The LBL factorization of Bunch for solving linear systems involving a symmetric indefinite tridiagonal matrix T is a stable, efficient method. It computes a unit lower triangular matrix L and a block 1×1 and 2×2 matrix B such that T = LBL . Choosing the pivot size requires knowing a priori the largest element σ of T in magnitude. In some applications, it is required to factor T as it is formed ...

The editing software used by the Economic Census offers a variety of imputation options, many of which employ statistical models. In prior censuses, the services sectors portion of the Economic Census has relied on industry average imputation as its primary statistical imputation model. This ratio imputation method uses weighted least squares estimates for no-intercept simple linear regression ...

We investigate the Mg–σ and –σ relations in a sample of 72 early-type galaxies drawn mostly from cluster and group environments using a homogeneous data-set which is well-calibrated onto the Lick/IDS system. The small intrinsic scatter in Mg at a given σ gives upper limits on the spread in age and metallicity of 49% and 32% respectively, if the spread is attributed to one quantity only and ...

A component-based approach is introduced for fast and flexible solution of parameter-dependent symmetric eigenproblems. Considering a generalized eigenproblem with symmetric stiffness and mass operators, we start by introducing a “σ-shifted” eigenproblem where the left hand side operator corresponds to an equilibrium between the stiffness operator and a weighted mass operator, with weight-param...

We consider the network dynamics of the soft consensus model and we investigate the dynamical behavior of two important measures of network structure, complexity and modularity. The dynamical mechanism of the soft consensus model is driven by the minimization of a cost function combining a collective measure of dissensus with an individual mechanism of opinion changing aversion. The dissensus m...

in this study, the role of interaction of pi electrons on the strength of simultaneous σ-hole interactions (pnicogen, chalcogen and halogen bonds) is investigated using the quantum chemical calculations. x-ben||taz∙∙∙y1,y2,y3 complexes (x = cn, f, cl, br, ch3 , oh and nh2, taz= s-triazine and y1,y2 and y3 denotes ph2f, hsf, and clf molecules) is introduced as a model. the results show that inte...

Several identities for the Riemann zeta-function ζ(s) are proved. For example, if s = σ + it and σ > 0, then ∞ −∞ (1 − 2 1−s)ζ(s) s 2 dt = π σ (1 − 2 1−2σ)ζ(2σ). Let as usual ζ(s) = ∞ n=1 n −s (ℜe s > 1) denote the Riemann zeta-function. The motivation for this note is the quest to evaluate explicitly integrals of |ζ(1 2 + it)| 2k , k ∈ N, weighted by suitable functions. In particular, the prob...

We introduce a new model of weighted automata: the desert automata. We show the decidability of the limitedness problem for desert automata by solving the underlying Burnside problem. As an application of this result, we give a positive solution to the so-called finite substitution problem which was open for more than 10 years: given recognizable languages K and L, decide whether there exists a...

We study the problem of minimizing the weighted number of late jobs to be scheduled on a single machine when processing times are equal. In this paper, we show that this problem, as well as its preemptive variant, are both strongly polynomial. When preemption is not allowed 1 | pj = p, rj | Σ wj Uj, the problem can be solved in O(n). In the preemptive case, 1 | pj = p, pmtn, rj | Σ wj Uj, the p...

The standard MR protocol of the spine included sagittal T1weighted and T2-weighted fast spin echo. Volume measurements are made by using a transparent template to overlay a grid of regularly spaced points over MRI scans of randomly selected patients (Figure 1). This point is counted as the full contact of the counter. Counts are made three times. The double or middle number is used. The volume ...