Sharif Digital Repository

In this thesis, we are going to extend hoeffding's inequality to supermartingale with differences bounded from above and compare this inequality with the other ones which derived in the past. After defining basic thorems, we introduce upper bounds which are derived for the probability that the sum of some independent random variables exceeds its mean by a positive number and also, compare to each o ther. In addition , we use these bounds and derive upper bounds of probability such as above for dependent random variables. Then, we introduce a n inequality which cover Hoeffding's inequality for ... 

In recent years, more attention was devoted to ECAE process than any other Severe Plastic Deformation (SPD) process. Repeatability of the process and high mechanical properties of the exit profile are the reasons of this attention. ECAE process carried out with conventional extrusion process, provides more strain and back pressure. In this thesis an analytical model based on upper Bound analysis and Bezier interpolation functions is presented and the effects of process parameters were studied. According to the presented model, reduction of inner corner angle φ, increases strain, strain rate and press force. Reduction of the outer corner angle ψ, causes the same effect. Moreover, decreasing... 

In this thesis, the effect of cognition in wireless networks is studied. In a wireless communica-tion network, cognition is the ability of a device to sense the transmissions of neighboring nodes and adapt its own transmission to the sensed environment. Cognitive radios are very attractive be-cause of the increasing need for more efficient use of frequency spectrum. The goal of this thesis is the analysis of cognitive radio networks from an information theoretic perspective and to this end statistical models of the wireless medium with a limited and tractable number of devices are uti-lized. We consider three different models in three parts of the thesis. First, we consider a new... 

The extrusion process of flat dies in non-symmetrical sections is among processes which in spite of enormous applications, has not been thoroughly understood due to complexities of analyzing the section deformation process. In these dies, a zone is formed during egression of billet from die in which the material is stationary and accordingly the material on profile of this zone shears. This zone is called the dead metal zone. Dead metal zone is a natural non-linear die and it is pragmatic to obtain the value of the deviation. In the present work, determine the curvature of the exit profile by using prediction of the dead metal zone profile is target. The dead metal zone profile is assumed... 

The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian man-ifold (M, g) such as the Laplace–Beltrami operator and Laplace-type operators. In the case of the Laplace–Beltrami operator, two aspects are investigated:
The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplace–Beltrami operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The proof relies on the... 

In this research, temperature distribution and roll force during steady state warm and hot rolling of 6061 Al alloy strip have been simulated, using finite element method and upper bound solution. At first, the velocity field and deformation zone shape have been determined, by means of upper bound solution, then using 2D finite element method, the temperature distribution within rolling and considering rate of heat of deformation, has been calculated. This model generalized for two pass steady state warm and hot rolling. Also, in order to evaluate the predictions, the experimental recorded of temperature variation, during hot rolling and temperature variation predicted by model has been... 

In this project, in order to model the flat rolling problems, an analytical method based on Bezier functions has been presented. To this goal, using the Bezier functions, the velocity field of the flat rolling has been stablished and the volume constancy condition and velocity boundary conditions have been considered in calculations. Using the achieved velocity field, the strain rate and strain fields has been determined. Then, with derived fields, power, pressure, and force of the deformation in flat-rolled billets from different materials such as copper, aluminium and steel have been calculated. To verify the accuracy of the results, the rolling process has been carried out on the... 

If we consider a point set on the plane as the vertices and straight-line segments between them as the edges of a graph, and weight of each edge is equal to its Euclidean length, from this kind of graphs, triangulation is the graph with maximum number of the edges. In a triangulation, dilation of any two vertices is equal to the ratio of their shortest path length to their Euclidean distance, and dilation of the triangulation is defined as the maximum dilation of any pair of its vertices. Dilation is a characteristic that shows how much a triangulation approximates a complete graph. In the minimum dilation triangulation problem, the objective is to find a triangulation of a given set of... 

