Controllability of an underactuated spacecraft with one thruster under disturbance

For an underactuated spacecraft using only one thruster, the attitude controllability with respect to the or- bit frame is studied in the presence of periodical oscillation disturbance, which provides a preconditional guide on de- signing control law for underactuated attitude control sys- tem. Firstly, attitude dynamic model was established for an underactuated spacecraft, and attitude motion was described using the special orthogonal group （SO （3））. Secondly, Liou- ville theorem was used to confirm that the flow generated by the drift vector of the underactuated attitude control system is volume-preserving. Furthermore, according to Poincar6＇s re- currence theorem, we draw conclusions that this drift field is weakly positively poisson stable （WPPS）. Thirdly, the suffi- cient and necessary condition of controllability was obtained on the basis of lie algebra rank condition （LARC）. Finally, the controllable conditions were analyzed and simulated in different cases of inertia matrix with the installed position of thruster.

Some properties of fuzzy positive implicative ideals in a BCK-algebras

In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.

LINEAR CONVERGENCE OF THE LZI ALGORITHM FOR WEAKLY POSITIVE TENSORS

We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim（LZI） algorithm for finding the largest eigenvalue of an irreducible nonnegative tensor, is established for weakly positive tensors. Numerical results are given to demonstrate linear convergence of the LZI algorithm for weakly positive tensors.

A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images

A small and weak target detection method is proposed in this work that outperforms all other methods in terms of real-time capability.It is the first time that two-dimensional(2D)images are processed using only one-dimensional1D structuring elements in a morphology-based approach,enabling the real-time hardware implementation of the whole image processing method.A parallel image readout and processing structure is introduced to achieve an ultra-low latency time on the order of nanoseconds,and a hyper-frame resolution in the time domain can be achieved by combining the row-by-row structure and the electrical rolling shutter technique.Experimental results suggest that the expected target can be successfully detected under various interferences with an accuracy of 0.1 pixels(1σ)under the worst sky night test condition and that a centroiding precision of better than 0.03 pixels(1σ)can be reached for static tests.The real-time detection method with high robustness and accuracy is attractive for application to all types of real-time small target detection systems,such as medical imaging,infrared surveillance,and target measurement and tracking,where an ultra-high processing speed is required.

Sobolev type embedding and weak solutions with a prescribed singular set

New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.

Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds

In this paper,the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation△_(p)u+au^(σ)=0 on complete noncompact Riemannian manifold,where a,σare two nonzero real constants with p≠2.Using the gradient estimate,they can get the corresponding Lionville theorem.On the other hand,by virtue of the Poincare inequality,they also obtain a Liouville theorem under some integral conditions with respect to positive weak solutions.

Embeddings of weighted Sobolev spaces and degenerate elliptic problems

New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.

Mathematical Analysis of a Chemotaxis-Type Model of Soil Carbon Dynamic

The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a chemotactic term, with the aim to account for the formation of soil aggregations in the bacterial and microorganism spatial organization(hot spot in soil). This is a spatial and chemotactic version of MOMOS(Modelling Organic changes by Micro-Organisms of Soil), a model recently introduced by M. Pansu and his group. The authors present here two forms of chemotactic terms, first a"classical" one and second a function which prevents the overcrowding of microorganisms.They prove in each case the existence of a nonnegative global solution, and investigate its uniqueness and the existence of a global attractor for all the solutions.