Generalized Galerkin Approximations for Pseudoinverses and Operator Equations of the First Kind

The main result of this paper is a basic theorem about generalized Galerkin approximations for pseudoinverses and operator equations of the first kind, which is presented as follows ：Let H be a Hilbert space, { Hn } a sequence of closed subspaces of H, Pn the orthogonal projection of H onto Hn, A∈B（H） and An∈B（Hn）. Suppose s-lim↑n→∞Hn=H, lim↑n→∞｜｜Pn°（A-An） ｜｜n=0,-↑R（An）=R（An）（n∈N）. Then the following four propositions are equivalent ： （a） sup↑n∈Nv∈An^-1 inf ｜｜υ｜｜〈∞ if un∈R（An） and lim↑n→∞un=0; （b） sup↑n∈N｜｜ An ｜｜ 〈∞; （c） if un∈R（An） and lim↑n→∞ un=u, then u∈R（A） and s-lim↑n→∞An^-1（un）=A^-1（u）; （d） if un∈R（An） and lim↑n→∞un=u.then u∈R（A） and lim↑n→∞Au^＋（un）=A^＋（u）. Furtherrnore, if any of the above propositions holds, we have thin N（A）=s-lim↑n→∞N（An ）,R（A） = s-lim↑n→∞R（An ）, -↑R（A） =R（A）.

Numerical Study on the Repeatability of 3R Planar Manipulators under Pseudoinverse Control

The repeatability and the drift properties for kinematically redundant manipulators under pseudoinverse control by simulation from th0e view of workspace is investigated. The conservative point and the conservative region are proposed, and the workspace of manipulator is divded into conservative region and non-conservative region. The repeatatility can be obtained if the closed path of the end effector is in the conservative region. The repeatability and properties of the drift for three DOF planar manipulator are studied under conditions of crank existence of four-bar linkage in mechanism,and some results are obtained by simnulaticn.

PSEUDOINVERSE DETERMINATION OF THE CIRCULATION IN PRYDZ BAY AND ITS ADJACENT OPEN OCEAN, ANTARCTICA

An inverse model is used to infer the circulation in Prydz Bay and its adjacent open ocean using hydrographic data obtained by the cruise of the 7th Chinese National Antarctic Research Expedition (CHINARE-7), 1990/91. Barotropic components are found to be strong in the study area, esp. at the Antarctic Divergence, and from a whole view, the velocity is rather small. In the open ocean, the flow is quasizonal, but outside the bay it shows a tendency of pressing onto the shelf from surface to bottom, and a feature of intensification just east of Fram Bank. We suggest here be the most important place to detect the possibility of the Antarctic Bottom Water formation. The meridional profiles of the distribution indicate a strong (relative to the ambient) core and a slope-trapped part into the bargain. In the southeastern part of the bay, there seems to exist a strong coastal current flowing westward. The computed upwelling centers are mainly situated in the west of the study region, as agrees quite well with the early hydrographic observations and the areas of high krill biomass.

ON STABLE PERTURBATIONS OF THE STIFFLY WEIGHTED PSEUDOINVERSE AND WEIGHTED LEAST SQUARES PROBLEM

In this paper we study perturbations of the stiffly weighted pseudoinverse （W^1/2 A）^＋W^1/2 and the related stiffly weighted least squares problem, where both the matrices A and W are given with W positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices A = A ＋ δA satisfy several row rank preserving conditions.

Unsupervised pseudoinverse hashing learning model for rare astronomical object retrieval

Searching for rare astronomical objects based on spectral data is similar to finding needles in a haystack owing to their rarity and the immense data volume gathered from large astronomical spectroscopic surveys.In this paper,we propose a novel automated approximate nearest neighbor search method based on unsupervised hashing learning for rare spectra retrieval.The proposed method employs a multilayer neural network using autoencoders as the local compact feature extractors.Autoencoders are trained with a non-gradient learning algorithm with graph Laplace regularization.This algorithm also simplifies the tuning of network architecture hyperparameters and the learning control hyperparameters.Meanwhile,the graph Laplace regularization can enhance the robustness by reducing the sensibility to noise.The proposed model is data-driven;thus,it can be viewed as a general-purpose retrieval model.The proposed model is evaluated in experiments and real-world applications where rare Otype stars and their subclass are retrieved from the dataset obtained from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope(Guo Shoujing Telescope).The experimental and application results show that the proposed model outperformed the baseline methods,demonstrating the effectiveness of the proposed method in rare spectra retrieval tasks.

A Principal Theorem of Generalized Galerkin's Schemes

In the present paper, the authors announce a newlyproved theorem of theirs. This theorem is of principal significance to numerical computation of solutions of variational equations.

A condition for the formation of Antarctic Bottom Water in Prydz Bay， Antarctica

Through Pseudoinverse inference of the circulation in Prydz Bay and its adjacent open ocean during January to March 1981, and comaing the results with that of 1991, we find that when the polar easterly hence the east wind drift is strong and extends its influence north of the slope, it is difficult for the Circumpolar Deep Water(CDW) to upweu onto the shelf, and congruently the Antarctic botom Water(AABW) cannot form in the bay by way of mixing scheme Of Forter and Carmack(1976). However, when the East Wind Drift weakens and confines itself over the shelf, the weSterly current will press on the slope and revolve anticyclonically so long as it is fairly strong. Such an anticyclonical Pattern manifests itseir mainly in the lower layer, and as a result, it will make the CDW upwell onto the shelf, providing an essential prerequisite for the formation of the AABW. We have analyzed this phenomenon from a dynamical view, and pointed out that the law of heat conduction accounts for its formation, in which the planetary and topographical beta effeCts play major roles.

