Perfect Convergence Research Articles

Pleading for European Comparative Administrative Law

This article pleads for reinforced communication and exchange between European and national courts, both in a vertical way, from the national to the European courts, and in a horizontal one, among national courts from different Member States. Building an integrated legal order needs a lot of communication and exchange between the constituent parts, quite more than is presently seen in the European Union. Courts at all levels will greatly benefit from knowing the case law from different jurisdictions which in the end are charged with the application of the same European rules. The barriers due to the specific legal traditions now separating different legal orders could be lowered thanks to a better mutual knowledge and understanding, making a shared European legal culture possible. 1 What is the Place for Comparative Law in Europe? The debate has been quite intense in the past years on the question of whether or not national legal systems are converging under the pressure of European law. In general terms, the question is probably begging different answers positioning themselves along the blurred line between a half full and half empty glass. Serious research will probably produce nuanced results, with more or less, a lot or very little convergence according to different issues, but then again the data from each sector will be liable to different readings, as has been the case concerning judicial review. A different question has been underlying the debate, this one focusing on the role, if any, for comparative law in Europe. To put it simply, the argument is that, provided that legal systems are converging, the same possibility of using comparative law will evaporate. This paper endeavours to show that comparative law’s role is now more important than ever as a direct result of the convergence process. While this process is very complex, it has the potential to last forever, as perfect convergence always eludes its pursuers. Research here has been massive, and positions varied: for a selection C. Kilpatrick, T. Novitz and P. Skidmore (eds.) The Future of Remedies in Europe (Oxford, Hart, 2000); more recently and for complete references see M. Eliantonio Europeanisation of Administrative Justice? (Groningen, Europa Law Publishing, 2008).

Comparison of Three Methods for Discretizing the Storage Term of the Richards Equation

We compared three methods for discretizing the storage term of the Richards equation: the traditional chain rule expansion approach (Method A), a mass conservative approach based on a mixed form of the Richards equation (Method B), and another mass conservative approach using a chord‐slope approximation for the specific moisture capacity (Method C). The results of three test problems indicated that Method A could not achieve a perfect global mass balance even if the iteration number in the Picard iteration scheme was large enough to bring a perfect solution convergence. Both Methods B and C successfully produced perfect mass balances. Method C produced step‐by‐step decreases in the global mass balance error as the Picard iteration level increased, which corresponded well with step‐by‐step decreases in the solution convergence error. Method B produced more accurate mass balances than Methods A and C for every Picard iteration level; when this method was used, the global mass balance error became negligible before the solution converged. Analytical evaluation of Method B revealed the mechanisms for removing the mass balance error. As the difference between the matric pressure head, ψ, lessens between the previous and current Picard iteration levels, the water retention curve becomes more linear in the region bounded by the two ψ values. As a result, the difference in the water content between two consecutive Picard iteration levels is accurately approximated by using the difference in the two ψ values, which results in a remarkable reduction in the mass balance error, allowing Method B to produce better results than Method C.

Finite-Dimensional Approximation Settings for Infinite-dimensional Moore–Penrose Inverses

After a brief survey of basic results about finite-dimensional approximation settings (such as mathematical frameworks of various projection methods, including the least-squares method, the dual least-squares method, and the Galerkin method) for infinite-dimensional Moore–Penrose inverses, this paper proceeds to a detailed study from the following aspects: For projection methods, we investigate convergence and weak convergence of their approximation setting to develop a unified theory on projection methods for infinite-dimensional Moore–Penrose inverses; this investigation yields a fundamental convergence theorem (Theorem 2.2), from which the criterion for convergence, the criterion for weak convergence, and the generalized dual least-squares method are derived. We also derive general results on the least-squares method, by which two flaws in Groestch's results are corrected. For nonprojection methods (whose approximation setting is a more general framework), we investigate weak perfect convergence of their approximation setting and provide a necessary and sufficient condition of such convergence holding (Theorem 3.2). Several examples are proposed as counterexamples to illustrate the differences between some important concepts or as concrete algorithms to show how the present work can help to analyze their behavior.

