New Results in Minimum-Comparison Sorting

We prove that sorting 13, 14 and 22 elements requires 34, 38 and 71 comparisons, respectively. This solves a long-standing problem posed by Knuth in his famous book The Art of Computer Programming, Volume 3, Sorting and Searching. The results are due to an efficient implementation of an algorithm for counting linear extensions of a given partial order. We also present some useful heuristics which allow us to decrease the running time of the implementation.     

Liquid / liquid ion-transfer processes at the dioctylphosphoric acid (N,N-didodecyl-N',N'-diethylphenylenediamine) / water (electrolyte) interface at graphite and mesoporous TiO2 substrates

Biphasic electrode systems are studied for the case of the oxidation of the water-insoluble liquid N,N-didodecyl-N',N'-diethylphenylenediamine (DDPD) neat and dissolved in bis(2-ethylhexyl) phosphate (HDOP) and immersed in aqueous electrolyte media. The oxidation process in the absence of HDOP is accompanied by transfer of the anion (perchlorate or phosphate) from the water into the organic phase. However, in the presence of HDOP, oxidation is accompanied by proton exchange instead. This electrochemically driven proton exchange process occurs over a wide pH range. Organic microdroplet deposits of DDPD in HDOP at basal plane pyrolytic graphite electrodes are studied by voltammetric techniques and compared in their behavior to organic microphase deposits in mesoporous TiO2 thin films. The mesoporous TiO2 thin film acts as a host for the organic liquid and provides an alternative biphasic electrode system compared to the random microdroplet/graphite system. Two types of mesoporous TiO2 thin-film electrodes, (i) a 300-400-nm film on ITO and (ii) a 300-400-nm film on ITO sputter-coated with a 20-nm porous gold layer, are investigated.     

Charge-Density-Wave Pseudogap and Two-Dimensional Superconductivity Within Strong-Coupling Description

We have considered the role of charge-density-pseudogap for phonon-mediated super-conductivity on two-dimensional lattice. The propagators that enter generalized Eliashberg equations have been renormalized to account for quasi-particle energies related to the formation of the pseudogap, which has been assumed to be of d-wave symmetry. We have evaluated the superconducting transition temperature T_c as a function of doping. It occurs that T_c for d-wave symmetry well reflects experimental behavior. Our results for the isotope shift exponent show that at low doping, the presence of the pseudogap may contribute to > 1/2 as well as to > 1/2 values.     

Analysis of VME-Bus communication protocol - RTCP-net approach

The paper discusses an RTCP-net approach to design and analysis of an example of VMEbus communication protocol. RTCP-nets are a novel Petri net class, based on time coloured Petri nets but were defined to give users powerful tools for easy and rapid design of real-time systems. Page templates are one of the main advantages of the new nets' design stage. Just modifying values of parameters in the page hierarchy graph is enough to change some features of a modelled system. Therefore, it is easy to experiment on different versions of the same model with very little additional effort. It is also very easy to reorganize page templates in order to model a different structure of a system.Relevant definitions and main properties of RTCP-nets are presented in the paper. A VMEbus communication protocol case study is used to demonstrate some applications of this approach.The work is carried out within KBN Research Project, Grant No. 4 T11C 035 24. Marcin Szpyrka received the M.S. degree in mathematics from the Rzeszów University (Poland) in 1997. He received the Ph. D. degree in computer science from AGH University of Science and Technology in Kraków (Poland) in 2000. Marcin Szpyrka is currently an assistant professor at the Institute of Automatics, AGH-UST. His research interests include: formal methods (Petri nets, process algebras), real-time systems and safety-critical systems. He has published over 40 papers and one book.     

Feedback min–max model predictive control using robust one-step sets

A solution to the infinite-horizon min–max model predictive control (MPC) problem of constrained polytopic systems has recently been defined in terms of a sequence of free control moves over a fixed horizon and a state feedback law in the terminal region using a time-varying terminal cost. The advantage of this formulation is the enlargement of the admissible set of initial states without sacrificing local optimality, but this comes at the expense of higher computational complexity. This article, by means of a counterexample, shows that the robust feasibility and stability properties of such algorithms are not, in general, guaranteed when more than one control move is adopted. For this reason, this work presents a novel formulation of min–max MPC based on the concept of within-horizon feedback and robust contractive set theory that ensures robust stability for any choice of the control horizon. A parameter-dependent feedback extension is also proposed and analysed. The effectiveness of the algorithms is demonstrated with two numerical examples.     

