Co and postseismic fault slip models of the 2022 M_(W)6.7 Menyuan earthquake reveal conjugated faulting tectonics at the central section of the Lenglongling fault

The 2022 M_(W)6.7 Menyuan earthquake ruptured the western end of the Tianzhu seismic gap,providing an opportunity to study the regional seismogenic characteristics and seismic hazards.Here we use interferometric synthetic aperture radar(InSAR)and seismic data to study the mainshock rupture,early afterslip and the second largest aftershock of the 2022 Menyuan earthquake sequences.Our modeling results show that the mainshock ruptured the Lenglongling fault and the Tuolaishan fault with a maximum slip of~3 m.Rapid postseismic transient deformation occurred at the center of the Lenglongling fault.Our afterslip modeling reveals that the majority of afterslip occurred in the deeper part of the Lenglongling fault.A high-angle conjugated faulting event is found at the middle section of the Lenglongling fault.We use the stress inversion to investigate the possible triggering mechanism of the conjugated rupture event.The results indicate the maximum principal stress direction is in~222°,forming a~22°angle between the conjugated fault of second largest aftershock and the mainshock.The calculated normal stress changes indicate the region is within a pull-apart stress field,which favors such a conjugated rupturing event.Our study will help understand the rupture behavior of such kind of conjugated fault in other regions.

THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES

The main aim of this paper is to discuss the following two problems: Problem I: Given X ∈ Hn×m (the set of all n×m quaternion matrices), A = diag(λ1,…, λm) EEEEE Hm×m, find A ∈ BSHn×n≥such that AX = X(?), where BSHn×n≥ denotes the set of all n×n quaternion matrices which are bi-self-conjugate and nonnegative definite. Problem Ⅱ2= Given B ∈ Hn×m, find B ∈ SE such that ||B-B||Q = minAE∈=sE ||B-A||Q, where SE is the solution set of problem I , || ·||Q is the quaternion matrix norm. The necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given.

Modified Lorentz Transformations and Space-Time Splitting According to the Inverse Relativity Model

Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fabric of space-time into a positive subspace-time that represents the space of causality and a negative subspace-time which represents a space without causality, thus, in the special case, we have new transformations for the coordinates of space and time modified from Lorentz transformations specific to each subspace, where the contraction of length disappears and the speed of light is no longer a universal constant. In the general case, we have new types of matric tensor, one for positive subspace-time and the other for negative subspace-time. We also find that the speed of the photon decreases in positive subspace-time until it reaches zero and increases in negative subspace-time until it reaches the speed of light when the photon reaches the Schwarzschild radius.

Relativistic Mechanics in Positive and Negative Subspace-Time according to the Inverse Relativity Model

In the second paper on the inverse relativity model, we explained in the first paper [1] that analyzing the four-dimensional displacement vector on space-time according to a certain approach leads to the splitting of space-time into positive and negative subspace-time. Here, in the second paper, we continue to analyze each of the four-dimensional vectors of velocity, acceleration, momentum, and forces on the total space-time fabric. According to the approach followed in the first paper. As a result, in the special case, we obtain new transformations for each of the velocity, acceleration, momentum, energy, and forces specific to each subspace-time, which are subject to the positive and negative modified Lorentz transformations described in the first paper. According to these transformations, momentum remains a conserved quantity in the positive subspace and increases in the negative subspace, while the relativistic total energy decreases in the positive subspace and increases in the negative subspace. In the general case, we also have new types of energy-momentum tensor, one for positive subspace-time and the other for negative subspace-time, where the energy density decreases in positive subspace-time and increases in negative subspace-time, and we also obtain new gravitational field equations for each subspace-time.

QSAR Studies on the Inhibitory Activityof Levofloxacin-thiadiazole HDACi Conjugates to Histone Deacetylases

A molecular electronegativity distance vector(M)based on 13 atomic types has been used to describe the structures of 19 conjugates(LHCc)of levofloxacin-thiadiazole HDAC inhibitor(HDACi)and related inhibitory activities(pH,i=1,2,6)of LHCc against histone deacetylases(HDACs,such as HDAC1,HDAC2 and HDAC6).The quantitative structure-activity relationships(QSAR)were established by using leaps-and-bounds regression analysis for the inhibitory activities(pH)of 19 above compounds to HDAC1,HDAC2 and HDAC6 along with M.The correlation coefficients(R~2)and the leave-one-out(LOO)cross validation Rfor the pH,pHand pHmodels were 0.976 and 0.949;0.985 and 0.977;0.976 and 0.932,respectively.The QSAR models had favorable correlations,as well as robustness and good prediction capability by R~2,F,R~2,A,Fand Vtests.Validated by using 3876 training sets,the models have good external prediction ability.The results indicate that the molecular structural units:–CH–(g=1,2),–NH,–OH,=O,–O–and–S–are the main factors which can affect the inhibitory activity of pH,pHas well as pHbioactivities of these compounds directly.Accordingly,the main interactions between HDACs inhibitor and HDACs are hydrophobic interaction,hydrogen bond,and coordination with Znto form compounds,which is consistent with the results in reports.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit （GPU） and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation （SSOR） technique and the incomplete Choleksy decomposition conjugate gradient algorithm （ICCG）. Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noise- contaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit （CPU）. Real airbome gravity-gradiometry data from Vinton salt dome （south- west Louisiana, USA） are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Research of the Conductive Structure of Crust and the Upper Mantle beneath the South-Central Tibetan Plateau

