For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75. For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements. Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.

This thesis addresses optimal control problems with elasticity for large deformations. A hyperelastic model with a polyconvex energy density is employed to describe the elastic behavior of a body. The two approaches to derive the nonlinear partial differential equation, a balance of forces and an energy minimization, are compared. Besides the conventional volume and boundary loads, two novel internal loads are presented. Furthermore, curvilinear coordinates and a hierarchical plate model can be incorporated into the formulation of the elastic forward problem. The forward problem can be solved with Newton\\\'s method, though a globalization technique should be used to avoid divergence of Newton\\\'s method. The repeated solution of the Newton system is done by a CG or MinRes method with a multigrid V-cycle as a preconditioner. The optimal control problem consists of the displacement (as the state) and a load (as the control). Besides the standard tracking-type objective, alternative objective functionals are presented for problems where a reasonable desired state cannot be provided. Two methods are proposed to solve the optimal control problem: an all-at-once approach by a Lagrange-Newton method and a reduced formulation by a quasi-Newton method with an inverse limited-memory BFGS update. The algorithms for the solution of the forward problem and the optimal control problem are implemented in the finite-element software FEniCS, with the geometrical multigrid extension FMG. Numerical experiments are performed to demonstrate the mesh independence of the algorithms and both optimization methods.

The main focus of this work lies in the simulation of the deformation of mechanical components which consist of nonlinear elastic, incompressible material and that are subject to large deformations. Starting from a nonlinear formulation one can derive a discrete problem by using linearisation techniques and an adaptive mixed finite element method. This turns out to be a saddle point problem that can be solved via a Bramble-Pasciak conjugate gradient method. With some modifications the simulation can be improved.:1. Introduction 2. Basics 3. Mixed variational formulation 4. Solution method 5. Error estimation 6. LBB conditions 7. Improvement suggestions

The elasticity of factor substitution between capital and labor is a crucial parameter in many economic fields. However, despite extensive research, there is no agreement on its value. Utilizing 738 estimates from 41 studies published between 1961 and 2016, this paper provides the first meta-regression analysis of capital-labor substitution elasticities for the U.S. economy. We show that heterogeneity in reported estimates is driven by the choice of estimation equations, the modeling of technological dynamics, and data characteristics. Based on the underlying meta-regression sample and a "best practice" specification, we estimate a long-run elasticity in the range of 0.6 to 0.7. For all estimated elasticities the hypothesis of a Cobb-Douglas production function is rejected.

In der vorliegenden Arbeit wird ein gemischtes Element gegen Locking-Effekte untersucht. Dazu wird ein Fünf-Feld-Hu-Washizu-Funktional (CoFEM-Element) für lineare und quadratische Hexaeder-Elemente unter einer hyperelastischen, isotropen, polykonvexen sowie einer transversal-isotropen Materialformulierung implementiert. Die resultierenden nichtlinearen Gleichungen werden mithilfe eines Mehrebenen-NEWTON-RAPHSON-Verfahren unter Beachtung einer konsistenten Linearisierung gelöst. Als repräsentatives Beispiel der numerischen Untersuchungen dient der einseitig eingespannte Cook-Balken mit einer quadratischen Druckverteilung am Rand. Zur Beurteilung des CoFEM-Elements wird das räumliche Konvergenzverhalten für unterschiedliche Polynomgrade und für verschiedene Netze unter Beachtung der algorithmischen Effizienz untersucht. / This paper presents a mixed finite element formulation of Hu-Washizu type (CoFEM) designed to reduce locking effects with respect to a linear and quadratic approximation in space. We consider a hyperelastic, isotropic, polyconvex material formulation as well as transverse isotropy. The resulting nonlinear algebraic equations are solved with a multilevel NEWTON-RAPHSON method. As a numerical example serves a cook-like cantilever beam with a quadratic distribution of in-plane load on the Neumann boundary. We analyze the spatial convergence with respect to the polynomial degree of the underlying Lagrange polynomials and with respect to the level of mesh refinement in terms of algorithmic efficiency.

