Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.

SDN Orchestration for Dynamic End-to-End Control of Data Center Multi-Domain Optical Networking

New and emerging use cases, such as the interconnection of geographically distributed data centers(DCs), are drawing attention to the requirement for dynamic end-to-end service provisioning, spanning multiple and heterogeneous optical network domains. This heterogeneity is, not only due to the diverse data transmission and switching technologies, but also due to the different options of control plane techniques. In light of this, the problem of heterogeneous control plane interworking needs to be solved, and in particular, the solution must address the specific issues of multi-domain networks, such as limited domain topology visibility, given the scalability and confidentiality constraints. In this article, some of the recent activities regarding the Software-Defined Networking(SDN) orchestration are reviewed to address such a multi-domain control plane interworking problem. Specifically, three different models, including the single SDN controller model, multiple SDN controllers in mesh, and multiple SDN controllers in a hierarchical setting, are presented for the DC interconnection network with multiple SDN/Open Flow domains or multiple Open Flow/Generalized Multi-Protocol Label Switching( GMPLS) heterogeneous domains. I n addition, two concrete implementations of the orchestration architectures are detailed, showing the overall feasibility and procedures of SDN orchestration for the end-to-endservice provisioning in multi-domain data center optical networks.

Non-hypergeometric Type of Polynomials and Solutions of Schrodinger Equation with Position-Dependent Mass

Using the coordinate transformation method, we study the polynomial solutions of the Schr6dinger equation with position-dependent mass （PDM）. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The issues related to normalization of the wavefunetions and Hermiticity of the Hamiltonian are also analyzed.

Active Error Compensating Welding Fixture System for Auto Body

The welding fixtures are the most important devices for an auto body welding assembly line. The current special fixtures used by many automotive manufactures are only fit for one or several specific welding processes, and the dimensional problem in the circle due to several variation sources accumulation has no adjustment. The active error compensating welding fixture system for auto body is designed and manufactured. The detecting model, coordinate transformation model, and adjusting model based on auto body coordinate system are presented. The dowel pin modular design is adopted in the structure of the fixture to suit different workpieces with some similar characteristics. The online detection and adaptive control system using eddy current sensors and adaptive adjusting devices is analyzed. Three kinds of the left rear wheel covers SGM60 are selected to test workpieces of the developed system, and the active error compensating experiments are performed in the lab for many times. Test results show the validity of mechanism reconfigurations, on-line detections and error compensations of the developed welding fixture.

SARC Model for Three-Dimensional Coordinate Transformation

In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The transformation procedure is divided into 4 steps: ① the original and object coordinates can be regarded as observations with errors; ② rigorous formula is firstly deduced in order to compute the first approximation of the transformation parameters by use of four common points and the transformation equation is linearized; ③ calculate the most probable values and variances of the seven transformation parameters by SARC model; ④ to demonstrate validity of SARC , an example is given.

A systematic strategy for multi-period heat exchanger network retrofit under multiple practical restrictions

A systematic strategy for retrofit of the multi-period heat exchanger network （HEN） on the basis of the multi- objective optimization is developed. In this three-stage procedure, a simplified multi-objective optimization model of the multi-period lIEN is first established and then solved to target the retrofit, aiming to minimizing the total annual cost and total annual CO2 emissions. The obtained Pareto front represents series of retrofit targets under different emission limitations, from which the most desirable one can be selected. The matching of the existing and the required heat exchangers is further implemented to finalize the retrofit, which will meet the practical retrofit requirements and matching restrictions. The application of the proposed procedure is illustrated through a case study of a HEN in a vacuum gas oil hydro-treating unit.

Kinematic modeling and analysis of novel eight-wheel lunar rover

A new kind of eight-wheel lunar rover is developed, which is a complex closed-chain system and has good capabilities of climbing slope, surmounting obstacles and adapting to uneven terrain. In this paper, the mechanical structure of the novel eight-wheel lunar rover is introduced, forward and inverse kinematic models of the rover are established according to the closed-chain coordinate transformation and instantaneous coincidence coordinate. Based on structural characteristics, its kinetic characteristics are analyzed. Wheel slippages are separated and calculated, and a method for closed-loop control modification using wheel slip estimation during the model establishment is proposed. The results can be applied to the motion control of lunar rover.