2-D Conductor Cross Section Reconstruction via Amplitudes of Backscattered Field in Near Regions

In this paper, an improved approach is presented to reconstruct two dimensional conduc- tor profile illuminated by incident plane waves of multiple frequencies and directions via amplitudes of backscattered field in near regions. Newton-Kantorovitch algorithm is adopted to cast the non- linear coupled integral equations into linearized form, method of moment is used to transform the above linearized integral equations into matrix form, the resulting ill-posed overdetermined linear equations are solved using pseudoinverse technique based on Gram-Schedmit orthogonal procedure. Initial values are determined by solving a nonlinear least aquare error problem to establish an equivat lent circular cylinder. The effects of various parameters on reconstruction quality are discussed with numerical results and analysis.

A Principal Theorem of Normal Discretization Schemes for Operator Equations of the First Kind

The authors announce a newly-proved theorem of theirs. This theorem is of principal significance to numerical computation of operator equations of the first kind.

BALANCE ROUTING TRAFFIC IN GENERALIZED SHUFFLE-EXCHANGE NETWORK

A methodology is proposed to handle problem that under equiproble address of packet traffic at the input port, Generalized Shuffle-Exchange Network (GSEN) routes traffic unevenly because of the unbalanced routing tags. The idea is to use routing tag according to probability, which can be evaluated by using Moore-Penrose inverse in matrix analysis. An instance is used to illustrate the idea, and the simulation is done to show the improvement in performance issues.

A Modified Direct Allocation Algorithm with Application to Redundant Actuators

Control allocation considers the problem of controlling instruction distribution for control systems with multiple and redundant actuators. This paper focuses on the direct allocation method, making the time requirement of the algorithm analogous compared with modified pseudoinverse redistribution methods, linear programming methods solved by simplex method, and sub-gradient optimization method. To reduce off-line computations of constructing the attainable moment set of actuators, a new approach based on the null space of the control effectiveness matrix is proposed, which is superior when the number of actuators is less than 10 compared with traditional method. To decrease on-line computations, an improvement method of searching the facet that is aligned with the desired moment is presented, shortening the search time by checking only the facets that lie around the desired moment. To find such facets, the vertices of the attainable moment set are normalized and saved during off-line computations. Simulation results show that at least 32.22% of off-line computation time would be saved using null space-based construction when the number of actuators is less than 10. In on-line computations, the modified method performs superiorly compared with the three aforementioned methods. Furthermore, it may solve the problem of control allocation efficiently when a remarkable large number of redundant actuators are configured.

Input-Constrained Hybrid Control of a Hyper-Redundant Mobile Medical Manipulator

To reduce the risk of infection in medical personnel working in infectious-disease areas, we proposed ahyper-redundant mobile medical manipulator (HRMMM) to perform contact tasks in place of healthcare workers.A kinematics-based tracking algorithm was designed to obtain highly accurate pose tracking. A kinematic modelof the HRMMM was established and its global Jacobian matrix was deduced. An expression of the trackingerror based on the Rodrigues rotation formula was designed, and the relationship between tracking errors andgripper velocities was derived to ensure accurate object tracking. Considering the input constraints of the physicalsystem, a joint-constraint model of the HRMMM was established, and the variable-substitution method was usedto transform asymmetric constraints to symmetric constraints. All constraints were normalized by dividing bytheir maximum values. A hybrid controller based on pseudo-inverse (PI) and quadratic programming (QP) wasdesigned to satisfy the real-time motion-control requirements in medical events. The PI method was used whenthere was no input saturation, and the QP method was used when saturation occurred. A quadratic performanceindex was designed to ensure smooth switching between PI and QP. The simulation results showed that theHRMMM could approach the target pose with a smooth motion trajectory, while meeting different types of inputconstraints.

The Stability of Banach Frames in Banach Spaces

In this paper, we give some equivalent conditions on a Banach frame for a Banach space by using the pseudoinverse operator. We also consider the stability of a Banach frame for a Banach space X with respect to Xd or an Xd-frame for a Banach space X under perturbation. These results generalize and improve the related works of Balan, Casazza, Christensen, Stoeva and Jian et al.

Carrier Frequency Offset Compensation for an Interleaved OFDMA Uplink

This paper reports an investigation of the carrier frequency offset （CFO） compensation in the uplink of the orthogonal frequency division multiple access （OFDMA） system with interleaved subcarrier assignment. The presence of CFOs between the transmitters and the uplink receiver will destroy the orthogonality among the different subcarriers, resulting in inter-carrier interference and multiuser interference. This paper proposes a pseudoinverse CFO compensation method based on the signal structure. The proposed method can compensate the CFOs of all users simultaneously and isolate the signals from all users at the same time. Compared with the existing CFO compensation methods, the new method provides a considerable signal-to-noise ratio gain on the bit error rate performance and has a relatively low implementation complexity.