THE STABILITY OF θ-METHODS FOR PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS

This paper deals with the numerical solution of initial value problems for pantograph differential equations with variable delays. We investigate the stability of one leg θ-methods in the numerical solution of these problems. Sufficient conditions for the asymptotic stability of θ-methods are given by Fourier analysis and Ergodic theory.

一种特殊的Θ-method求解比例尺方程的收敛性分析(英文)

介绍了用偏序的概念去研究用一种特殊的Θ-method求解比例尺方程的数值解和解析解的收敛性,然后证明了使用该种特殊的Θ-method求解该比例尺方程的数值解和解析解的收敛性.对这类研究的目前状况做一个简短的研究.

集成ISM与G1的建筑工人安全能力影响因素研究

为探究影响建筑工人安全能力的因素,提出一种集成解释结构模型(ISM)与序相关法(G1-Method)的因素分析法。首先,基于壳层模型(SHELL)与因子分析法,归纳与提取影响因素;其次,通过ISM构建工人安全能力影响因素多级递阶结构模型;最后,结合改进的G1-Method,计算因素间关联度及对安全能力的影响重要度。结果表明:所构建的安全能力影响因素结构模型包括安全认知能力、安全行为能力2个维度,以及16个影响因素。其中,安全观念、操作技能、环境适应是建筑工人安全能力形成的浅层因素,而安全教培、安全管理是安全能力形成的深层因素。同时,安全观念、安全教培、环境适应是安全认知能力的主要影响因素;操作技能、安全教培、安全管理是安全行为能力的主要影响因素。

Detection of Pulsation and Additional Components in Eclipsing Binary RS Sct

The eclipsing binary star RS Sct is a semi-detached system of theβLyrae type.This system was photometered for six nights in 2019 August,and 2020 June and August.The light and radial velocity curves were simultaneously analyzed to obtain the absolute physical and orbital parameters of the system,and the system geometry was determined.In this system,the primary component has filled its inner Roche lobe and the secondary component is close to filling it.Moreover,the change in the orbital period of this system was investigated.The presence of the third or fourth components and the mass transfer between the two components affect the orbital period of the system.In addition,the pulsation of the primary component was detected.Also,several frequencies with high signal-to-noise ratios were identified.According to the position of the primary component in the H-R diagram and the value of the obtained frequencies,this component is likely a delta-Scuti pulsator.

THE STABILITY OF THE θ-METHODS FOR DELAYDIFFERENTIAL EQUATIONS

This paper deals with the stability analysis of numerical methods for the solution of delay differential equations. We focus on the behaviour of three θ-methodsin the solution of the linear test equation u'(t)-A(t)u(t)+B(t)u( (t)) with (t)and A(t),B(t) continuous matrix functions. The stability regions for the threeθ-methods are determined.

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

The θ－Methods in Numerical Solution of Systems of Differential Equations with Two Delay Terms

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

Intensity distribution function and statistical properties of fast radio bursts

Fast Radio Bursts （FRBs） are intense radio flashes from the sky that are characterized by mil- lisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs that have been discovered. Their mean dispersion measure, after subtracting the contribution from the interstellar medium of our Galaxy, is found to be ~ 660 pc cm-3, supporting their being from a cosmological origin. Their energy released in the radio band spans about two orders of magnitude, with a mean value of ~ 10-39 erg. More interestingly, although the study of FRBs is still in a very early phase, the published collection of FRBs enables us to derive a useful intensity distribution function. For the 16 non-repeating FRBs detected by the Parkes telescope and the Green Bank Telescope, the intensity distribution can be described as dN/dFobs = （4.1± 1.3） × 103 F-obs1.1±0.2 sky-1 d-l, where Fobs is the observed radio obs fluence in units of Jy ms. Here the power-law index is significantly flatter than the expected value of 2.5 for standard candles distributed homogeneously in a flat Euclidean space. Based on this intensity distribution function, the Five-hundred-meter Aperture Spherical radio Telescope （FAST） is predicted to be able to detect about five FRBs for every 1000 h of observation time.

Wavelet Cleaning of Solar Dynamic Radio Spectrograms

By applying the state-of-the-art mathematical apparatus, the wavelet transformation, we explore the possibility of a dynamic cleaning of raw data ob- tained with the Chinese solar radio spectrographs over a wide wavelength range (from 0.7 to 7.6 GHz). We consider the problem of eliminating the interference caused by combination rates of data sampling (10-20 ins), and the low-frequency interference (4-30 s) caused by the receiving equipment changing its characteristics with time. It is shown that the best choice to reconstruct a signal suffering from amplitude, frequency and phase instabilities, is by means of wavelet transformation at both high and low frequencies. We analysed observational data which contained interferences of nonsolar origin such as instrumental effects and other man-made signals. A subsequent comparison of the reference data obtained with the acousto- optical receiver of the Siberian Solar Radio Telescope (SSRT) with the 'cleaned' spectra confirms the correctness of this approach.

Numerically investigating the peculiar periphery of a supernova remnant in the medium with a density gradient:the case of RCW 103

The young shell-type supernova remnant RCW 103 has peculiar properties in the X-ray morphology obtained with Chandra.The southeastern shell is brighter in the X-rays,and the curved border of the shell in this region is flatter than the other part.We investigate the formation of the peculiar periphery of the supernova remnant RCW 103 using 3D hydrodynamical simulation.Assuming that the supernova ejecta has been evolved in the medium with a density gradient,the detected shape of the periphery can be generally reproduced.For RCW 103,with the ejecta mass of 3.0 M,the density of the background material of 2.0 cm^(-3),and a gradient of 3.3-4.0 cm^(-3)pc^(-1),the X-ray periphery can be generally reproduced.The simulation turned out that the asymmetry of the SNR RCW 103 is mainly due to the inhomogeneous medium with a density gradient.

