When a nanostructure is coupled between two leads, the electron transmission probability as a function of energy, E, is used in the Landauer formula to obtain the electrical conductance of the nanodevice. The electron transmission probability as a function of energy, T (E), is calculated from the appropriate solution of the time independent Schrödinger equation. Recently, a large class of nanostructures called quantum dragons has been discovered. Quantum dragons are nanodevices with correlated disorder but still can have electron transmission probability unity for all energies when connected to appropriate (idealized) leads. Hence for a single channel setup, the electrical conductivity is quantized. Thus quantum dragons have the minimum electrical conductance allowed by quantum mechanics. These quantum dragons have potential applications in nanoelectronics. It is shown that for dimerized leads coupled to a simple two-slice (l = 2, m = 1) device, the matrix method gives the same expression for the electron transmission probability as renormalization group methods and as the well known Green's function method. If a nanodevice has m atoms per slice, with l slices to calculate the electron transmission probability as a function of energy via the matrix method requires the solution of the inverse of a (2 + ml) (2 + ml) matrix. This matrix to invert is of large dimensions for large m and l. Taking the inverse of such a matrix could be done numerically, but getting an exact solution may not be possible. By using the mapping technique, this reduces this large matrix to invert into a simple (l + 2) (l + 2) matrix to invert, which is easier to handle but has the same solution. By using the map-and-tune approach, quantum dragon solutions are shown to exist for single-layer planar rectangular crystals with different boundary conditions. Each chapter provides two different ways on how to find quantum dragons. This work has experimental relevance, since this could pave the way for planar rectangular nanodevices with zero electrical resistance to be found. In the presence of randomness of the single-band tight-binding parameters in the nanodevice, an interesting quantum mechanical phenomenon called Fano resonance of the electron transmission probability is shown to be observed.

This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation. Paper I concerns the solutions to non-linear parabolic equations with linear growth. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the Riesz measure associated with such solutions, and the Hölder continuityof the quotient of two such solutions up to the boundary. Paper 2 concerns the solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a Muckenhoupt weight of class 1+2/n. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the parabolic measure, and the Hölder continuity of the quotient of two such solutions up to the boundary. Paper 3 concerns a fractional heat equation. The first main result is that a solution to the fractional heat equation in Euclidean space of dimension n can be extended as a solution to a certain linear degenerate parabolic equation in the upper half space of dimension n+1. The second main result is the Hölder continuity of quotients of two non-negative solutions that vanish continuously on the latteral boundary of a Lipschitz domain. Paper 4 concerns the solutions to uniformly parabolic linear equations with complex coefficients. The first main result is that under certain assumptions on the opperator the bounds for the single layer potentials associated to the opperator are bounded. The second main result is that these bounds always hold if the opperator is realvalued and symmetric.

The sequence-dependent curvature and flexibility of DNA is critical for many biochemically important processes. However, few experimental methods are available for directly probing these properties at the base-pair level. One promising way to predict these properties as a function of sequence is to model DNA with a set of base-pair parameters that describe the local stacking of the different possible base-pair step combinations. In this dissertation research, we develop and study a computational model for predicting the diffusion coefficients of short, relatively rigid DNA fragments from the sequence and the base-pair parameters. We focus on diffusion coefficients because various experimental methods have been developed to measure them. Moreover, these coefficients can also be computed numerically from the Stokes equations based on the three-dimensional shape of the macromolecule. By comparing the predicted diffusion coefficients with experimental measurements, we can potentially obtain refined estimates of various base-pair parameters for DNA. Our proposed model consists of three sub-models. First, we consider the geometric model of DNA, which is sequence-dependent and controlled by a set of base-pair parameters. We introduce a set of new base-pair parameters, which are convenient for computation and lead to a precise geometric interpretation. Initial estimates for these parameters are adapted from crystallographic data. With these parameters, we can translate a DNA sequence into a curved tube of uniform radius with hemispherical end caps, which approximates the effective hydrated surface of the molecule. Second, we consider the solvent model, which captures the hydrodynamic properties of DNA based on its geometric shape. We show that the Stokes equations are the leading-order, time-averaged equations in the particle body frame assuming that the Reynolds number is small. We propose an efficient boundary element method with a priori error estimates for the solution of the exterior Stokes equations. Lastly, we consider the diffusion model, which relates our computed results from the solvent model to relevant measurements from various experimental methods. We study the diffusive dynamics of rigid particles of arbitrary shape which often involves arbitrary cross- and self-coupling between translational and rotational degrees of freedom. We use scaling and perturbation analysis to characterize the dynamics at time scales relevant to different classic experimental methods and identify the corresponding diffusion coefficients. In the end, we give rigorous proofs for the convergence of our numerical scheme and show numerical evidence to support the validity of our proposed models by making comparisons with experimental data. / text

