On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Agent Based Approaches to Engineering Autonomous Space Software

Current approaches to the engineering of space software such as satellite control systems are based around the development of feedback controllers using packages such as MatLab's Simulink toolbox. These provide powerful tools for engineering real time systems that adapt to changes in the environment but are limited when the controller itself needs to be adapted. We are investigating ways in which ideas from temporal logics and agent programming can be integrated with the use of such control systems to provide a more powerful layer of autonomous decision making. This paper will discuss our initial approaches to the engineering of such systems.Comment: 3 pages, 1 Figure, Formal Methods in Aerospac

The Andrews-Curtis Conjecture, Term Rewriting and First-Order Proofs

The Andrews-Curtis conjecture (ACC) remains one of the outstanding open problems in combinatorial group theory. In short, it states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of simple transformations. It is generally believed that the conjecture may be false and there are several series of potential counterexamples for which required simplifications are not known. Finding simplifications poses a challenge for any computational approach - the search space is unbounded and the lower bound on the length of simplification sequences is known to be at least superexponential. Various specialised search algorithms have been used to eliminate some of the potential counterexamples. In this paper we present an alternative approach based on automated reasoning. We formulate a term rewriting system ACT for AC-transformations, and its translation(s) into the first-order logic. The problem of finding AC-simplifications is reduced to the problem of proving first-order formulae, which is then tackled by the available automated theorem provers. We report on the experiments demonstrating the efficiency of the proposed method by finding required simplifications for several new open cases

Zinc oxide films obtained by sol-gel method from film-forming solutions

Thin ZnO films on silicon and quartz substrates were obtained from a film-enriched ethanolic solution based on Zn(NO3)2⋅6H2O and salicylic acid. The effect of salicylic acid on the processes occurring in the film-forming solution was studied by IR spectroscopy, proton-magnetic resonance, and viscometry methods. The formation of zinc salicylate nitrate in an ethanol solution is established, where salicylic acid exhibits a monodentate property in the carboxyl group. Thermal formation of zinc oxide was determined by thermal analysis and X-ray diffraction. The analysis of optical and electrophysical characteristics of ZnO films was carried out using spectroscopy, ellipsometry and also a block for measuring the electrophysical properties of thin-film materials. It was found that ZnO films were semiconductors of the electronic type, characterized by an optical band gap of 2.91–3.21eV, a surface resistance of 109–106 Q. and transparency coefficients in the visible spectral range of 0.80–0.96. It was shown that as the thickness of the ZnO films increased the resistance decreased

Evaluation of the international customs interaction effectiveness by the mirror comparison method of statistical data on foreign trade

Most of the strategic directions for improving customs administration in the Russian Federation, due to their specifics, involve interaction with the customs authorities of foreign states. The article discusses approaches to assessing the effectiveness of interstate customs interaction as a sub-type of the Russian customs service activity. The urgency of the problem lies in the fact that the basis of interstate customs interaction is the principle of minimizing possible customs risks. At the same time, the existing system of indicators used to evaluate the activities of customs authorities does not reflect the effectiveness of interaction in terms of the administration of these risks. The purpose of the study is to consider a process approach to assessing the effectiveness of customs cooperation in the concept of supply chain management. This approach involves an analysis of the activities of not a separate national customs administration, but an assessment of the integration of the actions of states in the context of concluded agreements on cooperation in the field of customs. A cross-border supply chain, according to the author, can have varying degrees of efficiency depending on the type of behavior of national customs administrations within it. The task of the study is to analyze the indicators of Russian and Chinese customs statistics of mutual trade by comparing “mirror” data on export-import transactions, extrapolating the trend of discrepancies to the dynamics of the development of customs cooperation between Russia and China, identifying elements that affect the gaps in mirror data. The results obtained suggest that, given a fairly definite and stable list of reasons for the discrepancies in the data of “mirror” customs statistics, their composition and degree of impact are different in each period of time and are a reflection of the level of interaction between the customs administrations of Russia and China. To verify the proposed approach, the trend of deviations of regional “mirror” statistics of bilateral trade between China and Russia is analyzed in the context of the cooperation key projects development between the Russian Far East and China customs administrations

Slow and fast micro-field components in warm and dense hydrogen plasmas

The aim of this work is the investigation of the statistical properties of local electric fields in an ion-electron two component plasmas for coupled conditions. The stochastic fields at a charged or at a neutral point in plasmas involve both slow and fast fluctuation characteristics. The statistical study of these local fields based on a direct time average is done for the first time. For warm and dense plasma conditions, typically $N_{e}\approx 10^{18}cm^{-3}$, $$, well controlled molecular dynamics (MD) simulations of neutral hydrogen, protons and electrons have been carried out. Relying on these \textit{ab initio} MD calculations this work focuses on an analysis of the concepts of statistically independent slow and fast local field components, based on the consideration of a time averaged electric field. Large differences are found between the results of these MD simulations and corresponding standard results based on static screened fields. The effects discussed are of importance for physical phenomena connected with stochastic electric field fluctuations, e.g., for spectral line broadening in dense plasmas.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Simulation of geological faults with discrete element method

We present an algorithm for simulation of the Earth’s crust tectonic movements and formation of the geological faults and near-fault damage zones. The algorithms are based on the Discrete Elements Method, and it is implemented using CUDA technology. We used to simulate faults formation due to different scenarios of tectonic movements. We considered the displacements with dipping angles varied from 30 to 90 degrees; i.e., up to vertical throw. For each scenario, we performed simulations for some statistical realizations. To characterize the simulated faults and damage zones, we consider the strains distribution and apply data clustering and Karhunen-Loeve analysis to distinguish between different forms of the fault zones. In particular, clustering analysis shows that displacements with high and low dip angles form completely different geological structures. Nearly vertical displacements, high dip angles, form wide V-shaped deformation zones, whereas the at displacements cause narrow fault-cores with rapidly decreasing strains apart from the fault core. Results of the presented simulations can be used to estimate mechanical and seismic properties of rocks in the vicinity of the faults and applied further to construct models for seismic modeling and interpretation, hydrodynamical simulations, history of matching simulation, etc

Thermalization of coupled atom-light states in the presence of optical collisions

The interaction of a two-level atomic ensemble with a quantized single mode electromagnetic field in the presence of optical collisions (OC) is investigated both theoretically and experimentally. The main accent is made on achieving thermal equilibrium for coupled atom-light states (in particular dressed states). We propose a model of atomic dressed state thermalization that accounts for the evolution of the pseudo-spin Bloch vector components and characterize the essential role of the spontaneous emission rate in the thermalization process. Our model shows that the time of thermalization of the coupled atom-light states strictly depends on the ratio of the detuning and the resonant Rabi frequency. The predicted time of thermalization is in the nanosecond domain and about ten times shorter than the natural lifetime at full optical power in our experiment. Experimentally we are investigating the interaction of the optical field with rubidium atoms in an ultra-high pressure buffer gas cell under the condition of large atom-field detuning comparable to the thermal energy in frequency units. In particular, an observed detuning dependence of the saturated lineshape is interpreted as evidence for thermal equilibrium of coupled atom-light states. A significant modification of sideband intensity weights is predicted and obtained in this case as well.Comment: 14 pages, 12 figures; the content was edite