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Darbe „Akcijų kainų kintamumo analizė“ nagrinėjami ir lyginami Baltijos (Lietuvos, Latvijos, Estijos) bei Lotynų Amerikos (Meksikos, Venesuelos) šalių duomenys. Atliekama pasirinktų akcijų kainų grąžų analizė. Jai naudojami trijų metų kiekvienos dienos duomenys (akcijų kainos). Pirmoje darbo dalyje supažindinama su bendra prognozavimo metodų teorija, aprašomi skirtingi, dažnai literatūroje ir praktikoje sutinkami modeliai. Antrojoje dalyje aprašyti prognozavimo metodai taikomi realiems duomenims, t.y. pasirinktoms akcijoms. Prognozuojama akcijų kainų grąža, kuri po to yra palyginama su realia reikšme, apskaičiuojamos prognozavimo metodų paklaidos. Pagrindinis darbo tikslas – atlikti lyginamąją prognozavimo modelių analizę su pasirinktomis akcijomis ir atrinkti tuos metodus, kurie duoda geriausius rezultatus. Darbo tikslui įgyvendinti naudojama SAS statistinio paketo ekonometrikos ir laiko eilučių analizės posistemė SAS/ETS (Time Series Forecasting System). / Most of empirical surveys in macro and financial economics are based on time series analysis. In this work, data of Baltic and Latin America countries is being analyzed and compared. Analysis of stock price returns is presented using daily long term (three years) period data. In the first part of this work general forecasting theory is presented, also different methods, frequently met in the literature and practice, are described. In the second part, forecasting models are being applied for real data. We present results of forecasting stock returns comparing them with real values. Also a precision of forecasts is being calculated, which let us to decide about propriety of each model. Consequently, the aim of this work is to forecast returns of stock price by various time series models and to choose the best one. The analysis was made using SAS statistical package and its econometrics and Time Series Analysis System (SAS/ETS).

Dažnai realių stochastinių sistemų dinamikos negalime aprašyti Markovo procesu, nes operacijų trukmės paprastai nėra pasiskirstę pagal eksponentinį dėsnį. Darbe buvo išnagrinėtas tokių atsitiktinių dydžių aproksimavimas dviejų eksponentinių atsitiktinių dydžių mišiniu. Paprasčiausioms sistemoms kartais galima gauti analizines formules sistemos būsenų stacionarioms tikimybėms suskaičiuoti, tačiau daugeliui sistemų to padaryti negalima. Būtent tokių sistemų tyrimui, panaudojus aproksimavimo algoritmus, buvo sukurta programinė įranga, kuri leidžia modeliuoti daugelį stochastinių sistemų. Magistro darbo užduotis: Sukurti stochastinių sistemų modelių aproksimavimo Markovo modeliais algoritmus ir programinę įrangą. Buvo iškelti tokie tikslai: Ištirti pasiskirstymo funkcijų aproksimavimo eksponentinių skirstinių mišiniu galimybes; Sukurti universalią programinę priemonę, kuri pagal pateiktą sistemos aprašymą, skaičiuotų jos stacionariąsias tikimybes bei funkcionavimo charakteristikas; Sukurtos programinės priemonės pagalba, sudaryti ir ištirti aptarnavimo sistemų ir vertybinių popierių įkainojimo modelius. Sukurta programinė įranga pasižymi universalumu ir paprastumu vartotojui. Sistemos funkcionavimą galima aprašyti turint minimalias C++ Builder programavimo kalbos žinias. Magistro darbe sukurta programinė įranga buvo pritaikyta aptarnavimo sistemoms modeliuoti, akcijų kainų dinamikai aprašyti bei opcionams įkainoti. / Application of numerical methods with approximation allows to extend a class of systems represented by Markovian processes under investigation compared with analytical methods. So a goal was stated to create algorithms for modeling stochastic systems approximating them by Markovian models. To reach this goal the following tasks were solved: Analyze possibilities to approximate stochastic systems’ models by Markovian models; Create a multipurpose software that would calculate stationary probabilities for given system described in an event-based language; Apply created software for models of service systems and stock valuation. Created software is universal and easy-to-use for anyone that has at least basic knowledge in C++ language. This software was applied for modeling of service systems, for description of share price variability as Markovian process and for option pricing.

