Sharif Digital Repository

In this thesis we study one of the applications of algebraic topology to computer science and define some tools to analyze concurrent programs. For this purpose a geometric space is corresponded to every concurrent program and a partial order is considered on this space, so every path on it corresponds to an execution of the program. Some of these paths which are dihomotop (homotop in partial ordered spaces) with each other induce the same execution of the program. By defining “Fundamental Category” in which objects are points of the space and morphisms are dihomotopy classes, the space that should be analyzed shrinks to a smaller one. By defining component category in the next step, without... 

In this thesis we study three versions of K−theory. The most well-known vesrsion is topological K−theory, a generalization of Grothendieck works on algebraic varieties to the topological setting by Atyiah and Hirzebruch. Since its birth it has been an indespensible tool in topology,differential geometry and index theory. In the early 1970s C∗−algebraic version of K−theory introduced through associating two abelian groups,K0(A)and K1(A)to a C∗−algebra like A. These functors proved to be a powerful machine, making it possible to calculate the K−theory of a great many C∗−algebras. At last,algebraic K−theory is dealig with linear algebra over a ring R by associating it, a sequence of abelian... 

In this thesis, we analyze and compare switching and CPSP cryptography systems. CPSP is a dynamic system which can act as synchronized or self-synchronized stream cipher under specific conditions. To do the comparison, first we have a brief review of cryptography fundamentals like stream cipher systems, synchronized stream ciphers, and self-synchronized ones. Then, we consider chaos systems in general form and then we present their role in cryptography systems, and in continue by introducing switching cryptography systems and also CPSP cryptography systems, and analyzing their relation with self-synchronized stream ciphers, we do our statistical tests on them  

The application of biocatalysts in organic reactions refers to the use of enzymes, purified or crude, to increase the reaction rate. The usage of biocatalysts in organic reactions have many advantages, including biocompatibility, ease of separation, high yield, reusability without losing activity, high selectivity, and the use of water as the solvent. Furthermore, the carbon–carbon bond formation is one of the most important reactions in the synthesis of organic compounds, drugs, and biomolecules. Using enzymes in organic reactions can provide insightful information about the enzymes catalytic activities and paves the way for systematic investigation of their mechanisms. The enzymes... 

In recent years, the emergence of semi-supervised learning methods has broadened the scope of machine learning, especially for pattern classification. Besides obviating the need for experts to label the data, efficient use of unlabeled data causes a significant improvement in supervised learning methods in many applications. With the advent of statistical learning theory in the late 80's, and the emergence of the concept of regularization, kernel learning has always been in deep concentration. In recent years, semi-supervised kernel learning, which is a combination of the two above-mentioned viewpoints, has been considered greatly.
Large number of dimensions of the input data along with... 

Portfolio generating functions are positive twice continuously differentiable functions of the common or ranked market weights. The return on such portfolios related to the market with a stochastic differential equation that has two components: the logarithmic change in the value of the generating function, and a drift process that is of bounded variation. The goal of this study is to generalized portfolio generating functions theorem for ’ functions, in order to cover some important functions in economic such as Gini coefficients  

At first the killing vector fields will be investigated. Conditions are introduced for the hypersurface of a Riemannian manifold with a killing vector field to be equipped with the same killing vector field. Then 2-killing vector field is studied and its relation with killing vector fields and monotone vector fields is presented. After that conformal vector fields are discussed and conditions are introduced in order that the Riemannian manifold equipped with a conformal vector field, isisometric to n-dimensional sphere with constant curvature. Finally we will present the conditions which conformal vector field is a 2-killing vector field. Then we will present the results in which the... 

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... 

A number of questions from a variety of areas of mathematics lead one to the problem of analyzing the topology of a simplicial complex. However, there are few general techniques available to aid us in this study. On the other hand, some very general theories have been developed for the study of smooth manifolds. One of the most powerful, and useful, of these theories is Morse Theory. We present a combinatorial adaptation of Morse Theory, which we call discrete Morse theory that may be applied to any simplicial complex (or more general cell complex). Our goal is to present an overview of the subject of discrete Morse Theory that is sufficient both to understand the major applications of the... 

In this thesis, we review the proof to standardness of Einstein solvamanifolds which is based on some results from Geometric Invariant Theory and stratification of topological spaces. Standardness is a very simple and yet powerful algebraic condition on the lie algebra of a solvmanifold which yields to remarkable existence and uniqueness and obstruction results  

In this thesis, we have shown that unique subgraphs of a graph have a key role in structure of the graph. Using unique subgraph which is called “anchor” here, the reconstruction of graphs is explained. Using anchor, we have shown that almost every n-vertex graph is determined by its 3log(n)-vertex subgraphs. In the second part of the thesis, a novel randomized algorithm is proposed for the graph isomorphism problem which is very simple and fast. It solves this problem with running time O(n^{2.373} \log(n)) for any pair of $n$-vertex graphs whose adjacency matrices are not strongly co-det. Strongly co-det pair of matrices have very special symmetric structure which can be disarranged to be... 

The main goal of this thesis is to classify minimal translation surfaces of three-dimensional Euclidean space. In pursuing that, a method will be introduced that constructs explicit examples. A translation surface is the sum of two regular curves α and β. A minimal surface is a surface, with zero mean curvature. Will be shown that besides the know examples (plane and surfaces of Scherk type) any minimal translation surfaces can be described Ψ(s, t) = α(s)+α(t) , where α is the unit speed curve and its curvature κα is a positive solution of (y ′ ) 2 + y 4 + c3y 2 + c 2 1 y −2 + c1c2 = 0 and its torsion is τ (s) = c1/κ(s) 2 . the above coefficients and their relations will be described  

A surfaceMin the Euclidean space is called a translation surfaceif it is given by the graph z(s,t)=f(s)+g(t), where f and gare smooth functions on some interval of R. These surfaces are called translation surfaces since its parameterization X(s,t)=(s,t,f(s)+g(t) ) can be written as the sum of two curves (translation), namely , X(s,t)=(s,0,f(s) )+(0,t,g(t) )
In this work , Minimal surfaces in Sol_3 and Nil_3have been studied,where Sol_3and Nil_3are two model geometry of the eight geometries of Thurston. We propose a similar problem in Sol_3 and Nil_3 changing the additive + in the Euclidean space by the group operation * of Sol_3 and Nil_3, such that we have X(s,t)=α(s)*β(t), where α... 

There are different approaches to the ideal closure of geodesic metric space with non-positive curvature in the sense of Busemann. We established relations between them with Andreev theorem. In this theorem we introduced a continuous surjection which coincides with identity mapping of Idx onto X. Due to we studied metric spaces, geodesics and their angles and also CATk domains. Then with asymptotic rays we introduced metric boundary and we produced compact metric space. Then we proved Andreev theorem with some theorems and lemmas. The Andreev theorem is correct for Alexandrov space. Finally we construct the counterexample showing that Busemann ideal closure can differ from the geodesic... 

In this work, we study spacelike surfaces in Minkowski space E3 1 foliated by pieces of circles that satisfy a linear Weingarten condition of type aH + bK=c, where a, b and c are constants and H and K denote the mean curvature and the Gauss curvature respectively. We show that such surfaces must be surfaces of revolution or surfaces with constant mean curvature H=0 or surfaces with constant Gauss curvature K=0