The purpose of this document is to study the application of Tensegrity principles on tensile textile constructions. This work studies the basic concept of Tensegrity unit, its classification according a previous researcher (Anthony Pugh) and the author’s contribution, focused on new generations of forms. Through the geometry and computer software, another typology and a constructive simple method is developed, bearing in mind, some aspects as important as system pretension to find its balance / El propósito de esta tesis es el estudio de la aplicación de los principios del tensegrity a las construcciones textiles atirantadas. El estudio del concepto básico de la unidad tensegrity, sus clasificaciones según investigadores anteriores (Anthony Pugh) y el aporte personal de nuevas generaciones de forma por medio de la geometría y programas informáticos, otra tipología y un método constructivo sencillo de realizar teniendo en cuenta aspectos tan importantes como la pretensión del sistema para buscar el equilibrio del mismo. La contribución clave de este prototipo en el campo de las estructuras ligeras es que es la primera vez que un anillo tensegrity ha sido utilizado en lugar de un anillo de compresión, para generar un domo completamente en tensegrity. Además se reemplazaron los tensores de los tensegritis tradicionales por membranas.

This diploma thesis deals with the solution of a construction of a corner gap site. A multifunctional house comprising three business establishments and nine residential units has been designed. Business premises will be used as stores. The apartments are designed for 4-member families. The multifunctional house has an atypical ground plan with a total area of 512 m2. The object has a basement and four above-ground floors, the business establishment is located on the first above-ground floor. The garage will be operated in automatic parking mode. The entire building is covered with a single-layer flat roof. The project is processed using the AutoCAD computer program.

The subject of my diploma thesis is the design of the pension with the possibility of wellness activities, which is located in the village of Holásky, on the level of documentation for the construction. The new building is located in the cadastral area Holásky. It is a three-storey, basement building in the shape of two bounce rectangles with separate parking for visitors to the pension and wellness. The supporting system consists of a reinforced concrete skeletal column system with a ceiling structure made of Spiroll core panels. Porotherm ceramic blocks with contact insulated facade according to ETICS are used for filling masonry. The roof structure is a single-skin flat roof.

Thesis dissertate power reactors and analyses techniques of an air-core power coils and inductors with ferromagnetic circuit and an air gap. Construction of the inductors verified the accuracy of the calculated values against the measured parameters. According to the outcome of this analysis, corrections of the design process are derived. Thesis design optimization to minimize size, weight, efficiency and in comparsion of these two factoctors.

The main topic of this thesis is the detailed design of new building in a secluded state administration buildings with a flat roof single shell. The building has two floors and no basement. Structural system used is brick. Vertical structures are made of Porotherm system and horizontal structures are made of monolithic reinforced concrete. The load is transferred to the monolithic strip foundation.

The topic of the thesis is the design of new residential building in Horni Loucky. The aim is to develop detailed documentation for construction. The work includes studies, drawings, text and part of the calculation. It is a detached residential building with ground plan dimensions of approximately 13.5 x 16,75 m. The building has 4 floors and a flat roof. The building is made of sand-lime bricks, ceilings are monolithic reinforced concrete. Roofing is made up of single shell flat roof. The building is located on undeveloped land in housing estates on flat terrain. Residential building contains 5 apartments, one of which is completely wheelchair and one workshop (eg hairdressing). At the building will be constructed parking area for the residents of the apartment building and premises.

The topic of the thesis is the design of new residential building in Uherské Hradiště. The aim is to develop detailed documentation for construction. The work includes studies, drawings, text and part of the calculation. It is a detached residential building with ground plan dimensions of approximately 16,5 x 26,5m. The building has 4 floors and a flat roof. The building is made of ceramic bricks, ceilings are monolithic reinforced concrete. Roofing is made up of single shell flat roof. The building is located on undeveloped land in housing estates on flat terrain. Residential building contains 16 apartments. Part of the 1st floor is also 6 separate garage.