Algebraic Solution for the Forward Displacement Analysis of the General 6-6 Stewart Mechanism

The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.

KINEMATIC ANALYSIS OF THE GENERAL SPATIAL 7R MECHANISM

The displacement, velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper, fused on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived. The derivation process and computation are considerably simple. A program written in Allanguage is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased. The results are verified by a numerical example. The researches of this paper and Ref. [5]found a base for establishing an expert system of spatial mechanism analysis in the future.

Temporal and Spectral Characteristics of Persistent Emission and Special Bursts of Magnetar SGR J1935+2154 Based on Insight-HXMT

In October 2022,the magnetar SGR J1935+2154 entered the active outburst state.During the episode,the InsightHXMT satellite carried out a long observation that lasted for 20 days.More than 300 bursts were detected,and a certain amount of persistent radiation signals were also accumulated.This paper mainly introduces the results of persistent radiation profile folding and period search based on Insight-HXMT data.At the same time,the burst phase distribution characteristics,spectral lag results of burst,the spectral characteristics of zero-lag bursts and the time-resolved spectral evolution characteristics of high-flux bursts are reported.We found that there is no significant delay feature during different energy bands for the bursts of SGR J1935+2154.The observed zero-lag burst does not have a unique spectrum.The time-resolved spectrum of the individual burst has consistent spectral types and spectral parameters at different time periods of the burst.We also find that the burst number phase distribution and the burst photon phase distribution have the same tendency to concentrate in specific regions of the persistent emission profile.

A Possible X-ray Quasi-periodic Oscillation in the Narrow-line Seyfert 1 Galaxy Mrk 142

A possible quasi-periodic oscillation(QPO) at frequency 7.045 × 10^(-5) Hz is found in the narrow-line Seyfert 1galaxy Mrk 142 in the data of XMM-Newton collected on 2020 April 11.We find that the QPO signal is statistically significantly larger than the 5σ level and highly coherent with quality factor Q > 5 at the 0.3–10 keV band by using the method of the Lomb–Scargle Periodogram,the Weighted Wavelet Z-transform and the REDFIT.We analyze the data in 0.3–0.6 keV,0.6–1 keV,1–3 keV and 3–10 keV energy bands,and find obvious QPO signals at 0.3–0.6 keV and 1–3 keV bands.We then analyze the time-average spectra and time variability at the QPO frequency of 7.045 × 10^(-5) Hz,and use a model to fit them.We find that the QPO signal mainly comes from the X-ray hot corona.

Radiation Spectral Analysis of 3D Dust Molecular Clusters(PAHs)and Peptoids under Ionization and Electric Field in ISM

Polycyclic aromatic hydrocarbons(PAHs),PANHs,and peptoids dust spectral calculations from the interstellar medium(ISM)are important for dust observations and theory.Our goal is to calculate the radiation spectrum of spherical PAHs dust clusters in a vacuum containing ionized and applied in the presence of an electric field.We propose a new simple computational model to calculate the size of three-dimensional spherical dust clusters formed by different initial dust structures.By the Vienna Ab-initio Simulation Package code,the density functional theory with the generalized approximation was used to calculate the electron density gradient and obtain the radiation spectrum of dust.When the radius of spherical dust clusters is~[0.009-0.042]μm,the dust radiation spectrum agrees well with the Z=0.02 mMMP stellar spectra,and the PAHs radiation spectrum of NGC 4676 at wavelengths of(0-5]μm and(5-10]μm,respectively.In the ionized state,the N-PAH,C_(10)H_(9)N,2(C_(4)H_(4))^(1+),and peptoids 4(CHON),(C_(8)H_(10)N_(2)O_(5))^(1+)dust clusters at 3.3μm,while the 2(C_(22)H_(21)N_(3)O_(2))^(1+),4(CHON)dust clusters at 5.2μm have obvious peaks.There is a characteristic of part of PAHs and peptoids clusters radiation at the nearinfrared wavelength of 2μm.However,especially after applying an electric field to the dust,the emission spectrum of the dust increases significantly in the radiation wavelength range[3-10]μm.Consequently,the dust clusters of PAHs,PANHs,and peptoids of the radius size~[0.009-0.042]μm are likely to exist in the ISM.