汉语的人称代词复数表示法

本文首先确定人称代词复数表示法的类型参项。然后对443个汉语方言的人称代词复数表示法进行归纳整理。现代汉语方言中使用的人称代词复数表示法共有4类24种复数表示法。用同样的方法来归纳44个少数民族语言,这些少数民族语言有3类9种复数表示法,没有汉语方言复杂。接下来本文讨论了汉语人称代词复数表示法中的一些问题。首先讨论的是人称代词复数表示法的出现顺序与山东方言中的"回头演变"现象。然后本文从认知-功能语言学的角度来讨论四种人称代词复数表示法的优劣,认为信息结构和信息编码的优势是增标法成为汉语人称代词复数表示法优势类型的主要原因。最后的"余论"简略地讨论了语言类型学应如何处理汉语这种方言复杂的方言,语言类型学的发展趋势及其与方言学、历史语言学的关系等问题。

Some Anzahl Theorems in Symmetric Matrices over Finite Local Rings (Ⅰ)

Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.

The seamless model for three-dimensional datum transformation

With extensive applications of space geodesy, three-dimensional datum transformation model has been necessarily used to transform the coordinates in the different coordinate systems.Its essence is to predict the coordinates of non-common points in the second coordinate system based on their coordinates in the first coordinate system and the coordinates of common points in two coordinate systems.Traditionally, the computation of seven transformation parameters and the transformation of noncommon points are individually implemented, in which the errors of coordinates are taken into account only in the second system although the coordinates in both two systems are inevitably contaminated by the random errors.Moreover, the coordinate errors of non-common points are disregarded when they are transformed using the solved transformation parameters.Here we propose the seamless (rigorous) datum transformation model to compute the transformation parameters and transform the non-common points integratively, considering the errors of all coordinates in both coordinate systems.As a result, a nonlinear coordinate transformation model is formulated.Based on the Gauss-Newton algorithm and the numerical characteristics of transformation parameters, two linear versions of the established nonlinear model are individually derived.Then the least-squares collocation (prediction) method is employed to trivially solve these linear models.Finally, the simulation experiment is carried out to demonstrate the performance and benefits of the presented method.The results show that the presented method can significantly improve the precision of the coordinate transformation, especially when the non-common points are strongly correlated with the common points used to compute the transformation parameters.

TGFβ signaling hyperactivation-induced tumorigenicity during the derivation of neural progenitors from mouse ESCs

Clinical therapies of pluripotent stem cells （PSCs）-based transplantation have been hindered by frequent development of terato- mas or tumors in animal models and clinical patients. Therefore, clarifying the mechanism of carcinogenesis in stem cell therapy is of great importance for reducing the risk of tumorigenicity. Here we differentiate Oct4-GFP mouse embryonic stem cells （mESCs） into neural progenitor cells （NPCs） and find that a minority of Oct4＋ cells are continuously sustained at Oct4＋ state. These cells can be enriched and proliferated in a standard ESC medium. Interestingly, the differentiation potential of these enriched cells is tightly restricted with much higher tumorigenic activity, which are thus defined as differentiation-resistant ESCs （DR-ESCs）. Transcriptomic and epigenomic analyses show that DR-ESCs are characterized by primordial germ cell-like gene sig- natures （Dazl, Rec8, Stro8, BUmp1, etc.） and specific epigenetic patterns distinct from mESCs. Moreover, the DR-ESCs possess germ cell potential to generate Sycp3＋ haploid cells and are able to reside in sperm-free spermaduct induced by busulfan. Finally, we find that TGFβ signaling is overactivated in DR-ESCs, and inhibition of TGFβ signaling eliminates the tumorigenicity of mESC-derived NPCs by inducing the full differentiation of DR-ESCs. These data demonstrate that these TGFβ-hyperactivated germ ceU-like DR-ESCs are the main contributor for the tumorigenicity of ESCs-derived target cell therapy and that inhibition of TGFβ signaling in ESC-derived NPC transplantation could drastically reduce the risk of tumor development. Keywords： embryonic stem cells, differentiation-resistant ESCs, tumorigenicity, germ cell, TGFβ signaling

Tracking with nonlinear measurement model by coordinate rotation transformation

A new filtering method is proposed to accurately estimate target state via decreasing the nonlinearity between radar polar measurements(or spherical measurements in three-dimensional(3D) radar) and target position in Cartesian coordinate. The degree of linearity is quantified here by utilizing correlation coefficient and Taylor series expansion. With the proposed method, the original measurements are converted from polar or spherical coordinate to a carefully chosen Cartesian coordinate system that is obtained by coordinate rotation transformation to maximize the linearity degree of the conversion function from polar/spherical to Cartesian coordinate. Then the target state is filtered along each axis of the chosen Cartesian coordinate. This method is compared with extended Kalman filter(EKF), Converted Measurement Kalman filter(CMKF), unscented Kalman filter(UKF) as well as Decoupled Converted Measurement Kalman filter(DECMKF). This new method provides highly accurate position and velocity with consistent estimation.