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[en] A method of determining the spectral shape of background radiation present in experimental spectra via a mathematical approach is presented. Elements of interest will be subtracted from an experimental spectrum using the linear correlation coefficient across a characteristic peak to determine their contribution. Once all elements of interest are removed, the remainder of the experimental spectrum should represent an approximation of the background. This approximation can then be used in conjunction with library least-squares to determine the background and elemental contributions to the unknown spectrum. - Highlights: • An approach for determining the background radiation spectral library is proposed. • The libraries of isotopes of interest will be subtracted from the unknown spectrum. • The linear correlation coefficient was used as a metric for this subtraction. • The background library was then used in a LLS fit to determine spectral contribution.
[en] This paper examines four variants of the weighted least squares (WLS) method used for decomposing spectra from channel counts of a Poisson distribution by estimating the bias of the channel counts by Monte Carlo method. It is shown that one of the modified methods yields the least bias. (author)
[en] The problem of adaptive estimates according to correlated observations is discussed. Investigation into adaptive procedure of estimation using the least square fir (LSF) while applying the dependent observations is conducted. Theorem on the LSF estimate consistency is proved. 3 refs
[en] User influence is generally considered as one of the most critical factors that affect information cascading spreading. Based on this common assumption, this paper proposes a theoretical model to examine user influence on the information multi-step communication in a micro-blog. The multi-steps of information communication are divided into first-step and non-first-step, and user influence is classified into five dimensions. Actual data from the Sina micro-blog is collected to construct the model by means of an approach based on structural equations that uses the Partial Least Squares (PLS) technique. Our experimental results indicate that the dimensions of the number of fans and their authority significantly impact the information of first-step communication. Leader rank has a positive impact on both first-step and non-first-step communication. Moreover, global centrality and weight of friends are positively related to the information non-first-step communication, but authority is found to have much less relation to it
[en] The paper illustrates and discusses some problems that should be taken into account, should the proposed use of fundamental constants in the definition of measurement units of the SI be implemented: (a) more base units being multi-dimensional, instead of fixing the present problems in this respect; (b) the multidimensionality in the definitions; (c) the use of CODATA adjusted values of the constants for this specific purpose; (d) formal issues in stipulating algebraic expressions of the definitions, and in respect to the rounding or truncation of the numerical values in their transformation from uncertain to exact values; (e) formal issues with the use of the integer number NA; (f) limitations that can arise from the stipulation of the values of several constants for the CODATA Task Group to continue performing in future meaningful least squares adjustments of the fundamental constants taking into account future data
[en] In this paper, we propose some new preconditioned GAOR methods for solving weighted linear least squares problems and discuss their comparison results. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Shen et al. (Appl Math Mech Engl Ed 33(3):375–384, 2012) and Wang et al. (J Appl Math, doi: 10.1155/2012/563586 , 2012) whenever these methods are convergent. Finally, numerical experiments are provided to confirm the theoretical results obtained in this paper.
[en] The 1973 CODATA-recommended values of the fundamental constants are listed. The basis for the least-squares analysis and some of its shortcomings are discussed. Although significant modifications of some of these numbers may be indicated by more recent experimental results, the tabulation should prove useful to the general user since it provides an identifiable set of values which are internally consistent to a precision of better than 0.1 part per million. 4 tables
[en] The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the POTFIT approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.