Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method

The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix.In this way,joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given.Compared with the general Newton iterative method,the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration.So the convergence domain is bigger than that of the general Newton iterative method.Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector.The inverse displacement analysis of the general 6R(six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random,the method can be applied to any other types of serial robots.

Pressure-Controlled Inverse Ratio Ventilation during General Anesthesia for Open Abdominal Surgery Improves Postoperative Pulmonary Function

Background: Studies have shown that pressure-controlled ventilation improves alveolar gas distribution. And inverse ratio ventilation has advantages of improving oxygenation in acute respiratory distress syndrome (ARDS) patients. However, the effects that pressure-controlled inverse ration ventilation in patients undergoes endotracheal intubation general anesthesia have not been assessed. Objective: To investigate whether pressure-controlled inverse ratio ventilation (PIV) would improve ventilatory and oxygenation parameters as well as lung function compared to conventional ventilation in patients undergoing open abdominal surgery. Interventions: In the conventional ventilation (CV) group, the ventilation strategy involved zero end-expiratory pressure and volume-controlled ventilation. In the pressure-controlled inverse ratio ventilation (PIV) group, the strategy involved P high starting at 7 cm H2O, P low starting at 4 cm H2O, T high at 4 s, T low at 2 s, and an inspiratory-to-expiratory time ratio of 2:1. The ΔP value was adjusted according to VT. Pressure levels were increased by 2 cm H2O until a maximal VT was observed. Inspired oxygen fraction (FIO2) was 1.0 and tidal volume (VT) was 6 mL/kg in both groups. Main Outcome Measures: The primary outcome is pulmonary function tests. Hemodynamic, ventilatory and oxygenation parameters were measured;visual analog scale (VAS) scores, and nausea and vomiting scores were also measured. Results: The PIV group tolerated pressure-controlled inverse ratio ventilation without significant hemodynamic instability. Mean airway pressure and static compliance were significantly higher in the PIV group than those in CV group (P P 2 h was well tolerated and improved respiratory compliance and lung function on the first postoperative day.

Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory

In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.

L^p APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX

As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.

General inverse of Stokes, Vening-Meinesz and Molodensky formulae

The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes’ formula, the general inverse Vening-Meinesz formula and the general Molodensky’s formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degen- erated into the classic ones.

Generalized inverses of tensors via a general product of tensors

We define the {i}-inverse （i = 1,2, 5） and group inverse of tensors based on a general product of tensors. We explore properties of the generalized inverses of tensors on solving tensor equations and computing formulas of block tensors. We use the {1}-inverse of tensors to give the solutions of a multilinear system represented by tensors. The representations for the {1}-inverse and group inverse of some block tensors are established.

INVERSE SCATTERING PROBLEM FOR ONE-DIMENSIONAL SCHRDINGER OPERATORS RELATED TO THE GENERAL STARK EFFECT

This paper disccusses the inverse scattering problem for one-dimensional Schrodinger operatorsrelated to the general Stark effect. We provide a ganeral framework which can be applied both to theStark-effect operator and the ordinary Schrodinger operator.

Improved Algorithms for Flush Airdata Sensing System

The Flush Airdata Sensing （FADS） system and its pressure model are presented briefly. The improved algorithm for calculating the impact pressure, static pressure and modifying coefficient are studied. First, the non-linear equations are simplified using Moore-Penrose inverse. Then the impact pressure and static pressure are computed with the improved iteration and BP neural network. Both the two improved algorithms meet the requirements of the flush airdata sensing system on precision, reliability and speed. BP neural network has great advantages on real-time requirements, for it needs only 5% time to reach the required precision comparing to the original algorithm.