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetryof the system without perturbation are given.The perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[Act.Phys.Sin.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.

New Continuum Observations of the Andromeda galaxy M31 with FAST

We present a new total intensity image of M31 at 1.248 GHz,observed with the Five-hundred-meter Aperture Spherical radio telescope(FAST)with an angular resolution of 4'and a sensitivity of about 16 mK.The new FAST image clearly reveals weak emission outside the ring due to its high sensitivity on large-scale structures.We derive a scale length of 2.7 kpc for the cosmic ray electrons and find that the cosmic ray electrons propagate mainly through diffusion by comparing the scale length at 4.8 GHz.The spectral index of the total intensity varies along the ring,which can be attributed to the variation of the spectra of synchrotron emission.This variation is likely caused by the change of star formation rates along the ring.We find that the azimuthal profile of the non-thermal emission can be interpreted by an axisymmetric large-scale magnetic field with varying pitch angle along the ring,indicating a complicated magnetic field configuration in M31.

The Doppler Effect and Spectral Energy Distribution of Blazars

The relativistic beaming model is adopted to discuss quantitatively the observational differences between radio-selected BL Lac objects (RBLs) and X-ray- selected BL Lac objects (XBLs), and between BL Lac objects and flat spectrum radio quasars (FSRQs). The main results are the following: (1) In the Doppler corrected color-color ( ) diagram, XBLs and FSRQs occupy separated regions, while RBLs bridge the gap between them. These properties suggest that similar intrinsic physical processes operate in all the objects under a range of intrinsic physical conditions. (2) Our results are consistent with the results of Sambruna, Maraschi and Urry (1996) from other methods. We show the ■xox introduced by Sambruna to be a good index for describing the energy distribution because it represents the intrinsic energy distribution and includes the Doppler correction. (3) The Doppler effect of relativistic beaming is the main mechanism, and the physical differences (such as magnetic fields, electron energies) are also important complementary factors for understanding the relation between XBLs and RBLs;

Quark nova model for fast radio bursts

Fast radio bursts （FRBs） are puzzling, millisecond, energetic radio transients with no discernible source; observations show no counterparts in other frequency bands. The birth of a quark star from a parent neutron star experiencing a quark nova - previously thought undetectable when born in isolation - provides a natural explanation for the emission characteristics of FRBs. The generation of unstable r-process elements in the quark nova ejecta provides millisecond exponential injection of electrons into the surrounding strong magnetic field at the parent neutron star＇s light cylinder via β-decay. This radio synchrotron emission has a total duration of hundreds of milliseconds and matches the observed spectrum while reducing the inferred dispersion measure by approximately 200 cm-3 pc. The model allows indirect measurement of neutron star magnetic fields and periods in addition to providing astronomical measurements of β-decay chains of unstable neutron rich nuclei. Using this model, we can calculate expected FRB average energies （- 1041 erg） and spectral shapes, and provide a theoretical framework for determining distances.

What determines the observational differences of blazars？

We examine the scenario that the Doppler factor determines the observational differences of blazars. Significantly negative correlations are found between the observational synchrotron peak frequency and the Doppler factor. After correcting the Doppler boosting, the intrinsic peak frequency has a tight linear relation with the Doppler factor. It is interesting that this relation is consistent with the scenario that the black hole mass governs both the bulk Lorentz factor and the synchrotron peak frequency. In addition, the distinction between the kinetic jet powers of BL Lac objects and fiat spectrum radio quasars disappears after the boosting factor δ2 is considered. The negative correlation between the peak frequency and the observational isotropic luminosity, known as the blazar sequence, also disappears after the Doppler boosting is corrected. We also find that the correlation between the Compton dominance and the Doppler factor exists for all types of blazars. Therefore, this correlation is unsuitable for examining the external Compton emission dominance.

