Conservation laws for non-potential operators

The aim of this work is to study the conservation laws of continuous means mechanics and also to extend the Hamiltonian method for these kind of systems in order to valid for non-potential operators through variational approach. Besides illustrating with various examples of mechanical applications we also introduce in this work the new technique in order to treat such problems as the non-potential problem.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

Linear prediction in optical spectroscopy

A linear prediction procedure is one of the approved numerical methods of signal processing. In the field of optical spectroscopy it is used mainly for extrapolation known parts of an optical signal in order to obtain a longer one or deduce missing signal samples. The first is needed particularly when narrowing spectral lines for the purpose of spectral information extraction. In the present paper the coherent anti-Stokes Raman scattering (CARS) spectra were under investigation. The spectra were significantly distorted by the presence of nonlinear nonresonant background. In addition, line shapes were far from Gaussian/Lorentz profiles. To overcome these disadvantages the maximum entropy method (MEM) for phase spectrum retrieval was used. The obtained broad MEM spectra were further underwent the linear prediction analysis in order to be narrowed.

Novel technology for preparation of optically active chemicals

Asymmetric synthesis using modified heterogeneous catalysts has gained lots of interest in the production of optically pure chemicals, such as pharmaceuticals, nutraceuticals, fragrances and agrochemicals. Heterogeneous modified catalysts capable of inducing high enantioselectivities are preferred in industrial scale due to their superior separation and handling properties. The topic has been intensively investigated both in industry and academia. The enantioselective hydrogenation of ethyl benzoylformate (EBF) to (R)-ethyl mandelate over (-)-cinchonidine (CD)-modified Pt/Al2O3 catalyst in a laboratory-scale semi-batch reactor was studied as a function of modifier concentration, reaction temperature, stirring rate and catalyst particle size. The main product was always (R)-ethyl mandelate while small amounts of (S)-ethyl mandelate were obtained as by product. The kinetic results showed higher enantioselectivity and lower initial rates approaching asymptotically to a constant value as the amount of modifier was increased. Additionally, catalyst deactivation due to presence of impurities in the feed was prominent in some cases; therefore activated carbon was used as a cleaning agent of the raw material to remove impurities prior to catalyst addition. Detailed characterizations methods (SEM, EDX, TPR, BET, chemisorption, particle size distribution) of the catalysts were carried out. Solvent effects were also studied in the semi-batch reactor. Solvents with dielectric constant (e) between 2 and 25 were applied. The enantiomeric excess (ee) increased with an increase of the dielectric coefficient up to a maximum followed by a nonlinear decrease. A kinetic model was proposed for the enantioselectivity dependence on the dielectric constant based on the Kirkwood treatment. The non-linear dependence of ee on (e) successfully described the variation of ee in different solvents. Systematic kinetic experiments were carried out in the semi-batch reactor. Toluene was used as a solvent. Based on these results, a kinetic model based on the assumption of different number of sites was developed. Density functional theory calculations were applied to study the energetics of the EBF adsorption on pure Pt(1 1 1). The hydrogenation rate constants were determined along with the adsorption parameters by non-linear regression analysis. A comparison between the model and the experimental data revealed a very good correspondence. Transient experiments in a fixed-bed reactor were also carried out in this work. The results demonstrated that continuous enantioselective hydrogenation of EBF in hexane/2-propanol 90/10 (v/v) is possible and that continuous feeding of (-)-cinchonidine is needed to maintain a high steady-state enantioselectivity. The catalyst showed a good stability and high enantioselectivity was achieved in the fixed-bed reactor. Chromatographic separation of (R)- and (S)-ethyl mandelate originating from the continuous reactor was investigated. A commercial column filled with a chiral resin was chosen as a perspective preparative-scale adsorbent. Since the adsorption equilibrium isotherms were linear within the entire investigated range of concentrations, they were determined by pulse experiments for the isomers present in a post-reaction mixture. Breakthrough curves were measured and described successfully by the dispersive plug flow model with a linear driving force approximation. The focus of this research project was the development of a new integrated production concept of optically active chemicals by combining heterogeneous catalysis and chromatographic separation technology. The proposed work is fundamental research in advanced process technology aiming to improve efficiency and enable clean and environmentally benign production of enantiomeric pure chemicals.

