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This master’s thesis has two major parts. The first part which includes chapters 1 to 8, describes the article A. Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math. 1, (1966)pp. 116-132, and expresses important facts about the Witt ring W(K) of quadratic forms over an arbitrary field K of characteristic unequal to 2. Among those, it is shown that the order of each element in the additive group of W(K) is a power of 2, the Witt ring doesn’t have any zero divisor of odd dimension and a necessary and sufficient condition for W(K) to be an integral domain is given. The connections between the square class number of a field and the cardinality of its Witt ring and, providing some... 

In this thesis, which is based on an article of Claus Scheiderer (Reference [21]), the relation between positive semi-definite elements of a semilocal ring, called psd, and elements of the ring which can be written as a sum of square elements of the ring and are called sos will be evaluated. In Chapter One, the concepts of prime cones, real spectrum of a ring and real ideals will be defined and then the relation between psd and sos elements in the total rings of quotients will be assessed. The Krull Valuation of an element which is a sum of squares will also be determined. In Chapter Two, the concept of totally positive elements in a ring will be defined and their properties will be... 

For a field of characteristic not two, the classical u-invariant is defined as the maximal dimension of anisotropic quadratic forms over F. Initially Kaplansky conjectured that u(F), when finite, is always a 2-power. Later Merkurjev constructed a field F such that u(F) = 6. This dissertation examines in detail the article: R. Elman, T. Y. Lam, Quadratic forms and the u-invariant. I. Math. Z. 131, 283-304 (1973). in which the notion of ”generalized u-invariant” (motivated by Pfister’s Local-Global Principle) was defined as the maximal dimension of anisotropic torsion quadratic forms over F. This is indeed a right generalization of the definition of the classical u-invariant since it not only... 

This master’s thesis has three chapters. In the first and second chapters provided all the necessary preparations for the third chapter to describes the following article: Lewis, D. W, Units in Witt rings, Commun. Algebra 18, no. 10, 3295-3306 (1990).The first chapter includes an introduction of quadratic forms and Witt ring on fields with characteristic unequal 2, studing W b(F) in the category of commutative rings and introduction of formally real and nonreal fields. In this chapter there are important theorems such as Witt’s Decomposition and Cancellation Theorem, Cassels Representation, Springer and Pfister’s Local-Global Principle. The second chapter introduces the discretely valuated... 

Let D be an F-central division algebra of index n. In this thesis a criterion for the triviality of the group G(D) = D^*/Nrd_(D/F) (D^*)D^' is presented and thus generalizing various related results published recently. To be more precise, it is shown that G(D) = 1 if and only if SK〗_1 (D) = 1 and (F^* )^2=(F^* )^2n. By using this, the role of some particular subgroups of D* in the algebraic structure of D is investigated. In this direction, it is proved that a division algebra D of prime index is a symbol algebra if and only if D* contains a non-abelian nilpotent subgroup  

Due to the large application of electro-sprays in various industries, the study of the stability of electro-hydrodynamic flows is important. This thesis examines the stability of cylindrical liquid jets in the presence of an axial electric field. The definition of this jet is a simplified model of electrospray, electrospinning. In this model, the stability of a free incompressible cylindrical flow with surface tensile strength, conductivity, polarization, viscosity, and dielectric constant is determined, irrespective of the solubility of the jet and the surrounding fluid (air), in the presence of uniform axial electric field has taken. This will be done by adding the forces generated by the... 

The Sato-Tate conjecture is an important conjecture regarding the distribution of the Frobenius traces of a family of elliptic curves over finite fields obtained from the reductions of an elliptic curve without CM over a number field modulo the prime ideals of its ring of integers. The statement is that the sequence of normalized Frobenius traces should follow a semicircle distribution. It was discovered by Mikio Sato and reformulated by John Tate in terms of L-functions around 1960. A complete proof of the conjecture for elliptic curves over totally real fields was published in 2008 by R. Taylor et al. under some mild technical assumptions. In addition to the original Sato-Tate conjecture,... 

Recently, parametric excitation has been proposed and experimentally proven to provide micro gyroscopes with robustness to parameter variations and enhancement of sensitivity. harmonic excitation gyroscopes are very sensitive to response of a resonance at the resonant frequency; therefore it has to be created accurately. However, parametric excitation gyroscopes are not sensitive as a result of wide bound of frequency at drive mode, accordingly it is not necessary to be formed accurately in the same way as harmonic excitation gyroscope.
The produced stress at combs have a significance effect on robustness, sensitivity and calibration curves of parametric excitation gyroscope, as a... 

In this thesis, we investigate the involutions of a Clifford algebra induced by involutions of orthogonal group in characteristic two. Several properties of these involutions, such as the relations between their invariants and their decompositions are studied. Also it is shown that a tensor product of quaternion algebras with involution can be expressed as the Clifford algebra of a suitable quadratic form with an involution induced by an involution of orthogonal group. Finally, in connection with the Pfister factor conjecture formulated by D. B. Shapiro, split tensor products of quaternion algebras with involution over a field of characteristic two are investigated  

In today‘s world, the need for travel to different places for various reasons like politics, business and entertainment is unavoidable. This demonstrates the importance of the airline industry and the attention is achieved from the society. Different airlines try various strategies to satisfy more customers of this industry and of course more benefit would arise. These strategies would work more efficiently based on the outcome of a sound research on the exact needs of the customers, their perceived quality and expectations, and the gaps between the two and how they can be filled. This research follows the aim of understanding customer satisfaction for airline industry in Kish Island .In... 

Network Function Virtualization (NFV) is a new paradigm for designing modern computer networks and data centers. NFV leverages the IT virtualization technologies to virtualize entire classes of network node functions into building blocks that may connect, or chain together to create communication services. In this research, we analysed and designed two offline and online algorithms for the problem of join optimization over placement and routing of network function chains in data centers. In the offline case, we showed that traditional randomized rouding works well and by help of chrnoff bound, we derive a new bound on performance gap. The online algorithm in both performance and resource... 

Hydroxyapatite (HA) is crucial in orthopedic and dental applications due to its similarity to hard tissues of body. Creating a coating with high adhesion, high corrosion resistance, and mechanical properties on orthopedic and dental implants can result in reducing the healing period, as well as increasing the durability of the implant. HA coating can cause the surface of the implant and bones to be strongly bonded together, letting the cells grow on it. Besides, titanium plasma sprayed (TPS) implants have been commercialized in the past decades due to their superior performance compared to uncoated implants in terms of bone-to-implant contact and bone retention. In this project, by using... 

Aluminum alloys are widely used in many applications in aerospace and automotive industries. Therefore, the study of the effects of different parameters such as chemical composition, temperature, strain, strain rate and recovery and recrystallization phenomena being more effective on controlling of microstructure and final properties of product, are more important. In this research, deformation behavior of AlMg6 alloy has been studied from two theoretical and experimental views as described below: In ambient temperature deformation, the mechanical properties in correlation on the microstructures developed at different temperatures have been assessed. The results of tensile test demonstrated...