Defining the We-map Reference Frames and Providing Mathematical Expressions for Transformation Relations

We-map is an interactive mobile map that can be easily communicated and applied on personal electronic devices,such as personal computers and mobile phones.Therefore,the study of direction systems and coordinate systems is critical,and exploring reference frames is essential in direction and coordinate systems.Despite its significance,existing research on We-map lacks specific solutions for the exploration of reference frames is indispensable for the establishment of accurate direction and coordinate systems.In this paper,we endeavor to address this gap by elucidating the significance of We-map reference frames,defining them with mathematical constraints,summarizing their nature and characteristics,deriving their transformation relationships and representing them through mathematical formulars and equations.Our work contributes to the fundamental theory of We-map and provides valuable systems and support for the mathematical foundation of We-map,map production,and platform development.Ultimately,this research serves to advance the development of We-map.

FIRST INTEGRALS AND INTEGRAL INVARIANTS FOR VARIABLE MASS NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

The first integrals and their conditions of existence for variable massnonholonomic system in noninertial relerence frames are obtained,and the canonicalequations and the variation equations of the system are extended. It is proved that using the first integral we can construct the integral invariant of the system.Finally,a series of deductions and an example are given.

INTEGRAL THEORY FOR THE DYNAMICS OF NONLINEAR NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

This paper establishes the integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frame. Firstly, based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system. Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively. Thirdly, derives canonical equation and variation equation and by using the first integral constructs integral invariant. And then, establishes the basic integral variants and the integral invariant of Poincare-Cartan type. Finally, we give a series of deductions.

THE PRINCIPLES OF LEAST ACTION OF VARIABLE MASS NONHOLONOMIC NONCONSERVATIVE SYSTEM IN NONINERTIAL REFERENCE FRAMES

This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.

Trial by fire:Testing the paleolongitude of Pangea of competing reference frames with the African LLSVP

Paleogeography can be reconstructed using various crust-or mantle-based reference frames that make fundamentally different assumptions.The various reconstruction models differ significantly in continental paleolongitude,but it has been difficult to assess which models are more valid.We suggest here a "LLSVP test",where an assumed correlation between present-day large low velocity shear-wave provinces and the paleogeography of supercontinent Pangea at breakup ca.200 million years ago can be used to assess the relative accuracy of published reconstructions.Closest correlations between continental paleolongitude and the African LLSVP are achieved with mantle-based reference frames(moving hotspots and true polar wander),whereas shallower crustbased reference frames are shown to be invalid.The relative success of mantle-based frames,and thus the importance of the depth of reference frame,supports the notion that mantle convection is largely vertical compared to the horizontal plate motion of tectonics.

Thermodynamic Properties of Spherically-Symmetric, Uniformly-Accelerated Reference Frames

We aim to study the thermodynamic properties of the spherically symmetric reference frames with uniform acceleration, including the spherically symmetric generalization of Rindler reference frame and the new kind of uniformly accelerated reference frame. We find that, unlike the general studies about the horizon thermodynamics, one cannot obtain the laws of thermodynamics for their horizons in the usual approaches, despite that one can formally define an area entropy （Bekenstein-Hawking entropy）. In fact, the common horizon for a set of uniformly accelerated observers does not always exist, even though the Hawking-Unruh temperature is still well-defined. This result indicates that the Hawking-Unruh temperature is only a kinematic effect, and to gain the laws of thermodynamics for the horizon, one needs the help of dynamics. Our result is in accordance with those from the various studies about the acoustic black holes.

Electrodynamics in Noninertial Reference Frames

The electrodynamics both in RF with prescribed law of motion and in FR with prescribed structure is considered. Parallel comparison for solutions in “uniformly accelerated” NRF M?ller system and in uniformly accelerated rigid NFR in the space of the constant curvature is carried out. The stationary criterion is formulated. On the basis of this criterion, one of the “eternal physical problems” concerning the field at uniformly accelerated charge motion is considered. The problems of electromagnetic wave spreading, Doppler’s effect and field transformations are discussed.

