Sharif Digital Repository

Geographical environments can be modeled through the medium of TINs, in which some discrete points are sampled as vertices, and the union of polygonal faces, particularly triangles, constitutes its surface. As regards the two-dimensional space, the TIN boundary is an x-monotone path and we focus on this case. If the number of vertices is too large to be stored or some sampled points should be removed due to a lack of vital information, the necessity of TIN simplification arises. On top of this situation, if a point observer locates on or above the TIN, the points visible to the observer have more priorities to be considered in the simplified TIN. For example, human eyes can see the closer or... 

In present study, bioelectrochemical degradation of oxalate as a substance which its concentration in kidney leads to urolithiasis in a microfluidic microbial fuel cell (MFC) was investigated. In addition, to define a novel application for the microfluidic MFC, measurement and monitoring of oxalate concentration were studied. This application can introduce the system as an implantable medical device for medical usage of urolithiasis and hyperoxaluria diseases. In this work, by designing and fabrication of two MFCs including a large-scale and microfluidic one, and measuring the outlet concentration of oxalate in the large-scale system, the outlet concentration of oxalate at microfluidic MFC... 

Tropical algebraic geometry is a fairly new branch in geometry which is called so in honor of Brazilian mathematician Imre Simon who was pioneer of this field.The set equipped with the addition and multiplication is a semifield.Algebraic geometry objects like algebraic varieties can be defined over.Polynomials and rational functions are defined over.The functions that they define are piecewise linear and concave functions and the set of points where they are nonlinear is a tropical variety which is a concave polyhedral. Thus, tropical algebraic geometry is a piecewise linear version of algebraic geometry.Another approach to tropical algebraic geometry comes back to the works of Russian... 

For a simple polygon in the plane, the visibility graph is a graph whose vertices are the vertices of the polygon and there is an edge between two vertices if and only if their corresponding vertices see each other in the polygon. Two points of the polygon see each other if the line segment connecting them lies completely inside (or on the boundary of) the polygon. Although computing the visibility graph of a polygon has been solved efficiently, its reverse problem after three decades is still an open problem. The reverse problem is known as recognition and reconstruction visibility graphs. Recognizing visibility graphs is to determine the necessary and sufficient conditions on a graph to be... 

Semiconductor-based photo catalysts, titanium dioxide (TiO2) especially, have been extensively studied for the oxidative photo destruction of organic pollutants in wastewaters and hydrogen production as a green energy source. Much effort has been made to remove the restrictions on the use of TiO2 and challenges related to the recovery of powdery photocatalysts. In this study, copper oxide (CuO) and Zirconium oxide (ZrO2) were used to synthesize nanocomposites. Composition of TiO2/CuO and TiO2/ZrO2 with different weight percentages of second dioxide was synthesized by chemical methods and structural properties of samples were studied by X-ray diffraction and scanning electron microscopy.... 

Here, the properties of separability of linkages are studied. In general, a linkage is a simple polygonal chain embedded in 3-space with disjoint, straight-line edges, which are fixed-length bars. The internal vertices are called joints. If the two end points are connected then the linkage is a closed linkage, otherwise it is an open linkage. By imposing restrictions on the way the bars in joints can move, three kinds of linkages as rigid, revolute and flexible can be introduced. A motion in a linkage is the motion of its vertices that preserves the length of the bars, and adheres the restrictions on joints. A collection of linkages are said to be separatable if for any distance d, there is... 

This study consists of two parts: steady state calculations and neutron noise calculations in the frequency domain for two rectangular and hexagonal geometries. In the steady state calculation, the neutron diffusion and its adjoint equations are approximated by two-dimensional coordinates in two-group energy and are solved using the average current nodal expansion method. Then, by considering the node size in the dimensions of a fuel assembly, different orders of flux expansion are investigated. For verification purposes, the calculations have been performed by power iteration method for two test problems of BIBLIS-2D and IAEA-2D. For rectangular geometry with increasing flux expansion order... 

The widespread use of nuclear energy leads to obtain detailed information, such as neutron flux distribution (power) which is very effective in designing and evaluating the reactor safety. The neutron flux (power) reconstruction method uses the homogeneous flux distribution and the heterogeneous form function in a fuel assembly to calculate the heterogeneous power in the fuel rods. Therefore, this method has been widely developed in the last two decades. This study investigates to calculate two-dimensional and two-group neutron flux (power) in the fuel rod for both quadrilateral and hexagonal geometry related to core results by using nodal method. To achieve a more complete program and join... 

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.... 

The ever-increasing demand for wireless communication has raised the need for better utilization of bandwidth and energy. Intelligent Reflecting Surface (IRS) is an emerging technology that has been proposed for the sixth generation of wireless communication. In this thesis, we study the essential role these surfaces can play in improving the physical layer security.First, we consider a relatively realistic scenario for the location of the eavesdroppers. In this scenario, we will assume that the transmitters, users, and eavesdroppers all use a single antenna configuration, and the eavesdroppers are placed randomly across the studied region. Two notable parameters in physical layer security,... 