In recent years, stochastic-flow networks (SFNs) have been extensively applied to many problems such as distribution, power transmission, and telecommunication. In quality management and decision making, an important task is to design some performance indices in order to measure the performance of an SFN. The system reliability and unreliability are such two common performance indices.Hitherto, several research works have been conducted for evaluating these two performance indices.One approach for evaluating the reliability of SFNs is determining all the upper or lower boundary points (respectively, UBPs or LBPs).Here, we study four problems to determine: (1) all the UBPs in a two-terminal... 

Energy of graphs first defined by Ivan Gutman in 1978[1]. Let G be a graph with (0,1)-adjacency matrix A and let λ_1≥⋯≥λ_n be eigenvalues of A. Grap h energy is defined as the sum of absolute values of the eigenvalues of A and is shown by ɛ(G). let H_1,…,H_k be the vertex-disjoint induced subgraphs of graph G, it is proved that energy of G is at least equal to the sum of energy of H_i subgraphs, where the summation is over i. Also by partitioning edges of G to L_1,…,L_k subgraphs, energy of G is at most equal to sum of energy of L_i subgraphs , where the summation is over i. In this thesi s we study energy of graphs, specially... 

A mathematical model has been proposed to estimate the deformation pattern and the required power in cold plate rolling using the stream function method and upper bound theorem. In the first place admissible velocity distributions as well as the geometry of deformation zone were derived from the proposed stream functions. Then, the optimum velocity field was obtained by minimization of the power function computed based on the upper bound theorem. Then a steady state heat transfer equation has been solved in whole model using finite element method. In order to verify the predictions, rolling experiments on aluminum plates were conducted and also, a finite element analysis performed employing... 

In this research two stage deep drawing has been analyzed by the upper bound method. During this study, the deep drawings of cylindrical parts have been analyzed. In this method, for the first stage the whole deformation region is divided into five zones including punch bottom, punch radius, between punch and die, die radius and flange. Then, the geometric equations of each zones is generated by sweeping the section curves defined on the boundary of each zone. The velocity fields are expressed in a similar manner by sweeping the boundary velocity functions. At each stage, with the change of height between punch and die, the point location is changed and movement and tension in the sheet are... 

In this research, the extrusion of composite AA6061-SiC has been investigated and the temperature distribution field and energy required for the process has been predicted. In this regard, to predict the flow behavior of material, hot extrusion tests conformed at various ranges of temperatures and strain rates. Afterward, the finite element method coupled with the upper bound technique to calculate the temperature distribution and energy required during hot extrusion. This model has also used for wire drawing and cold extrusion processes. The present model is capable of considering various process parameters such as speed of extrusion, reduction and the initial billet/die temperature on the... 

More than 70% of the components used in aerospace, aircraft and defence industries Are made of aluminum alloys. The 7xxx series of Al alloys such as AA7075 and AA7175 are typical alloys utilized in the mentioned industries. For these alloys, the optimization of the extrusion process in term of reaching a maximum extrusion quality without jeoparding the extrudate, the surface and microstructural properties is far more complex than other aluminum alloys. It is generally accepted that product properties are closely correlated to microstructure. So it is of paramount importance to understand the way in which the structure is modified and how the forming parameters i.e. temperature, ram speed,... 

Nowadays, information gathering based on wireless sensor network (WSN) has formed various applications and it also seems to be spreading more in future. Wireless sensor network, is a network composed of multiple nodes, without any infrastructure, each having one or more sensors, wireless communications unit, processing unit, memory, and power supply. Memory capacity, computation power, and power supply are usually considered as valuable resources and limited in nodes. Most of sensor nodes are located in a dense mode and they are susceptible to failure. Therefore network topology may vary dynamically. A sensor network can support real-time communications independent of its type of structure... 

In this study, a two-hole die with unsymmetrical T-shape holes has been investigated. At first, a kinematically admissible velocity field in outlet of die has determined. Then, appropriate length of die has calculated by upper bound method. Finally, suitable position of holes has achieved in aspect of minimum pressure and curvature. To calculate curvature of exit profile, a realistic deviation function has been defined. To validation of results, finite element simulation and physical modeling have been used. Analytical, experimental and finite element results have decent agreement to each other