Realization of an Optimal Dynamic Geodetic Reference Frame in China:Methodology and Applications

China Geodetic Coordinate System 2000(CGCS2000)has been used for several years as a formal published reference frame.The coordinates of all global navigation satellite system(GNSS)stations in China need to be corrected to align with the CGCS2000 frame.Different strategies can be adopted for the realization of an optimal reference frame.However,different strategies lead to different results,with differences as great as several decimeters when GNSS station coordinates are transformed into CGCS2000-defined coordinates.The two common methods for the coordinate correction of a GNSS station are quasi-stable adjustment under CGCS2000 and plate movement correction,and the differences between their results can be greater than 10 cm.In this study,a statistic method called"supervised clustering"is applied to the selection of GNSS reference stations;a new scheme named"partition spacing"for the grouping of all processed GNSS stations is proposed;and the plate movement correction method is used to correct the coordinates of all GNSS stations from the GNSS epoch to the CGCS2000 epoch.The results from the new partitioning method were found to be significantly better than those from the conventional station-blocking approach.When coordinates from the stations without grouping were used as the standard,the accuracy of all the three-dimensional coordinate components from the new partitioning method was better than 2 mm.The root mean squares(RMSs)of the velocities in the x,y,and z directions resulting from the supervised clustering method were 0.19,0.45,and 0.32 mm∙a1,respectively,which were much smaller than the values of 0.92,0.72,and 0.97 mm∙a1 that resulted from the conventional approach.In addition,singular spectrum analysis(SSA)was used to model and predict the position nonlinear movements.The modeling accuracies of SSA were better than 3,2,and 5 mm in the east(E),north(N),and up(U)directions,respectively;and its prediction accuracies were better than 5 mm and 1 cm for the horizontal and vertical domains,respectively.

Three-party reference frame independent quantum key distribution protocol

We present a three-party reference frame independent quantum key distribution protocol which can be implemented without any alignment of reference frames between the sender and the receiver.The protocol exploits entangled states to establish a secret key among three communicating parties.We derive the asymptotic key rate for the proposed protocol against collective attacks and perform a finite-size key security analysis against general attacks in the presence of statistical fluctuations.We investigate the impact of reference frame misalignment on the stability of our protocol,and we obtain a transmission distance of 180 km,200 km,and 230 km for rotation of reference framesβ=π/6,β=π/8 andβ=0,respectively.Remarkably,our results demonstrate that our proposed protocol is not heavily affected by an increase in misalignment of reference frames as the achievable transmission distances are still comparable to the case where there is no misalignment in reference frames(whenβ=0).We also simulate the performance of our protocol for a fixed number of signals.Our results demonstrate that the protocol can achieve an effective key generation rate over a transmission distance of about 120 km with realistic 107 finite data signals and approximately achieve 195 km with 109 signals.Moreover,our proposed protocol is robust against noise in the quantum channel and achieves a threshold error rate of 22.7%.

Application of time series modeling to a national reference frame realization

This paper presents an option for modern dynamic terrestrial reference system realization in Uzbekistan for user needs. An additive model is explored to predict patterns of time series and investigate means of constructing forecast time series models in the future. The main components(trend, periodical, and irregular) of the KIUB(DORIS) and KIT3, TASH, MADK, and MTAL(GNSS) international stations coordinate time series were investigated. It was shown that seasonal nonlinear trends occurred both in the height(U) component of all stations and the east(E) component of high mountainous stations such as MTAL and MADK. The seasonal periodical portion of the time series determined from the additive model has a complicated pattern for all sites and can be explained as both hydrological signals in the region and improvement of observational quality. Amplitudes of the best-fitting sinusoids in the North component ranged between 1.73 and 8.76 mm; the East component ranged between 0.82 and 11.92 mm; and the Up component ranged between 3.11 and 40.81 mm. Regression analysis of the irregular portion of the height component of the two techniques at the Kitab station using tropospheric parameters(pressure and temperature) was confirmed as only 57% of the stochastic portion of the time series.

