Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.

Probiotic lactobacilli and bifidobacteria in the mouth – in vitro studies on saliva-mediated functions and acid production

Probiotic lactobacilli and bifidobacteria in the mouth – in vitro studies on saliva-mediated functions and acid production Probiotics are viable bacteria which, when used in adequate amounts, are beneficial to the health of the host. Although most often related to intestinal health, probiotic bacteria can be found also in the mouth after consumption of products that contain them. This study aimed at evaluating the oral effects of probiotic bacteria already in commercial use. In a series of in vitro studies, the oral colonisation potential of different probiotic bacteria, their acid production and potential saliva-mediated effects on oral microbial ecology were investigated. The latter included effects on the salivary pellicle, the adhesion of other bacteria, and the activation of the peroxidase system. Streptococcus mutans, Streptococcus gordonii, Aggregatibacter actinomycetemcomitans and Helicobacter pylori were used as bacterial indicators of the studied phenomena. There were significant differences between the probiotic strains in their colonisation potential. They all were acidogenic, although using different sugars and sugar alcohols. However, their acid production could be inhibited by the peroxidase system. Based on the results, it can be suggested that probiotic bacteria might influence the oral microbiota by different, partly species or strain-specific means. These include the inhibition of bacterial adhesion, modification of the enamel pellicle, antimicrobial activity, and activation of the peroxidase system. To conclude, probiotic strains differed from each other in their colonisation potential and other oral effects as evaluated in vitro. Both positive and potentially harmful effects were observed, but the significance of the perceived results needs to be further evaluated in vivo.

A primeira lei da termodinâmica dos processos homogêneos

Thermodynamics of homogeneous processes, which corresponds to the very special situation in thermodynamics of continuous media, is used to discuss the first law. An important part of this work is the exposition of some typical mathematical errors, frequently found in the traditional presentation of thermodynamics. The concepts of state and process functions are discussed, as well as reverse and reversible processes, temporality and its implications on thermodynamics, energy reservoirs and symmetry. Our proposal is to present the first law by using a time dependent viewpoint coherent with mechanics and the foundations of that viewpoint.

Sintonização de estados quânticos: um estudo numérico do oscilador harmônico quântico

The quantum harmonic oscillator is described by the Hermite equation.¹ The asymptotic solution is predominantly used to obtain its analytical solutions. Wave functions (solutions) are quadratically integrable if taken as the product of the convergent asymptotic solution (Gaussian function) and Hermite polynomial,¹ whose degree provides the associated quantum number. Solving it numerically, quantization is observed when a control real variable is "tuned" to integer values. This can be interpreted by graphical reading of Y(x) and |Y(x)|², without other mathematical analysis, and prove useful for teaching fundamentals of quantum chemistry to undergraduates.

Mathematical equation correction to spectral and transport interferences in high-resolution continuum source flame atomic absorption spectrometry: determination of lead in phosphoric acid

In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.

Analysis of electricity distribution network operation business models and capitalization of control room functions with DMS

Electricity distribution network operation (NO) models are challenged as they are expected to continue to undergo changes during the coming decades in the fairly developed and regulated Nordic electricity market. Network asset managers are to adapt to competitive technoeconomical business models regarding the operation of increasingly intelligent distribution networks. Factors driving the changes for new business models within network operation include: increased investments in distributed automation (DA), regulative frameworks for annual profit limits and quality through outage cost, increasing end-customer demands, climatic changes and increasing use of data system tools, such as Distribution Management System (DMS). The doctoral thesis addresses the questions a) whether there exist conditions and qualifications for competitive markets within electricity distribution network operation and b) if so, identification of limitations and required business mechanisms. This doctoral thesis aims to provide an analytical business framework, primarily for electric utilities, for evaluation and development purposes of dedicated network operation models to meet future market dynamics within network operation. In the thesis, the generic build-up of a business model has been addressed through the use of the strategicbusiness hierarchy levels of mission, vision and strategy for definition of the strategic direction of the business followed by the planning, management and process execution levels of enterprisestrategy execution. Research questions within electricity distribution network operation are addressed at the specified hierarchy levels. The results of the research represent interdisciplinary findings in the areas of electrical engineering and production economics. The main scientific contributions include further development of the extended transaction cost economics (TCE) for government decisions within electricity networks and validation of the usability of the methodology for the electricity distribution industry. Moreover, DMS benefit evaluations in the thesis based on the outage cost calculations propose theoretical maximum benefits of DMS applications equalling roughly 25% of the annual outage costs and 10% of the respective operative costs in the case electric utility. Hence, the annual measurable theoretical benefits from the use of DMS applications are considerable. The theoretical results in the thesis are generally validated by surveys and questionnaires.