Railways, Airports and Sea Container Operators as Publicly Listed Companies – Financial Performance and Shareholder Value Creation Perspective

Logistics infrastructure and transportation services have been the liability of countries and governments for decades, or these have been under strict regulation policies. One of the first branches opened for competition in EU as well as in other continents, has been air transports (operators, like passenger and freight) and road transports. These have resulted on lower costs, better connectivity and in most of the cases higher service quality. However, quite large amount of other logistics related activities are still directly (or indirectly) under governmental influence, e.g. railway infrastructure, road infrastructure, railway operations, airports, and sea ports. Due to the globalization, governmental influence is not that necessary in this sector, since transportation needs have increased with much more significant phase as compared to economic growth. Also freight transportation needs do not correlate with passenger side, due to the reason that only small number of areas in the world have specialized in the production of particular goods. Therefore, in number of cases public-private partnership, or even privately owned companies operating in these sub-branches have been identified as beneficial for countries, customers and further economic growth. The objective of this research work is to shed more light on these kinds of experiments, especially in the relatively unknown sub-branches of logistics like railways, airports and sea container transports. In this research work we have selected companies having public listed status in some stock exchange, and have needed amount of financial scale to be considered as serious company rather than start-up phase venture. Our research results show that railways and airports usually need high fixed investments, but have showed in the last five years generally good financial performance, both in terms of profitability and cash flow. In contrary to common belief of prosperity in globally growing container transports, sea vessel operators of containers have not shown that impressive financial performance. Generally margins in this business are thin, and profitability has been sacrificed in front of high growth – this also concerns cash flow performance, which has been lower too. However, as we examine these three logistics sub-branches through shareholder value development angle during time period of 2002-2007, we were surprised to find out that all of these three have outperformed general stock market indexes in this period. More surprising is the result that financially a bit less performing sea container transportation sector shows highest shareholder value gain in the examination period. Thus, it should be remembered that provided analysis shows only limited picture, since e.g. dividends were not taken into consideration in this research work. Therefore, e.g. US railway operators have disadvantage to other in the analysis, since they have been able to provide dividends for shareholders in long period of time. Based on this research work we argue that investment on transportation/logistics sector seems to be safe alternative, which yields with relatively low risk high gain. Although global economy would face smaller growth period, this sector seems to provide opportunities in more demanding situation as well.

Using the best linear predictor (BLP) in the selection between and among half-sib progenies of the CMS-39 maize population

Data of corn ear production (kg/ha) of 196 half-sib progenies (HSP) of the maize population CMS-39 obtained from experiments carried out in four environments were used to adapt and assess the BLP method (best linear predictor) in comparison with to the selection among and within half-sib progenies (SAWHSP). The 196 HSP of the CMS-39 population developed by the National Center for Maize and Sorghum Research (CNPMS-EMBRAPA) were related through their pedigree with the recombined progenies of the previous selection cycle. The two methodologies used for the selection of the twenty best half-sib progenies, BLP and SAWHSP, led to similar expected genetic gains. There was a tendency in the BLP methodology to select a greater number of related progenies because of the previous generation (pedigree) than the other method. This implies that greater care with the effective size of the population must be taken with this method. The SAWHSP methodology was efficient in isolating the additive genetic variance component from the phenotypic component. The pedigree system, although unnecessary for the routine use of the SAWHSP methodology, allowed the prediction of an increase in the inbreeding of the population in the long term SAWHSP selection when recombination is simultaneous to creation of new progenies.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Linear competitive inhibition of human tissue kallikrein by 4-aminobenzamidine and benzamidine and linear mixed inhibition by 4-nitroaniline and aniline

Hydrolysis of D-valyl-L-leucyl-L-arginine p-nitroanilide (7.5-90.0 µM) by human tissue kallikrein (hK1) (4.58-5.27 nM) at pH 9.0 and 37ºC was studied in the absence and in the presence of increasing concentrations of 4-aminobenzamidine (96-576 µM), benzamidine (1.27-7.62 mM), 4-nitroaniline (16.5-66 µM) and aniline (20-50 mM). The kinetic parameters determined in the absence of inhibitors were: Km = 12.0 ± 0.8 µM and k cat = 48.4 ± 1.0 min-1. The data indicate that the inhibition of hK1 by 4-aminobenzamidine and benzamidine is linear competitive, while the inhibition by 4-nitroaniline and aniline is linear mixed, with the inhibitor being able to bind both to the free enzyme with a dissociation constant Ki yielding an EI complex, and to the ES complex with a dissociation constant Ki', yielding an ESI complex. The calculated Ki values for 4-aminobenzamidine, benzamidine, 4-nitroaniline and aniline were 146 ± 10, 1,098 ± 91, 38.6 ± 5.2 and 37,340 ± 5,400 µM, respectively. The calculated Ki' values for 4-nitroaniline and aniline were 289.3 ± 92.8 and 310,500 ± 38,600 µM, respectively. The fact that Ki'>Ki indicates that 4-nitroaniline and aniline bind to a second binding site in the enzyme with lower affinity than they bind to the active site. The data about the inhibition of hK1 by 4-aminobenzamidine and benzamidine help to explain previous observations that esters, anilides or chloromethyl ketone derivatives of Nalpha-substituted arginine are more sensitive substrates or inhibitors of hK1 than the corresponding lysine compounds.