Reference-frame-independent quantum key distribution with an untrusted source

Reference frame independent quantum key distribution(RFI-QKD) allows two legitimate parties to share the common secret keys with the drift of reference frames. In order to reduce the actual requirements of RFI-QKD protocol on light source and make it more suitable for practical applications, this paper gives a specific description of RFI-QKD protocol with an untrusted source and analyzes the practical security of this protocol based on the two-way "plug and play" structure commonly used in practical systems. In addition, we also investigate the performance of RFI-QKD with an untrusted source considering statistical fluctuations based on Chernoff bound. Using simulations, we compare the secret key rate of RFIQKD with an untrusted source to RFI-QKD with trusted source. The results show that the performance of RFI-QKD with an untrusted source is similar to that of RFI-QKD with trusted source, and the finite data size clearly effects the performance of our protocol.

Houston16:A stable geodetic reference frame for subsidence and faulting study in the Houston metropolitan area,Texas,U.S.

Houston,Texas,is one of the earliest regions to employ continuous GPS technology for land subsidence monitoring.Currently,there are over 200 permanent GPS stations located in the greater Houston area.The need for a consistent and stable reference frame to precisely interpret local ground deformation has become critically important since the 1990s,because of the significant spreading of subsidence.We have established a stable Houston reference frame,designated Houston16,using publicly available GPS observations(>5 years)from 15 Continuously Operating Reference Stations(CORS)located outside of the greater Houston area.Applications of the reference frame in subsidence and faulting studies are demonstrated in this article.Houston16 is aligned in origin and scale with the International GNSS Reference Frame of 2008(IGS08).A 7-parameter method was employed to transform the GPS-derived positional time series from IGS08 to Houston16.The primary product of this study is the seven parameters for transforming Earth-Centered-Earth-Fixed XYZ coordinates from IGS08 to Houston16.The frame stability of Houston16 is approximately 1 mm/year.Houston16 will be updated every few years to mitigate degradation of the frame’s stability with time and to synchronize with future updates of the IGS reference frame.

Impact of the terrestrial reference frame on the determination of the celestial reference frame

Currently three up-to-date Terrestrial Reference Frames(TRF) are available, the ITRF2014 from IGN, the DTRF2014 from DGFI-TUM, and JTRF2014 from JPL. All use the identical input data of space-geodetic station positions and Earth orientation parameters, but the concept of combining these data is fundamentally different. The IGN approach is based on the combination of technique solutions, while the DGFI is combining the normal equation systems. Both yield in reference epoch coordinates and velocities for a global set of stations. JPL uses a Kalman filter approach, realizing a TRF through weekly time series of geocentric coordinates. As the determination of the CRF is not independent of the TRF and vice versa, the choice of the TRF might impact on the CRF, Within this work we assess this effect.We find that the estimated Earth orientation parameter(EOP) from DTRF2014 agree best with those from ITRF2014, the EOP resulting from JTRF2014 show besides clear yearly signals also some artifacts linked to certain stations. The estimated source position time series however, agree with each other better than ±1 μas. When fixing EOP and station positions we can see the maximal effect of the TRF on the CRF. Here large systematics in position as well as proper motion arise. In case of ITRF2008 they can be linked to the missing data after 2008. By allowing the EOP and stations to participate in the adjustment,the agreement increases, however, systematics remain.

Extended intrinsic mean spin tensor for turbulence modelling in non-inertial frame of reference

We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.

NOETHER’S THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS RELATIVE TO NON-INERTIAL REFERENCE FRAME

The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.

A Quaternion Solution of the Motion in a Central Force Field Relative to a Rotating Reference Frame

The paper presents a quaternion approach of giving a closed form solution of the motion in a central force field relative to a rotating reference frame. This new method involves two quaternion operators: the first one transforms the motion from a non-inertial reference frame to a inertial one with a very significant consequence of vanishing all the non-inertial terms (Coriolis and centripetal forces);the second quaternion operator provides the solution of the motion in the noninertial reference frame by applying it to the solution in the inertial reference frame. This process will govern the inverse transformation of the motion and is proved on two particular cases, the Foucault Pendulum and Keplerian motions problems relative to rotating reference frames.

