Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

Moments of inertia of triaxial nuclei in covariant density functional theory

The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted by Allmond and Wood[J.M.Allmond and J.L.Wood,Phys.Lett.B 767,226(2017)].We find that the CDFT MoIs are generally smaller than the experimental values but exhibit qualitative consistency with the irrotational flow and experimental data for the relative MoIs,indicating that the intermediate axis exhibites the largest MoI.Additionally,it is found that the pairing interaction collapse could result in nuclei behaving as a rigid-body flow,as exhibited in the^(186-192)Os case.Furthermore,by incorporating enhanced CDFT MoIs(factor of f≈1.55)into the 5DCH,the experimental low-lying energy spectra and deformation parameters are reproduced successfully.Compared with both CDFT and the triaxial rotor model,the 5DCH demonstrates superior agreement with the experimental deformation parameters and low-lying energy spectra,respectively,emphasizing the importance of considering shape fluctuations.

The deterministic condition for the ground reaction force acting point on the combined knee valgus and tibial internal rotation moments in early phase of cutting maneuvers in female athletes

Background:Combined knee valgus and tibial internal rotation(VL+IR)moments have been shown to stress the anterior cruciate ligament(ACL)in several in vitro cadaveric studies.To utilize this knowledge for non-contact ACL injury prevention in sports,it is necessary to elucidate how the ground reaction force(GRF)acting point(center of pressure(CoP))in the stance foot produces combined knee VL+IR moments in risky maneuvers,such as cuttings.However,the effects of the GRF acting point on the development of the combined knee VL+IR moment in cutting are still unknown.Methods:We first established the deterministic mechanical condition that the CoP position relative to the tibial rotational axis differentiates the GRF vector’s directional probability for developing the combined knee VL+IR moment,and theoretically predicted that when the CoP is posterior to the tibial rotational axis,the GRF vector is more likely to produce the combined knee VL+IR moment than when the CoP is anterior to the tibial rotational axis.Then,we tested a stochastic aspect of our theory in a lab-controlled in vivo experiment.Fourteen females performed 60˚cutting under forefoot/rearfoot strike conditions(10 trials each).The positions of lower limb markers and GRF data were measured,and the knee moment due to GRF vector was calculated.The trials were divided into anterior-and posterior-CoP groups depending on the CoP position relative to the tibial rotational axis at each 10 ms interval from 0 to 100 ms after foot strike,and the occurrence rate of the combined knee VL+IR moment was compared between trial groups.Results:The posterior-CoP group showed significantly higher occurrence rates of the combined knee VL+IR moment(maximum of 82.8%)at every time point than those of the anterior-CoP trials,as theoretically predicted by the deterministic mechanical condition.Conclusion:The rearfoot strikes inducing the posterior CoP should be avoided to reduce the risk of non-contact ACL injury associated with the combined knee VL+IR stress.

Implementing and evaluating an automatic centroid moment tensor procedure for the Indonesia region and surrounding areas

The purpose of this research was to suggest an applicable procedure for computing the centroid moment tensor(CMT)automatically and in real time from earthquakes that occur in Indonesia and the surrounding areas.Gisola software was used to estimate the CMT solution by selecting the velocity model that best suited the local and regional geological conditions in Indonesia and the surrounding areas.The data used in this study were earthquakes with magnitudes of 5.4 to 8.0.High-quality,real-time broadband seismographic data were provided by the International Federation of Digital Seismograph Networks Web Services(FDSNWS)and the European Integrated Data Archive(EIDA)Federation in Indonesia and the surrounding areas.Furthermore,the inversion process and filter adjustment were carried out on the seismographic data to obtain good CMT solutions.The CMT solutions from Gisola provided good-quality solutions,in which all earthquake data had A-level quality(high quality,with good variant reduction).The Gisola CMT solution was justified with the Global CMT(GCMT)solution by using the Kagan angle value,with an average of approximately 11.2°.This result suggested that the CMT solution generated from Gisola was trustworthy and reliable.The Gisola CMT solution was typically available within approximately 15 minutes after an earthquake occurred.Once it met the quality requirement,it was automatically published on the internet.The catalog of local and regional earthquake records obtained through this technology holds great promise for improving the current understanding of regional seismic activity and ongoing tectonic processes.The accurate and real-time CMT solution generated by implementing the Gisola algorithm consisted of moment tensors and moment magnitudes,which provided invaluable insights into earthquakes occurring in Indonesia and the surrounding areas.

