Sharif Digital Repository

In elliptic curves equation, if the number of solution is infinite, complication of calculation increase quickly. Even the simplest solutioncan be large. y2 + y = x35115523309x − 140826120488927 The x-coordinate number of smallest solution has 5454 digits. The theorem of Mordell and Weil states that “The set E(Q) of rational solutions has the structure of an infinitely generated abelian group.” E(Q) = (Z)rankE(Q) ⊕T Can the rank be arbitrary large? The current record is rank(E)=28.Manjul Behargava has recently made progress on the study of the average rank for all elliptic curves with rational coefficient. Every such curve has a unique equation of the form y2 = x3 +Ax+B, where A and B are... 

An algebraic number field is a finite extension of Q. Let K be an algebraic number field. Each element 2 K satisfies an equation n + a1n1 + ::: + an with coefficients a1; :::; an 2 Q and is an algebraic integer if it satisfies such an equation with coefficients a1; :::; an 2 Z. algebraic integers form a subring.Let K be an algebraic number field of degree n. Let OK denote the ring of integers of K. The field K is said to possess a power basis if there exists an element 2 OK such that OK = Z + Z + + Zn1. A field having a power basis is called monogenic. In this thesis we consider that there exists infinitely many dihedral quintic fields with a power basis that is shown by lavallee [18]  

Let K, k be two fields and GK be the Galois group of separable closure of K. By a Galois representation of dimension n of GK we mean a homomorphism ρ : GK → GLn(k) of topological groups. In this thesis we want to introduce the theory of Galois representations according to the Taylor’s paper [20] which has written based on his speech in international mathematical conference (ICM 2004). In general we want to build a suitable background for the reader who wants to read the Taylor’s paper with presenting the concepts related to Galois representations such as p-adic and l-adic representations, geometric representations, modular forms, L-function of a Galois representation, Weil-Deligne... 

In this thesis, we studied the representation of Galois groups and modular forms.Also, we presented the Serre’s conjecture which has been proven in two papers published in 2005 and 2008. Moreover, the main aim of this text is presenting the Fontaine-Mazur and Serre’s conjecture  

According to increasingly utilization of different frequency spots, RF receivers are allways under the threats of compression and desensitization because of large out-of-band or in-band blockers. The IC technologies afford fast, low-resistance switches as scaling keeps going on. With this mind, the Linear Periodic Time Varying circuits, in which the switches play the most dominant role, will be a sensible candidate for the concerns of blocker detection and rejection. Furthermore, nowadays’ receivers should be reconfigureable so as to be tunable at different frequency bands and satisfy contrastive standards. In this regard, the LPTV filters provide vast range of tunablity not only with... 

LetK be a biquadratic field. M.-N. Gras and F. Tanoe gave a necessary and sufficient condition that K is monogenic by using a diophantine equation of degree 4 [13]. We consider algebraic extension fields of higher degree. Let F be a Galois extension field over the rationals Q whose Galois group is 2-elementary Abelian. then we shall prove that F of degree graeter than 8, is monogenic if and only if F being field of n'th primitive root of unity under a suitable condition for the case of degree 8  

In this paper Alexander Berkovich and Hamza Yesilyurt revisit old conjectures of Fermat and Euler regarding the representation of integers by binary quadratic form x2 + 5y2. Making use of Ramanujan’s 1 1 summation formula, they establish a new Lambert series identity for Σ1 n;m=1 qn2+5m2 . Conjectures of Fermat and Euler are shown to follow easily from this new formula. But they do not stop there. Employing various formulas found in Ramanujan’s notebooks and using a bit of ingenuity, they obtain a collection of new Lambert series for certain infinite products associated with quadratic forms such as x2+6y2, 2x2+3y2, x2+15y2, 3x2+5y2, x2+27y2, x2+5(y2+z2+w2), 5x2+y2+z2+w2. In the process, they... 

Nitrogen compounds are becoming increasingly important in wastewater management, because of the many effects that nitrogenous material can have on the environment that need nitrogen removal. In this study, the performance of a submerged fixed bed reactor in nitrogen removal, constructed two anoxic and aerobic sections under Modified Ludzack-Ettinger process was investigated. Laboratory experiments were conducted at a constant COD concentration of 350 mg/lit, hydraulic retention times of 8, 12 and 18 hours and influent ammonia loading rate between 0.128 and 0.955 g NH3/m2.day. Nitrogen removal efficiency was obtained between 80.4 and 97.3%, and COD removal efficiency was achieved between 88.9... 

Circular polarization (CP) is one of the common polarization types used in wireless systems for frequency identification (RFID), global positioning (GPS) and wireless local area networks (WLAN), since it can provide greater flexibility in orientation angle between transmitter and receiver, and better mobility and weather penetration than the linearly polarized antennas. Magnetic permeability in ferrites can be tuned by external magnetic field ; So ferrites can be good candidates for new reconfigurable CP antenna technology. In this project, we will consider circularly polarized slot antenna with a wide axial ratio beamwidth that consists of a normally magnetized ferrite substrate mounted... 

Distribution power systems are undergoing a fundamental transition with the introduction of microgrids (MGs) and proliferation of renewable energy sources inspired mainly by privacy and environmental concerns. In this regard, energy management methods employed by utilities should take into account the intermittent nature of RESs power production while coping with the independent operation of MGs. Transactive energy (TE) is an emerging concept which utilizes economic-based mechanisms to facilitate the dynamic and decentralized management of active agents of the system. However, the energy transactions between transactive agents could have adverse impacts on the technical aspect of the system... 

Let C(S) and C(T) denote the sup-normed Banach spaces of real or complex-valued continuous functions on the compact Hausdorff spaces S and T, respectively. A linear map H:C(T)→C(S) is called separating if, for x,y∈C(T), xy≡0 implies HxHy≡0. In the second chapter of this thesis, we will show that any continuous separating map is a continuous multiple of a composition map. Moreover, it will be proved that any linear separating isomorphism of C(T) onto C(S) is continuous. We will also define separating and biseparating maps on the rings of continuous functions equipped with the compact-open topology. In addition, vector-valued separating maps will be investigated. For example, assume that C(T)... 

In this dissertation, transportation networks with two classes of vehicles, including conventional vehicles and autonomous vehicles, have been studied. Four problems, including traffic assignment problem with two classes, congestion pricing problem for conventional vehicles, network design problem for autonomous vehicles, and simultaneous congestion pricing and network design problem, have been modeled and algorithms to solve them are presented. In this study, a dynamic penalty function algorithm is used to solve the congestion pricing problem, and a heuristic algorithm is used to solve the network design problem. Besides, the two-class traffic assignment problem is solved using the... 

Three-dimensional (3D) computational fluid dynamics (CFD) was used in this study to investigate single and multi phase flow behavior related to three stages of ESP pump. Compared to experimental measurements, the numerical prediction for single phase flow of water is matched very well. Furthermore, the effects of viscosity and pump rotational speed for oil were investigated and the results show that by increasing oil viscosity and decreasing rotational speed, the pump head and efficiency reduced. ESP performance under two phase oil-methane flow and the effect of oil viscosity, rotational speed, intake pressure, gas bubble diameter, oil rate and gas volume fraction were studied. ESP boosting...