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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 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... 

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  

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,... 

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  

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... 

Enanthioselective synthesis of biological molecules are so important in synthetic chemistry, and because of their biological activities, β-amino carbonyl compounds have earned so much attention in this area of chemistry. Mannich reaction is a classical method for synthesis of these molecules. The Mannich reaction is a three-component reaction between an enolizable CH-acidic carbonyl compound, an amine, and an aldehyde producing β-amino carbonyl compounds. But acidic or basic difficult circumstances, long reaction time, low yield and enantioselectivity, are the drawbacks of classical methods. In this project, we used titania-based solid acid as an enantioselective catalyst to overcome these... 

This thesis contains two parts .In the first part a catalyst such as AlCl3/Al20 has been demonstrated to catalyze Michael addition reaction of amines to a,�- unsaturated compounds with high yields , short reaction time and under solvent-free condition.The Michael addition to a,�- unsaturated compounds produces quantitively the mono addition products.The next part is about olefins epoxidation . Alkene epoxidation is a useful reaction in organic synthesis. Epoxides play an important role in industrial intermediates for the production of fine chemicals as well as pharmaceuticals .The hydrogen peroxide has been used as an oxidant because it is considered as an economical and appropriate reagent... 

This thesis contains four chapters. In first chapter the role of water in organic reactions as a ecofriendly solvent, computational chemistry and dynamic nuclear magnetic resonance were studied. In the second chapter synthesis of new 4-hydroxy pyrrole derivatives in water were reported. For the synthesis of these compounds arylglyoxal derivatives, 1,3-dicarbonyl compounds and ammonium acetate were used. The reaction conditions are very mild. The third chapter contains the synthesis of new (4 or 5)-Aryl-2-aryloeil-(1H)-imidazole compounds in aqueous media. We also investigated the tauto-isomerisation of isomeric imidazoles during this reaction using DNMR technique. In forth chapter a... 

Purification of waste water containing metal ions, is one of major environmental problems which have threaten human’s life, other creatures and even agricultural products by means of polluting suberranean water. Copper ion is one of dangerous heavy metals that exists in potable water and agricultural uses, due to serious problems in health of humans and aquatic. In recent years, different methods for purification of waste water containing heavy metal ions have been published. Right now, thorough these methods such as: filtration, coagulation, precipitation and adsorption are being used, which have their own advantages and disadvantages.In this research, new method for purification of waste... 

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... 

Albert proposed the cyclic algebraof the degree 4 in1934. After that more studies were conducted on thecyclic algebras on F in conditions in which L = F(µ )nis an extention of F, for in the Albert’s example it wasmanifest that 2|[F(µ ) : F]. In a paper in the same yearnAlbert proposed a condition for an F-division algebrato be cyclic. In this thesis, a theorem will be proposedin which for the condition (n=1) the Albert’s theoremwill be the result. Moreover, F-division rings of the pndegree are investigated. the required means is modularspectral factorization which was for the ?rst time de?nedin clusters by Merkuryev. Finally a condition will beproposed for the fact that F-division... 

Network management includes a wide range of topics such as performance, security, monitoring, debugging and so on. The network monitoring plays a vital role and can cover a wide range of network management requirements. Monitoring is the only way to know the correct network performance in accordance with the network design. In order to understand what is happening on the network and how network performance over time, the network should have a reporting system. Today, the reporting is done using network monitoring tools. In traditional networks, network monitoring is done using additional hardware which imposes high costs, complexity and also additional traffic overheads to the network. But...