Chapter 1 discusses the econometric pitfalls associated with the use of patent production functions to study the invention process. It then goes on to argue that a sound understanding of the invention process necessarily requires an understanding of the propensity to patent. The empirical analysis carried out in Chapter 1 seeks to explain the proportion of inventions patented – a potential metric for the propensity to patent – from an international sample of manufacturing firms. <p><p>Chapter 2 proposes a methodology to filter out the noise induced by varying patent practices in the R&D-patent relationship. The methodology explicitly decomposes the patent-to-R&D ratio into its components of productivity and propensity. It is then applied to a novel data set of priority patent applications in four countries and six industries.<p><p>Chapter 3 takes stock of the literature on the role of fees in patent systems while Chapter 4 presents estimates of the price elasticity of demand for patents at the trilateral offices (that is, in the U.S. Japan and Europe). The estimation of dynamic panel data models of patent applications suggests that the long-term price elasticity is about -0.30.<p> / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

The aim of this thesis was to find anomalies of elastic properties induced by topological changes of the Fermi surface. The latter are called &amp;quot;Lifshitz transitions&amp;quot;. Lifshitz transitions are an interesting subject to study because a topological change of the Fermi surface results in a van Hove singularity of the density of states at the Fermi energy, which again induces an anomaly in the free energy and therefore yield anomalies of observable physical quantities. In all cases the question arose, if the corresponding van Hove singularities are large enough to cause anomalies in the elastic properties, which are measurable by nowadays experimental techniques and computable within the accuracy reachable in nowadays computer calculations. The calculations have been done with the Full-Potential nonorthogonal Local-Orbital minimum-basis band-structure code FPLO. To shift the van Hove singularities through the Fermi energy we used hydrostatic pressure, which is mimicked in the computations by decreasing the volume of the unit cell. The materials under consideration had been YCo5 and LaCo5 as examples for magnetic compounds and the element Osmium as an example for a non-magnetic material. All these materials exhibit hexagonal symmetry. In the case of YCo5 our calculations yield a first order Lifshitz transition. Here, an extraordinarily large peak in the spin-up part of the DOS, which is caused by a nearly dispersionless band in the hexagonal plane, crosses the Fermi level under a pressure of about 21 GPa. Thus, the spin-up 3d states become partly depopulated, which results in a drop of the total magnetic moment of 35%. Therefore the transition can be regarded as a transition from strong to weak ferromagnetism. Further, the transition results in a volume collapse of 1.4%. Though the volume collapse is isomorphic, it exhibits the following anisotropy: while the lattice constant in the hexagonal plane is almost smoothly contracting with increasing pressure, the lattice constant in c-direction collapses at the transition-pressure. This volume collapse has been verified in experiment. Analogous calculations have been performed for the compound LaCo5, which is isoelectronic to YCo5. Here as well we predict a first order Lifshitz transition, taking place at a pressure of about 23 GPa. The mechanism of the transition is the same than in YCo5. Again we find a volume collapse under pressure together with a decrease of the magnetic moment. The relative volume change amounts to 1.3%. Like in YCo5, the unit cell dimensions in the hexagonal plane are decreasing almost smoothly with pressure while in c-direction the lattice constant collapses at the transition-pressure. For LaCo5 there are no such experiments done so far to the best of our knowledge. For Osmium we found, that LDA reproduces the ground state volume very well. Furthermore, we could detect three Lifshitz transitions taking place at very high pressures of about 72 GPa, 81 GPa, and 122 GPa. At first, a hole ellipsoid appears at the Gamma-point (V=24.6Å^3, P=72 GPa), then a neck is created at the symmetry-line LH (V=24.2Å^3, P=81 GPa), and finally a hole ellipsoid