Sharif Digital Repository

Simultaneous triangulation of matrices is a subject with a rich literature. There are many well known theorems available, such as McCoy theorem or Burnsides. In the nite dimensional case since the all the topologies on vector spaces are the same, there is a little bit diculty and most of the arguments are from linear algebra. In this thesis we study the simultaneous triangulation of sub algebras of K(X),with X a innite dimensional Banach space. We will give a denition of simultaneous triangulation which is independent of the notion of Basis and totally relies on Invariant subspaces. This denition coincides with the denition of simultaneous triangulation in nite dimensional case. Then we will... 

The aim of this thesis is to study invariants of Diophantine forms and equations. These invariants are the transformations that do not change the original equations and forms. This thesis has a different view to the concept of invariants from Hlibertian view. Based on this new definition, by having one of the solutions of the equation, new solutions can be found with invariant method. The number of these solutions can be finite or infinite. In case of infinite solutions this method is more important. The focus of this thesis is on forms and linear invariants. The most important result in this text is about two main theorems that can classify the invariants of all completely decomposable... 

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 recent years, sparse representation has had a variety of applications in computer vision such as noise reduction, image reconstruction, classification and dimension reduction. In this project, we aim to provide a method of matching the keypoints obtained from the Scale Invariant feature Transform (SIFT) algorithm. In this algorithm is used descriptor instead of intensity . The proposed method, first, extracts the salient points from the images and learns a dictionary-based descriptors corresponding to the points. Then, using the dictionary, it obtains the sparse coefficients for each salient point by which, it determines the correspondence of the salient points in the two images using SVD... 

Order reduction is a very important issue in Control Theory. A growing need for order reduction models in different fields such as simulation, identification, and design of control system shows this significance. Actually, a high-order system makes a great deal of complexity in designing hardware of control system, debugging, and implementation. Till nowadays, many repetitive as well as nonrepetitive methods with various criteria have been introduced to find low-order models. In this research, order reduction of linear time invariant system models is analyzed. The selected criterion for measuring error between original system and reduced order system is the norm of H1 because it is not only... 

In normal diffusion, the mean-square displacement (MSD) of a Brownian particle is proportional to time. However, diffusion in disordered systems, i.e. transport on fractal geometries, does not follow the classical laws of BM, and this leads to many anomalous physical properties. In the anomalous regime, the most famous definition of anomaly is the deviation of MSD, from the ‘normal’ linear dependence on time ⟨r2(t)⟩ ta. Specifically, we study the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time (MFPT) of two sided and subordinated diffusion on the different fractal curves (loop-erased random... 

In this thesis, we study a homological invariant in Knot theory, called Khovanov homology. The main property of this invariants is that it gives us the Jones polynomial, as its graded Euler characteristic. Besides, the functor (1+1) TQFT, from the category of closed one-manifolds to the category of vector spaces is employed in its construction. By making some changes to this functor and defining another functor and some other steps, the so-called Lee spectral sequence is derived which starts from Khovanov homology and converges to another homological invariant of links, called Lee-Khovanov homology. Computation of this homology is very simple. By using this spectral sequence, a numerical... 

Knot theory is the study of ambient isotopy classes of compact 1–manifolds in a 3-manifold. In classical knot theory this 3-manifold is R3 or S3. This field has experienced a great transformative advances in recent years because of its strong connections with and a number of other mathematical disciplines including topology of 3-manifolds and 4-manifolds, gauge theory, representation theory, categorification, morse theory, symplectic geometry and the theory of pseudo-holomorphic curves. In this thesis we start with classical knot theory, introducing some of its (classical) invariants like unknotting number, Seifert genus and slice genus of a knot, knot group and finally Alexander Polynomial... 

In this thesis, stability and stabilization of fractional-order linear time invariant swarm systems are studied. In recent years it has been proved that the exact model of dynamic agents in most of the swarm systems can be modeled more accurate by fractional order differential equations. Stating the motivation of choosing this subject, the achievements of the thesis can be divided into two general parts: Investigating the stability of fractional-order swarm systems and how to stabilize such systems. After introducing the fractional-order systems and fractional-order model of swarm systems in the introduction part, the literature review is presented in Chapter 2. In Chapter 3 the results... 

