Broadband third-order optical nonlinearities of layered franckeite towards mid-infrared regime

The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.

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.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

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.

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.

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.

Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem

The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.

基于LQ-moments的洪水频率分布参数计算方法研究

为改善频率曲线高尾部对实测洪水大值段的拟合效果,提高大重现期洪水设计值精度,研究LQmoments(LQM)法在洪水频率分布参数估计中的应用。LQM法是L-moments(LM)法的扩展方法,具有较好的不偏性和稳健性。以6个年最大洪峰流量系列为例,进行P-Ⅲ分布和GEV分布LQM法的参数估计,以累积相对偏差平方和(δ)、RMSE和平均绝对误差(MAE)为标准,评价和比较LQM法和LM法对P-Ⅲ和GEV分布参数的估计精度和拟合效果。结果表明,P-Ⅲ分布LQM法取得了很好的拟合效果,6个洪峰流量系列中,5个系列的最优参数估计方法为LQM法,其中3个系列的最优分布为P-Ⅲ分布;与LM法相比,LQM法能更好地拟合洪水序列大值部分,提高大重现期设计值估计精度,是洪水频率分布参数估计的有效方法。

Moment Redistribution Effect of the Continuous Glass Fiber Reinforced Polymer-Concrete Composite Slabs Based on Static Loading Experiment

This study aimed to investigate the moment redistribution in continuous glass fiber reinforced polymer(GFRP)-concrete composite slabs caused by concrete cracking and steel bar yielding in the negative bending moment zone.An experimental bending moment redistribution test was conducted on continuous GFRP-concrete composite slabs,and a calculation method based on the conjugate beam method was proposed.The composite slabs were formed by combining GFRP profiles with a concrete layer and supported on steel beams to create two-span continuous composite slab specimens.Two methods,epoxy resin bonding,and stud connection,were used to connect the composite slabs with the steel beams.The experimental findings showed that the specimen connected with epoxy resin exhibited two moments redistribution phenomena during the loading process:concrete cracking and steel bar yielding at the internal support.In contrast,the composite slab connected with steel beams by studs exhibited only one-moment redistribution phenomenon throughout the loading process.As the concrete at the internal support cracked,the bending moment decreased in the internal support section and increased in the midspan section.When the steel bars yielded,the bending moment further decreased in the internal support section and increased in the mid-span section.Since GFRP profiles do not experience cracking,there was no significant decrease in the bending moment of the mid-span section.All test specimens experienced compressive failure of concrete at the mid-span section.Calculation results showed good agreement between the calculated and experimental values of bending moments in the mid-span section and internal support section.The proposed model can effectively predict the moment redistribution behavior of continuous GFRP-concrete composite slabs.

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.

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.

Construction of a complete set of similarity invariants using pseudo-Zernike moments

To resolve the completeness and independence of an invariant set derived by the traditional method, a systematic method for deriving a complete set of pseudo-Zernike moment similarity （translation, scale and rotation） invariants is described. First, the relationship between pseudo-Zernike moments of the original image and those of the image having the same shape but distinct orientation and scale is established. Based on this relationship, a complete set of similarity invariants can be expressed as a linear combination of the original pseudo-Zernike moments of the same order and lower order. The problem of image reconstruction from a finite set of the pseudo-Zernike moment invariants （PZMIs） is also investigated. Experimental results show that the proposed PZMIs have better performance than complex moment invariants.

Retrieving Microphysical Properties and Air Motion of Cirrus Clouds Based on the Doppler Moments Method Using Cloud Radar

Radar parameters including radar reflectivity, Doppler velocity, and Doppler spectrum width were obtained from Doppler spectrum moments. The Doppler spectrum moment is the convolution of both the particle spectrum and the mean air vertical motion. Unlike strong precipitation, the motion of particles in cirrus clouds is quite close to the air motion around them. In this study, a method of Doppler moments was developed and used to retrieve cirrus cloud microphysical properties such as the mean air vertical velocity, mass-weighted diameter, effective particle size, and ice content. Ice content values were retrieved using both the Doppler spectrum method and classic Z-IWC （radar reflectivity-ice water content） relationships; however, the former is a more reasonable method.

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.

On the Spectral Moments of Wind Waves

In order to obtain high order spectral moments, the residual moment M(w(n))(i) = integral(0)(wn) w(i)S(w)dw, as proposed by Denis s, is presented for approximate estimation of spectral moment m(i) = integral(0)(infinity) w(i)S(w)dw. Glazman's partial averaging idea is discussed. It is pointed out that Glazman's method and definition of non-dimensional spectral moment can not be used to estimate spectral moments for engineering purposes and that method is not supported by theory and computation. The non-dimensional spectral moment of PM spectrum, which should be expressed as [GRAPHICS] is related to wind speed. The 0 - 8th moments of PM spectrum are estimated for wind speeds of 10, 20 and 30 m/s and some discussions are given.

Series expansion feasibility of singular integral in method of moments

When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.

CALCULATING RESPONSE SPECTRAL MOMENTS BY COMPLEX MODAL ANALYSIS

Response spectral moments are useful for system reliability analysis.Usually,spectral mo- ments are calculated by the frequency domain method.Based on the time domain modal analysis of random vibrations,the authors present a new method for calculating response spectral moments through response correlation functions.The method can be applied to both classical and non-classical damping cases and to three kinds of random excitations,i.e.,white noise,band-limited white noise, and filtered white noise.