Convergence Analysis of the Numerical Solution for Cathode Design of Aero-engine Blades in Electrochemical Machining

As a main difficult problem encountered in electrochemical machining (ECM), the cathode design is tackled, at present, with various numerical analysis methods such as finite difference, finite element and boundary element methods. Among them, the finite element method presents more flexibility to deal with the irregularly shaped workpieces. However, it is very difficult to ensure the convergence of finite element numerical approach. This paper proposes an accurate model and a finite element numerical approach of cathode design based on the potential distribution in inter-electrode gap. In order to ensure the convergence of finite element numerical approach and increase the accuracy in cathode design, the cathode shape should be iterated to eliminate the design errors in computational process. Several experiments are conducted to verify the machining accuracy of the designed cathode. The experimental results have proven perfect convergence and good computing accuracy of the proposed finite element numerical approach by the high surface quality and dimensional accuracy of the machined blades.

Convergence of European spot market prices for natural gas? A real-time analysis of market integration using the Kalman Filter

This letter provides a textbook example of an econometric analysis of the integration between two commodity markets and the subsequent price convergence or absence thereof. Price relations between spot markets are analysed for natural gas in Europe. The European market for natural gas is currently undergoing a liberalization process with the aim of creating a single, unified market. Time-varying coefficient estimation models are used, applying the Kalman filter to test whether price convergence between different locations is really taking place. The results reveal that the construction of a pipeline between the UK and Zeebrugge (Belgium) has led to almost perfect price convergence between these locations in the time period under consideration; on the other hand, liberalization on the European continent does not seem to be working so far.

Comparing 10 Methods for Solution Verification, and Linking to Model Validation

Grid convergence is often assumed as a given during computational analyses involving discretization of an assumed continuum process. In practical use of finite difference and finite element analyses, perfect grid convergence is rarely achieved or assured, and this fact must be addressed to make statements about model validation or the use of models in risk analysis. We have previously provided a 4-step quantitative implementation for a quantitative V&V process. One of the steps in the 4-step process is that of Solution Verification. Solution Verification is the process of assuring that a model approximating a physical reality with a discretized continuum (e.g. finite element) code converges in each discretized domain to a converged answer on the quantity of subsequent validation interest. The modeling reality is that often we are modeling a problem with a discretized code because it is neither continuous spatially (e.g. contact and impact) nor smooth in relevant physics (e.g. shocks, melting, etc). The typical result is a non-monotonic convergence plot that can lead to spurious conclusions about the order of convergence, and a lack of means to estimate residual solution verification error or uncertainty at confidence. We compare ten techniques for grid convergence assessment, each formulated to enablemore » a quantification of solution verification uncertainty at confidence and order of convergence for monotonic and nonmonotonic mesh convergence studies. The more rigorous of these methods require a minimum of four grids in a grid convergence study to quantify the grid convergence uncertainty. The methods supply the quantitative terms for solution verification error and uncertainty estimates needed for inclusion into subsequent model validation, confidence, and reliability analyses. Naturally, most such methodologies are still evolving, and this work represents the views of the authors and not necessarily the views of Lawrence Livermore National Laboratory.« less

The Basic Principles for Stable Approximations to Orthogonal Generalized Inverses of Linear Operators in Hilbert Spaces

ABSTRACT This work presents some basic principles concerned with two general settings for stable approximating orthogonal generalized inverses in Hilbert spaces. In these two settings, perfect convergence and perfect uniform convergence are two important concepts for making theoretical or numerical analysis. Our basic principles characterize the two important concepts by some necessary conditions: stability with other compensated conditions. These basic principles include as simple corollaries some well-known results.

Endogenous distribution and equilibrium growth: a note

Does distributive conflict diminish during the course of economic development? This article outlines a model in which distribution, the tax rate and growth evolve endogenously over time. When voting occurs over a tax on capital, we show that the growth rate is maximized at the political equilibrium in the long run. When voting occurs over a general income tax, we show that the growth rate is maximized at the political equilibrium in both the short and long run. These results suggest that the transitional dynamics of growth models with redistributive politics lead to growth-maximizing outcomes, as distributive conflict diminishes in the course of development. This implies that the democratic process leads to greater consensus over policy choices, with a perfect convergence of interest across individuals with respect to the tax rate.