Vernal pools are small, seasonally filling wetlands found throughout forests of north eastern North America. Vernal pools have been proposed as potential 'hot spots' of carbon cycling. A key component of the carbon cycle within vernal pools is the decomposition of leaf litter. I tested the hypothesis that leaf litter decomposition is more rapid within vernal pools than the adjacent upland. Leaf litter mass losses from litterbags incubated in situ within vernal pools and adjacent upland habitat were measured periodically over one year and then again after two years. The experiment was carried out at 24 separate vernal pools, over two replicate years. This is a novel degree of replication in studies of decomposition in temporary wetlands. Factors influencing decomposition, such as duration of flooding, water depth, pH, temperature, and dissolved oxygen were measured. Mass loss was greater within pools than adjacent upland after 6 months, equal after 12 months, and lower within pools than adjacent upland after 24 months. This evidence suggests that vernal pools of Central Ontario are 'hot spots' of decomposition up to 6 months, but not after 12 and 24 months. In the long term, vernal pools may reduce decomposition rates, compared to adjacent uplands.

This study compares four recently developed decline curve methods and the traditional Arps or Fetkovich approach. The four methods which are empirically formulated for shale and tight gas wells are: 1. Power Law Exponential Decline (PLE). 2. Stretched Exponential Decline (SEPD). 3. Duong Method. 4. Logistic Growth Model (LGM). Each method has different tuning parameters and equation forms. The main objective of this work is to determine the best method(s) in terms of Estimated Ultimate Recovery (EUR) accuracy, goodness of fit, and ease of matching. In addition, these methods are compared against each other at different production times in order to understand the effect of production time on forecasts. As a part of validation process, all methods are benchmarked against simulation. This study compares the decline methods to four simulation cases which represent the common shale declines observed in the field. Shale wells, which are completed with horizontal wells and multiple traverse highly-conductive hydraulic fractures, exhibit long transient linear flow. Based on certain models, linear flow is preceded by bilinear flow if natural fractures are present. In addition to this, linear flow is succeeded by Boundary Dominated Flow (BDF) decline when pressure wave reaches boundary. This means four declines are possible, hence four simulation cases are required for comparison. To facilitate automatic data fitting, a non-linear regression program was developed using excel VBA. The program optimizes the Least-Square (LS) objective function to find the best fit. The used optimization algorithm is the Levenberg-Marquardt Algorithm (LMA) and it is used because of its robustness and ease of use. This work shows that all methods forecast different EURs and some fit certain simulation cases better than others. In addition, no method can forecast EUR accurately without reaching BDF. Using this work, engineers can choose the best method to forecast EUR after identifying the simulation case that is most analogous to their field wells. The VBA program and the matching procedure presented here can help engineers automate these methods into their forecasting sheets.

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Certain hydrogel forming de novo proteins that utilize different crosslinking methods are studied experimentally on a rheometer. The stress reaxation modulus of CRC, a telechelic, triblock protein, is shown to be that of a stretched exponential function with a value of β ≅ 0.5. The insertion of an integrin binding domain and changes in pH within the range 6.5–8.5 are shown not to significantly affect the resulting rheological behavior. A selective chemical crosslinker is used on CRC hydrogel systems and is shown to change the rheological behavior of the system to that of a combination of a chemically and physically crosslinked system. Chemically crosslinked hydrogels composed of W6, a wheat gluten-based protein, demonstrate a storage modulus weakly dependent on the angular frequency that is much greater than the loss modulus, with a modulus concentration dependence of c^9/4.

In this thesis, the free vibration analysis of anisotropic laminated composite shells of revolution (ALCSOR) is studied. The governing equations are kinematic, constitutive, and motion equations. Geometrically linear strain-displacement equations of Reissner-Naghdi shell theory in combination with first-order shear deformation theory in which transverse shear and rotatory inertia effects are taken into consideration. The constitutive relations are for macrosopically ALCSOR in which statically equivalent force and moment resultants, instead of internal stresses for a single layer, are introduced. Equations of motion for the free vibration problem are obtained by the Hamilton&amp / #8217 / s principle. The derived governing equations for the free vibration analysis of ALCSOR are initially formulated into a system of partial differential equations in terms of fundamental variables. Then, those partial differential equations are reduced to a system of first order ordinary differential equations by applying finite exponential Fourier Transform method resulting in a two point boundary value problem. It has been demonstrated that the application of the finite exponential Fourier transform made it possible to solve the governing equations, comprising the full anisotropic form of the constitutive equations, which was otherwise impossible to solve with the classical Fourier decomposition method. First, the boundary value problem formulated is reduced to a series of initial value problems, then the multisegment numerical integration is used in combination with the frequency trial method in order to find the critical modes within a given range of natural frequencies. A computer code DALSOR is written for the solution of the natural frequencies and mode shapes of mascroscopically ALCSOR. DALSOR is applicable to any general boundary condition at both ends of the shell, and allows for variation of all elastic and geometric properties in the meridional direction. Numerical results are presented, and mainly discussions on the method of solution and the effect of macroscopic anisotropy on modal characteristics, mainly natural frequencies, are made. Various case studies are performed primarily on cylindrical shells in order to investigate the effects of mainly fiber orientation angle, stacking sequence, arbitrary boundary conditions at the edges of the shell, thickness-to-radius ratio on the modal characteristics, mainly natural frequencies. Application of the method of solution has also been demonstrated for a truncated composite spherical shell.

