Sharif Digital Repository

Grothendieck’s theory of dessin d’enfant makes a connection between piecewise flat metrics and conformal structures on a compact surface R on one hand, and the defining equation for R whose coefficients lie in an algebraic number field on the other. This connection is realized by a combinatorial structure (a dessin) on a given surface R.In this thesis we begin by briefly reviewing Grothendieck’s theory of dessin d’enfant and Belyi’s theorem and also the approximation of a Belyi map via Thurston’s theory of circle packings.We then introduce a method for computing the explicit equation of the Riemann surface and Belyi map associated to a dessin. Also we explain how the absolute Galois group... 

In this thesis, zero-divisor ideal graphs and geometric zero-divisor graphs are introduced and are partially studied. We begin by studying the relation between the zero-divisor graph and zero-divisor ideal graph associated to principal ideal rings. We also investigate some of the basic properties of the zero-divisor ideal graphs, including their girth and diameter. Then, we introduce the geometric zero-divisor graphs associated to reduced schemes and study their basic properties to some extent. Finally, we conclude by characterizing all reduced schemes whose associated geometric zero-divisor graph contains a vertex which is... 

This thesis is devoted to study some asymptotic behaviors of Poisson Voronoi tessellation in the Euclidean space as dimension of the space tends to infinity. First we use Blaschke-Petkantschin formula to prove that the variance of volume of the typical cell tends to zero exponentially in dimension. It is also shown that the volume of intersection of the typical cell with the co-centered ball of volume converges in distribution to the constant . Next we consider the linear contact distribution function of the Poisson Voronoi tessellation and compute the limit when dimension goes to infinity. As a byproduct, the chord length distribution and the geometric covariogram of the typical cell are... 

The main purpose of this thesis is to study computational questions related to compact Riemann surfaces (algebraic curves) with main emphasis on the theory of Grothendieck’s dessins d’enfants; where recovering the explicit formula of a Belyi map from the corresponding dessin on a topological surface is important. Some applications such as investigating the modular j-function and also certain classes of modular curves are included in this thesis along with a summary of attempts toward generalizing the Belyi theorem to complex dimension two.First two chapters contain necessary prerequisites on compact Riemann surfaces and a short introduction to the theory of dessins d’enfants and Belyi... 

Learning of shape classes from a set of given data is of special practical importance in computer vision. Large variations in the surrounding objects makes the problem of shape learning a very di°cult one. These di°culties may vary according to diferences in pose and part articulations of shapes. Despite all of the problems, large applications of this problem in areas such as tracking, object recognition and text recognition inspires many groups to work on it. In this thesis we aim to investigate a solution for this problem  

The focus of this thesis is the computation of the discrepancy for any given distribution of points on S2. The problem of the distribution of points on the sphere has a long history and Thomson’s Problem, inspired by early atomic theory dating back to 1904, was a landmark. While Thomson’s Problem is based on the Coulomb potential, the discrepancy measures the deviation of the number of points in a set from the expected one. The Polar Coordinates method was introduced in the context of Thomson’s problem. In this thesis the order of the growth of the discrepancy for this method is investigated and a modification of it is shown to lead to the best known results. In addition a new algorithm is... 

The meaning and the nature of space and it’s essential properties seems to be one of the oldest problems which has been continuing to occupy human’s mind during centuries. It can be counted as a common ground between philosophy, mathematics, physics and even art. However this thesis concentrates on the philosophical and mathematical attitudes, neglecting the other aspects of the issue. Prima facie, it appears that the concept of space is essentially mingled with geometry, the science which seems to investigate the essentials of space. Taking it for granted, Kant regarded space, and so Euclidean geometry which dominates it, as an indispensible and necessary structure of the human’s mind.... 

Using interpolation and starting with Bernoulli numbers, posed by Leopold and Kubota, the aspect of adic function was constructed as adic analogues of the Dirichlet functions.Studing Galois module theory of ideal class group and his favorite structure extensions and modules related to them,Iwasawa found a new method for constructing adic functions by using Stickelberger’s elements.These results wich established by Iwasawa are known as Iwasawa Theory and they have many application in Algebriac Number Theory. Iwasawa’s most remarkable disconvry is the facet that at least in some important cases, there is a similar deep algebraic and analytic dichotomy in arithmetic of extensions. A... 

