Sharif Digital Repository

Hyperbolic branching Brownian motion is a branching diffusion process in which individual particles follow independent Brownian paths in the hyperbolic plane H2, and undergo binary fission(s) at rate λ > 0. It is shown that there is a phase transition in λ : For λ ≤ 1/8 the number
of particles in any compact region of H2 is eventually 0, w.p.1, but for λ > 1/8 the number of particles in any open set grows to ∞ w.p.1. In the subcritical case (λ ≤ 1/8) the set Λ of all limit points in ∂H2 (the boundary circle at ∞) of particle trails is a Cantor set, while in the supercritical case (λ > 1/8) the set Λ has full Lebesgue measure. For λ ≤ 1/8 it is shown that w.p.1 the Hausdorff dimension of Λ... 

In this essay we focus on the question of whether a 3-manifold (possibly with bound- ary) like M supports a codimension-1 transversely oriented foliation like F , such that F is transverse to ∂M and does not have Reeb components. If such foliation exists, then ∂M is necessarily a (possibly
empty) union of tori and (based on the works of Novikov, Reeb and Rosenberg) M is either S2 × S1(with F being the prod- uct foliation) or M is irreducible. In a paper by David Gabai, which we discuss, the sufficiency of these conditions is proved in case of non-trivial second homology group.Furthermore, from the works of Thurston it is concluded that compact leaves of such foliation are norm minimizing... 

Given a principal bundle a characteristic class is an element of the cohomology al- gebra of the classifying space of structure group of the bundle with coefficients in a commutative ring with unit ,which have a functorial property .When the structure groupe of the bundle is a Lie group and the coefficient ring is the real or complex num- bers , the Chern–Weil approach provides a geometric construction of char-acteristic classes. Classical Chern–Weil formalism relates geometry to topology, assigning to the cur- vature of a connection, de Rham cohomology classes of the underlying manifold.This theory developped in the 40’s by Shiing-ShenChern and Andre Weil which can be seen as a generalisation... 

One of the most important applications of artificial intelligence, and especially deep learning is image captioning. Given an image, the task is to automatically produce a sentence, describing the image. Image captioning has several real world applications like helping the blind understanding the images, generating automatic captions for the social media, etc. In the past, several different methods for image captioning have been used, but after the emergence of deep learning, like many other areas, image captioning algorithms have been improved significantly. In this thesis, I talk about a specific method for image captioning, called ”Deep Compositional Captioning. In this method, at first... 

In the present study, the Ricci curvature is defined on the graphs by using two methods and the lower bounds are obtained. In the first method, which is related to Bakry and Emery, a definition for Ricci curvature and lower bounds would be obtained by using Curvature-Dimension inequalities.The second method which is related to Ollivier, is based on the fact that in Riemannian Geometry,the Ricci Curvature controls the velocity of convergence and divergence of emanated geodesics from a same source. Next, the more Curvature-Dimension inequalities for Ricci curvature would be obtained by using local clustering. Finally, the Bonnet-Myers theorem would be proved on the graphs.
 

In this thesis, the aim is to stating some of the noncommutative geometry(NCG) applications in formulating and describing the gravity. So, in the first chapter, we will work on some of metric aspects of NCG. In this chapter, we will review elements of the spin geometry, specifically we will define the Dirac operator which is the most important object in this thesis. Then, we will try to find counterparts of some of Riemannian geometric notions like integral and distance in the NCG framework. We will define some notions such as noncommutative infinitesimals, Dixmier trace, Wodzicki residue, noncommutative integral and spectral triples. Then, in the second chapter, we will work on some of the... 

In this thesis, a discrete exterior calculus is studied. Discrete exterior calculus is an attempt to create a discrete analogy of differential geometry and topology which is potentially applicable in computer science and physics. At first, simplicial complexes are presented as approximation of smooth manifolds. Then discrete forms and discrete exterior derivative are defined. We will observe that Stokes, theorem can be stated and proved in discrete analogy too. We will obtain Hodge operator by using dual complex and after that discrete Laplacian and Heat kernel will be calculated by using Hodge operator. In addition, we will define discrete vector field independent of discrete forms and then... 