Unexpected beauty

Unexpected beauty

Osmium nanoislands spontaneously deposited on a Pt(111) electrode: an XPS, STM and GIF-XAS study

Scanning tunneling microscopy (STM) characterized adlayers of spontaneously deposited osmium on a Pt(111) electrode were investigated using ex-situ X-ray photoemission spectroscopy (XPS) and in-situ grazing incidence fluorescence X-ray absorption spectroscopy (GIF-XAS). After a single spontaneous deposition, monoatomic (or nearly monoatomic) nanoislands of osmium are formed. The island diameter varies from 2 to 5 nm depending on the Os coverage, which in turn is adjusted by varying the concentration of the Os precursor salt (OsCl3) in the deposition bath and/or by the deposition time. XPS reveals three oxidation states: a metallic Os (the 4f7/2 core level binding energy of 50.8 eV), Os(IV) (51.5 eV) and Os(VIII) (52.4 eV). The metallic osmium exists at potentials below 500 mV (vs. RHE) while above 500 mV osmium is oxidized to Os(IV). Electrodissolution of osmium begins above 900 mV and occurs simultaneously with platinum oxidation. At ca. 1200 mV V versus the RHE reference, the oxidation state of some small amounts of osmium that survive dissolution is the Os(VIII). We demonstrate, for the first time, that mixed or odd valencies of osmium exist on the platinum surface at potentials higher that 800 mV. In-situ GIF-XAS measurements of an Os LIII edge also reveal the presence of three Os oxidation states. Namely, below the electrode potential of 400 mV, the X-ray fluorescent energy at maximum absorption is 10.8765 keV, and is characteristic of the metallic Os. In the potential range between 500 and 1000 mV this energy is gradually shifted to higher values, assignable to higher valencies of osmium, like Os(IV). This tendency continues to higher potentials consistent with the third, highly oxidized osmium form present, most likely Os(VIII). The variation of the “raw edge jump height” of Os with the electrode potential, which is equivalent to a drop in osmium surface concentration, demonstrates that the electrochemical stripping of Os begins below 1.0 V versus RHE, as expected from voltammetry. Also, the observed intensity of the white line of Os in the 100–400 mV region is larger than the value reported for metallic bulk Os. This discrepancy may result from the difference in the electronic properties of the metallic Os layers on Pt(111) and the metallic bulk Os: in the potential region between 100 and 400 mV, the 5d electrons in Os and Pt form a mixed electronic band, and the density of electronic states near the Fermi level, the main factor determining the white line intensity, may not be the same as in metallic bulk. The presented results on osmium adlayers are much more comprehensive than those available in our previous work due to the combined STM, GIF-XAS and XPS investigations. A nearly perfect convergence of the in situ and ex situ data is one of the main research outcomes of this project. Finally, platinum XPS spectra taken in the context of Os electrooxidation from the electrode surface are also presented and conclusions are made, that up to 900 mV platinum remain metallic, irrespective of a significant osmium oxidation on its surface.

Observer-based iterative learning control for a class of time-varying nonlinear systems

In this brief, we propose an observer-based iterative learning control (ILC) scheme for the tracking problem of a class of time-varying nonlinear systems. First, a state observer is derived for the system under consideration, and sufficient conditions for the boundedness and the convergence to zero of the estimation error are given. Thereafter, an iterative learning rule - based on the proposed state observer - ensuring the boundedness of the tracking error is derived. Moreover, it is shown that if the initial state variables are known, it is possible to obtain a perfect convergence to zero, over a finite tracking horizon, when the number of iterations tends to infinity. By associating a state observer with the ILC scheme it is possible to avoid the use of state and output time-derivative measurements which are generally necessary in contraction mapping based ILC design for nonlinear systems without zero relative degree.

It Was Not Death for I Stood Up…and Fragged the Dumb-Ass MoFo Who'd Wasted Me

It Was Not Death for I Stood Up…and Fragged the Dumb-Ass MoFo Who'd Wasted Me

On Convergence of Interpolation to Analytic Functions

In the present paper, both the perfect convergence for the Lagrange interpolation of analytic functions on [−1, 1] and the perfect convergence for the trigonometric interpolation of analytic functions on [− π , π ] with period 2 π are discussed.