With the super-wide band magnetoteiluric sounding data of the JUong （吉隆）-Cuoqin （措勤） profile （named line 800） which was completed in 2001 and the Dingri （定日）-Cuomai （措迈） profile （named line 900） which was completed in 2004, we obtained the strike direction of each MT station by strike analysis, then traced profiles that were perpendicular to the main strike direction, and finally obtained the resistivity model of each profile by nonlinear conjugate gradients （NLCG） inversion. With these two models, we described the resistivity structure features of the crust and the upper mantle of the center-southern Tibetan plateau and its relationship with Yalung Tsangpo suture： the upper crust of the research area is a resistive layer with resistivity value range of 200-3 000 Ω.m. The depth of its bottom surface is about 15-20 km generally, but the bottom surface of resistive layer is deeper in the middle of these two profiles. At llne 900, it is about 30 km deep, and even at line 800, it is about 38 km deep. There is a gradient belt of resistivity at the depth of 15-45 km, and a conductive layer is beneath it with resistivity even less than 5 Ω.m. This conductive layer is composed of individual conductive bodies, and at the south of the Yalung Tsangpo suture, the conductive bodies are smaller with thickness about 10 km and lean to the north slightly. However, at the north of the Yalung Tsangpo suture, the conductive bodies are larger with thickness about 30 km and also lean to the north slightly. Relatively, the conductive bodies of line 900 are thinner than those of line 800, and the depth of the bottom surface of line 900 is also shallower. At last, after analyzing the effect factors to the resistivity of rocks, it was concluded that the very conductive layer was caused by partial melt or connective water in rocks. It suggests that the middle and lower crust of the center-southern Tibetan plateau is very thick, hot, flabby, and waxy.

Explicit Iterative Methods of Second Order and Approximate Inverse Preconditioners for Solving Complex Computational Problems

Explicit Exact and Approximate Inverse Preconditioners for solving complex linear systems are introduced. A class of general iterative methods of second order is presented and the selection of iterative parameters is discussed. The second order iterative methods behave quite similar to first order methods and the development of efficient preconditioners for solving the original linear system is a decisive factor for making the second order iterative methods superior to the first order iterative methods. Adaptive preconditioned Conjugate Gradient methods using explicit approximate preconditioners for solving efficiently large sparse systems of algebraic equations are also presented. The generalized Approximate Inverse Matrix techniques can be efficiently used in conjunction with explicit iterative schemes leading to effective composite semi-direct solution methods for solving large linear systems of algebraic equations.

Three-dimensional conjugate gradient inversion of magnetotelluric sounding data

Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn＇ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified.

Application of a compound controller based on fuzzy control and support vector machine to ship's boiler-turbine coordinated control system

Multivariables, strong coupling, nonlinearity, and large delays characterize the boiler-turbine coordinated control systems for ship power equipment. To better deal with these conditions, a compound control strategy based on a support vector machine （SVM） with inverse identification was proposed and applied to research simulating coordinated control systems. This method combines SVM inverse control and fuzzy control, taking advantage of the merits of SVM inverse controls which can be designed easily and have high reliability, and those of fuzzy controls, which respond rapidly and have good anti-jamming capability and robustness. It ensures the controller can be controlled with near instantaneous adjustments to maintain a steady state, even if the SVM is not trained well. The simulation results show that the control quality of this fuzzy-SVM compound control algorithm is high, with good performance in dynamic response speed, static stability, restraint of overshoot, and robustness.

Three-dimensional conjugate gradient inversion of magnetotelluric full information data

Based on the analysis of impedance tensor data, tipper data, and the conjugate gradient algorithm, we develop a three-dimensional （3D） conjugate gradient algorithm for inverting magnetotelluric full information data determined from five electric and magnetic field components and discuss the method to use the full information data for quantitative interpretation of 3D inversion results. Results from the 3D inversion of synthetic data indicate that the results from inverting full information data which combine the impedance tensor and tipper data are better than results from inverting only the impedance tensor data （or tipper data） in improving resolution and reliability. The synthetic examples also demonstrate the validity and stability of this 3D inversion algorithm.