On the development of object functions and restrictions for shapes made with a turret punch press

This study presents the information required to describe the machine and device resources in the turret punch press environment which are needed for the development of the analysing method for automated production. The description of product and device resources and their interconnectedness is the starting point for method comparison the development of expenses, production planning and the performance of optimisation. The manufacturing method cannot be optimized unless the variables and their interdependence are known. Sheet metal parts in particular may then become remarkably complex, and their automatic manufacture may be difficult or, with some automatic equipment, even impossible if not know manufacturing properties. This thesis consists of three main elements, which constitute the triangulation. In the first phase of triangulation, the manufacture occuring on a turret punch press is examined in order to find the factors that affect the efficiency of production. In the second phase of triangulation, the manufacturability of products on turret punch presses is examined through a set of laboratory tests. The third phase oftriangulation involves an examination of five industry parts. The main key findings of this study are: all possible efficiency in high automation level machining cannot be achieved unless the raw materials used in production and the dependencies of the machine and tools are well known. Machine-specific manufacturability factors for turret punch presses were not taken into account in the industrial case samples. On the grounds of the performed tests and industrial case samples, the designer of a sheet metal product can directly influence the machining time, material loss, energy consumption and the number of tools required on a turret punch press by making decisions in the way presented in the hypothesis of thisstudy. The sheet metal parts to be produced can be optimised to bemanufactured on a turret punch press when the material to be used and the kinds of machine and tool options available are known. This provides in-depth knowledge of the machine and tool properties machine and tool-specifically. None of the optimisation starting points described here is a separate entity; instead, they are all connected to each other.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Cognitive Functions After Traumatic Brain Injury. A 30-year Follow-up Study

Many cognitive deficits after TBI (traumatic brain injury) are well known, such as memory and concentration problems, as well as reduced information-processing speed. What happens to patients and cognitive functioning after immediate recovery is poorly known. Cognitive functioning is flexible and may be influenced by genetic, psychological and environmental factors decades after TBI. The general aim of this thesis was to describe the long-term cognitive course after TBI, to find variables that may contribute to it, and how the cognitive functions after TBI are associated with specific medical factors and reduced survival. The original study group consisted of 192 patients with TBI who were originally assessed with the Mild Deterioration Battery (MDB) on average two years after the injury, during the years 1966 – 1972. During a 30-year follow-up, we studied the risks for reduced survival, and the mortality of the patients was compared with the general population using the Standardized Mortality Ratio (SMR). Sixty-one patients were re-assessed during 1998-2000. These patients were evaluated with the MDB, computerized testing, and with various other neuropsychological methods for attention and executive functions. Apolipoprotein-E (ApoE) genotyping and magnetic resonance imaging (MRI) based on volumetric analysis of the hippocampus and lateral ventricles were performed. Depressive symptoms were evaluated with the short form of the Beck depression inventory. The cognitive performance at follow-up was compared with a control group that was similar to the study group in regard to age and education. The cognitive outcome of the patients with TBI varied after three decades. The majority of the patients showed a decline in their cognitive level, the rest either improved or stayed at the same level. Male gender and higher age at injury were significant risk factors for the decline. Whereas most cognitive domains declined during the follow-up, semantic memory behaved in the opposite way, showing recovery after TBI. In the follow-up assessment, the memory decline and impairments in the set-shifting domain of executive functions were associated with MRI-volumetric measures, whereas reduction in information-processing speed was not associated with the MRI measures. The presence of local contusions was only weakly associated with cognitive functions. Only few cognitive methods for attention were capable of discriminating TBI patients with and without depressive symptoms. On the other hand, most complex attentional tests were sensitive enough to discriminate TBI patients (non-depressive) from controls. This means that complex attention functions, mediated by the frontal lobes, are relatively independent of depressive symptoms post-TBI. The presence of ApoE4 was associated with different kinds of memory processes including verbal and visual episodic memory, semantic memory and verbal working memory, depending on the length of time since TBI. Many other cognitive processes were not affected by the presence of ApoE4. Age at injury and poor vocational outcome were independent risk factors for reduced survival in the multivariate analysis. Late mortality was higher among younger subjects (age < 40 years at death) compared with the general population which should be borne in mind when assessing the need for rehabilitation services and long-term follow-up after TBI.

