Long periods of regular astronomical latitude-longitude measurements on observatories participating in determination of Earth´s rotation parameters are frequently used for estimation of corrections to star catalogue mean places and proper motions. The proposed method is the extension and generalization of the usually exploited chain method. It is possible to estimate simultaneously the corrections of declinations and right ascensions for instruments which determine both latitude and longitude. Additional unknowns - amplitudes of short-periodic terms (e.g. corrections to nutation amplitudes, tidal variations, nearly diurnal polar motion, instrumental parameters and refraction anomalies) can be included into total adjustment. It is not necessary to fulfil the condition of closing the chain. The constraint for unknown parameters is the minimum of choosen guadratic form. The problem is solved by using the theory of generalized inverse of matrices. The method is demonstrated on determination of the right ascension corrections from observations with visual transit instrument. Another applications of proposed method are outlined.
In the current work, a new notion of n-weak amenability of Banach algebras using homomorphisms, namely (ϕ, ψ)-n-weak amenability is introduced. Among many other things, some relations between (ϕ, ψ)-n-weak amenability of a Banach algebra A and Mm(A), the Banach algebra of m × m matrices with entries from A, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra L 1 (G) is (ϕ, ψ)-n-weakly amenable for any bounded homomorphisms ϕ and ψ on L 1 (G).
In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as "hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.
We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.
Let $\Omega$ be a bounded open subset of $\mathbb{R}^{n}$, $n>2$. In $\Omega$ we deduce the global differentiability result \[u \in H^{2}(\Omega, \mathbb{R}^{N}) \] for the solutions $u \in H^{1}(\Omega, \mathbb{R}^{n})$ of the Dirichlet problem \[ u-g \in H^{1}_{0}(\Omega, \mathbb{R}^{N}), -\sum _{i}D_{i}a^{i}(x,u,Du)=B_{0}(x,u,Du) \] with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems.
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.
There are several ways that can be implemented in a vehicle tracking system such as recognizing a vehicle color, a shape or a vehicle plate itself. In this paper, we will concentrate ourselves on recognizing a vehicle on a highway through vehicle plate recognition. Generally, recognizing a vehicle plate for a toll-gate system or parking system is easier than recognizing a car plate for the highway system. There are many cameras installed on the highway to capture images and every camera has different angles of images. As a result, the images are captured under varied imaging conditions and not focusing on the vehicle itself. Therefore, we need a system that is able to recognize the object first. However, such a system consumes a large amount of time to complete the whole process. To overcome this drawback, we installed this process with grid computing as a solution. At the end of this paper, we will discuss our obtained result from an experiment.
The split graph $K_r+\overline {K_s}$ on $r+s$ vertices is denoted by $S_{r,s}$. A non-increasing sequence $\pi =(d_1,d_2,\ldots ,d_n)$ of nonnegative integers is said to be potentially $S_{r,s}$-graphic if there exists a realization of $\pi $ containing $S_{r,s}$ as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for $\pi $ to be potentially $S_{r,s}$-graphic. They are extensions of two theorems due to A. R. Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series 4 (1979), 251–267 and An Erdős-Gallai type result on the clique number of a realization of a degree sequence, unpublished).