Genetic programming based approaches to identification and fault diagnosis of non-linear dynamic systems

System identification is one of the most important research directions. It is a diverse field which can be employed in many different areas. One of them is the model-based fault diagnosis. Thus, the problems of system identification and fault diagnosis are closely related. Unfortunately, in both cases, the research is strongly oriented towards linear systems, while the problem of identification and fault diagnosis of non-linear dynamic systems still remains open. There are, of course, many more or less sophisticated approaches to this problem, although they are not as reliable and universal as those related to linear systems, and the choice of the method to be used depends on the application. The purpose of this paper is to provide a new system identification framework based on a genetic programming technique. Moreover, a fault diagnosis scheme for non-linear systems is proposed. In particular, a new fault detection observer is presented, and the Lyapunov approach is used to show that the proposed observer is convergent under certain conditions. It is also shown how to use the genetic programming technique to increase the convergence rate of the observer. The final part of this paper contains numerical examples concerning identification of chosen parts of the evaporation station at the Lublin Sugar Factory S.A., as well as state estimation and fault diagnosis of an induction motor.     

A fault-tolerant control strategy for non-linear discrete-time systems: application to the twin-rotor system

In this paper, an active fault-tolerant control scheme is proposed in the case of actuator faults. In particular, the general idea of integrating fault identification and control schemes, which takes into account the fault estimation error is first presented in a linear context. As a result, the so-called separation principle for the controller and the fault identification scheme is developed. Subsequently, the proposed approach is extended to a class of non-linear systems. Similarly to the linear case, it is proven that using a suitable control strategy and a faulty identification scheme it is possible to obtain an integrated fault-tolerant control framework, which takes into account the fault identification error. As a result, a non-linear counterpart of the above-mentioned separation principle is developed. Finally, the last part of the paper shows the application results obtained using a twin-rotor system that confirm the high performance of the proposed approach.     

Monitoring of transient temperature and thermal stresses in pressure components of steam boilers

Two methods of solving the transient inverse heat conduction problens in complex shaped elements are presented in this paper. The time-space temperature distribution in whole element cross-section is reconstructed using the measured temperature histories at several points placed inside the element or on its easily accessible outer surface. Thermal stresses are then evaluated involving Finite Element Analysis. In both methods the heat transfer coefficient at the element inner surface is the unknown value. Four examples are presented, two for one method showing the high accuracy of the presented methods and possibility of their practical application.     

X-ray Microtomography Analysis of the Aluminum Alloy Composite Reinforced by SiC After Friction Stir Processing

Despite many years of using friction stir processing (FSP), there are many unexplained aspects concerning the processes which appear during FSP: determining the direction of flow and mixing of the materials and the degree of mixing and microstructure fragmentation in specific areas. This paper presents the impact of FSP on the micro- and macrostructure of the composite with hypo-eutectic Si matrix reinforced by SiC particles. The analysis of the structure of the processed area in FSP in the relation to the microstructure of the base material has been made using x-ray microtomography. The results of these studies have been juxtaposed with studies using microscopic methods (light microscopy and SEM). The microtomography images revealed an additional separation on the advancing side and the weld nugget, where on the basis of a 3D reconstruction a layer microstructure on the direction of linear movement of the tool has been demonstrated. The analyses have revealed a limited flow of the material above the weld nugget. The main advantages of the research method applied were the possibility to show the invisible or barely visible elements of the microstructure using standard test methods and the ability to analyze the microstructure changes uninterruptedly in different directions in the volume of the material.     

The Characteristics of the Superconducting and Magnetic Phases in the Polycrystalline Samples of Ruthenocuprates of Nominal Compositions RuSr2GdCu2O8, Ru0.98Sr2GdCu2O8 and Ru0.5Sr2GdCu2.5O8−δ

The temperature dependencies of the resistivity for the superconducting ruthenocuprates of nominal compositions RuSr₂GdCu₂O₈, Ru_0.98Sr₂GdCu₂O₈ and Ru_0.5Sr₂GdCu_2.5O_8?δ were examined for the magnetic field dependent characteristics of the superconducting transitions. The effect of the insignificant diminishing of the Ru/Cu ratio in parent RuSr₂GdCu₂O₈ was confirmed as relevant for the stabilisation of the superconducting phase. Noted differences in the compared characteristics are interpreted for possible inhomogeneous nucleation of the superconducting phase in the parent ruthenocuprate. The phase anisotropy in RuSr₂GdCu₂O₈ and Ru_0.98Sr₂GdCu₂O₈, in presence of the compounds Ru magnetism, appears to be a cause of a significant softening of the H _c2(T) phase line. An anomalous lowering of the magnetoresistivity was observed in the approx. 10 K range above the onset of the superconducting transition, which may suggest the presence of enhanced superconducting fluctuations in the samples. The positive magnetic field shift of the temperatures, which limit the magnetoresistivity and the specific heat signatures of the magnetic ordered state of the Ru sublattice, suggests probing the influence of the ferromagnetic Ru interactions in an effective metallic-like conduction channel present in the samples. Superconducting characteristics of the Ru_0.5Sr₂GdCu_2.5O_8?δ reveal a significant contribution of the Gd paramagnetic signal at low temperatures, interpreted for the presence of a significant anisotropy of the superconducting phase. It is concluded that the Ru–Cu substituted phases of ruthenocuprates may present an opportunity to investigate the effectively anisotropic superconducting phase despite its comparatively high T _c in the compounds related to the 123-type cuprate superconductor.