NADPH-Dependent Thioredoxin System In Regulation of Chloroplast Functions

Photosynthesis, the process in which carbon dioxide is converted into sugars using the energy of sunlight, is vital for heterotrophic life on Earth. In plants, photosynthesis takes place in specific organelles called chloroplasts. During chloroplast biogenesis, light is a prerequisite for the development of functional photosynthetic structures. In addition to photosynthesis, a number of other metabolic processes such as nitrogen assimilation, the biosynthesis of fatty acids, amino acids, vitamins, and hormones are localized to plant chloroplasts. The biosynthetic pathways in chloroplasts are tightly regulated, and especially the reduction/oxidation (redox) signals play important roles in controlling many developmental and metabolic processes in chloroplasts. Thioredoxins are universal regulatory proteins that mediate redox signals in chloroplasts. They are able to modify the structure and function of their target proteins by reduction of disulfide bonds. Oxidized thioredoxins are restored via the action of thioredoxin reductases. Two thioredoxin reductase systems exist in plant chloroplasts, the NADPHdependent thioredoxin reductase C (NTRC) and ferredoxin-thioredoxin reductase (FTR). The ferredoxin-thioredoxin system that is linked to photosynthetic light reactions is involved in light-activation of chloroplast proteins. NADPH can be produced via both the photosynthetic electron transfer reactions in light, and in darkness via the pentose phosphate pathway. These different pathways of NADPH production enable the regulation of diverse metabolic pathways in chloroplasts by the NADPH-dependent thioredoxin system. In this thesis, the role of NADPH-dependent thioredoxin system in the redox-control of chloroplast development and metabolism was studied by characterization of Arabidopsis thaliana T-DNA insertion lines of NTRC gene (ntrc) and by identification of chloroplast proteins regulated by NTRC. The ntrc plants showed the strongest visible phenotypes when grown under short 8-h photoperiod. This indicates that i) chloroplast NADPH-dependent thioredoxin system is non-redundant to ferredoxinthioredoxin system and that ii) NTRC particularly controls the chloroplast processes that are easily imbalanced in daily light/dark rhythms with short day and long night. I identified four processes and the redox-regulated proteins therein that are potentially regulated by NTRC; i) chloroplast development, ii) starch biosynthesis, iii) aromatic amino acid biosynthesis and iv) detoxification of H₂O₂. Such regulation can be achieved directly by modulating the redox state of intramolecular or intermolecular disulfide bridges of enzymes, or by protecting enzymes from oxidation in conjunction with 2-cysteine peroxiredoxins. This thesis work also demonstrated that the enzymatic antioxidant systems in chloroplasts, ascorbate peroxidases, superoxide dismutase and NTRC-dependent 2-cysteine peroxiredoxins are tightly linked up to prevent the detrimental accumulation of reactive oxygen species in plants.

Orthogonal function method in modelling paper web quality variation

This work is devoted to the analysis of signal variation of the Cross-Direction and Machine-Direction measurements from paper web. The data that we possess comes from the real paper machine. Goal of the work is to reconstruct the basis weight structure of the paper and to predict its behaviour to the future. The resulting synthetic data is needed for simulation of paper web. The main idea that we used for describing the basis weight variation in the Cross-Direction is Empirical Orthogonal Functions (EOF) algorithm, which is closely related to Principal Component Analysis (PCA) method. Signal forecasting in time is based on Time-Series analysis. Two principal mathematical procedures that we used in the work are Autoregressive-Moving Average (ARMA) modelling and Ornstein–Uhlenbeck (OU) process.

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.