appears at the L-point (V=23.2 Å^3, P=122 GPa). Due to a degeneracy in the band structure, the hole ellipsoid at the L-point appears at the same pressure when the necks, situated at the symmetry-lines LH merge at L. The corresponding van Hove singularities in the DOS are very tiny and thus no anomalies in the elastic properties could be detected. Furthermore, we showed that the kink in c/a at 25 GPa and at 27 GPa found by Occelli et al. [Occelli et al., Phys. Rev. Lett. 93, 095502 (2004)] and Ma et al. [Ma et al., Phys. Rev. B 72, 174103 (2005)], respectively, is not statistically significant and that (c/a)(P) can be fitted equally well by a smooth function as by piece-wise linear functions as proposed in these references. / Das Ziel dieser Arbeit war es, Anomalien in den elastischen Eigenschaften zu finden, die durch topologische Änderungen der Fermifläche - genannt &amp;quot;Lifschitz Übergänge&amp;quot; - hervorgerufen werden. Lifschitz Übergänge sind ein interessantes Forschungsgebiet, denn die topologische Änderung der Fermifläche führt zu einer van Hove Singularität in der Zustandsdichte, die an der Fermienergie liegt und eine Anomalie in der freien Energie hervorruft und deswegen zu Anomalien in beobachtbaren physikalischen Größen führt. In allen Fällen kam die Frage auf, ob die entsprechenden van Hove Singularitäten groß genug sind, um mit heutigen Methoden meßbare und berechenbare Anomalien in den elastischen Eigenschaften zu verursachen. Die Daten wurden mit dem Computerprogramm FPLO (Full-Potential nonorthogonal Local-Orbital minimum-basis band-structure scheme) berechnet. Um die van Hove Singularitäten durch die Fermienergie zu schieben, verkleinerten wir das Volumen der Einheitszelle, um hydrostatischen Druck zu simulieren. Als zu untersuchende Stoffe wurden YCo5 und LaCo5 als Beispiele für magnetische Verbindungen gewählt und Osmium als Beispiel für ein nicht magnetisches Element. Im Falle von YCo5 fanden wir einen Lifschitz Übergang erster Ordnung. Hier springt ein besonders großer Peak im Spin-auf Teil der Zustandsdichte unter einem Druck von ca. 21 GPa über die Fermienergie. Dadurch werden die Spin-auf 3d Zustände teilweise unbesetzt und das magnetische Moment verringert sich um 35%. Deswegen kann man den Übergang als einen Übergang von starkem Ferromagnetismus zu schwachem Ferromagnetismus bezeichnen. Das Volumen verkleinert sich hierbei um 1.4%. Obwohl dieser Volumenkollaps isomorph ist, zeigt er folgende Anisotropie: während die Gitterkonstante in der hexagonalen Ebene mit zunehmendem Druck mehr oder weniger glatt kontrahiert, kollabiert am Übergangsdruck die Gitterkonstante in c-Richtung. Dieser Volumenkollaps wurde vom Experiment verifiziert. Analoge Rechnungen wurden für die Verbindung LaCo5, die isoelektronisch zu YCo5 ist, durchgeführt. Auch hier sagen wir einen Lifschitz Übergang erster Ordnung voraus, der bei einem Druck von ca. 23 GPa stattfinden wird. Der Mechanismus dieses Übergangs ist der selbe wie in YCo5. Wiederum finden wir einen Volumenkollaps unter Druck zusammen mit einer Verringerung des magnetischen Moments. Die relative Volumenänderung beträgt hier 1.3%. Wie in YCo5 verläuft hier die Kontraktion der Gitterkonstante in der hexagonalen Ebene mehr oder weniger glatt, während die Gitterkonstante in c-Richtung am Übergang kollabiert. Für LaCo5 existieren unseres Wissens hierzu noch keine Experimente. Im Falle von Osmium fanden wir drei Lifschitz Übergänge bei sehr hohen Drücken von ca. 72 GPa, 81 GPa, und 122 GPa. Zuerst bildet sich ein Lochellipsoid am Gamma-Punkt (V=24.6Å^3, P=72 GPa), dann bildet sich ein Hals an der Symmetrielinie LH (V=24.2Å^3, P=81 GPa), und zum Schluß erscheint ein Lochellipsoid am L-Punkt (V=23.2 Å^3, P=122 GPa). Auf Grund einer Entartung in der Bandstruktur taucht das Lochellipsoid am L-Punkt an dem Druck auf, an dem sich auch die Hälse auf der Symmetrielinie LH bei L verbinden. Die entsprechenden van Hove Singularitäten in der Zustandsdichte sind jedoch extrem klein und deswegen können keine Anomalien in den elastischen Eigenschaften detektiert werden. Desweiteren zeigten wir, daß der Knick in c/a, den Occelli et al. [Occelli et al., Phys. Rev. Lett. 93, 095502 (2004)] bei 25 GPa und Ma et al. [Ma et al., Phys. Rev. B 72, 174103 (2005)] bei 27 GPa fanden, statistisch nicht relevant ist und daß (c/a)(P) genauso gut von einer glatten Funktion gefittet wird als von stückweise linearen Funktionen.

