Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear systemthat produces, with a tolerance index ǫ, the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.
The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.
The study makes an attempt to model a complete vibrating guitar including its non-linear features, specifically the tension-compression of truss rod and tension of strings. The purpose of such a model is to examine the influence of design parameters on tone. Most experimental studies are flawed by uncertainties introduced by materials and assembly of an instrument. Since numerical modelling of instruments allows for deterministic control over design parameters, a detailed numerical model of folk guitar was analysed and an experimental study was performed in order to simulate the excitation and measurement of guitar vibration. The virtual guitar was set up like a real guitar in a series of geometrically non-linear analyses. Balancing of strings and truss rod tension resulted in a realistic initial state of deformation, which affected the subsequent spectral analyses carried out after dynamic simulations. Design parameters of the guitar were freely manipulated without introducing unwanted uncertainties typical for experimental studies. The study highlights the importance of acoustic medium in numerical models.
The present work focuses on the modeling and analysis of mechanical properties of structural steel. The effect of major alloying elements namely carbon, manganese and silicon has been investigated on mechanical properties of structural steel. Design of experiments is used to develop linear models for the responses namely Yield strength, Ultimate tensile strength and Elongation. The experiments have been conducted as per the full factorial design where all process variables are set at two levels. The main effect plots showed that the alloying elements Manganese and Silicon have positive contribution on Ultimate tensile strength and Yield strength. However, Carbon and Manganese showed more contribution as compared to Silicon. All three alloying elements are found to have negative contribution towards the response- Elongation. The present work is found to be useful to control the mechanical properties of structural steel by varying the major alloying elements. Minitab software has been used for statistical analysis. The linear regression models have been tested for the statistical adequacy by utilizing ANOVA and statistical significance test. Further, the prediction capability of the developed models is tested with the help of test cases. It is found that all linear regression models are found to be statistically adequate with good prediction capability. The work is useful to foundrymen to choose alloying elements composition to get desirable mechanical properties.
We studied the thermophilous grass Bromus erectus in Central Europe to determine its pattern of population genetic structure and genetic diversity, using ISSR-PCR fingerprinting to analyze 200 individuals from 37 populations. We found three genetic groups with a clear geographic structure, based on a Bayesian approach. The first group occurred west and south of the Alps, the second east and north of the Alps, and the third was formed by four genetically depauperated populations in Germany. The populations from Germany formed a subset of the Bohemian-Moravian populations, with one private allele. Two differentiation centers, one in the Atlantic- Mediterranean and the second in the Pannonian-Balkan area, were recognized by species distribution modeling. The geographic distribution of the genetic groups coincides with the syntaxonomic split of the Festuco-Brometea class into the Festucetalia valesiaceae and Brometalia erecti orders. We found a statistically significant decrease in mean ISSR bands per individual from south to north, and to a lesser extent from the east to west. The former was explained by Holocene long-distance migrations from southern refugia, the latter by the difference in the gradient of anthropopression. We hypothesize a cryptic northern shelter of the species in Central Europe in the putative Moravian-Bohemian refugium.
Adsorption experiments of nitric oxide in nitrogen carrier gas were held on activated carbon in a fixed bed flow system. Breakthrough curves describing the dependence of exit concentrations of nitric oxide on time were matched with theoretical response curves calculated from the linear driving force model (LDF). The model assumes Langmuir adsorption isotherm for the description of non-linear equilibrium and overall mass transfer coefficient for mass transfer mechanism. Overall mass transfer coefficients were obtained by the method of least squares for fitting numerically modelled breakthrough curves with experimental breakthrough curves. It was found that LDF model fits all the breakthrough curves and it is a useful tool for modelling purposes.
The national total expenditure of a country is precipitated on several factors of which revenue generated could be one and very significant. This paper therefore examines the contribution of some selected sources of Nigerian government revenue to total national expenditure. Statistical and econometric techniques used for the data analysis are unit root test, cointegration test, combined estimators’ analysis, the error correction model (ECM) and the feasible generalized linear (FGLS) estimators. Results showed that the variables are non stationary but are stationary at first difference. The long-run relationship of total expenditure on oil revenue, non-oil revenue, federation account and federal retained revenue revealed that the variables are co-integrated and required the use of combined estimators. The effect of non-oil revenue and federal retained revenue is very significant. Investigations on the short-run modeling necessitated the use of FGLS estimators. The effect of ECM and federal retained revenue is very significant. Consequently, other sources of revenue apart from federal retained revenue need to be enhanced and tailored towards improving economic growth and development through national expenditure.
One of the most important problems concerning contaminant transport in the ground is the problem related to the definition of parameters characterizing the adsorption capacity of ground for the chosen contaminants relocating with groundwater. In this paper, for chloride and sulfate indicators relocating in sandy ground, the numerical values of retardation factors (Ra) (treated as average values) and pore groundwater velocities with adsorption (ux/Ra) (in micro-pore ground spaces) are taken into consideration. Based on 2D transport equation the maximal dimensionless concentration values (C*max c) in the chosen ground cross-sections were calculated. All the presented numerical calculations are related to the unpublished measurement series which was marked in this paper as: October 1982. For this measurement series the calculated concentration values are compared to the measured concentration ones (C*max m) given recently to the author of this paper. In final part of this paper the parameters characterizing adsorption capacity (Ra, ux/Ra) are also compared to the same parameters calculated for the two earlier measurement series. Such comparison also allowed for the estimation of a gradual in time depletion of adsorption capacity for the chosen sandy ground.
A simulation-based optimization approach to design of phase excitation tapers for linear phased antenna arrays is presented. The design optimization process is accelerated by means of Surrogate-Based Optimization (SBO); it uses a coarse-mesh surrogate of the array element for adjusting the array’s active reflection coefficient responses and a fast surrogate of the antenna array radiation pattern. The primary optimization objective is to minimize side-lobes in the principal plane of the radiation pattern while scanning the main beam. The optimization outcome is a set of element phase excitation tapers versus the scan angle. The design objectives are evaluated at the high fidelity level of description using simulations of the discrete electromagnetic model of the entire array so that the effects of element coupling and other possible interaction within the array structure are accounted for. At the same time, the optimization process is fast due to SBO. Performance and numerical cost of the approach are demonstrated by optimizing a 16-element linear array of microstrip antennas. Experimental verification has been carried out for a manufactured prototype of the optimized array. It demonstrates good agreement between the radiation patterns obtained from simulations and from physical measurements (the latter constructed through superposition of the measured element patterns).