Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Development of Light Weight Structures to Provide Blast-Resistant Designs

In the past, blast-resistant designs for structures were often constructed with massive type structural systems, which relied more on brute strength than on finesse to achieve the required blast resistance. However, structures composed of COLD-FORMED steel components, such as sheet metal and metal studs, have shown great promise in providing blast resistance with the added benefits of low cost and ease of construction. Some examples of using such structures to provide containment for package handling facilities (PHF) are described in the paper for situations where blast containment is needed, such as a potential package bomb being discovered during the package vetting process. Results from tests and analytic data are used to illustrate aspects of design peculiar to such types of applications. Designs for specific capacities of PHF are described.

Contour tracking using weighted structure tensor based variational level set

A novel contour tracking method using weighted structure tensor based variational level set is proposed in this paper.The image is first converted to weighted structure tensor field by extracting apositive definite symmetric covariance matrix for each pixel.Then,a level set method is employed to represent object contour implicitly which separates the image domain into two areas each modeled by tensor field based Gaussian mixture model separately.By solving agradient flow equation of energy functional with respect to the level set,the object contour will converge to its real profile in the newly arrived frame.Experimental results on several video sequences demonstrate the better performance of our method than the other two contour tracking algorithms.

Fuzzy Earthwork Dynamic Allocation and Optimization for Construction of High Concrete Face Rockfill Dam

Due to the complexity of earthwork allocation system for the construction of high concrete face rockfill dam,traditional allocation and planning are not able to function properly in the construction process with strong randomness.In this paper,the working mechanism of earthwork dynamic allocation system is analyzed comprehensively and a solution to fuzzy earthwork dynamic allocation is proposed on the basis of uncertain factors in the earthwork allocation of a hydropower project.Under the premise of actual situation and the experience of the construction site,an all-coefficient-fuzzy linear programming mathematical model with fuzzy parameters and constraints for earthwork allocation is established according to the structure unit weighted ranking criteria.In this way,the deficiency of certain allocation model can be overcome.The application results indicate that the proposed method is more rational compared with traditional earthwork allocation.

Structural Stability of Weighted Digraph with Continuous Vertex Values

In this paper, we give a sufficient condition about the stability of weighted digraph, which exceeds Roberts original judgement extremely.

EFFECT OF TOXIC METAL ON THE STRUCTURAL DRY WEIGHT OF A PLANT： A MODEL

A two compartment mathematical model for the individual plant growth under the stress of toxic metal is studied. In the model it is assumed that the uptake of toxic metal by the plant is through root compartment. The toxic metal present in the soil interfere with the uptake and distribution of essential nutrients in plant causing decrease in the nutri- ent uptake eventually damaging the root structure. In the model it is further assumed that the resistance to nutrient transport from root to shoot compartment increases and nutrient use efficiency decreases due to the presence of toxic metal. In order to visualize the effect of toxic metal on plant growth, we have studied two models, that is, model for plant growth with no toxic effect and model for plant growth with toxic effect. From the analysis of the models the criteria for plant growth with and without toxic effects are derived. The numerical simulation is done using Matlab to support the analytical results.

Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

The Sasaki–Ricci Flow on Sasakian 3-Spheres

We show that on a Sasakian 3-sphere the Sasaki-Ricci flow initiating from a Sasakian metric of positive transverse scalar curvature converges to a gradient Sasaki-Ricci soliton.We also show the existence and uniqueness of gradient Sasaki-Ricci soliton on each Sasakian 3-sphere.