Relevance vector machine technique for the inverse scattering problem

A novel method based on the relevance vector machine（RVM） for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine（SVM） based approach.

Comparison of CS,CGM and CS-CGM for Prediction of Pipe’s Inner Surface in FGMs

The cuckoo search algorithm(CS)is improved by using the conjugate gradient method(CGM),and the CS-CGM is proposed.The unknown inner boundary shapes are generated randomly and evolved by Lévy flights and elimination mechanism in the CS and CS-CGM.The CS,CGM and CS-CGM are examined for the prediction of a pipe’s inner surface.The direct problem is two-dimensional transient heat conduction in functionally graded materials(FGMs).Firstly,the radial integration boundary element method(RIBEM)is applied to solve the direct problem.Then the three methods are compared to identify the pipe’s inner surface with the information of measured temperatures.Finally,the influences of timepoints,measurement point number and random noise on the inverse results are investigated.It is found that the three algorithms are promising and can be used to identify the pipe’s inner surface.The CS-CGM has higher accuracy and faster convergence speed than the CS and CGM.The CS and CS-CGM are insensitive to the initial values.The CGM and CS-CGM are more insensitive to the measurement noises compared with the CS.With the increase of timepoints and measurement points,and with the decrease of measurement noises,the inverse results are more accurate.

A multiphase direct aperture optimization for inverse planning in radiotherapy

Optimization of the inverse planning becomes critical because it follows the invention of intensity modulated radiotherapy(IMRT) to shorten the previous "trial-and-error" treatment process and increase efficiency.In this paper, the inverse planning is used to direct aperture optimization in the ARTS(Accurate/Advanced Radiotherapy System). The objective function was quadratic, both tolerance and dose-volume constraint types are supported. The memory efficient conjugate gradient algorithm is used to cope with its large data.Furthermore, to fully exploit the solution space, a shortest path sub-procedure is coupled into the whole algorithm, thus giving further possibility decreasing the objective function. Two clinical cases are tested, indicating that the applicability of this algorithm is promising to clinical usage.

GENERALIZED CONJUGATE-GRADIENT ALGORITHM AND ITS APPLICATIONS TO SEISMIC TRACE INVERSION

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Inverse estimation for unknown fouling geometry on inner wall of forced-convection pipe

A conjugate gradient method （CGM） based on the inverse algorithm is used to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall. It is assumed that no prior information is available about the functional form of the unknown profile. Therefore, the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined using the simulated exact and inexact temperature measurements. The results show that the excellent estimation of the fouling-layer profile can be obtained for the test case considered in this study. The technique presented in this study can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a predefined criterion.

Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation

Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation （FD-RTE） to probe the internal structure of the medium is investigated in the present work. The forward model of FD-RTE is solved via the finite volume method （FVM）. The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient （MCG） method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure.

Inverse Learning Control of Nonlinear Systems Using Support Vector Machines

An inverse learning control scheme using the support vector machine (SVM) for regression was proposed. The inverse learning approach is originally researched in the neural networks. Compared with neural networks, SVMs overcome the problems of local minimum and curse of dimensionality. Additionally, the good generalization performance of SVMs increases the robustness of control system. The method of designing SVM inverse learning controller was presented. The proposed method is demonstrated on tracking problems and the performance is satisfactory.

RandWPSO-LSSVM反演方法及其在大型地下工程中的应用

根据粒子群算法(PSO)和支持向量机(SVM)的特点和局限性,对其进行改进,建立随机权重粒子群最小二乘支持向量机(RandWPSO-LSSVM)反演模型,由正交设计、均匀设计和三维有限元数值计算给出学习和测试样本,反演糯扎渡水电站大型调压井工程区的围岩力学参数和初始地应力场。研究表明:RandWPSO对LSSVM预测模型的优化效果明显比PSO好;反演得到工程区x向和y向侧压力系数分别为2.641 5和2.083 1,微新岩体、弱风化下层、弱风化上层、全强风化层岩体、断层等围岩的弹性模量分别为24.849 2,10.898 7,2.839 8,0.270 4和0.651 3 GPa;反馈计算得到的位移相对实测位移误差较小,验证反演参数的合理性,也表明所建立的RandWPSO-LSSVM反演模型合理可靠,可有效指导大型地下工程参数设计和施工稳定性分析。

有关共轭点和对称共轭点的星像函数逆函数的Hermitian Toeplitz行列式

S_(c)^(*)和S_(sc)^(*)分别称为有关共轭点的星像函数类、有关对称共轭点的星像函数类,得到了其逆函数的Hermitian Toeplitz行列式的估计.