Sharif Digital Repository

The Weil group WF is assigne to every local field F. Langlands Correspondence is a bijetion between semisimple two-dimensional Deligne representations of Weil Group WF and irreducible representations of GL2(F) which fixes assigned L-functions and local constants. In this thesis we have classified an important class of irreducible representations of GL(2) over local fields called Principal Series. We also tried to give a taste of Langlands Correspondence to the reader. First we explain preliminaries and introduce locally profinite groups and their smooth representations. Then we classify representations of GL2(F) when F is finite. Then we study GL2(F) when F is a local field. Finally we... 

The k-center problem—covering a set of points using k congruent balls with minimum radius—is a well-known clustering model in computer science with a wide range of applications. The k-center is a well known NP-Hard problem. In this thesis, we focus on the k-center problem with outliers in high dimensional data streams. Due to increase in data size, we focus on the data stream model of the problem. Moreover, in real-world applications, where input points are noisy, it is very important to consider outliers. In this thesis, we study 1-center and 2-center with outliers in high dimensional data streams in Euclidean space. We provide a 1:7-approximation streaming algorithm for 1-center with z... 

Szemeredi's theorem is one of the significant theorems in additive combinatorics which was started by Van Der Waerden's theorem in 1927. Erdos and Turan conjectured generalized versions of Van Der Waerden's theorem in several ways included Szemeredi's theorem. In 1975 Szemeredi proved the conjecture using complicated combinatorial methods. In 1977 H. Furstenberg proved Szemeredi's theorem via the Ergodic theory approach which led to prove polynomial Szemeredi's theorem and multi-dimensional Szemeredi's theorem. The Ergodic approach is the only known approach so far to these generalizations of this theorem which is named Ergodic Ramsey theory and led to some other problems in Ergodic theory... 

In majority of the (standalone or grid-connected) PV Systems, predefined rule-based algorithms are utilized in order to manage and control the flow of power. The function of these algorithms is to send the generated energy from solar panels either to load for consumption, or to battery for storage, or to the grid for sale. Their performance is based on predefined instructions and regardless of load change and consumption patterns. Therefore the total efficiency of these systems depend greately upon individual user’s load type and consumption pattern. In current research, an optimum and dynamic energy management algorithm is proposed using dynamic programming (DP) method, in order to increase... 

In this monograph, we investigate the long-time behavior of stochastic delay equations. Our approach is random dynamical systems, and we solve our equation in the rough path point of view. Namely, we deal with the singular case, i.e., when the delay terms also are appearing in the diffusion part. Although we can solve the equation using the classical tools of stochastic analysis, the main obstacle is the lack of flow property. More precisely, the solution does not depend continuously on the initial value. To solve this problem, we define this property differently. We will show how we can generate a flow property on fields of Banach spaces using rough path theory. As a consequence, we prove...