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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

A Local Reference Frame Construction Method Based on the Signed Surface Variation

A fast local reference frame(LRF)construction method based on the signed surface variation is proposed,which can adapt to the real-time applications such as self-driving,face recognition,object detection.The z-axis of the LRF is generated based on the concavity of the local surface of keypoint.The x-axis is constructed by the weighted vector sum of a set of projection vectors of the local neighborhoods around keypoint.The performance of the proposed LRF is evaluated on six standard datasets and compared with six state-of-the-art LRF construction methods(e.g.,BOARD,FLARE,SHOT,RoPS and TOLDI).Experimental results validate the high repeatability,robustness,universality and time efficiency of our method.

Numerical Simulation of the Mechanical Stirring Process in a Tannin-Based Foaming Precursor Resin

Tannin foam is a new functional material.It can be widely applied to the automobile industry,construction industry,and packaging industry due to its wide range of raw materials,renewable,easily degraded,low cost and almost no pollution.Preparing tannin foam is a very complex process that includes high temperature,two phases,mechanical agitation,and phase change.To investigate the influence of the stirring velocity and paddle shape,simulation was calculated by making use of the volume of fluid(VOF)method and multiple reference frame(MRF)method in a three-dimensional flow field of tannin-based foaming precursor resin.The gas holdup and velocity magnitude were analysed with various conditions of mechanical velocities and paddle shape in the stirring flow field.The result shows the higher the velocity,the greater the disturbance and paddle shape between the eggbeater and the Rushton turbine,obviously the paddle shape of the eggbeater with a wider range of agitation,which can entrap more air into the tannin-based foaming precursor resin in a short time.Especially when the speed is 1500 rpm,the flow field of the Rushton turbine comes out of a ditch,which decreases the efficiency of mass transfer;there is less air to mix into the tannin-based foaming precursor resin,which causes unevenness.At the same time,the eggbeater shows the marvelous capability of hybrid as it has two vortexes and multiple cycles that make a difference from the Rushton turbine,which has only one vortex and two upper and lower loops;the structure makes the flow field more stable allowed evenness of flow field tannin-based foaming precursor resin.The results reveal that it is beneficial for tannin-based foaming precursor resin to use an eggbeater with a speed of 1500 rpm to reduce the consumption of resources while obtaining a uniform flow field.

The Transference Number

The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion(often a cation)is transported from one electrode to the other.The cation transference number is an important transport parameter that affects this rate.The purpose of this perspective is to distinguish between approximate and rigorous methods used in the literature to measure the transference number.We emphasize the fact that this parameter is dependent on the reference frame used in the analysis;care must be taken when comparing values obtained from different sources to account for differences in reference frames.We present data obtained from a well-characterized electrolyte.We compare rigorously determined transference numbers in two reference frames with values obtained by an approximate method.We conclude with a qualitative discussion of the relationship between the transference number and salt concentration gradients that are obtained when current is drawn through a battery。

Relativity of a Free Will Concept Depending on Both Conscious Indeterminism and Unconscious Determinism

Free will is difficult to classify with respect to determinism or indeterminism, and its phenomenology in consciousness often shows both aspects. Initially, it is felt as unlimited and indeterminate will power, with the potentiality of multiple choices. Thereafter, reductive deliberation is led by determinism to the final decision, which realises only one of the potential choices. The reductive deliberation phase tries to find out the best alternative and simultaneously satisfying vague motivations, contextual conditions and personal preferences. The essential sense of free will is the introduction of personal preferences, which allows a higher diversity of reactions to vague motivations. With an oversimplified model of determinism as a chain of events, incompatibilists define ＂free＂ as ＂undetermined＂ so that determinism becomes incompatible with any free choice between alternatives. In consciousness, free will requires a more complex model of network determinism as well as the consideration of unconsciousness as a causal factor. When ＂free＂ defined as ＂undetermined＂ is applied to the context of consciousness, it should be reinterpreted as ＂unconscious of being determined＂ or not aware of underlying determinism. Lacking information on determinism generates a feeling of ＂free＂ in consciousness and, therefore, gives the impression of indeterminism. Lacking information may be induced by an uncertain future without determined events--an unconscious past with biological reactions suddenly emerging from the unconsciousness or an unknown present unable to distinguish determinism of complex events. Therefore, at the level of human consciousness, the experience of free will is associated with apparent indeterminism although it is based on unconscious determinism. The concepts of compatibilism and incompatibilism are only two different aspects of the same phenomenon and correspond to consciousness and unconsciousness. Nevertheless, they can be considered together with a free will concept based on relativity depending on two different reference frames--the first person＇s experience frame or the Laplace＇s demon frame with knowledge on every molecule of the universe. Only relativity of the free will concept avoids the contradiction between ＂free＂ and ＂unfree＂ for the same phenomenon and could be a compromise for considering compatibilism and incompatibilism equally.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software,the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ωturbulence model,Eulerian−Eulerian two-fluid model,and multi-reference flame method.The mixing process in the tank was calculated by tracer method.The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase.When the rotating speed exceeds 93 r/min,the relative power demand remains basically constant.The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution.When the inclination angle is 50°,the relative power demand reaches the maximum.An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

Characterization of the Engineering Flow in a Miniaturised Bioreactor by Computational Fluid Dynamics

Three approaches based on computational fluid dynamics(CFD) techniques have been assessed for their ability to describe the engineering flow environment in a miniaturized mechanically agitated bioreactor. The three approaches tested were the source-sink(SS), the multiple reference frames(MRF) and the sliding grids(SG). In all the cases, the predictions of the velocity components agree with reported experimental data. However, the analysis of the results of the turbulent intensities predicted by the three approaches indicates the MRF and the SG techniques under predicted turbulent intensities are comparable to both experimental measurements and the SS method. The predicted power number and pumping number based on the SS approach are closer to typical reported experimental values compared to those obtained from the MRF and SG methods.