Moment magnitudes of two large Turkish earthquakes on February 6,2023 from long-period coda

Two large earthquakes(an earthquake doublet)occurred in south-central Turkey on February 6,2023,causing massive damages and casualties.The magnitudes and the relative sizes of the two mainshocks are essential information for scientific research and public awareness.There are obvious discrepancies among the results that have been reported so far,which may be revised and updated later.Here we applied a novel and reliable long-period coda moment magnitude method to the two large earthquakes.The moment magnitudes(with one standard error)are 7.95±0.013 and 7.86±0.012,respectively,which are larger than all the previous reports.The first mainshock,which matches the largest recorded earthquakes in the Turkish history,is slightly larger than the second one by 0.11±0.035 in magnitude or by 0.04 to 0.18 at 95%confidence level.

Analysis of rockburst mechanism and warning based on microseismic moment tensors and dynamic Bayesian networks

One of the major factors inhibiting the construction of deep underground projects is the risk posed by rockbursts.A study was conducted on the access tunnel of the Shuangjiangkou hydropower station to determine the evolutionary mechanism of microfractures within the surrounding rock mass during rockburst development and develop a rockburst warning model.The study area was chosen through the combination of field studies with an analysis of the spatial and temporal distribution of microseismic(MS)events.The moment tensor inversion method was adopted to study rockburst mechanism,and a dynamic Bayesian network(DBN)was applied to investigating the sensitivity of MS source parameters for rockburst warnings.A MS multivariable rockburst warning model was proposed and validated using two case studies.The results indicate that fractures in the surrounding rock mass during the development of strain-structure rockbursts initially show shear failure and are then followed by tensile failure.The effectiveness of the DBN-based rockburst warning model was demonstrated using self-validation and K-fold cross-validation.Moment magnitude and source radius are the most sensitive factors based on an investigation of the influence on the parent and child nodes in the model,which can serve as important standards for rockburst warnings.The proposed rockburst warning model was found to be effective when applied to two actual projects.

GPU-acceleration 3D rotated-staggered-grid solutions to microseismic anisotropic wave equation with moment tensor implementation

To improve the accuracy of microseismic inversion,seismic anisotropy and moment tensor source should be carefully considered in the forward modelling stage.In this study,3D microseismic anisotropy wave forward modelling with a moment tensor source was proposed.The modelling was carried out based on a rotated-staggered-grid(RSG)scheme.In contrast to staggered-grids,the RSG scheme defines the velocity components and densities at the same grid,as do the stress components and elastic parameters.Therefore,the elastic moduli do not need to be interpolated.In addition,the detailed formulation and implementation of moment-tensor source loaded on the RSG was presented by equating the source to the stress increments.Meanwhile,the RSG-based 3D wave equation forward modelling was performed in parallel using compute unified device architecture(CUDA)programming on a graphics processing unit(GPU)to improve its efficiency.Numerical simulations including homogeneous and anisotropic models were carried out using the method proposed in this paper,and compared with other methods to prove the reliability of this method.Furthermore,the high efficiency of the proposed approach was evaluated.The results show that the computational efficiency of proposed method can be improved by about two orders of magnitude compared with traditional central processing unit(CPU)computing methods.It could not only help the analysis of microseismic full wavefield records,but also provide support for passive source inversion,including location and focal mechanism inversion,and velocities inversion.

