A Concise Guide to Complex Hadamard Matrices

Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,..., 16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12,14 and 16, which we could not find in the existing literature.     

The Mechanochemical Synthesis of NaNbO3 Using Different Ball-Impact Energies

We studied the mechanochemical synthesis of NaNbO₃ from a starting-powder mixture of sodium carbonate and Nb₂O₅ using ball-impact energies of 15 and 370 mJ/hit. Based on the results of a quantitative phase analysis we propose a mechanism for the mechanochemical synthesis of NaNbO₃. During milling a condition is established, where the amounts of perovskite, X-ray diffraction -amorphous phase and residual carbonate in the mixture do not change with increasing milling time. Similarly, the NaNbO₃ crystallite size and the quantity of microstrains reach final values that are independent of the applied ball-impact energy.     

Elasto-Plastic Springback of Beams Subjected to Repeated Bending/Unbending Histories

This contribution investigated repeated elastoplastic pure plane bending/unbending process of beams made of material with an elastic-linear hardening rheological model. The attention is focused on beams with cross sections which have at least one axis of symmetry and are initially straight or have constant radius of curvature. Elastoplastic deflection states of beams after repeated bending/unbending process are determined using the large displacement theory. Experiments were conducted to verify the theory for beams made of aluminium alloy AA 5050-H38 with rectangular cross sections. It is shown that maximal relative difference between experimental and theoretical results in the case of a largely curved beams after repeated bending/unbending process is 1.27%.     

Integration of a laser interferometer and a CMM into a measurement system for measuring internal dimensions

In order to improve the existing comparative procedure for calibrating internal dimensions, we have developed a new measurement set-up for traceable absolute measurements. It consists of a co-ordinate measuring machine (CMM) and a laser interferometer (LI). The LI serves as a traceable measurement system, while the CMM is only used as a guiding system for the measuring probe. Extended research focused on defining probe parameters such as diameter, bending and indentation, as well as probing head repeatability and other error sources. The final goal of the research was to determine uncertainty of measurement under existing laboratory conditions. The main outcomes of the research and final uncertainty of measurement are presented in this article.     

Low-Temperature Sintering of K0.5Na0.5NbO3 Ceramics

The objective of this work was to lower the sintering temperature of K_0.5Na_0.5NbO₃ (KNN) without reducing its piezoelectric properties. The KNN was sintered using 0.5, 1, 2, and 4 mass% of (K, Na)-germanate. The influence of the novel sintering aid, based on alkaline germanate with a melting point near 700°C, on the sintering, density, and piezoelectric properties of KNN is presented. The alkaline-germanate-modified KNN ceramics reach up to 96% of theoretical density at sintering temperatures as low as 1000°C, which is approximately 100°C less than the sintering temperature of pure KNN. The relative dielectric permittivity (ɛ/ɛ₀) and losses (tanδ), measured at 10 kHz, the piezo d ₃₃ coefficient, the electromechanical coupling and mechanical quality factors ( k _p, k _t, Q _m) of KNN modified with 1 mass% of alkaline germanate are 397, 0.02, 120 pC/N, 0.40, 0.44, and 77, respectively. These values are comparable to the best values obtained for KNN ceramics sintered above 1100°C.     

A rigorous design method for binary cellular neural networks

In order to be able to take full advantage of the great application potential that lies in cellular neural networks (CNNs) we need to have successful design and learning techniques as well. In almost any analogic CNN algorithm that performs an image processing task, binary CNNs play an important role. We observed that all binary CNNs reported in the literature, except for a connected component detector, exhibit monotonic dynamics. In the paper we show that the local stability of a monotonic binary CNN represents sufficient condition for its functionality, i.e. convergence of all initial states to the prescribed global stable equilibria. Based on this finding, we propose a rigorous design method, which results in a set of design constraints in the form of linear inequalities. These are obtained from simple local rules similar to that in elementary cellular automata without having to worry about continuous dynamics of a CNN. In the end we utilize our method to design a new CNN template for detecting holes in a 2D object. © 1998 John Wiley Sons, Ltd.     

Seeding effects on the mechanochemical synthesis of 0.9Pb(Mg1/3Nb2/3)O3–0.1PbTiO3

A systematic investigation of the seeding effects on the mechanochemical synthesis of lead magnesium niobate – lead titanate 0.9Pb(Mg_1/3Nb_2/3)O₃–0.1PbTiO₃ (PMN–10PT), one of the most studied relaxor-ferroelectric material for electrocaloric applications, is reported. The perovskite crystallisation process was followed by X-ray diffraction using the Rietveld refinement method and transmission electron microscopy. Compared to the mixed-oxides case which requires 143 h of high-energy milling, the milling time needed to obtain a phase-pure PMN–10PT perovskite using PT seeds is reduced almost twice. The presence of PT seeds leads to faster transitions from the amorphous to pyrochlore and to perovskite phases compared to the mixed-oxides case. A sintering study demonstrates, for the first time, that a second, metastable, pyrochlore phase is taking part in the processes of perovskite formation. The PMN–10PT ceramic prepared from the PT-seeded powder exhibits electrocaloric properties comparable to reported values for PMN–10 PT prepared from oxides.     

The Contemporary Approach to CALR-Positive Myeloproliferative Neoplasms

CALR mutations are a revolutionary discovery and represent an important hallmark of myeloproliferative neoplasms (MPN), especially essential thrombocythemia and primary myelofibrosis. To date, several CALR mutations were identified, with only frameshift mutations linked to the diseased phenotype. It is of diagnostic and prognostic importance to properly define the type of CALR mutation and subclassify it according to its structural similarities to the classical mutations, a 52-bp deletion (type 1 mutation) and a 5-bp insertion (type 2 mutation), using a statistical approximation algorithm (AGADIR). Today, the knowledge on the pathogenesis of CALR-positive MPN is expanding and several cellular mechanisms have been recognized that finally cause a clonal hematopoietic expansion. In this review, we discuss the current basis of the cellular effects of CALR mutants and the understanding of its implementation in the current diagnostic laboratorial and medical practice. Different methods of CALR detection are explained and a diagnostic algorithm is shown that aids in the approach to CALR-positive MPN. Finally, contemporary methods joining artificial intelligence in accordance with molecular-genetic biomarkers in the approach to MPN are presented.