Sharif Digital Repository

In this thesis, we exmine a group of optimization methods called trust region methods for solving semidefinite programming problems. Nowadays, many application problems can be cast as semidefinite programming and problems with very large size are encountered every year. So, having a powerful method for solving such problems is very important. Trust region approach present a new scheme for constructing efficient algorithms to solve semidefinite programming problems.When using interior point methods for solving semidefinite programs (SDPs), one needs to solve a system of linear equations at every iteration. For large problems, solving the system of linear equations can be very expensive. In... 

Power transformer is one of the most important equipment in the power system which plays a key role in the reliability and quality of power delivery. Among numerous failure modes of a typical power transformer, the turn-to-turn fault (TTF) is one of the most prominent reasons for its unplanned outage. A turn-to-turn fault quite often begins with the degradation of the winding insulation between two adjacent turns, then in a short time, this low-level fault can progress to a large number of turns and results in the transformer costly damages. Therefore, it is vital to detect TTF at an early stage and prevent its progression to a catastrophic disaster. The conventional percentage differential... 

large-scale data collection from multiple sources to a single entity, such as a cloud provider, poses a challenging problem for implementing centralized machine learning algorithms. Constraints such as privacy protection and restrictive access policies that prevent accessing personally identifiable information hinder the development of centralized machine learning algorithms in important and sensitive domains like healthcare. However, from early disease detection to discovering new drugs, leveraging artificial intelligence in this domain is a fun-damental necessity. As a potential solution, federated learning has been proposed, allowing data owners (users) to jointly train a shared machine... 

The use of distributed generation (DG) units provides several advantages for the utility distribution grid. Mostly power electronics converter is used as an interface to connect a DG unit to a utility grid. A DG unit normally operates in a grid-connected mode. In this mode, the host grid dominantly dictates the voltage amplitude and frequency of the local load at the point of common coupling (PCC) and the DG unit controls its real/reactive power components. Separation of the DG unit and its dedicated load from the host grid is called islanding. Subsequent to the formation of an island, due to the lack of control over the voltage magnitude and frequency, the islanded DG system becomes... 

Many spacecrafts and satellites have long flexible components, the most common ones are the satellites with flexible solar panels, which are used to provide the satellite energy. The governing equations of the satellite rigid motion along with the solar panels vibrations are the combination of the coupled partial and ordinary differential equations. Various reasons, such as the satellite maneuvers and the external disturbances, cause the vibration of panels. Due to the dependence between the governing equations of the satellite rigid motion and the flexible components vibrations, these vibrations affect the satellite rigid dynamics and the control aims; therefore, in addition to the... 

Nowadays, micro systems in many area of science and technology have special importance and status. The main function of these systems is based on the deformation of a beam at micro scale. Therefore study of behavior and control of micro-beams will have a great importance. Among micro-beams, clamped-free and clamped-clamped micro beams that actuated by piezoelectric and electrostatic actuators have wider applications. For example, clamped-free micro-beams are used in atomic force microscopy (AFM), micro switches, mass sensors and micro-accelerometers and clamped-clamped micro-beams are used in micro mirrors and Grating Light Valves (GLV). In this thesis, the studied system is clamped-free... 

Turbulence can distort and corrupt the image in quite a few ways when light from a distance star or another astronomical object enters the Earth's atmosphere. It is inevitable that all images produced by any telescope on ther Earth are blurred by these distortions. Adaptive Optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions: it aims at correcting the deformations of an incoming wavefront by deforming a mirror in order to compensate for the distortion. The research work reported in this thesis presents a solution to the surface shape control problems in a Deformable Mirror system. Our first goal is to derive equations that... 

Precise adjustment of orientation is vital in many important applications of satellites. Besides, in order to have sustainable power source and to reduce heavy costs of launching deployable solar arrays with large area to mass ratio are utilized. The vibrations in these flexible parts and attitude dynamics of the main hub influence eachother mutually. Thus, simultaneous attitude and vibrations control is of noticeable significance. In this thesis considering new details such as multi-section solar panels, the governing dynamic partial differential equations (PDE) are derived via Hamilton principle. In order that errors arised from discretized models be eliminated and just using regular... 

A prey-predator fishery model with stage structure for prey is discusing in this thises. The adult preyand predator populations are harvested in the proposed system. The dynamic behavior of the model system is discussed. It is observed that singularity induced bifurcation phenomena is appeared when variation of the economic interest of harvesting is taken into account. We have incorporated state feedback controller to stabilize the model system in the case of positive economic interest. Fishing effort used to harvest the adult prey and predator population is used as a control to develop a dynamic framework to investigate the optimal utilization of the resource. Simulation results show that the... 

