Sharif Digital Repository

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... 

The classical theory of Tannakian categories concerns tensor categories with fiber functors over the categories of vector spaces. Our main problem in this thesis, is to investigate the case of fiber functors to more general tensor categories. More precisely, suppose F : C → D be a fiber functor (i.e. k-tensor exact) between two k-tensor categories, over a field k. Then does there exist a Hopf algebra A in D, naturally associated with F, such that C is equivalent to the category of comodules over A, and F becomes equal under this equivalence to the forgetful functor from the category of comodules over A to D?We will show that the answer is affirmative for semisimple categories D,if F has a... 

Because of environmental problems of fossil fuel energies and the rise in petroleum products, the tendencies to the renewable sources like wind power and solar power have been increased. In some particular applications like electric vehicles, satellites power system and all stand-alone unites that are using solar and wind powers are the only solutions. On the other hand, because of intermittent behavior of renewable sources, use of back-up supplies e.g. batteries are necessary to make a balance in power consumptions and productions. To interface between different ports some independent two port converters are used in traditional techniques. Multiport converters, used in... 

Let K be a field and S=K[x0,…,xn-1] be the polynomial ring in n variables over the field K. Let G be a finite undirected graph without loops or multiple edges with the vertex set V(G)={0,…,n-1} and the edge set E(G). One can associate a squarefree quadratic monomial ideal I(G)=of S to the graph G. The ideal I (G) is called the edge ideal of G in S. It is an algebraic object whose invariants can be related to the properties of G and vice versa. The graph G is called Cohen–Macaulay over K (Gorenstein over K) if the ring S/I (G) is Cohen–Macaulay (Gorenstein). Let n ≥ 2 be an integer. The Grimaldi graph represented by G(n) is obtained by letting all the elements of... 

Cancer is one of the main causes of death among all people around the world. This shows that more and more attention should be paid to cure cancer. One of the most common cancer treatments is radiation therapy. Among all radiation therapy treatments, Intensity-Modulated Radiation Therapy is a very effective and flexible ways to treat cancer. There are numerous mathematical problems to find the perfect treatment plan. One of these mathematical problems is Fluence Map Optimization in which we try to find the best dose intensity for each tumor and surrounding organs. The main purpose in this problem is to minimize the number of cancerous cells which are being destroyed while minimizing the... 

Perovskite solar cells with 25.5% efficiency and fast and cheap manufacturing process are among the most promising technologies in this field to replace silicon cells. Despite the challenges of stability and toxicity to these cells, their manufacturing technology has recently shifted to the development of large-scale manufacturing methods in module dimensions. In the present study, the fabrication of perovskite cells in large dimensions to achieve the perovskite module has been aimed and studied that to achieve this, the method of large-scale spraying and printing using the vacuum system was used to create cell-forming films and, consequently, to make the final cell and module. To... 

Jean-Pierre Serre in 1955, in his famous article “Faisceaux Algébriques Cohérents” asked if there is any finitely generated projective module on polynomial rings which is not free. Or equivalently: is there any non-trivial algebraic vector bundle over an affine space? The negative answer to this question is known as Serre’s conjecture and it was an open problem in algebra and affine algebraic geometry until 1976, when it was proved independently by Quillen and Suslin. The challenge of solving this question and its consequences led to a vast amount of research in commutative algebra, homological algebra and algebraic K-theory and inspired generalizations and similar questions. In this thesis... 

Recent stringent HC and CO emission regulations are because of increasing consciousness of the perilous influences of exhaust emissions. The chief attempt to pass the standards is to decrease the emissions during cold-start, due to catalytic converters are not efficient until they arrive a light-off temperature. It has been discovered that 50% to 80% of the controlled HC and CO emissions are sent out from tailpipe of automotive during the cold-start. Therefore, in order to minimize the cold-start emissions and fast light-off of catalytic converters, it is important to understand the catalytic converter characteristics and techniques for rapid warm-up catalyst. This thesis describes a... 

Nowadays, in the presence of different types of computer attacks and different methods of eavesdropping on network communications, nobody can deny the importance of cryptography. Hardware Security Modules that are specifically designed for this purpose are widely used as a fast and reliable tool for encrypting data in computer networks. In this project, using the common and well-known FPGA platform and by leveraging the reconfigurability feature of this platform and also by adding a network protocol detection module to the traditional architecture of Hardware Security Modules, a novel module has been designed and implemented that can encrypt and decrypt data in a communication network, at... 

The Emergence of modern wireless communication standards and the need to use the frequency spectrum efficiently has made communication system designers exert complex modulation schemes. One of the results of such designs that has a direct impact on the design procedure of power amplifiers is that there will be signals with high peak to average power ratio.The obvious consequence of this manner in the design of communication systems would be the reduction of power amplifier efficiency due to its operation in its back-off region. The solution will be to use load modulated power amplifiers such as Doherty amplifier which brings up the problem of limited bandwidth.In this thesis, we tackle this... 

