On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

Badania procedur obliczeniowych pod kątem zastosowań w symulacji drgań skrętnych w układzie kierowniczym motocykla z uwzględnieniem luzu i tarcia

The torsional vibrations that occur in the motorcycle steering system pose a significant problem for motorcyclist's safety. These vibrations are particularly conspicuous in the motorcycles operated with high dynamic loads, where the impact of freeplay and friction emerges due to mechanical wear. The vibrations generated in the motorcycle steering system in the presence of freeplay and friction have peculiar nonlinear nature typical of stick-slip processes. Due to the threshold-like phenomena reflected in the nonlinearities related to freeplay and friction, it is difficult to simulate the behaviour of such systems and comprehensive preliminary research must be first carried out for this purpose. In this paper, simulation tests of the torsional vibrations that occur in a simplified equivalent model of the steering system (torsional pendulum) have been described. A mathematical model of the system has been given, inclusive of an original method of generating external inputs. Computer software developed in the Matlab-Simulink environment has been presented. The impact of computational procedures on simulation results, including impact of the method used to implement the slick-slip model in the simulation program, impact of the type of the algorithms used to integrate differential equations, and impact of the preset numerical parameters, has been analysed.Drgania skrętne występujące w układzie kierowniczym stanowią istotny problem dla bezpieczeństwa użytkownika motocykla. Drgania te są szczególnie widoczne w motocyklach eksploatowanych przy dużych obciążeniach dynamicznych. Wówczas, na skutek zużycia mechanicznego, znacząco objawia się wpływ luzu i tarcia. Drgania generowane w układzie kierowniczym motocykla w obecności luzu i tarcia mają osobliwy nieliniowy charakter procesów stick-slip. Z uwagi na progowy charakter nieliniowości związanych z luzem i tarciem oraz zmienność struktury modelu, realizacja symulacji takich układów jest trudna i wymagająca rozległych badań wstępnych. W niniejszej pracy relacjonowane są testy symulacyjne drgań skrętnych występujących w uproszczonym zastępczym modelu układu kierowniczego (wahadło torsyjne). Podano matematyczny model układu, w tym także oryginalny sposób generowania wymuszeń zewnętrznych. Przedstawiono oprogramowanie w środowisku Matiab-Simulink. Badany jest także wpływ procedur obliczeniowych na wyniki symulacji, w tym: wpływ sposobu implementacji modelu stick-slip w programie symulacyjnym, wpływ rodzaju zastosowanych algorytmów całkowania równań różniczkowych, a także wpływ zadawanych parametrów numerycznych

Metoda analizy drgań skrętnych w układzie kierowniczym motocykla na płaszczyźnie fazowej

A vibration analysis method has been described, where time functions are represented in the “phase plane”; for free vibrations, the representations are classic phase portraits. In the case of vibrations forced with sinusoidal inputs, the representations are Lissajous figures and their stroboscopic expansions to “Poincaré maps”. For the purposes of presentation of the research method proposed, the analyses of free and forced vibrations of a system close to the motorcycle steering system have been described, with the system being modelled and simulated in the Matlab-Simulink environment and with the stick-slip processes being taken into account. The calculation results depict not only the essence of the method of analysing vibrations in the phase plane but also the impact of selected model parameters (in this case, related to freeplay and friction) and measurement disturbances on the representation results. The analysis method shown is a solution alternative to the classic spectral analyses.W pracy prezentowana jest metoda analizy drgań wykorzystująca odwzorowania przebiegów czasowych na tzw. płaszczyźnie fazowej i dla przypadku drgań swobodnych są to klasyczne portrety fazowe. W przypadku drgań wymuszonych przebiegami sinusoidalnie zmiennymi są to zobrazowania typu figury Lissajous oraz ich stroboskopowe rozwinięcia do tzw. map Poincare. W celu prezentacji proponowanej metody badawczej relacjonowane są analizy drgań swobodnych i wymuszonych dotyczące układu zbliżonego do układu kierowniczego (UK) motocykla modelowanego i symulowanego w środowisku Matlab-Simulink, z uwzględnieniem procesów stick-slip. Wyniki obliczeń obrazują nie tylko istotę metody analizy drgań na płaszczyźnie fazowej, ale także wpływ wybranych parametrów modelu (tu dotyczących luzu i tarcia), a także zakłóceń pomiarowych na wyniki zobrazowań. Prezentowana metoda analizy stanowi alternatywne rozwiązanie względem klasycznych analiz widmowych