Becoming as Creative Involution?: Contextualizing Deleuze and Guattari's Biophilosophy

Becoming as Creative Involution?: Contextualizing Deleuze and Guattari’s Biophilosophy Mark Hansen As several recent critical studies have conclusively demonstrated, biological research and theory form a central reference point in Gilles Deleuze’s philosophy.1 From his early major work culminating in Difference and Repetition of 1968, through his collaboration with Félix Guattari on Capitalism and Schizophrenia (especially, A Thousand Plateaus of 1980), to his final work on Leibniz and geophilosophy (The Fold, and with Guattari again, What is Philosophy?), Deleuze has framed his account of individuation and agency through an evolving critical engagement with evolutionary thinking. Rooted in his early rehabilitation of Henri Bergson’s 1907 Creative Evolution, Deleuze’s heretical “evolutionism” draws widely and irreverently on the advances of recent biology; and yet, for all its gesturing toward biological theory, it remains distinctly philosophical in flavor. Not only was Deleuze’s very interest in biology overdetermined from the beginning by his desire to redress the almost total neglect of Bergson as a philosopher, but (more importantly for my purposes) his ongoing engagement with biological theory (and with Bergsonism itself) has been marshaled to support a metaphysics of the virtual that is, for all its resonances with recent developments in biology, at odds with the distinct priority biological theory (and the Bergson of Creative Evolution) places on processes of actualization. Laying bare this différend between science and philosophy motivates the first strand of my argument in this paper: an attempt to unpack and clarify the genealogy of Deleuze’s changing, though lifelong, engagement with Bergson. Essentially, after starting off from a point of seemingly perfect convergence between philosophy and biology—Bergson’s notion of the élan vital—Deleuze drives an ever-widening wedge between the biological notions he appropriates from neo-evolutionism and what he increasingly comes to view as a model of creative evolution too fundamentally bound up with both humanism and a residual representationalism. As I shall argue, what compels Deleuze to distance himself from creative evolution and from a certain Bergson is his (paradoxically very Bergsonian) philosophical aim of furnishing a metaphysics for contemporary science, that is, a metaphysics of the virtual.2 Against such a metaphysics, I shall insist, against such metaphysics and with the support of contemporary biologists, that a certain priority be granted processes of actualization. Still, despite Deleuze’s distancing from creative evolution, something substantial persists across his changing relation to both Bergson and biology: namely, his commitment to a notion of internal difference, or difference in itself. This commitment motivates Deleuze’s initial adherence to Bergson’s creative evolutionism no less than his later “break” with Bergson over the status of intensity as well as the correlated model of creative involution he develops together with Guattari. The initial impetus driving Deleuze’s effort to rehabilitate the fraught notion of the élan vital and with it, the very career of Bergson as philosopher, was nothing other than the notion of internal difference. As he reconstructs it in his 1956 essay, “Bergson’s Conception of Difference,” and then again in his 1966 Bergsonism, the élan vital introduces an explosive force internal to the process of evolution (internal difference) that is capable of accounting for the positive power of time as a source of creative invention. With the progress of his own philosophical career, Deleuze soon found reason to temper his initial adherence to Bergsonism—and specifically, to Bergson’s derivation of internal difference from qualitative difference—without in any way abandoning his own commitment to internal difference. As early as Difference and Repetition (1968), Deleuze traces qualitative difference or difference in kind (together with quantitative difference or difference in degree) to a fluid continuum of intensity, thereby eschewing Bergson’s argument that qualitative difference is itself one of two tendencies being differentiated and thus, a tendency internal to difference that, as Deleuze puts it, “show[s] the way in which a thing varies qualitatively in time” (Bergsonism 32). By attending to what is at stake in this shift concerning the source of internal difference, I shall correlate Deleuze’s break with Bergson over the role of intensity with the generalized philosophical Aufhebung of biology that underwrites his introduction (in Difference and...

