Results 1 - 10 of 5869
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[en] The integral is calculated and the system of orthogonal polynomials with weight equal to the corresponding integrand is constructed. This weight decreases polynomially, therefore only finitely many of its moments converge. As a result the system of orthogonal polynomials is finite. Systems of orthogonal polynomials related to 5H5-Dougall's formula and the Askey integral is also constructed. All the three systems consist of Wilson polynomials outside the domain of positiveness of the usual weight
[en] The paper suggests a general approach to deriving upper bounds for the spectral radii of weighted digraphs. The approach is based on the generalized Wielandt lemma (GWL), which reduces the problem of bounding the spectral radius of a given block matrix to bounding the Perron root of the matrix composed of the norms of the blocks. In the case of the adjacency matrix of weighted graphs and digraphs where all the blocks are square positive (semi)definite matrices of the same order, the GWL takes an especially nice simple form. The second component of the approach consists in applying known upper bounds for the Perron root of a nonnegative matrix. It is shown that the approach suggested covers, in particular, the known upper bounds of the spectral radius and allows one to describe the equality cases.
[en] In low-level radioanalysis it is usually necessary to test the sample net counts against some ''Critical Level'' in order to determine if a given result indicates detection. This is an interpretive review of the work by Nicholson (1963), Currie (1968) and Gilbert (1974). Nicholson's evaluation of three different computational formulas for estimation of the ''Critical Level'' is discussed. The details of Nicholson's evaluation are presented along with a basic discussion of the testing procedures used. Recommendations are presented for calculation of confidence intervals, for reporting of analytical results, and for extension of the derived formula to more complex cases such as multiple background counts, multiple use of a single background count, and gamma spectrometric analysis
[en] In this study, stability conditions of receding horizon control (RHC) based on a horizon size are proposed for linear discrete systems. The proposed stability conditions present a relevant horizon size which can guarantee the stability of RHC even though a final state weighting matrix does not satisfy non-increasing monotonicity of optimal cost. Therefore, the possible range of the final state weighting matrix ensuring the stability of RHC is extended to zero and also it can be applied to the stability problems of other forms of model predictive control like the conventional stability conditions
[en] One of the control techniques that could replace the present conventional PID controllers in nuclear plants is the linear quadratic regulator (LQR) method. The most attractive feature of the LQR method is that it can provide the systematic environments for the control design. However, the LQR approach heavily depends on the selection of cost function and the determination of the suitable weighting matrices of cost function is not an easy task, particularly when the system order is high. The purpose of this paper is to develop an efficient and reliable algorithm that could optimize the weighting matrices of the LQR system
[en] Let D be the unit disc in the complex plane C and H a class of holomorphic functions in D distinguished by a restriction on their growth in a neighbourhood of the boundary of the disc which is stated in terms of weight functions of moderate growth. Some results which describe the sequences of zeros for holomorphic functions in classes H of this type are obtained. The weight functions defining H are not necessarily radial; however the results obtained are new even in the case of radial constraints. Conditions for meromorphic functions in D ensuring that they can be represented as a ratio of two functions in H sharing no zeros are investigated. Bibliography: 28 titles.