This study estimates the price and income elasticity coefficients of electricity demand in the mining sector of South Africa for the period ranging from April 2006 to March 2019. A time varying parameter (TVP) model with the Kalman filter is applied to monitor the evolution of the elasticity estimates. The TVP model can provide a robust estimation of elasticities and can detect any outliers and structural breaks. The results indicate that income and price elasticity coefficients of electricity demand are lower than unit. The income elasticity of demand has a positive sign and it is statistically significant. This indicates that mining production – used as a proxy for mining income – is a significant determinant of electricity consumption in the mining sector. In its final state income elasticity is estimated at 0.15 per cent. On the contrary, price does not play a significant role in explaining electricity demand. In fact, the price elasticity coefficient was found to be positive which is contrary to normal economic convention. This lack of response is attributed mainly to the mining sector’s inability to respond, rather than an unwillingness to do so. A fixed coefficient model in a form of Ordinary Least Squares (OLS) is used as a benchmark model to estimate average price and income elasticity coefficients for the period. The results of the OLS regression model confirm that price does not play a significant role in explaining electricity consumption in the mining sector. An average price elasticity coefficient of -0.007 has been estimated. Income elasticity was estimated at 0.11 for the period under review. The CUSUM of squares test indicate that parameters of the model are unstable. The Chow test confirms 2009 as a breakpoint in the data series. This means that elasticity coefficients of electricity demand in the mining sector are time variant. Thus the OLS results cannot be relied upon for inference purposes. The Kalman filter results are superior. This study cautions policy makers not to interpret the seeming lack of response to price changes as an indication that further prices increases could be implemented without hampering electricity consumption in the sector. Furthermore, it recommends that the electricity pricing policy should take into account both the negative impacts of rapid price increases and the need to invest in long-term electricity infrastructure in order to improve the security of energy supply. A long term electricity price path should be introduced in order to provide certainty and predictability in the price trajectory. This would allow all sectors of the economy sufficient time and space to make investment and operational decisions that would have the least adverse effects on economic growth and job creation. / Economics / M. Com. (Economics)

In the theoretical part of the thesis, different methods of testing frost susceptibility in the Czech Republic and other countries of the European Union are compared. The practical part of the thesis deals with laboratory testing of frost susceptibility of concrete and mixed recycled materials using the direct method of frost heave tests as well as determining the California Bearing Ratio (CBR) and design module of elasticity using the cyclic triaxial test. Suitability of materials for construction of road infrastructure is then assessed on the basis of the results of these tests.

In 2022, food prices increased rapidly, prompting this investigation into how the price shock has impacted consumer behavior. Previous studies have found that price shocks affect low- income households with children the most. A switch to more calorie-dense food and a decreased consumption of snacks. This study aims to estimate the price elasticity of various food products and to identify how the elasticities differ among various types of households. The elasticities are calculated using OLS regression on receipt data from Coop. Results show that household variables, including income level, presence of children, shopping location, and organic product preferences, significantly impact the price elasticity of food products. Low-income households without children, living outside major cities and their suburbs, have a higher price elasticity, meaning these shoppers are more sensitive to price changes. The same tendencies were observed for all products even though the exact parameters could only be proven for a third of the products. The findings have important implications for understanding how price changes affect consumer behavior and can inform food policy decisions. / Under 2022 ökade livsmedelspriserna kraftigt, vilket inspirerade denna undersökning av hur prischocken har påverkat konsumenternas beteende. Tidigare studier visar att prischocker har störst påverkan på låginkomsthushåll med barn. Även en övergång till mer kaloririk mat och en minskad konsumption av snacks har observerats. Syftet med denna studie är att uppskatta priselasticiteten för olika livsmedel och identifiera hur elasticiteten skiljer sig åt mellan olika typer av hushåll. Elasticiteterna beräknas med hjälp av en OLS-regression på kvittodata från Coop. Resultaten visar att hushållsvariabler, inklusive inkomstnivå, barn i hushållet, varans inköpsplats och val av ekologiska produkter, påverkar priselasticiteten för livsmedel markant. Hushåll med låg inkomst utan barn, som bor utanför större städer och deras förorter, har en högre priselasticitet, vilket innebär att dessa kunder är mer priskänsliga. Samma tendenser observerades för alla produkter även om de exakta parametrarna endast kunde bevisas för en tredjedel av produkterna. Resultaten har viktiga implikationer för förståelsen av hur prisförändringar påverkar konsumentbeteenden och kan även informera livsmedelspolitiska beslut.