Geometrical reconstructions and electronic relaxations of silicon surfaces. I. An electron density topological study of H-covered and clean Si(111)(1×1) surfaces

The relaxations of the first three interlayer distances in the H-covered Si(111)(1×1) surface were calculated using a fully periodic Hartree–Fock approach and a finely tuned slab model. All computed relaxations fall well within the error bounds of the experiment, provided the relevant geometrical parameters and the basis set of the first layer Si atoms (Si1) are both optimized. The quantum theory of atoms in molecules is applied on the wave functions of Si bulk and of H-covered or clean Si(111)(1×1) slabs so as to shed light on how the electronic perturbation caused by H adsorption and surface formation propagates and dampens through the first Si atoms layers. In the H-covered surface, the large charge transfer from Si1 to H induces a noticeable asymmetry in and strengthening of the surface Si1–Si2 back bonds, whereas in the clean slab the same bonds are found to be weakened compared to the bulk in agreement with the well-known tendency of this system to evolve in favor of other reconstructions. The negatively charged hydrogen layer in the Si(111)(1×1)–H slab is almost entirely counterbalanced by the first two silicon layers with the Si1 atoms bearing more than 94 percent of the compensating positive charge. The hydrogen and Si1 atoms in the H-covered surface polarize in such a way as to oppose the electric field created by charge transfer into the surface double layer. The effect of H-coverage is to reverse the outwards polarization of Si1 atoms present in the clean system and to enhance its magnitude. Due to the surface electric field, the atomic energies in both slabs are not found to converge towards bulk values even for the atoms of the innermost layers, although the other calculated local and integrated properties exhibit an almost perfect convergence beyond the first two or three atomic layers. In the H-covered slab, the Si1 atoms have their interatomic surface completely isolated from the outside through their interaction with H atoms, while Si2 are found to be the only surface silicon atoms in agreement with the experimental observation that passivant substitution or oxidation are mediated by Si2 and never occur directly at Si1 atoms.

Asymptotically perfect and relative convergence of productivity

In this paper we examine the extent to which countries are converging in per capita productivity levels. We propose to use cluster analysis in order to allow for the endogenous selection of converging countries. We formally define convergence in a time series analytical context, derive the necessary and sufficient conditions for convergence, and introduce a cluster analytical procedure that distinguishes several convergence clubs by testing for these conditions using a multivariate test for stationarity. We find a large number of relatively small convergence clubs, which suggests that convergence might not be such a widespread phenomenon. Copyright © 2000 John Wiley & Sons, Ltd.

Terminal attractor optical associative memory with adaptive control parameter

The control parameter dependence in terminal attractor (TA) optical associative memory is investigated. With adaptive setting of the control parameter in the dynamics of the TA model for dynamic iteration, perfect convergence of the associative memory for pattern recognition is achieved. With numerical simulations, the optimal control parameter in the TA model associative memory is determined. The optimal control parameter is also used in an optical experiment. The experimental results show that the target pattern can be successfully associated.

Absolute, perfect, and unconditional convergence of double series

Absolute, perfect, and unconditional convergence of double series

Etude analytique et numérique de la réponse en vibration à hautes fréquences d'éprouvettes de fatigue vibratoire des métaux. Application aux aciers

In the present paper, the so-called ultrasonic fatigue or fatigue at very high frequency has been studied in the materials elastic behaviour case while neglecting the thermal effects that influence the mechanical fields. The determination of mechanical fields and specimen resonance length has been done both analytically and numerically. The numerical method used for this calculation is the finite element method (FEM). Martensitic steel Soleil A2 and austenitic steel ICL 472 BC have been considered in order to compare the two methods (analytical and numerical). It is shown that a perfect convergence is obtained between the two solutions

Unipolar terminal-attractor-based neural associative memory with adaptive threshold and perfect convergence

A perfectly convergent unipolar neural associative-memory system based on nonlinear dynamical terminal attractors is presented. With adaptive setting of the threshold values for the dynamic iteration for the unipolar binary neuron states with terminal attractors, perfect convergence is achieved. This achievement and correct retrieval are demonstrated by computer simulation. The simulations are completed (1) by exhaustive tests with all of the possible combinations of stored and test vectors in small-scale networks and (2) by Monte Carlo simulations with randomly generated stored and test vectors in large-scale networks with an M/N ratio of 4 (M is the number of stored vectors; N is the number of neurons ≤ 256). An experiment with exclusive-oR logic operations with liquid-crystal-television spatial light modulators is used to show the feasibility of an optoelectronic implementation of the model. The behavior of terminal attractors in basins of energy space is illustrated by examples.