More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201

Aerodynamic Noise Prediction for a Rod-Airfoil Configuration using Large Eddy Simulations

Aerodynamic noise produced by aerodynamic interaction between a cylinder (rod) and an airfoil in tandem arrangement is investigated using large eddy simulations. Wake from the rod convects with the flow, impinges of the airfoil to produce unsteady force which acts as a sound source. This rod-airfoil interaction problem is a model problem for noise generation due to inflow or upstream-generated turbulence interacting with a turbomachine bladerow or a wind turbine rotor. The OpenFoam and Charles (developed by Cascade Technologies) solvers are chosen to carry out the numerical simulations. The airfoil is set at zero angle of attack for the simulations. The flow conditions are specified by the Reynolds number (based on the rod diameter), Red = 48 K, and the flow Mach number, M = 0.2. Comparisons with measured data are made for (a) mean and root-mean-squared velocity profiles in the rod and airfoil wakes, (b) velocity spectra in the near field, and (c) far-field pressure spectra and directivity. Near-field flow data (on- and off-surface) is used with the Ffowcs Williams-Hawkings (FW-H) acoustic analogy as well as Amiet’s theory to predict far-field sound

Energy radiation of moving cracks

The energy radiated by moving cracks in a discrete background is analyzed. The energy flow through a given surface is expressed in terms of a generalized Poynting vector. The velocity of the crack is determined by the radiation by the crack tip. The radiation becomes more isotropic as the crack velocity approaches the instability threshold.Comment: 7 pages, embedded figure

About Zitterbewegung and electron structure

We start from the spinning electron theory by Barut and Zanghi, which has been recently translated into the Clifford algebra language. We "complete" such a translation, first of all, by expressing in the Clifford formalism a particular Barut-Zanghi (BZ) solution, which refers (at the classical limit) to an internal helical motion with a time-like speed [and is here shown to originate from the superposition of positive and negative frequency solutions of the Dirac equation]. Then, we show how to construct solutions of the Dirac equation describing helical motions with light-like speed, which meet very well the standard interpretation of the velocity operator in the Dirac equation theory (and agree with the solution proposed by Hestenes, on the basis --however-- of ad-hoc assumptions that are unnecessary in the present approach). The above results appear to support the conjecture that the Zitterbewegung motion (a helical motion, at the classical limit) is responsible for the electron spin.Comment: LaTeX; 11 pages; this is a corrected version of work appeared partly in Phys. Lett. B318 (1993) 623 and partly in "Particles, Gravity and Space-Time" (ed.by P.I.Pronin & G.A.Sardanashvily; World Scient., Singapore, 1996), p.34

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16

AAL platform with a “de facto” standard communication interface (TICO): Training in home control in special education

Framed within a long-term cooperation between university and special education teachers, training in alternative communication skills and home control was realized using the “TICO” interface, a communication panel editor extensively used in special education schools. From a technological view we follow AAL technology trends by integrating a successful interface in a heterogeneous services AAL platform, focusing on a functional view. Educationally, a very flexible interface in line with communication training allows dynamic adjustment of complexity, enhanced by an accessible mindset and virtual elements significance already in use, offers specific interaction feedback, adapts to the evolving needs and capacities and improves the personal autonomy and self-confidence of children at school and home. TICO-home-control was installed during the last school year in the library of a special education school to study adaptations and training strategies to enhance the autonomy opportunities of its pupils. The methodology involved a case study and structured and semi-structured observations. Five children, considered unable to use commercial home control systems were trained obtaining good results in enabling them to use an open home control system. Moreover this AAL platform has proved efficient in training children in previous cognitive steps like virtual representation and cause-effect interaction