Novel two dimensional and three dimensional antenna array geometries for smart antenna application are introduced. MMSE beamforming algorithm, using these arrays, in presence of signal, noise and interferences is implemented. Beamforming approach is used for every type of array assuming uniform and log-normal distributions for the interference amplitudes. Equal volume cylindrical or prism type arrays with circular, hexagonal, triangular, square and star cross sections with equal number of elements are considered for comparison. Novel geometries consisting of rotated cross sections are studied as well. In each case the relative SIR’s are compared in these geometries, showing that the... 

More than 70 weight percentage of using parts in diverse industries (such as military, civil, automobile productions and etc.) are produceed by the casting processes. For each one of the casting procceses, mold cavity is requisite for arrived molten metal in the mold cavity to get eventuated as a solidified part. Based on mold ilk, if the mold is permanent, the cast part must be capable to be remoeved from the the mold inside. For the non-permanent mold (asssuming multi-piece and non-monolithic), if the model requires to be removed from the mold inside after molding and before casting, only model (no cast part) has to be moldable (why for removing the solidified cast part from the... 

Guarding terrains(or covering terrains) is a well known problem in the field of visibility and computational geometry. The aim of this problem is to select a minimal set of elements (such as points on terrain, line segment, points above terrain ,...),as guard set, such that every point of the terrain is visible from at least one member of the guard set.
This problem was introduced in 2-dimensions as art gallery problem. Various types of this problem have been defiend and studied in the literature. Guarding 3-dimensional terrains is an example of this problem. In 3-dimentional case, the guarded terrain can be modeled with triangulated irregullar network(TIN), as one of the surface models,... 

Using the achievements of differential geometry an extended form of descent equations is worked out which leads to a set of modified consistent anomalies. A gauge invariant partition function is also defined for gauge theories with the standard quantization results. It is shown that the (extended) descent equations and consequently the (modified) consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally. Moreover Translation-invariant products are discussed in the setting of α-cohomology and it is shown that loop calculations of Translation-invariant quantum field theories are entirely determined by α-cohomology class of star product in all... 

Many geometric problems have algorithms that exist on paper for them, such as the Convex Hull problem [1], Minimum Spanning Tree [2], Voronoi Diagram [3], Closest Pair of Points [4], Largest Empty Circle [5], Smallest Enclosing Circle [6], and more. In all of these problems, the assumption is that a certain number of points are given as input, and we must perform various operations on these points based on the nature of the problem. Furthermore, a stronger assumption is that these points are given to us precisely, but in reality, this is not the case, and for various reasons, it is not possible to determine the exact locations of these points. Therefore, it can be said that we are dealing... 

In this research, we consider the question of finding approximate bounds on some of computational geometry problems with uncertain data. We use color spanning set to model the uncertainty. Given a set of n points colored with m colors in d-dimension. The problem of minimum diameter in color spanning set model is finding a set of m points with distinct colors so as to minimize diameter of the points. We give an algorithm with an approximation factor (1 + ϵ) with running time O(21ϵd .ϵ−2d.n3) which improves the previous results. Next,we consider a new problem of finding bounds on unit covering in color-spanning set model:Minimum color spanning-set ball covering problem is to select m points of... 

In this research, we want to find a point of the kernel in an unknown star-shaped polygon by a robot with minimal sensing, such that the path is not far from the optimum path. The robot has a gap sensor which detects the dicontinuities (gaps) in its visibility polygon and detects the direction of gaps. The robat can move toward or against these gaps. Also, the robot has a compass, and detects the North, the West, the South and the East. The robot detects the position of gaps between these directions, and also, can move along these directions. In this research, we present an on-line algorithm, by which this robot can find a point of the kernel in an unknown star-shaped polygon. The... 

Along with improvement of technology and need for access to energy resources, existence of pipelines such as gas, oil and water pipes is vital for our lives. These pipes will be eroded and damaged over time. With the prediction of the defects and tracking of pipeline paths, the probability of sudden damages is greatly reduced. In this research, at first various non-destructive methods of monitoring the pipelines are investigated and it is shown that the laser method is the most comprehensive and non-destructive inspection method and then the background of the chosen method is examined. Also, the hardware aspect of the system and the proper layout of the laser sensors are determined on the... 

One of the ultimate goals in robotics is to design autonomous robots. Among other things, this means a robot has to be able to plan its own motion. To be able to plan a motion, a robot must have some knowledge about the environment in which it is moving. Some of this information can be provided by a floor plan. For other information the robot will have to rely on its sensors. In this thesis, we consider that the environment is unknown for the robot. So, the robot uses weak sensor to planning its motion. The sensor can distinguish between colors. The robot can follow the colors. Therefore, we need to specify the umber of colors in which the robot can navigate by them. We propose an efficient...