Properties of BL Lac Objects with Redshift ≤ 0.2

We present a large sample which includes 82 BL Lac objects with red- shifts below 0.2 from recent literature. We find strong correlations in both flux and luminosity between the radio (5 GHz) and optical bands (5500 A). The correlations in other bands are very weak. Five TeV BL Lacs and two suspect sources are found to have similar properties as high- frequency- peaked BL Lacs (HBLs). Our results suggest that both the radio and optical emissions are from the same radiation mech- anism in the SSC model. The TeV BL Lac candidates should be HBLs or HBL-like objects with small redshifts.

Ryanodine receptor-protein regulator interaction revealed a general molecular mechanism of channel inhibition

Ryanodine receptors (RyR) are the major Ca2+ release channels in both cardiac and skeletal muscle, they play a crucial role in the Ca2+ signaling pathway that govern the

A low-latency pipeline for GRB light curve and spectrum using Fermi/GBM near real-time data

Rapid response and short time latency are very important for Time Domain Astronomy, such as the observations of Gamma-ray Bursts（GRBs） and electromagnetic（EM） counterparts of gravitational waves（GWs）. Based on near real-time Fermi/GBM data, we developed a low-latency pipeline to automatically calculate the temporal and spectral properties of GRBs. With this pipeline, some important parameters can be obtained, such as T_（90） and fluence, within ～ 20 min after the GRB trigger.For ～ 90% of GRBs, T90 and fluence are consistent with the GBM catalog results within 2σ errors.This pipeline has been used by the Gamma-ray Bursts Polarimeter（POLAR） and the Insight Hard Xray Modulation Telescope（Insight-HXMT） to follow up the bursts of interest. For GRB 170817 A, the first EM counterpart of GW events detected by Fermi/GBM and INTEGRAL/SPI-ACS, the pipeline gave T90 and spectral information 21 min after the GBM trigger, providing important information for POLAR and Insight-HXMT observations.

Spectral indices for radio emission of 228 pulsars

We determine spectral indices of 228 pulsars by using Parkes pulsar data observed at 1.4 GHz, among which 200 spectra are newly determined. The indices are distributed in the range from -4.84 to -0.46. Together with known pulsar spectra from literature, we tried to find clues to the pulsar emission process. The wealCcorrelations between the spectral index, the spin-down energy loss rate E and the poten- tial drop in the polar gap Aψ hint that emission properties are related to the particle acceleration process in a pulsar＇s magnetosphere.

New Features of the Pulsar B0950+08 Radiation at the Frequency of 111 MHz

Results of long time observations of the pulsar B0950+08 are given.These observations were carried out at the LPA radio telescope at the frequency of 111 MHz from January of 2016 to May of 2019(450 days).A strong variability in emission of this pulsar has been detected with changes in signal to noise ratios hundreds of times.Part of the long-time flux density variability can be explained by refractive scintillations in the interstellar medium.The existence of radiation between the interpulse(IP)and main pulse(MP)was confirmed.It was more powerful than at high frequencies.We detected the unusual IP and precursor(Pr)radiation on 2017 August 1.On the basis of 65 strong IPs we found the correlations between energies of IP and Pr and between the phase of IP and the distance Pr–IP.It is shown that the observed peculiarities of this pulsar can be explained in the frame of the aligned rotator model.We estimated distances of radiation levels from the center of the neutron star.The calculated value of the initial period of 0.2 s means that not all pulsars are born with millisecond periods.The large age of the pulsar(6.8 million years)and the small angle between its magnetic moment and the rotation axis(less than 20°)confirm the suggestion related to pulsar evolution with respect to alignment.

