordinate

如何保证零注入节点的注入功率在状态估计结果中严格为0是电力系统状态估计研究中的重要问题。在直角坐标下,由于零注入约束为线性约束,可使用修正牛顿法来有效地解决这一问题。因此,借鉴直角坐标下修正牛顿法的思路,提出了极坐标下的修正牛顿法和修正快速解耦估计。这些方法的计算流程与传统的极坐标下的牛顿法和快速解耦估计非常相似,计算速度与大权重法相当,同时能够保证零注入约束严格满足。仿真结果验证了所得结论。

BCS Ground State and XXZ Antiferromagnetic Model as SU（2）,SU（1,1） Coherent States：AN Algebraic Diagonalization Method

An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.

DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

Application of spline element and state space method for analysis of dynamic response of elastic rectangular plates is presented. The spline element method is used for space domain and the state space method in control theory of system is used for time domain. A state variable recursive scheme is developed, then the dynamic response of structure can he calculated directly. Several numerical examples are given. The results which are presented to demonstrate the accuracy and efficiency of the present method are quite satisfactory.

Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties: Factorization method

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrrdinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU（1, 1） dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.

STATE SPACE METHODS FOR DECENTRALIZED H_∞ CONTROL

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Generalized Lanczos method for systematic optimization of tensor network states

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.

BCS Ground State and XXZ Antiferromagnetic Model as SU(2), SU(1,1) Coherent States: An Algebraic Diagonalization Method

An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.

Quick and Simple Spectrophotometric Method of Identification of the Thermal State of Meat on the Basis of Composition and Content of Free Nucleotides

At present, there is no method for identifying meat frozen in a thermal state acceptable for production control. The role of free nucleotides in the processes of refrigeration and storage of meat, affecting the structural and mechanical properties of muscle tissue, the formation of taste and its biological value is known. In this article we compared methods for identifying the thermal state of meat based on the determination of the composition and content of free nucleotides by high-performance liquid chromatography (HPLC) and spectrophotometry [SF]. High-purity reference substances were used: free nucleotides—ATP, ADP, AMP, IMP and nucleosides-inosine and hypoxanthine. It has been experimentally established that the characteristic peaks of the absorption spectra for extracts of free nucleotides of meat frozen depended from thermal state of meat. The content of ATP is 21.8 times higher in meat frozen in a fresh state, and the amount of IMF is 12.3 times lower than in meat frozen after cooling. The results of studies of meat frozen using the HPLC method and the developed SF method show the adequacy of the data obtained by both methods. SF-method based on the determination of the optical density of the extracts of free nucleotides is recommended to justify the choice of technological process meat defrost modes.

Meta-Analysis of Bushen Huoxue Method in the Treatment of Recurrent Spontaneous Abortion Due to Prethrombotic State

Objective:To evaluate the effectiveness and safety of Bushen Huoxue prescription in the treatment of recurrent spontaneous abortion(RSA)due to prethrombotic state(PTS).Methods:Databases such as CNKI,WanFang,VIP,CBM,PubMed,Embase,and Cochrane Library were searched for randomized controlled trials on Bushen Huoxue prescription in treating RSA due to PTS from inception to March 2021;meta-analysis was performed by RevMan Version 5.3.0 following quality evaluation.Results:Seven trials were included,with 496 patients;the meta-analysis indicated that Bushen Huoxue prescription has advantages on the improvement of total clinical effective rate[RR=1.22,95%CI(1.10,1.35),Z=3.80(P=0.0001)],embryo survival rate at pregnancy of 12 weeks[RR=1.25,95%CI(1.10,1.41),Z=3.53(P=0.0004)],D-dimer levels[SMD=-1.59,95%CI(-2.20,-0.97),Z=5.07(P<0.00001)],and fibrinogen levels[MD=-1.00,95%CI(-1.29,-0.70),Z=6.61(P<0.00001)],but the statistical heterogeneity was significant;in terms of incidence of adverse reactions,there was no statistical difference between Bushen Huoxue prescription and western medicine.Conclusion:Compared with western medicine alone,Bushen Huoxue prescription alone or in combination with western medicine showed significant advantages in improving the overall clinical efficiency,embryonic survival rate at 12 weeks of pregnancy,and reducing D-dimer values as well as fibrinogen levels,without any significant difference in the incidence of adverse effects;however,the number of included studies is small and there are drawbacks,such as small sample size and low quality;therefore,high-quality clinical studies with large sample size and rigorous trial designs are needed in the future to provide a reliable basis for the effectiveness and safety of TCM in reducing the incidence of RSA due to prethrombotic state.

State space solution to 3D multilayered elastic soils based on order reduction method

Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.

Methods for Derivation of Density Matrix of Arbitrary Multi-Mode Gaussian States from Its Phase Space Representation

We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation.An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values.As an example,we apply our method to the derivation of three-mode symmetric continuous variable entangled state.Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.

Electronic States of Difluorocarbene Calculated by Multireference Configuration Interaction Method

We investigate the geometries and energies of seven electronic states X-1A1, A1B1, a-3B1, B-1A2,b-3A2, C1B2 and c-3B2 of CF2 carbene using internally contracted multireference configuration interaction methods including Davidson correction （icMRCIq-Q） with different basis sets aug-cc-pVXZ （X=T, Q, 5）. For the first time, the potential energy curves of electronic states of CF2 related icMRCI＋Q/aug-cc-pVTZ level. The ab initio results will and dynamics of electronic states of CF2 radical. to the lowest dissociation limit are calculated at the further increase our understanding of the structures