In the thesis "On Boundaries of Statistical Models" problems related to a description of probability distributions with zeros, lying in the boundary of a statistical model, are treated. The distributions considered are joint distributions of finite collections of finite discrete random variables. Owing to this restriction, statistical models are subsets of finite dimensional real vector spaces. The support set problem for exponential families, the main class of models considered in the thesis, is to characterize the possible supports of distributions in the boundaries of these statistical models. It is shown that this problem is equivalent to a characterization of the face lattice of a convex polytope, called the convex support. The main tool for treating questions related to the boundary are implicit representations. Exponential families are shown to be sets of solutions of binomial equations, connected to an underlying combinatorial structure, called oriented matroid. Under an additional assumption these equations are polynomial and one is placed in the setting of commutative algebra and algebraic geometry. In this case one recovers results from algebraic statistics. The combinatorial theory of exponential families using oriented matroids makes the established connection between an exponential family and its convex support completely natural: Both are derived from the same oriented matroid. The second part of the thesis deals with hierarchical models, which are a special class of exponential families constructed from simplicial complexes. The main technical tool for their treatment in this thesis are so called elementary circuits. After their introduction, they are used to derive properties of the implicit representations of hierarchical models. Each elementary circuit gives an equation holding on the hierarchical model, and these equations are shown to be the "simplest", in the sense that the smallest degree among the equations corresponding to elementary circuits gives a lower bound on the degree of all equations characterizing the model. Translating this result back to polyhedral geometry yields a neighborliness property of marginal polytopes, the convex supports of hierarchical models. Elementary circuits of small support are related to independence statements holding between the random variables whose joint distributions the hierarchical model describes. Models for which the complete set of circuits consists of elementary circuits are shown to be described by totally unimodular matrices. The thesis also contains an analysis of the case of binary random variables. In this special situation, marginal polytopes can be represented as the convex hulls of linear codes. Among the results here is a classification of full-dimensional linear code polytopes in terms of their subgroups. If represented by polynomial equations, exponential families are the varieties of binomial prime ideals. The third part of the thesis describes tools to treat models defined by not necessarily prime binomial ideals. It follows from Eisenbud and Sturmfels' results on binomial ideals that these models are unions of exponential families, and apart from solving the support set problem for each of these, one is faced with finding the decomposition. The thesis discusses algorithms for specialized treatment of binomial ideals, exploiting their combinatorial nature. The provided software package Binomials.m2 is shown to be able to compute very large primary decompositions, yielding a counterexample to a recent conjecture in algebraic statistics.

This thesis consists of a summary and five papers, dealing with self-normalized sums of independent, identically distributed random variables, and three-decision procedures for directional conclusions. In Paper I, we investigate a general set-up for Student's t-statistic. Finiteness of absolute moments is related to the corresponding degree of freedom, and relevant properties of the underlying distribution, assuming independent, identically distributed random variables. In Paper II, we investigate a certain kind of self-normalized sums. We show that the corresponding quadratic moments are greater than or equal to one, with equality if and only if the underlying distribution is symmetrically distributed around the origin. In Paper III, we study linear combinations of independent Rademacher random variables. A family of universal bounds on the corresponding tail probabilities is derived through the technique known as exponential tilting. Connections to self-normalized sums of symmetrically distributed random variables are given. In Paper IV, we consider a general formulation of three-decision procedures for directional conclusions. We introduce three kinds of optimality characterizations, and formulate corresponding sufficiency conditions. These conditions are applied to exponential families of distributions. In Paper V, we investigate the Benjamini-Hochberg procedure as a means of confirming a selection of statistical decisions on the basis of a corresponding set of generalized p-values. Assuming independence, we show that control is imposed on the expected average loss among confirmed decisions. Connections to directional conclusions are given.