Fourier methods for testing multivariate independence

Recently a power study of some popular tests for bivariate independence based on ranks has been conducted. An alternative class of tests appropriate for testing not only bivariate, but also multivariate independence is developed, and their small-sample performance is studied. The test statistics employ the familiar equation between the joint characteristic function and the product of component characteristic functions, and may be written in a closed form convenient for computer implementation. Simulations on a distribution-free version of the new test statistic show that the proposed method compares well to standard methods of testing independence via the empirical distribution function. The methods are applied to multivariate observations incorporating data from several major stock-market indices. Issues pertaining to the theoretical properties of the new test are also addressed.     

A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution

Goodness-of-fit statistics are considered which are appropriate for generalized families of distributions, resulting from exponentiation. The tests employ a variation of the data determined by the cumulative distribution function of the corresponding non-generalized distribution. The resulting test, which makes use of the Mellin transform of the transformed data, is shown to be consistent. Simulation results for the case of the generalized Rayleigh distribution show that the proposed test compares well with standard methods based on the empirical distribution function.     

On modified Runge-Kutta trees and methods

Modified Runge-Kutta (mRK) methods can have interesting properties as their coefficients may depend on the step length. By a simple perturbation of very few coefficients we may produce various function-fitted methods and avoid the overload of evaluating all the coefficients in every step. It is known that, for Runge-Kutta methods, each order condition corresponds to a rooted tree. When we expand this theory to the case of mRK methods, some of the rooted trees produce additional trees, called mRK rooted trees, and so additional conditions of order. In this work we present the relative theory including a theorem for the generating function of these additional mRK trees and explain the procedure to determine the extra algebraic equations of condition generated for a major subcategory of these methods. Moreover, efficient symbolic codes are provided for the enumeration of the trees and the generation of the additional order conditions. Finally, phase-lag and phase-fitted properties are analyzed for this case and specific phase-fitted pairs of orders 8(6) and 6(5) are presented and tested.     

P-stability, Trigonometric-fitting and the numerical solution of the radial Schrödinger equation

In this paper we will study the importance of the properties of P-stability and Trigonometric-fitting for the numerical integration of the one-dimensional Schrödinger equation. This will be done via the error analysis and the application of the studied methods to the numerical solution of the radial Schrödinger equation.     

Fabrication of TiC-Reinforced Composites by Vacuum Arc Melting: TiC Mode of Reprecipitation in Different Molten Metals and Alloys

TiC crystals were developed and grown through a melt dissolution and reprecipitation mechanism, in different alloy matrices (pure Fe, 316L, Fe-22 at.%Al, Ni-25at.%Al, and pure Co) through the use of Vacuum Arc Melting (VAM) process. The TiC surfaces exhibit a characteristic faceted mode of growth which is explained in terms of classic nucleation and crystal growth theories and is related with the well-known Jackson factor of crystal growth. Different morphologies of the finally solidified TiC grains are observed (dendritic, radially grown, isolated blocky crystals, particle clusters), the establishment of which may be most likely related with solidification progress, cooling rate, and melt compositional considerations. An initial, rough and qualitative phase identification shows a variety of compounds, and the attempts to define specific phase crystallographic-orientational relationships led to rather random results.     

Synthesis of probabilistic models for quality-of-service software engineering

An increasingly used method for the engineering of software systems with strict quality-of-service (QoS) requirements involves the synthesis and verification of probabilistic models for many alternative architectures and instantiations of system parameters. Using manual trial-and-error or simple heuristics for this task often produces suboptimal models, while the exhaustive synthesis of all possible models is typically intractable. The EvoChecker search-based software engineering approach presented in our paper addresses these limitations by employing evolutionary algorithms to automate the model synthesis process and to significantly improve its outcome. EvoChecker can be used to synthesise the Pareto-optimal set of probabilistic models associated with the QoS requirements of a system under design, and to support the selection of a suitable system architecture and configuration. EvoChecker can also be used at runtime, to drive the efficient reconfiguration of a self-adaptive software system. We evaluate EvoChecker on several variants of three systems from different application domains, and show its effectiveness and applicability.     

Post deposition annealing studies of lanthanum aluminate and ceria high-k dielectrics on germanium

Germanium MOS transistors with high-k gates are good alternatives for the replacement of SiO₂ in order to improve the performance of modern devices. Especially rare-earth oxides on germanium deposited by molecular beam deposition (MBD) have shown improved electrical properties compared to previous used HfO₂ with a germanium oxynitride (GeON) interfacial layer. In this work we report on the influence of ex situ post-annealing treatment with forming gas on the electrical characteristics of LaAlO₃/Al₂O₃/nGe and CeO₂/nGe MIS capacitors. We have observed an improvement of the electrical characteristics after forming gas anneal (FGA) for LaAlO₃/Al₂O₃/nGe in contrast to CeO₂/nGe which shows no clear trend regarding the influence of FGA.     

A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems

We examine a nonlinear explicit two-step method of fourth algebraic order and infinite phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Applying special vector arithmetic with respect to an analytic function, the method can be extended to be vector-applicable for multidimensional problems. Numerical results to illustrate the efficiency of the method are presented and sensitivity analysis indicates the validity of the method in the frequency regime.     

Role of cation demixing and quasicrystal formation and breakup on the stability of smectitic colloids

The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory has been extensively used to explain colloid stability. This study investigated the effect of demixing of monovalent and divalent cations and crystalline swelling on the breakup and formation of smectite quasicrystals (QCs) and how these processes affect flocculation and dispersion of natural soil clay–humic complexes. The results indicated that in a Ca-dominated system the formation of large QCs enhanced flocculation and that increasing the concentration of Na⁺, K⁺, or NH₄⁺ resulted in the breakup of large Ca-QCs, which enhanced dispersion. In low ionic strength systems, dispersion was caused by expanded double layers (DLVO) and the formation of small QCs. X-ray diffraction analyses showed that as large Ca-QCs breakup, monovalent cations resided primarily on the external surfaces and Ca²⁺ was preferentially retained in the interlayers. In high ionic strength systems increasing concentrations of monovalent cations also decreased the size of QCs but the effect was partially counteracted by compression of double layers between QCs. X-ray diffraction analyses indicated that monovalent cations were sorbed on both the external surfaces and in the interlayers in high ionic strength systems.