Determining the moment of inertia of triaxial Mars with updated global gravity models

The principal moments of inertia(PMIs)with the principal axes are usually taken as the dynamic figure parameters of Mars;they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations.These PMIs are natural and significant for the geodetic,geophysical,and geodynamic problems of Mars,which are functions of internal density distributions.In this study,a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion.We deduced the polar oblateness J^(2)and the equatorial ellipticity J_(22)of Mars to be 1.9566×10^(−3)and 6.3106×10^(−5),respectively.The preferred principal moments of inertia of Mars are A=2.66589×1036 kg·m^(2),B=2.66775×10^(36)kg·m^(2),and C=2.68125×10^(36)kg·m^(2).These values indicate that Mar is slightly triaxial.The equatorial principal moment of inertia of the Martian core is 1.46008×10^(35)kg·m^(2),accounting for~5.47%of the planet’s PMI;this result is critical for investigating the density and size of the core of Mars,and the planet’s free core nutation.

Band engineering of valleytronics WSe_(2)–MoS_(2)heterostructures via stacking form,magnetic moment and thickness

Spin-valley polarization and bandgap regulation are critical in the developing of quantum devices.Here,by employing the density functional theory,we investigate the effects of stacking form,thickness and magnetic moment in the electronic structures of WSe_(2)–MoS_(2)heterostructures.Calculations show that spin-valley polarization maintains in all situations.Increasing thickness of 2H-MoS_(2)not only tunes the bandgap but also changes the degeneracy of the conduction band minimums(CBM)at K/K_(1) points.Gradual increase of micro magnetic moment tunes the bandgap and raises the valence band maximums(VBM)atΓpoint.In addition,the regulation of band gap by the thickness of 2H-MoS_(2)and introduced magnetic moment depends on the stacking type.Results suggest that WSe_(2)–MoS_(2)heterostructure supports an ideal platform for valleytronics applications.Our methods also give new ways of optical absorption regulation in spin-valley devices.

Unusual magnetic relaxation in a single-molecule magnet with toroidal magnetic moments

We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions.The structural study shows that the symmetry changes from one polar point group(mm2)at room temperature to another polar point group(m)at low temperature.Magnetic studies and theory calculations illustrate that the vortex distribution of magnetic dipoles in the triangular dysprosium clusters forms a toroidal magnetic moment.Interestingly,the analysis of AC magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes,corresponding to the Raman,Orbach,and QTM relaxation pathways,respectively.The sum of three modified Debye functions is successfully used to describe the multiple relaxation behavior.

Dynamic connectedness and network in the high moments of cryptocurrency,stock,and commodity markets

This study examines the connectedness in high-order moments between cryptocurrency,major stock(U.S.,U.K.,Eurozone,and Japan),and commodity(gold and oil)markets.Using intraday data from 2020 to 2022 and the time and frequency connectedness models of Diebold and Yilmaz(Int J Forecast 28(1):57–66,2012)and Barunik and Křehlik(J Financ Econom 16(2):271–296,2018),we investigate spillovers among the markets in realized volatility,the jump component of realized volatility,realized skewness,and realized kurtosis.These higher-order moments allow us to identify the unique characteristics of financial returns,such as asymmetry and fat tails,thereby capturing various market risks such as downside risk and tail risk.Our results show that the cryptocurrency,stock,and commodity markets are highly connected in terms of volatility and in the jump component of volatility,while their connectedness in skewness and kurtosis is smaller.Moreover,jump and volatility connectedness are more persistent than that of skewness and kurtosis connectedness.Our rolling-window analysis of the connectedness models shows that connectedness varies over time across all moments,and tends to increase during periods of high uncertainty.Finally,we show the potential of gold and oil as hedging and safe-haven investments for other markets given that they are the least connected to other markets across all moments and investment horizons.Our findings provide useful information for designing effective portfolio management and cryptocurrency regulations.

Analytical Investigation into the Rotational Performance of Glulam Bolted Beam-Column Connections under Coupled Bending Moment and Shear Force

Considering the glulam beam-column connection form and the number of bolts,monotonic loading test and finite element analysis was carried out on 9 connection specimens in 3 groups to study the rotational performance and failure mode of the connection.The test results revealed that compared with U-shaped connectors,T-shaped connectors can effectively improve the ductility of connections,and the increase in the number of bolts can reduce the initial stiffness and ductility of connections.By theoretical analysis,formulas for calculating the initial stiffness and ultimate moment of connections were deduced.Subsequently,the moment-rotation theoretical model of connections was established based on the formulas,which were validated according to the test data and simulation results.The proposed model can not only improve the current theoretical system of heavy-duty glulam beam-column structure but also provide a theoretical basis for calculating the mechanical properties of the glulam beam-column connection.