With the emergence and development of ultra broadband communication systems incorporating ultrashort pulses, the design of suitable receiver structures became one the most significant problems in such systems; since due the limited bandwidth and speed of current electronic devices, most of the existing receiver structures cannot be used properly. In the field of radio communications, the design of simple and low power consumption receivers for ultrawideband (UWB) and millimeter wave band communication systems, which do not rely on complex channel estimation mechanisms, is of much interest. In ultrashort light pulse optical communication systems –and specially coherent optical CDMA systems–... 

In this research, INS error will be corrected with the help of the unscented kalman filter, by combining the IMU sensors and flight consecutive images information. Measurement equation of the Kalman filter is the epipolar Constraint of geometry of two consecutive images of the camera. In epipolar Constraint, the common points of two consecutive images of the camera field of view have an important role. This points will be extracted by SIFT and SURF algorithms. These algorithms have many mistakes in the process of images matching, but in this research, a solution based on the error covariance of the position of the ground point corresponding to the two common points of two images is presented... 

Molecular communication (MC), which has stimulated a great deal of interest in recent years, is a new paradigm for communication among nanoscale biological machines. In MC, molecules are carriers of information and information is encoded into concentration, type or releasing time of molecules. One of the issues in the problem of finding more explicit bounds on the capacity.An approach for bounding mutual information in the low SNR regime using the symmetrized KL divergence is introduced and its applicability to Poisson channels is shown. To the best of our knowledge, the first upper bound on the capacity of Poisson channel with a maximum transmission constraint in the low SNR regime is... 

In this thesis we introduce the objective method for solving combinatorial probability problems and combinatorial optimization. For introducing this method, we consider its application in solving problems such as graphs maximal partial matching problem. Then we introduce mean-field model, which has a close relationship with this method. Finally we use this method to discuss perfect mathching with minimal cost in complete graphs, and using obtaind theorems and concepts from solving this problem, like involution invariance and standard construction, we find an answer for random assigment problem, which is one of the most practical problems in the class of optimization problems  

Because of advancing fractional calculus and modeling physical phenomena by using fractional calculus more accurately than that by using integer calculus, and also existing uncertainties in models of real world systems, robust stability and performance analysis of fractional order systems are necessary. This thesis deals with the robust -stability analysis of LTI fractional order systems from kind of uncertain typical fractional order systems (UTFOS) and the robust stability analysis of LTI fractional order systems with delays from kind of uncertain retarded type systems (URTS) and uncertain neutral type systems (UNTS) with interval uncertainties. The coefficients of the numerator and the... 

The accuracy, speed, and ability to do work in hazardous environments has led to the development of robots in everyday life. Accordingly, research on quadruped robots for use in military environments is expanding. Designing control algorithms for walking and stepping on quadruped robots is one of the most important parts of the design of these robots, which creates complex movements despite the lack of sophisticated equipment in the robots. One of the robot gaiting control methods is dynamic based method that is based on the robot’s dynamics and resistant to perturbations. Trajectory based method is another robot gaiting control method that is inspired from CPG algorithm and has learning... 

Image retrieval refers to the task of finding images related to a query image within an image set. Due to ever-increasing volumes of data, it has become increasingly necessary to find suitable and efficient methods for searching in massive databases. In this thesis, modern image retrieval techniques developed within the last 15 years have been studied, with an aim to satisfy three primary constraints of efficiency, accuracy, and low memory usage. Our focus has been on content-based retrieval; meaning that instead of using text and other information, we directly utilize image features for analysis and processing. To achieve this, we studied two established techniques, the bag-of-words model,... 

Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an
SLE with <2. This lies outside the... 

The focus of this thesis is on robust control of hybrid systems using tube-based model predictive control. Hybrid systems are systems that contain both continuous and discrete components. The hybrid nature of these systems can stem from inherent switching behavior that occurs in many dynamical or digitally controlled systems, or from approximation of nonlinear systems. The ability of these systems to model a vast amount of physical phenomena has been attracted a lot of attention from control society. Although much effort have been made on the control of “nominal” hybrid systems, robust stabilization of these systems still seems to be immature. One of the most successful approaches toward...