Form Of Spline Research Articles

Construction of programmed motion of manipulating robots in the form of fourth-order splines

A method is proposed for constructing programmed motion in the form of fourth-order splines. Expressions are obtained for locating the spline coefficients for certain boundary conditions having practical applications.

Spline-Based Adaptive Control of Distributed Parameter Systems

In this paper spline functions are used for designing an alternative - more practical - approach to modeling and to control of a class of continuous-time linear distributed parameter systems. The key step or submitted approach is the simultaneous spline approximation of both the signals and of the kernels of integral operator describing the system. This approximation under acceptable assumptions permits to create simple, finite-dimensi onal and parametric models easily lmplementabl e for adaptive control purposes. The control synthesis is based on the Integral continuous-time and continuous-space loss functional. Choosing suitable spline approximation the functional can be converted to the matrix quadratic form. The minimization is then performed via quadratic programming met hod. The control signals are continuous-time functions and are generated by the controller in the form of polynomial splines of defined dogree. The restrictions on amplitude and speed changes of the signals are introduced. The results of simulation experiments are given.

Polynomial splines and nonparametric regression

Let (X, Y) ∈ [0, 1]d × R be a random vector and let the conditional distribution of Y given X = x have mean θ(x) and satisfy an appropriate moment condition. It is assumed that the density function of X is bounded away from zero and infinity on [0, 1]d. Suppose that θ(x) is known to be a general d-dimensional smooth function of x only. Consider an estimator of θ having the form of a polynomial spline with simple knots at equally spaced grids over [0, 1]d where the coefficients are determined by the method of least-squares based on a random sample of size n from the distribution of (X, Y). It is shown that this estimator achieves the optimal rates of convergence for nonparametric regression estimation as defined in Stone [14] under L 2 norm and supnorm, respectively.

Analysis of rail track structures (ARTS)

The computer program ARTS for the static non-linear analysis (with or without allowing any element to take tension) of track structures is presented. The finite element method is used and a choice of hexahedronal, pentahedronal and beam elements is provided which can model non-homogeneous isotropic elastic material properties. The program allows the calculation of contact forces between two structures (i.e. the ground and the tie/rail system). There are two techniques for describing the material non-linearity. Triaxial test data for ballast or granular material may be processed in a cubical spline form to allow for variable Young's modulus and Poisson's ratio, or a hyperbolic model may be employed. This permits the program to take into account the ballasts' stress path dependence. Elements can be selected as permitted, or not, to take tension. If permitted to take tension then the stress-strain or Poisson's ratio-strain characteristics are identical in tension and compression. Initial elastic properties may be imposed or body and surcharge conditions may be input allowing the program to calculate initial stresses and thus properties. A sample analysis has been selected to demonstrate the general problem solving procedure and the input and output descriptions.

On approximation by splines of solution of boundary problem

For the boundary problem$$y'' + p(x) y' + q(x) y = r(x), \; y(a) = Y_a, \; y(b) = Y_b$$we give the approximate solution method of fourth order of accuracy in the form of cubic spline. For truncated problem ($p(x) \equiv 0$) we establish the prior estimates of error.

Statistical error analysis of electrode construction for electrostatic spline lenses

It is easy to calculate approximately the electrode shapes for a given axial potential distribution by neglecting its high-order derivatives. The lens with the electrodes determined this way has different optical properties than that with the original axial potential distribution. These differences were calculated for a large number of randomly generated samples with axial potential distributions in the form of cubic splines. The differences were found to be about ±5%–10% for the focal lengths and the chromatic aberration coefficients. The spherical aberration coefficients for the constructed electrode systems usually have smaller values than those of the original lens models, but the differences are larger. The conclusion is that this simple electrode construction method is usually accurate enough for practical lens design.