Analysis of interval constants in calendars affiliated with the Shoushili

We study interval constants that are related to motions of the Sun and Moon, i.e., the Qi, Intercalation, Revolution and Crossing interval, in calendars affiliated with the Shoushi calendar （Shoushili）, such as Datongli and Chiljeongsannaepyeon. It is known that these interval constants were newly introduced in the Shoushili calendar and revised afterward, except for the Qi interval constant, and the revised values were adopted in later calendars affiliated with the Shoushili. We first investigate the accu- racy of these interval constants and then the accuracy of calendars affiliated with the Shoushili in terms of these constants by comparing times for the new moon and the maximum solar eclipse calculated by each calendar with modem methods of calcula- tion. During our study, we found that the Qi and Intercalation interval constants used in the early Shoushili were well determined, whereas the Revolution and Crossing interval constants were relatively poorly measured. We also found that the interval constants used by the early Shoushili were better than those of the later one, and hence better than those of Datongli and Chiljeongsannaepyeon. On the other hand, we found that the early Shoushili is, in general, a worse calendar than Datongli for use in China but a better one than Chiljeongsannaepyeon for use in Korea in terms of times for the new moon and when a solar eclipse occurs, at least for the period 1281 - 1644. Finally, we verified that the times for sunrise and sunset in the Shoushili-Li-Cheng and Mingshi are those at Beijing and Nanjing, respectively.

Spatial dependence of high energy electrons and their radiations in pulsar wind nebulae

We investigate the spatial dependence of high energy electrons and their radiations in pulsar wind nebulae （PWNe）. By assuming a time-dependent broken power-law injection and spatial dependence of convection velocity, magnetic field strength and diffusion coefficient on the radial distance of an expand- ing system, we numerically solve the Fokker-Planck transport equation including convection, diffusion, adiabatic loss and radiative loss in spherical coordinates, and investigate the effects of magnetic field, PWN age, maximum energy of electrons, and diffusion coefficient on electron spectra and non-thermal photon emissions. Our results indicate that （1） electron spectra and the corresponding photon spectra are a function of radial distance r of the expanding system; （2） for a given expansion velocity, the increase of the PWN age causes a slower decrease of the convection velocity （V ∝ r-β） and a more rapid decrease of the magnetic field strength （B ∝ r-1＋β）, but a more rapid increase of the diffusion coefficient （k∝ r1-β） because the index β decreases with the PWN age; and （3） the lower energy part of the electron spectra is dominated by convection and adiabatic loss, but the higher energy part is dominated by the competition between syn- chrotron loss and diffusion, and such a competition is a function of radial distance. Therefore the diffusion effect has an important role in the evolution of electron spectra as well as non-thermal photon spectra in a PWN.

f and g series solutions to a post-Newtonian two-body problem with parameters β and γ

Classical Newtonian f and g series for a Keplerian two-body problem are extended for the case of a post-Newtonian two-body problem with parameters β and γ. These two parameters are introduced to parameterize the post-Newtonian approximation of alternative theories of gravity and they are both equal to1 in general relativity. Up to the order of 30, we obtain all of the coefficients of the series in their exact forms without any cutoff for significant figures. The f and g series for the post-Newtonian two-body problem are also compared with a Runge-Kutta order 7 integrator. Although the f and g series have no superiority in terms of accuracy or efficiency at the order of 7, the discrepancy in the performances of these two methods is not quite distinct. However, the f and g series have the advantage of flexibility for going to higher orders.Some examples of relativistic advance of periastron are given and the effect of gravitational radiation on the scheme of f and g series is evaluated.

More Emission Cones: Multi-frequency Simulation of the Pulse Profiles of PSR J0437-4715

Pulsar radio emission beams have been studied observationally for a long time, and the suggestion is that they consist of the so-called core and conal components. To reproduce these components is a challenge for any emission model, and that the pulse profile of pulsars changes with frequency presents even a greater challenge. Assuming a local surface magnetic structure (to produce the core or central beam) and a global dipole magnetic field (to produce the conal beams), Gil & Krawczyk (1997) applied curvature radiation to the pulse profile simulation of PSR J0437-4715 (hereafter the GK model). Here we present an alternative multi-frequency simulation of the same profiles within the framework of the Inverse Compton Scattering (ICS) model. It is obtained from our simulation (1) that besides the core, the inner cone and the outer cone, there is an outer-outer cone; (2) that the emission components of the core and cones evolve strongly with frequency. Some important differences between the ICS model and the GK model are discussed, which need to be tested by further observations.

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.