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be so small (β = 10-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magnetic energy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magnetic energy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of the corresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as to whether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope. This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed to be detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.

Three pulsars discovered by FAST in the globular cluster NGC 6517 with a pulsar candidate sifting code based on dispersion measure to signal-to-noise ratio plots

We report the discovery of three new pulsars in the globular cluster(GC)NGC 6517,namely NGC 6517 E,F and G,made with the Five-hundred-meter Aperture Spherical radio Telescope(FAST).The spin periods of NGC 6517 E,F and G are 7.60 ms,24.89 ms and 51.59 ms,respectively.Their dispersion measures are 183.29,183.713 and 185.3 pc cm^(-3),respectively,all slightly larger than those of the previously known pulsars in this cluster.The spin period derivatives are at the level of 1×10^(-18) s s^(-1),which suggests these are recycled pulsars.In addition to the discovery of these three new pulsars,we updated the timing solutions of the known isolated pulsars,NGC 6517 A,C and D.The solutions are consistent with those from Lynch et al.but with smaller timing residuals.From the timing solution,NGC6517 A,B(position from Lynch et al.),C,E and F are very close to each other on the sky and only a few arcseconds from the optical core of NGC 6517.With currently published and unpublished discoveries,nine pulsars have been discovered in NGC 651,ranking it 6 thfor GCs with the most known pulsars.The discoveries take advantage of the high sensitivity of FAST and a new algorithm used to check and filter possible candidate signals.

浅析对供应商4M变更的规范管理

随着顾客对产品的个性化需求越来越细化,为了适应这种市场化的要求,大型企业一方面需要遵循严格的产品规范要求,同时又需要对市场变化做出迅速反应,满足不同客户的需求。产品多样小批量的生产变化对提供产品服务的企业运营提出了很大的挑战,同时对管控产品质量的风险加大。文章通过研究对供应商4M变更管理规范的要求,探讨企业在实际生产过程中针对供应商4M变更的规范管理,有效防范供应商产品4M变更的风险,使企业在当前的生产模式中竞争地位不断增强。

Comparative dissolution study on counterfeit medicines of PDE-5 inhibitors

Counterfeit medicines are a growing problem in both developing and industrialised countries. In general the evaluation of these medicines is limited to the identification and the dosage of the active ingredients. In this study in vitro dissolution tests were conducted on two sets of counterfeit medicines containing PDE-5 inhibitors （sildenafil citrate and tadalafil）. The dissolution profiles were statistically compared to the ones of the genuine products using the f2-method and a comparison at each time point using the Cochran test. The results showed low equivalences between counterfeit and genuine products as well as higher variations around the mean dissolution value at the different time points for the counterfeit products.

Inverse Shadowing and Weak Inverse Shadowing Property

In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing property with respect to classes . In addition we study relation between minimality and weak inverse shadowing property with respect to class and relation between expansivity and inverse shadowing property with respect to class .

A Computational Study with Finite Difference Methods for Second Order Quasilinear Hyperbolic Partial Differential Equations in Two Independent Variables

In this paper we consider the numerical method of characteristics for the numerical solution of initial value problems (IVPs) for quasilinear hyperbolic Partial Differential Equations, as well as the difference scheme Central Time Central Space (CTCS), Crank-Nicolson scheme, ω scheme and the method of characteristics for the numerical solution of initial and boundary value prob-lems for the one-dimension homogeneous wave equation. The initial deriva-tive condition is approximated by different second order difference quotients in order to examine which gives more accurate numerical results. The local truncation error, consistency and stability of the difference schemes CTCS, Crank-Nicolson and ω are also considered.

Modeling the rail surface unevenness of a high-precision radio telescope

This study proposed a coarse-fine mixed model for describing the rail surface unevenness of an ultra-large fully steerable radio telescope （Qi Tai Telescope） with a diameter of 110 meters. The rail surface unevenness includes information on error arising from two different scales, i.e., the long-period- short-change and the short-period-long-change. Consequently, in this study an idea of a mixed model was proposed, in which trigonometric and fractal functions were, respectively, used to describe infor- mation on error from two scales. Key parameters were determined by using the least squares method and the wavelet transform method, and finally, a specific mathematical expression of the model was obtained by optimization. To validate the effectiveness of the new modeling method, the mixed model was then used to describe the rails of the Green Bank Telescope, the Large Millimeter Telescope, and a radio telescope in Miyun, Beijing. A comparative study revealed that the maximum error was less than 15 %, thus the result was superior to those of existing modeling methods.

THE NUMERICAL STABILITY OF THE θ-METHOD FOR DELAYDIFFERENTIAL EQUATIONS WITH MANY VARIABLEDELAYS

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations(DDEs)where a,b1,b2,. ..,bm and yo ∈ C, 0 < λm ≤ λm-1 ≤ ... ≤λl < 1. A sufficient condition such that the differential equations are asymptotically stable isderived.And it is shown that the linear θ-method is AGPm-stable if and only if1/2≤θ-≤ 1.

Rankin-Selberg coefficients in large arithmetic progressions

Let(λ_f(n))_(n≥1)be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f.We prove that,for any fixedη>0,under the Ramanujan-Petersson conjecture for GL_(2)Maass forms,the Rankin-Selberg coefficients(λ_f(n)^(2))_(n≥1)admit a level of distributionθ=2/5+1/260-ηin arithmetic progressions.

Interpolation of Morrey-Campanato and related smoothness spaces

We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.