Noether Theorem and Its Inverse Theorem in Canonical Formalism for Nonholonomic Nonconservative Singular System

Classical Noether theorem and its generalization are given in configuration space and expressed in terms of Lagrange variables. The Noether Theorems 1, 2 in phase space for holonomic singluar system (of which the Lagrangian function is singular) are discussed, Here the Noether theorem and its inverse theorem in canonical formalism for nonholonomic nonconservative singular system are further investigated. Consider a nonholonomic nonconservative system whose motion is described in

A FURTHER GENERALIZATION OF THE MODIFIED MBIUS INVERSION FORMULA

Ⅰ. INTRODUCTIONThe Mbius inversion formula in number theory has been modified recently by Chen to account for the continuous variables such

CRITERION OF POSITIVE DEFINITENESS OF MATRICES AND SOLUTION OF INVERSE PROBLEM FOR SYSTEM OF LINEAR EQUATIONS

The class of symmetric definitely positive matrices is extremely important in the matrix theory. At present, positive definiteness of a symmetric matrix can be shown by determining the signs of its all ordered principal minors or the signs

The least squares problem of the matrix equation A_1X_1B_1~T+A_2X_2B_2~T=T

The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.

REESSE Unified Recursive Algorithm for Solving Three Computational Problems

Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is designed by the authors, which can not only seek directly the multiplicative inverse and the greatest common divisor, but also solve directly a simple congruence for general solutions. This paper presents the definition and the two valuable properties of a simple congruence, analyzes in detail the reduction and recursion process of solving simple congruences, induces the recursive formula for solving simple congruences, and describes formally and implements in C language the recursive algorithm. At last, the paper compares REESSE with the extended Euclidean algorithm in thought, applicability and time complexity.

The Boundedness of Nonlinear Control Systems

In this paper we consider nonlinear control sysfemdx/dt=A（t）x+B（t）f（x）,（1）Where x（t）∈Rn is the state vector,A（t）=(aij（t）)n×nis the System matrix,B（t）,an nxr time-varying matrix,is the input matrix;f（x）∈Rr is nonlinearvector function,and A（t）,B（t）∈c[t0,∞),f（x）∈c[x0,∞)Here we are to discuss thc boundedness of system（1）in various cases ofmatrix A（t）,and the following results shall be obtained.In this paper,weshall use the results of Bihari and other authors.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the General Linear Model

In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.

AN INDIRECT METHOD FOR DETERMINATION OF PARAMETERS IN THE FORECAST MODEL

An indirect method for determining some parameters in a forecast model has been developed, by which the program of the original model with little modification can be used as a subroutine of the inversion system and the optimum estimate of the parameters can be obtained by calling the subroutine time after time. It is specially useful for the sophisticated numerical weather prediction model. It may also be utilized to improve the forecast timely in case of obvious differences between the recent observations and the forecasts. The effect of the method is verified by numerical simulation tests with simple models.

Reducible solution to a quaternion tensor equation

We establish necessary and sufficient conditions for the existence of the reducible solution to the quaternion tensor equation A*N C*NB=C via Einstein product using Moore-Penrose inverse,and present an expression of the reducible solution to the equation when it is solvable.Moreover,to have a general solution,we give the solvability conditions for the quaternion tensor equation A1*N C1*MB1+a1*C2*MB2+A2*NC3*MB2=e,which plays a key role in investigating the reducible solution to A*NC*NB=e.The expression of such a solution is also presented when the consistency conditions are met.In addition,we show a numerical example to illustrate this result.

Fractional Fourier transform on R^(2)and an application

We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.

GPGPU Accelerated Fast Convolution Back-Projection for Radar Image Reconstruction

This paper describes a parallel fast convolution back-projection algorithm design for radar image reconstruction. State-of-the-art general purpose graphic processing units （GPGPU） were utilized to accelerate the processing. The implementation achieves much better performance than conventional processing systems, with a speedup of more than 890 times on NVIDIA Tesla C1060 supercomputing cards compared to an Intel P4 2.4 GHz CPU. 256×256 pixel images could be reconstructed within 6.3 s, which makes real-time imaging possible. Six platforms were tested and compared. The results show that the GPGPU super-computing system has great potential for radar image processing.