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, . . .This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution  

In this thesis, we first define the pseudo-distance p on the group of Hamiltonian diffeomorphisms.Using the concept of displacement energy, we show that the pseudo-distance p is degenerate and if the manifold is closed, p will be zero for each p = 1; 2; 3; : : : Then, we introduce Lagrangian submanifolds and prove that if L R2n is a rational Lagrangian submanifold, we have the following inequality e(L) ≥ 1γ(L). : Finally, using the above inequality and the concept of displacement energy, for M = R2n we prove that 1 is non-degenerate. Therefore, the hypothesis for 1 to be a metric, are satisfied. This metric is called Hofer’s metric  

Non-overlapping Cameras in multi-camera systems have become prevalent in robotics and computer vision research; therefore, it is possible to cover the wide field of view, and researches have been done for computing extrinsic parameters of cameras. These cameras do not have any overlap in their views, so obtaining the corresponding point in their images is somehow impossible. Light and shadow geometry is analogous to Structure from Motion problem. In this thesis,we study Structure from Motion problem and have tried to propose an approach for estimating extrinsic parameters of non-overlapping cameras in Multi-camera systems. We formulate the problem by using light and shadow geometry and... 

In this study, different metal oxides were impregnated on the surface of ZSM-5 employed as photocatalysis for degradation of methylene blue dye used in the presence of ultraviolet light. The final products were characterized by powder X-ray diffraction (XRD) and fourier transform infrared (FT-IR) method. According to the proposed mechanism for the photocatalytic degradation of methylene blue based on these results, it was found that the reaction followed from the first-order mechanism. The results indicated that rate constant for pure ZSM-5 was 9.3〖 ₓ10〗^(-3) (min-1). Furthermore the impregnated ZSM-5 having 12% zinc oxide demonstrated the highest photocatalytic activity with rate constant... 

Disturbance is one of the inseparable components of the mechanical systems which cannot be avoided. In these systems a number of inner and outer sources exist which are the cause of disturbance. Abrupt changes in torque, uncertainty in parameters, mechanical impulses and external forces on robot’s parts all can be mentioned as examples which introduce disturbance that affects the output of mechanical and robotic systems. Therefore, disturbance rejection is considered indispensable in robotic control systems. There are number of problems which are associated with disturbance rejection. In several methods, mostly optimization based methods, system fails to completely reject the disturbance and... 

In this project, after studies about red mud, a product of the Bayer process in production of Alumina, its properties, and characteristics, red mud samples, taken from Jajarm Alumina production unit, were studied, tested, and processed. After primary preparation, characteristic determination experiments were performed on these wastes that contain iron oxide, TiO2, Al2O3, etc., and some of their physical, chemical and mineralogical characteristics were determined. These experiments include chemical analysis, XRD, XRF, compressive strength measurement, grain size distribution, prosity, etc. Considering the properties of this substance and its ceramic usages, processess of making ceramic... 

Nowadays, microfluidic flow appears in many applications, such as medical, biological, and chemical industries. Where as, micromixing, which deals with mixing of microfluidic flow in micro channels, appears to be an important issue to many researchers. In such systems, molecular diffusion plays an important role. On the other hand, lattice Boltzmann method is a relatively new simulation technique for complex fluid systems and has become interesting to many researchers in computational physics. In this study, computational simulation of such mixing process, using LBM is the main objective. Different obstacle layouts inside a microchannel have been investigated. Chaotic advection and jet... 

In the past few decades there has been rapid advance in the use of digital cameras in different fields of art and science. Photo editing softwares have provided extensive facilities for their users and graphic softwares have astonished people with artificial yet fabulous images. Under these circumstances, recognition and distinction of authentic images from digitally-manipulated ones have become a critically important but notoriously daunting task. Users of the internet and computers need to recognize authentic images from the manipulated ones, or distinguish a composite photo from an original one. Digital image forensicsa was born as a response to these demands and has so far provided...