The Explanation of the Michelson-Morley Experiment Results by Means Universal Frame of Reference

It is commonly thought that the Michelson-Morley experiment from 1887 and Kennedy-Thorndike experiment from 1932 demonstrated that the universal frame of reference (ether) does not exist and that the velocity of light in vacuum is absolutely constant. The analysis of this experiment led to the creation of the Special Theory of Relativity (STR). The article explains why Michelson-Morley and Kennedy-Thorndike experiments could not detect the universal frame of reference. In this article, a different transformation of time and position than the Lorentz transformation is derived on the basis of the geometric analysis of the Michelson-Morley and Kennedy-Thorndike experiments. The transformation is derived based on the assumption that the universal frame of reference (UFR) exists. UFR is a frame of reference in which the velocity of light is constant in every direction. In inertial frames of reference moving in the UFR, the velocity of light may be different. The article has derived the formula for relative speed and patterns for the maximum and minimum speed of light that can be measured in the inertial system. Finally, the anisotropy of the microwave background radiation has been explained by using the presented theory. According to the body kinematics model presented in this article, anisotropy of cosmic microwave background is the Doppler effect for observer moving in the UFR.

Video Compressed Sensing Reconstruction Based on Multi-Dimensional Reference Frame Multi Hypothesis Rediction

In this paper,a video compressed sensing reconstruction algorithm based on multidimensional reference frames is proposed using the sparse characteristics of video signals in different sparse representation domains.First,the overall structure of the proposed video compressed sensing algorithm is introduced in this paper.The paper adopts a multi-reference frame bidirectional prediction hypothesis optimization algorithm.Then,the paper proposes a reconstruction method for CS frames at the re-decoding end.In addition to using key frames of each GOP reconstructed in the time domain as reference frames for reconstructing CS frames,half-pixel reference frames and scaled reference frames in the pixel domain are also used as CS frames.Reference frames of CS frames are used to obtain higher quality assumptions.Themethod of obtaining reference frames in the pixel domain is also discussed in detail in this paper.Finally,the reconstruction algorithm proposed in this paper is compared with video compression algorithms in the literature that have better reconstruction results.Experiments show that the algorithm has better performance than the best multi-reference frame video compression sensing algorithm and can effectively improve the quality of slowmotion video reconstruction.

Content based error resilience coding using redundant coding, reference frame modification, and mode decision

Quality degradation occurs during transmission of video streaming over the error-prone network. By jointly using redundant slice, reference frame selection, and intra/inters mode decision, a content and end-to-end rate-distortion based error resilience method is proposed. Firstly, the intra/inter mode decision is implemented using macro-block(MB) refresh, and then redundant picture and reference frame selection are utilized together to realize the redundant coding. The estimated error propagation distortion and bit consumption of refresh MB are used for the mode and reference frame decision of refresh MB. Secondly, by analyzing the statistical property in the successive frames, the error propagation distortion and bit consumption are formulated as a function of temporal distance. Encoding parameters of the current frame is determined by the estimated error propagation distortion and bit consumption. Thirdly, by comparing the rate-distortion cost of different combinations, proper selection of error resilience method is performed before the encoding process of the current frame. Finally, the MB mode and bit distribution of the primary picture are analyzed for the derivation of the texture information. The motion information is subsequently incorporated for the calculation of video content complexity to implement the content based redundant coding. Experimental results demonstrate that the proposed algorithm achieves significant performance gains over the LA-RDO and HRP method when video is transmitted over error-prone channel.

Decoy-state reference-frame-independent quantum key distribution with both source errors and statistical fluctuations

Reference-frame-independent quantum key distribution （RFI QKD） can generate secret keys without the alignment of reference frames, which is very robust in real-life implementations of QKD systems. However, the performance of decoy-state RFI QKD with both source errors and statistical fluctuations is still missing until now. In this paper, we investigate the performance of decoy-state RFI QKD in practical scenarios with two kinds of light sources, the heralded single photon source （HSPS） and the weak coherent source （WCS）, and also give clear comparison results of decoy-state RFI QKD with WCS and HSPS. Simulation results show that the secret key rates of decoy-state RFI QKD with WCS are higher than those with HSPS in short distance range, but the secret key rates of RFI QKD with HSPS outperform those with WCS in long distance range.