We estimate the order of weighted approximations of functions and their derivatives by using the means of mixed series of Legendre polynomials. As the main result, we obtain estimates of the order of approximation of ...
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We estimate the order of weighted approximations of functions and their derivatives by using the means of mixed series of Legendre polynomials. As the main result, we obtain estimates of the order of approximation of a function and its derivatives by the Valle-Poussin means and their derivatives.
In this paper, by a new concept and method we shall give practical and numerical solutions of linear singular integral equations by combining the two theories of the Tikhonov regularization and reproducing kernels.
In this paper, by a new concept and method we shall give practical and numerical solutions of linear singular integral equations by combining the two theories of the Tikhonov regularization and reproducing kernels.
In the paper, the problem of uniform approximation of a continuous function defined on an interval is considered. The approximating functions have absolutely continuous derivatives of order (n - 1) and derivatives of ...
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In the paper, the problem of uniform approximation of a continuous function defined on an interval is considered. The approximating functions have absolutely continuous derivatives of order (n - 1) and derivatives of order n bounded in absolute value. An alternance criterion for a best approximation element in this class is given. This criterion generalizes the criterion for the best approximation element obtained by N. P. Korneichuk in the class of Lipschitz functions.
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently larg...
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We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes. Moreover, patterning process can be performed by an effective algorithm. We also show that Turing's or Meinhardt's type reaction-diffusion models can be approximated by genetic networks. These results exploit the fundamental fact that the genes form functional units and are organized in blocks. Due to this modular organization, the genes always are capable to construct any new patterns and even any time sequences of new patterns from old patterns. Computer simulations illustrate some analytical results. Copyright (c) 2005 John Wiley & Sons, Ltd.
The aim of this paper is the analysis of the bias contained in star catalogues, these errors can be obtained by means of kinematics or dynamical methods. In this paper a general method, suitable when the sample is not...
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The aim of this paper is the analysis of the bias contained in star catalogues, these errors can be obtained by means of kinematics or dynamical methods. In this paper a general method, suitable when the sample is not homogeneous is presented.
We shall discuss the relations among sampling theory (Sinc method), reproducing kernels and the Tikhonov regularization. Here, we see the important difference of the Sobolev Hilbert spaces and the Paley–Wiener spaces...
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Let B be a convex polytope in the d-dimensional Euclidean space. We consider an interpolation of a function f at the vertices of B and compare it with the interpolation of f and its derivative at a fixed point y is an...
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Let B be a convex polytope in the d-dimensional Euclidean space. We consider an interpolation of a function f at the vertices of B and compare it with the interpolation of f and its derivative at a fixed point y is an element of B. The two methods may be seen as multivariate analogues of an interpolation by secants and tangents, respectively. For twice continuously differentiable functions, we establish sharp error estimates with respect to a generalized L-p norm for 1 <= p <= infinity. The case p = 1 is of special interest since it provides analogues of the midpoint rule and the trapezoidal rule for approximate integration over the polytope P. In the case where P is a simplex and p > 1, this investigation covers recent results by S. Waldron [SIAM J. Numer. Anal., 35 (1998), pp. 1191-1200] and by M. Stampfle [J. Approx. Theory, 103 (2000), pp. 78-90].
In this article we shall give practical and numerical solutions of the Laplace equation on multidimensional spaces and show the numerical experiments by using computers. Our method is based on the Dirichlet principle ...
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We shall give very and surprisingly simple approximate real inversion formulas of the Gaussian convolution (the Weierstrass transform) for the first-order Sobolev Hilbert space on the whole real line by using best app...
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