Here, we first ivestigate some available nonsmooth algorithms indentilying their drawbacks, and then provide some guidelines to avert these drawbacks. We divide the algorithms to two main classes, first order and second order. The main drawback of the second order class of algorithm is that there does not exist any suitable method to approximate the generalized second order derivative. To solve this problem, we construct a uniform approximation for the generalized Hessian matrix of an SC1 function. Using the discrete gradient and the extended second order derivative, we define the discrete Hessian matrix. We construct a sequence of sets, where each set is composed of discrete Hessian... 

In this thesis, first we will have a brief review on hash functions and related concepts.Then, we will descibe the hash function, Cubehash, which is one of the competitors in the competition held by NIST for selecting SHA-3 standard. Next, we will describe an attack based on linearization of differential paths in hash functions and apply this attack on Cubehash. At the end, we will discuss the results of this attack on Cubehash  

The aim of this thesis is to investigate recent methods for Image Processing(Any signal process which it’s input is an image and it’s ouput is an image or a set of Image parameters) using Calculus of variation tools. Methods which are to be investigated has been divided into two well known parts of Image Processing : Image Restoration and Image Segmentation.Image Processing Chapter includes two sections: one calculus of variations methods(energy method), other methods based on PDEs(heat equation and Malik-Perona equation). In studing each of this methods, It has been tried to include experimental results and negative and positive points of them.In Image Segmentation Chapter, first... 

In this thesis,we consider aperiodic predator–ysystem with mutualinter ference andimpulses. By constructing a suitable Lyapunov function and using the compar-ison the orem of impulsive differential equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. We also present some examples to verify our main results  

Stochastic Partial Differential Equations have many applications in other area of science. In this thesis we investigate two pproaches in SPDE.The first approach is semigroup and the second is variational method.Our main purpose is stability of these equations  

Social enterprises are organisations comprised of two conflicting logics: social and commercial. However, simultaneous commitment to both logics often leads to tensions, making social enterprises fragile organisations at the risk of mission drift. The extant literature on hybridity highlights two important overall strategies – integration and differentiation - for managing tensions. However, integration or differentiation alone can create additional problems, which is especially true in the case of differentiation, creating a situation comparable to black and white, with a salient faultline and heated conflicts. In this inductive qualitative case study, responding to the recent call in the... 

In 1952, Choquet-Bruhat proved the well-posedness of the Cauchy problem for Einstein’s equation, and demonstrated that a given initial data on a Cauchy hypersurface in spacetime propagates forward in time as a solution to the wave equation. It took nearly half a century for mathematicians to build the necessary tools and techniques for proving the stability of the most basic solution of Einstein’s vacuum equations (EVE), namely Minkowski spacetime. In 1993, Christodoulou and Klainerman showed the global nonlinear stability of this solution using the concept of a double null gauge. The Schwarzschild solution, introduced by Karl Schwarzschild in 1916 for spherically symmetric spacetimes as an... 

First, stabilization problem of an integer order-nonlinear differential inclusion (IO-NDI) in the form of tracking problem is investigated and discussed while control inputs are subjected to the sector and dead-zone nonlinearities. Based on two the well-known theorems, the mentioned differential inclusion is modeled by a nonlinear system possessing polytopic uncertainties. For tackling the mentioned problem, sliding mode control (SMC) approach is applied and developed. Second, two issues including stability analysis and stabilization problem of a fractional order-linear differential inclusion (FO-LDI) are studied for both fractional order derivatives and separately. For solving these... 

Nowadays, continuous systems such as strings, bars, beams and plates have become widespread in science and engineering applications. To achieve the control purposes of continuous systems, most of engineers use discretization techniques to reduce the governing partial differential equation (PDE) into a set of ordinary differential equations (ODEs). From practical point of view, this model reduction can cause many problems such as in-domain measurement and actuation and control spillover. This thesis attempts to investigate the problem of vibration control of nonclassical microscale beams using the partial differential equation control theory which eliminates spillover instabilities. To this... 

In this thesis we investigating two models of cancer invasion .First, a general mathematical model of cancer invasion is presented. In this model there are three factors: tumor cell, extracellular matrix and enzyme. The model consists of a parabolic partial differential equation (PDE) describing the evolution of tumor cell density , an ordinary differential equation modeling of extracellular matrix and a parabolic PDE governing the evolution of the matrix degrading enzyme concentration. This model is investigated in two special versions for existence and uniqueness of global solutions. In the first model we neglect the remodeling term, this model is named the chemotaxis-haptotaxis model.... 

In this thesis, first, the modeling method of neural fields is precisely presented. Then, Existence and Stability of different solutions of one dimensional neural fields like Standing Pulses, Traveling Waves and ... are investigated in three different models of neural fields. In order for proving Existence and Stability of the solutions the mathematical tools like Fourier transform and Evans function are applied. All the models which analysed in this thesis have the following Integro-Differential Equation form:
τ
∂u(x, t)
∂t
= −u(x, t) +
∫ +∞
−∞
w(x, y)f[u(y, t)]dy + I(x, t) + s(x, t)
and also in some models the parameters might be changed