Complete moment convergence for ND random variables under the sub-linear expectations

In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.

Measurement of remanent magnetic moment using a torsion pendulum with single frequency modulation method

In Tian Qin spaceborne gravitational-wave detectors, the stringent requirements on the magnetic cleanliness of the test masses demand the high resolution ground-based characterization measurement of their magnetic properties. Here we present a single frequency modulation method based on a torsion pendulum to measure the remanent magnetic moment mr of 1.1 kg dummy copper test mass, and the measurement result is(6.45 ± 0.04(stat) ± 0.07(syst)) × 10^(-8)A · m^(2). The measurement precision of the mr is about 0.9 n A · m^(2), well below the present measurement requirement of Tian Qin. The method is particularly useful for measuring extremely low magnetic properties of the materials for use in the construction of space-borne gravitational wave detection and other precision scientific apparatus.

Explaining Pomeranchuk Effect by Parity of Magnetic Moments of Leptons and Hadrons for Superconductivity in 3He and Graphene*

The mystery of superconductivity has intrigued scientists for 110 years now. The author in 2014 specifically predicted the superconductivity in carbon, sulfur and hydrogen compounds and generally predicted carbonaceous, hydrogeneous and sulfurous compounds in 2005 with reference to scattering to asymmetric orbital motions and associated spin and orbital exchanges between nuclei and electrons. The emphasis was in 2005 upon stronger electron and nuclear interactions and electron-phonon effects. But here the author develops more the un-gerade parity of the p and f orbitals and their contributions to the superconductivity at lower pressures and higher temperatures. On the bases of such, the role of parity from the origin and inflation of the Universe is noted and dark and bright energies and matters in the mature Universe are reasoned. Moreover, the superconductors are all reasoned by positive and negative nuclear magnetic moments (NMMs) with availability of un-gerade parities of p and f subshells and their orbitals. In addition to superconductivity, such positive and negative NMMs by Little Effect is presented for explaining Pomeranchuk Effect and thereby further explaining superconductivity and superfluidity of 3He. On the bases of successes of Little Effect via positive and negative NMMs, in particular negative NMMs of 3He, the superconductivity in twisted graphene is explained and also its recently discovered Pomeranchuk Effect.

pth-Moment Stabilization of Hybrid Stochastic Differential Equations by Discrete-Time Feedback Control

The given unstable hybrid stochastic differential equation is stabilized in the sense of p th-moment exponential stability.We achieve the results by feedback controls based on the discrete-time state and mode observations.The upper bound on the duration between two consecutive observations is obtained as well.Finally,a numerical example is given to verify the validity of the theoretical conclusions.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Moment tensor and stress inversion solutions of acoustic emissions during compression and tensile fracturing in crystalline rocks

We investigate the accuracy and robustness of moment tensor(MT)and stress inversion solutions derived from acoustic emissions(AEs)during the laboratory fracturing of prismatic Barre granite specimens.Pre-cut flaws in the specimens introduce a complex stress field,resulting in a spatial and temporal variation of focal mechanisms.Specifically,we consider two experimental setups:(1)where the rock is loaded in compression to generate primarily shear-type fractures and(2)where the material is loaded in indirect tension to generate predominantly tensile-type fractures.In each test,we first decompose AE moment tensors into double-couple(DC)and non-DC terms and then derive unambiguous normal and slip vectors using k-means clustering and an unstructured damped stress inversion algorithm.We explore temporal and spatial distributions of DC and non-DC events at different loading levels.The majority of the DC and the tensile non-DC events cluster around the pre-cut flaws,where macro-cracks later develop.Results of stress inversion are verified against the stress field from finite element(FE)modeling.A good agreement is found between the experimentally derived and numerically simulated stress orientations.To the best of the authors’knowledge,this work presents the first case where stress inversion methodologies are validated by numerical simulations at laboratory scale and under highly heterogeneous stress distributions.