On maximum norm contractivity of second order damped single step methods

In this paper we consider A(θ)-stable finite difference methods for numerical solutions of dissipative partial differential equations of parabolic type. Combining two rational approximation methods with different orders of accuracy, where the lower order method is applied n ₀ times (n ₀ fixed) at each time step, we prove the existence of a second order method which is contractive for all time steps. Moreover, we shed light on the conditions on the lower order method which are sufficient (and sometimes necessary) to obtain the optimal order of accuracy. For the one-dimensional heat equation we construct a family of numerical methods which are contractive in the maximum norm for all values of the discretization parameters. We also present numerical examples to illustrate our results. Received: May 2002 / Accepted: January 2003     

The ring transformations of 1,2,3,4-diepoxybutane (2,2′-bioxirane) catalysed by various aluminosilicates

The transformations of a molecule containing two adjacent epoxide rings, 2,2-bioxirane that is, were studied over various acidic aluminosilicates (HZSM-5, HY-FAU, AlMCM-41), for the first time, In the 373–473 K temperature range, in a pulse reactor, a ring-opening–ring-enlargment reaction producing furan only occured over the zeolites and it was the predominant reaction on AlMCM-41 as well. The driving force of this transformation route is water formation via elimination from 2,2-bioxirane. Suprising is the lack of the mono- or dialdehyde, the would-be products of the cleavage of the sterically more hindered C–O bonds – an acid-catalysed reaction typical for alkyl-substituted oxiranes.     

The behaviour of the multi-layer perceptron and the support vector regression learning methods in the prediction of NO and NO2 concentrations in Szeged, Hungary

The main aim of this paper is to predict NO and NO₂ concentrations 4 days in advance by comparing two artificial intelligence learning methods, namely, multi-layer perceptron and support vector machines, on two kinds of spatial embedding of the temporal time series. Hourly values of NO and NO₂ concentrations, as well as meteorological variables were recorded in a cross-road monitoring station with heavy traffic in Szeged, in order to build a model for predicting NO and NO₂ concentrations several hours in advance. The prediction of NO and NO₂ concentrations was performed partly on the basis of their past values, and partly on the basis of temperature, humidity and wind speed data. Since NO can be predicted more accurately, its values were considered primarily when forecasting NO₂. Time series prediction can be interpreted in a way that is suitable for artificial intelligence learning. Two effective learning methods, namely, multi-layer perceptron and support vector regression are used to provide efficient non-linear models for NO and NO₂ time series predictions. Multi-layer perceptron is widely used to predict these time series, but support vector regression has not yet been applied for predicting NO and NO₂ concentrations. Three commonly used linear algorithms were considered as references: 1-day persistence, average of several day persistence and linear regression. Based on the good results of the average of several day persistence, a prediction scheme was introduced, which forms weighted averages instead of simple ones. The optimization of these weights was performed with linear regression in linear case and with the learning methods mentioned in non-linear case. Concerning the NO predictions, the non-linear learning methods give significantly better predictions than the reference linear methods. In the case of NO₂, the improvement of the prediction is considerable, however, it is less notable than for NO.     

Nanocomposite bulk of mechanically milled Al-Pb samples consolidated pore-free by the high-energy rate forming technique

It is shown that pore-free bulk samples were produced by the high-energy rate forming axis-symmetrical powder compaction method for different application purposes in case of the very different, immiscible Al and Pb metal pair. The starting Al-Pb nanocomposites were made by mechanical milling of atomized Al and Pb powders either in a SPEX 9000 or a Fritsch Pulverisette 4 mill. Due to the conditions that milling was carried out in air, the PbO layer, originally existing at the surface of the atomized Pb powder, ruptured and was also dispersed in the composite. The presence of the nano PbO particles was proven by XRD and TEM (BF, DF, SAED). When the energy of milling was high, the PbO crystallites became so small that they could hardly be seen by XRD technique. Local distribution of the PbO nanoparticles was still visible in a TEM, using the process diffraction method. Both XRD and SAED proved to be useful for the evaluation of the results of the milling process and compaction.     