Gauss' theory of the arithmetic of quadratic forms appeared in Disquisitiones Arithmeticae (1801) and in particular Gauss presented a composition law for binary quadratic forms and related it to the arithmetic of quadratic extensions of Q. In the series of papers of “Higher Composition Laws” Manjul Bhargava gave a far reaching generalization of Gauss' composition law and extended it to binary cubic, and a number of other cases. He obtained six composition laws one of which the classical one of Gauss. Since the work of Gauss has had deep impact on number theory and in particular on the arithmetic of quadratic fields, one expects that Bhargava’s theory to lead to new insights in... 

In a solar central system plant about 40% of energy losses occurs in the heliostat field. Furtheremore, half of the investment costs for construction of the plant is related to the heliostat field. Therefore, an optimal design of the heliostat field is necessary for reduction of levelized cost of energy in solar tower power plants. In this study, in order to optimally design the heliostat field, first energy performance of the helistat field in one year is simulated. Solar power and sun’s position at each moment of the day is determined by mathematical relations. Then, loss factors in the field are modelled and heliostat field layout is designed by an algorithm. Finally, by using PSO... 

Today, due to the scarcity of fossil energy resources, security of energy supply, and increasing environmental concerns, we need to develop new technologies to promote energy-saving and reduce greenhouse gas emissions. One of the suitable options for this purpose is to use the simultaneous production of electric power, cooling, and heating. Meanwhile, trigeneration systems that provide part of their energy needs from the sun, due to the free solar energy source and low environmental impact, can be an ideal technology for clean and safe scattered production. The present study has suggested a trigeneration system of cooling, heating, and power generation based on the organic Rankin cycle and... 

Today, due to increasing electricity consumption and demand, the use of conventional systems such as thermal, hydro and nuclear power plants is not enough to convert energy. Over the past century, scientists have sought to discover new technologies for exploiting different forms of energy and converting them into high-efficiency electrical energy. One of these ways is to use the phenomenon of magnetohydrodynamics (magnetic fluid dynamics) to convert thermal energy directly into electrical energy. Magnetohydrodynamics is a theoretical field that studies the dynamics of fluids with electrical conductivity. Induction magneto-hydrodynamic generators use ionized hot plasma (a quasi-neutral gas of... 

The power generation system of this type of power plants operates on the air flowing through the power plant’s chimney and colliding with the turbine blades within the chimney. When the solar collector warms the nearby air and thus expands the air by absorbing the sunlight, a difference is created in the density. Then, this difference in the density creates the phenomenon of buoyancy, making the air pass to the top of the chimney through the collector.This study simulated and optimized a solar chimney power plant. The simulation and optimization were performed based on the information of Manzanares Solar Chimney Power Plant in Spain (located in 150 km from the south of Madrid). It was... 

The issue under discussion in this paper is to optimize the fuel consumption of the Toyota Prius hybrid car. In order to solve this problem, the ADVISOR design model used by NREL in the Matlab / Simulink environment has been used. Various parts of this model are described. The optimization performed on this issue is based on the emotional controller. This controller works by simulating learning in animals based on encouraging and punishing them. With the introduction of the controller, the model and its inclusion in the fuel consumption control and its implementation have achieved good results. In the initial state and the controller in the model, the fuel consumption was 4.9 liters per 100... 

In this thesis, an attempt has been made to provide a smart and innovative system to optimize fuel consumption in cars by using the combination of engineering sciences, aerospace, and machine learning. Considering the current challenges of societies, the economic importance of saving fuel, as well as recent developments in the fields of machine learning and reinforcement learning, this research tries to improve the performance of cars in order to minimize the air resistance force of car bodies. In this regard, deep neural networks have been used to learn the dynamics of aerodynamic forces and reinforcement learning algorithms, especially DDPG (Deep Deterministic Policy Gradient), have been...