Convergence theory of extrapolated iterative methods for a certain class of non-symmetric linear systems

Summary A variety of iterative methods considered in [3] are applied to linear algebraic systems of the formAu=b, where the matrixA is consistently ordered [12] and the iteration matrix of the Jacobi method is skew-symmetric. The related theory of convergence is developed and the optimum values of the involved parameters for each considered scheme are determined. It reveals that under the aforementioned assumptions the Extrapolated Successive Underrelaxation method attains a rate of convergence which is clearly superior over the Successive Underrelaxation method [5] when the Jacobi iteration matrix is non-singular.     

The effect of transverse shear onto the singular solutions of a complete spherical shell

Green's functions for the field variables of a complete sphere subjected to normal surface traction are obtained with “free space” properties. Further, self-equilibrated singular solutions of the variables associated with tangentially applied point loads and concentrated surface moments are constructed. The solution formulae are derived within the framework of the improved theory of thin shells and thus incorporate the effect of transverse shear in the equilibrium of the shell element. Despite the complex character of the solution, expressed in terms of complex Legendre functions, the closed form of it reveals the effects of the new assumptions (presence of shear strains) onto the singular behavior of the associated kernels. Numerical results for the field variables demonstrate the differences between the two theories, classical and improved.     

Neue Additionsverbindungen von Germaniumtetrajodid mit organischen Basen

Four new stable addition compounds have been prepared by reaction of germanium tetraiodide with various tertiary amines. It is a case of adducts of 1:4 composition, in contrast to the 1:5 addition compound with triethylamine, which we have also prepared and investigated for comparison. Formation, properties, analytical results, conductometric measurements and spectral data (IR and¹H-NMR) of these adducts are described and discussed in terms of possible structural types and the nature of the bonding.

     

On the existence of weakly maximal optimal stationary programs for an infinite dimensional growth model

In this paper we consider a discrete-time, infinite horizon growth model for a multisector economy with an infinite dimensional commodity space, and we establish the existence of a weakly maximal optimal stationary program.     

The impact of special days in call arrivals forecasting: A neural network approach to modelling special days

A key challenge for call centres remains the forecasting of high frequency call arrivals collected in hourly or shorter time buckets. In addition to the complex intraday, intraweek and intrayear seasonal cycles, call arrival data typically contain a large number of anomalous days, driven by the occurrence of holidays, special events, promotional activities and system failures. This study evaluates the use of a variety of univariate time series forecasting methods for forecasting intraday call arrivals in the presence of such outliers. Apart from established, statistical methods, we consider artificial neural networks (ANNs). Based on the modelling flexibility of the latter, we introduce and evaluate different methods to encode the outlying periods. Using intraday arrival series from a call centre operated by one of Europe’s leading entertainment companies, we provide new insights on the impact of outliers on the performance of established forecasting methods. Results show that ANNs forecast call centre data accurately, and are capable of modelling complex outliers using relatively simple outlier modelling approaches. We argue that the relative complexity of ANNs over standard statistical models is offset by the simplicity of coding multiple and unknown effects during outlying periods.     

An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver

Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can be relaxed in various ways, including via mixed-integer linear programming (MIP), nonlinear programming, and linear programming. There is a tradeoff between the quality of the bounds and CPU time requirements of these relaxations. Unfortunately, these tradeoffs are problem-dependent and cannot be predicted beforehand. This paper proposes a new dynamic strategy for activating and deactivating MIP relaxations in various stages of a branch-and-bound algorithm. The primary contribution of the proposed strategy is that it does not use meta-parameters, thus avoiding parameter tuning. Additionally, this paper proposes a strategy that capitalizes on the availability of parallel MIP solver technology to exploit multicore computing hardware while solving MINLPs. Computational tests for various benchmark libraries reveal that our MIP activation strategy works efficiently in single-core and multicore environments.     

Existence and multiplicity of solutions for asymptotically linear, noncoercive elliptic equations

First we prove the existence of a nontrivial smooth solution for a p-Laplacian equation with a (p − 1)-linear nonlinearity and a noncoercive Euler functional, under hypotheses including resonant problems with respect to the principal eigenvalue of (-D_p, W^1,p₀(Z)){(-{\it \Delta}_p,\,W^{1,p}_0(Z))} . Then, for the semilinear problem (i.e., p = 2), assuming nonuniform nonresonance at infinity and zero, we prove a multiplicity theorem which provides the existence of at least three nontrivial solutions, two being of opposite constant sign. Our approach combines minimax techniques with Morse theory and truncation arguments.