Determining nonlinear dynamic behavior of structures is always one of the main goals of structure and earthquake engineers. The Modal Incremental Dynamic Analysis (MIDA) is one of the newest methods for analyzing the seismic behavior of structures. Indeed, this method has superseded the exact IDA method which is too complicated and prolix. Although, this method represents approximate results, high accuracy, fastness and low cost procedure made it an efficient and useful technique. Many researchers have used this method and investigated the accuracy of that and achieved proper results. Up to now no one has applied this method on structures which are equipped with dampers. In the procedure of... 

Analog-to-digital conversion and signal processing has been increasing due to its many advantages. So that mostly we prefer to convert signal from analog area to digital samples, then they are processed and finaly put the result signal at the system output. How ever because the restriction of the sampling rate, Prevent the spread of digital processing for the high-frequency signal (RF). In recent years, ADCs sampling rate rise up to several GHz (for example ADC with 4 GSPS and 12 bits for TI) that output of the these ADCs by powerful and fast FPGAs are processed but According to Shannon theorem band width of these ADCs is not desirable.the goal of this thesis uses of the compressed sensing... 

Over the past decade there has been dramatic increase in fossil fuel’s usage; As a consequence, world now faces problems such as: air pollution, climate change, global warming and ozone layer depletion. In addition, depletion of the fossil energy resources is growing as a serious issue. Renewable energy(RE) sources are the most promising solution to these problems. Global investment in clean energy was increased by 16% in 2014 and solar power is anticipated to become the world’s largest source of electricity by 2050 .The German government has planned to achieve a goal of 8 percent renewables for gross power consumption by 2050 .RE is still more expensive than traditional one and faces a... 

Increasing dynamics of mobile users intensifies the Doppler effect and degrades the performance of the communication system. Considering Fourier kernel-based modulation, in this research, we focus on dealing with the Doppler effect and compensating non-ideal communication channel response suffered from the Doppler-delay spread. In the first step, we study Zak transform and present a new transform for 2-D representation of time signals. This mapping is a well-known transformation that can be considered as a generalized discrete-time Fourier transform in the field of signal processing and can be used to represent a signal in the delay-Doppler domain. After providing a new 2-D transform, we... 

Anti-lock brakes car as one of the most fundamental and vehicle stability control system is considered. Solenoid valves, one-way valves, Accumulator, damper orifices and other components is a crucial role in the anti-lock system performance, so that the performance of the system and thus affect the dynamic performance of the vehicle. This is the most important part of the anti-lock brake System and These components are all new brake system.In this study a complete modeling of hydraulic control unit and obtain sufficient data to model the dynamic behavior of the hydraulic control unit to be seen. operators working in higher frequencies are weak and virtually reached saturation and efficient... 

In this thesis we have studied slotted and unslotted ALOHA random access optical CDMA packet switching networks with a chip-level receiver structure. We used generalized optical orthogonal codes (GOOC) and Overlapping PPM (OPPM) signaling technique to improve system performance. The impact of physical layer parameters such as GOOC code cross correlation value and OPPM overlapping index on key performance benchmarks such as network throughput and delay are analyzed. We have also studied the stability of the network based on the number of backlogged users, using expected state drift. It has been shown that using GOOC instead of strict OOC improves the network average delay and throughput.... 

It is necessary to evaluate dosimetry accuracy in the framework of advanced methods for radiation therapy such as Intensity Modulated Radiation Therapy (IMRT) to ensure reliability of a proposed treatment. The ability of the Monte Carlo codes to model linear accelerator (LINAC) and to calculate the exact dose distribution in clinical radiation therapy is one of the reasons to use such codes. The purpose of this project is to validate a treatment planning system with BEAMnrc and DOSXYZnrc Monte Carlo codes. In this study, the dose distribution obtained from DOSXYZnrc in considered to be thr main criterion with which the dose distribution obtained from treatment planning system is assessed and... 

Breast cancer has been one of the main causes of women's deaths in recent years. Today, various methods are used to treat this disease, among which intensity-modulated radiation therapy is one of the most common methods. The goal of radiation therapy is to destroy cancer cells while protecting the surrounding healthy tissues. In left breast cancer, due to the proximity of the heart and breast tissue, we are at risk of delivering an excessive dose to the heart and increasing cardiac complications after the treatment. In addition, due to the irregular and unpredictable breathing movements of the patient during the treatment and the resulting uncertainty, we face more challenges. In order to... 

Studies regarding Multiple Input - Multiple Output synthetic aperture radars, shows promising advances in synthetic aperture imaging. Compared to conventional SAR, MIMO-SAR encompasses desirable features, namely: lower background noise, better detection rate, easier implementation of imaging modes etc. Signals used in these radars, are required to have specific properties such as orthogonality, large time-bandwidth product, high Doppler tolerance and qualified ambiguity function. Also because of the specific geometry of SAR imaging, these signals should remain orthogonal in respectively large Doppler shifts and time offsets. Through the past years, many signals are suggested in the... 

The goal of this project, has been designing a downhole camera, which captures images from environment of a well and transmits that to the surface. High temperature and pressure of well environment and corrosion and limitation in data transmission rate which is because of mono conductor cable, are the challenges of designing this system. For doing that, first, the principles of image compression are explained. Then, based on that, an image compression system based on wavelet transform has been designed. Its components are examined too. For making the introduced system resistant to the high pressure and temperature, using an isolated case is suggested. For implementation, an...