Modelling of centre differential control

In this article we present a simplified model of centre differential control. At the beginning, the introduction highlights important role of center differential control and tests carried out using mathematical models. This work contains the full development of a model, consisting of: the equations which describe the vehicle, the structure of the model, important values and parameters used in the simulation. All these components allow you to expand an existing model, thus is not necessary to create it from the beginning. It presents detailed equations which were realized by a simulation model with a simplified block diagram illustrating the structure of the model and on the next the full structure. Then a concept of a simplified torque of split control system was described and which will be continue as the basis for the simulation model. The action of the control system is presented by the simulation model implemented in Matlab Simulink. Model refers to a linear motion in different road conditions and using the control of centre differential. In the following defines the parameters and data used in the model and the fifth chapter contains sample waveforms of model variables along with their brief description. The last two points are synthetic applications and supporting literature

Selected methods for improving operating conditionsof three-phase systems working in the presenceof current and voltage deformation – part II

The paper includes a summary of long-time research conducted by a research team in the Institute of Electrical Engineering and Computer Science at Silesian University of Technology. The research work has principally been related to selected problems in the field of analysis and synthesis of systems aimed at symmetrisation and improvement of some power quality parameters. This paper constitutes the second part of the report on the research. It has been devoted to three-phase system symmetrisation as well as effective elimination of higher harmonics and substantial improvement of power quality by means of hybrid active power filters

Selected methods for improving operating conditions of three-phase systems working in the presence of current and voltage deformation – part I

The paper includes a summary and a background of long-time research conducted by a research team in the Institute of Electrical Engineering and Computer Science at SilesianUniversity of Technology. The researchwork has principally been related to selected problems in the field of analysis and synthesis of systems aimed at symmetrisation and improvement of some power quality parameters. This paper constitutes a first part of the report on the research. It has been devoted to effective elimination of higher harmonics and reactive power compensation by means of parallel active power filters. The other problem discussed in this paper is related to this issue and it is very important from the economic point of view; it addresses optimal sizing and placement of active power filters in investigated power networks

Application of Acoustic Emission Method to Determine Critical Stress in Fibre Reinforced Mortar Beams

The objective of this investigation was to test the effectiveness of the Acoustic Emission (AE) mea- surements in determining the critical stresses during four-point bending of mortar beams. Within the measuring procedure the parameter σcr/σ300 was calculated and analysed. Additionally, the influence of cement replacement by high calcium fly ash (HCFA) on the process of crack healing was discussed. Mortar beams with different content of HCFA and reinforced by steel microfibres were prepared for tests. After curing in standard conditions the beams were subjected to four-point bending test in order to introduce the pre-cracking. Thereafter the beams were cured in the lime water and loaded after 56 and 112 days in the same way as for the first time. Additionally the microstructure of mortars was studied in a stereo optical microscope as well in an electron scanning microscope including the Energy Dispersive X-ray analysis (EDX). The results of microstructural characterization of mortar containing HCFA from lignite combustion are presented. The applied load level slightly exceeded the critical stress, producing intense crack growth processes however did not significant affected the load capacity of the beams. During the consecutive loading the decreasing tendency of σcr/σ300 ratio was noted. The obtained results confirm that the latter parameter can be applied as a measure of the composite degradation level for the elements carrying the repeated loads of amplitude close to the critical stress of the structure and also that the cement replacement with HCFA influences the process of crack healing