Design curve determination for two-layered wire rope strand using p-version finite element code

Parametric analysis of a two-layered axially loaded strand is performed using the recently developed p-version finite element code, which describes the geometry well and takes into account all possible inter-wire motions and frictional contact between the wires. A special nonlinear contact theory was developed based on the Hertz-theory. It is assumed that the wires have homogenous, isotropic, linear elastic material properties. The developed code is a tool for designing wire rope strands that require low computer resources and short computational time. Case studies are performed to verify and demonstrate the efficiency and applicability of the method. Design curves are presented according to the strand geometry parameters such as helix angle and ratio of the wire radius in the different layers. The optimal geometry parameters for a given strand can be determined using these design curves.     

Time-Resolved and Spatio-Temporal Analysis of Complex Cognitive Processes and their Role in Disorders like Developmental Dyscalculia

The aim of this article is to report on the importance and challenges of a time-resolved and spatio-temporal analysis of fMRI data from complex cognitive processes and associated disorders using a study on developmental dyscalculia (DD). Participants underwent fMRI while judging the incorrectness of multiplication results, and the data were analyzed using a sequence of methods, each of which progressively provided more a detailed picture of the spatio-temporal aspect of this disease. Healthy subjects and subjects with DD performed alike behaviorally though they exhibited parietal disparities using traditional voxel-based group analyses. Further and more detailed differences, however, surfaced with a time-resolved examination of the neural responses during the experiment. While performing inter-group comparisons, a third group of subjects with dyslexia (DL) but with no arithmetic difficulties was included to test the specificity of the analysis and strengthen the statistical base with overall fifty-eight subjects. Surprisingly, the analysis showed a functional dissimilarity during an initial reading phase for the group of dyslexic but otherwise normal subjects, with respect to controls, even though only numerical digits and no alphabetic characters were presented. Thus our results suggest that time-resolved multi-variate analysis of complex experimental paradigms has the ability to yield powerful new clinical insights about abnormal brain function. Similarly, a detailed compilation of aberrations in the functional cascade may have much greater potential to delineate the core processing problems in mental disorders.     

General relativistic hypercomputing and foundation of mathematics

Looking at very recent developments in spacetime theory, we can wonder whether these results exhibit features of hypercomputation that traditionally seemed impossible or absurd. Namely, we describe a physical device in relativistic spacetime which can compute a non-Turing computable task, e.g. which can decide the halting problem of Turing machines or decide whether ZF set theory is consistent (more precisely, can decide the theorems of ZF). Starting from this, we will discuss the impact of recent breakthrough results of relativity theory, black hole physics and cosmology to well established foundational issues of computability theory as well as to logic. We find that the unexpected, revolutionary results in the mentioned branches of science force us to reconsider the status of the physical Church Thesis and to consider it as being seriously challenged. We will outline the consequences of all this for the foundation of mathematics (e.g. to Hilbert’s programme). Observational, empirical evidence will be quoted to show that the statements above do not require any assumption of some physical universe outside of our own one: in our specific physical universe there seem to exist regions of spacetime supporting potential non-Turing computations. Additionally, new “engineering” ideas will be outlined for solving the so-called blue-shift problem of GR-computing. Connections with related talks at the Physics and Computation meeting, e.g. those of Jerome Durand-Lose, Mark Hogarth and Martin Ziegler, will be indicated.     

Preparation and characterization of hydroxyapatite from eggshell

Hydroxyapatite (HAp) was successfully produced by using recycled eggshell. The observed phases of the synthesised materials were dependent on the mechanochemical activation method (ball milling and attrition milling). The structures of the HAp were characterized by X-ray diffraction, scanning electron microscopy and infrared spectroscopy. Attrition milling proved to be more efficient than ball milling, as resulted nanosize, homogenous HAp even after milling.