On a family of biquadratic fields that do not admit a unit power integral basis

2019 ◽  
Vol 94 (1-2) ◽  
pp. 1-19
Author(s):  
Japhet Odjoumani ◽  
Alain Togbe ◽  
Volker Ziegler
Keyword(s):  
Integral Basis ◽  
Unit Power ◽  
Biquadratic Fields

On biquadratic fields that admit unit power integral basis

2011 ◽  
Vol 133 (3) ◽  
pp. 221-241 ◽  
Author(s):  
Attila Pethő ◽  
Volker Ziegler
Keyword(s):  
Integral Basis ◽  
Unit Power ◽  
Biquadratic Fields

Integers of Biquadratic Fields

1970 ◽  
Vol 13 (4) ◽  
pp. 519-526 ◽  
Author(s):  
Kenneth S. Williams
Keyword(s):  
Explicit Form ◽  
Integral Domain ◽  
Minimal Polynomial ◽  
Rational Numbers ◽  
Integral Basis ◽  
Squarefree Integers ◽  
Biquadratic Fields ◽  
Rational Integral

Let Q denote the field of rational numbers. If m, n are distinct squarefree integers the field formed by adjoining √m and √n to Q is denoted by Q(√m, √n). Since Q(√m, √n) = Q(√m, √n) and √m + √n has for its unique minimal polynomial x4 —2(m + n)x2 + (m - n)2, Q(√m, √n) is a biquadratic field over Q. The elements of Q(√m, √n) are of the form a0 + a1√m + a2√n + a3√mn, where a1, a2, a3 ∊ Q. Any element of Q(√m, √n) which satisfies a monic equation of degree ≥ 1 with rational integral coefficients is called an integer of Q(√m, √n). The set of all these integers is an integral domain. In this paper we determine the explicit form of the integers of Q(√m, √n) (Theorem 1), an integral basis for Q(√m, √n) (Theorem 2), and the discriminant of Q(√m, √n) (Theorem 3).

Bicyclic Bicubic Fields

1990 ◽  
Vol 42 (3) ◽  
pp. 491-507 ◽  
Author(s):  
Charles J. Parry
Keyword(s):  
Class Number ◽  
Unit Group ◽  
Rational Numbers ◽  
Integral Basis ◽  
Number Problem ◽  
Biquadratic Fields ◽  
Abelian Fields ◽  
Extensive Body ◽  
Fundamental Units

There is an extensive body of literature on the bicyclic biquadratic fields. These fields provide the simplest examples of abelian noncyclic extensions of Q. In sharp contrast, there is a dearth of literature on the bicyclic bicubic extensions of the rational numbers. These fields together with the abelian noncyclic octic extensions provide the next simplest abelian noncyclic extensions.In this article, we shall study abelian bicyclic bicubic extensions of Q of degree 9. Hasse [4, v-ix] has stated as important objectives: the computation of an integral basis, the determination of class number and the calculation of fundamental units for abelian fields. In this article, we will solve the first problem completely, and show that the solution to the unit problem leads to a solution of the class number problem. Moreover, we shall give a method for determining the unit group up to a subgroup which has index 1 or 3 and so determine the class number up to a factor of 3.

scholarly journals Increase of power and efficiency of the 900 MW supercritical power plant through incorporation of the ORC

2013 ◽  
Vol 34 (4) ◽  
pp. 51-71 ◽  
Author(s):  
Paweł Ziółkowski ◽  
Dariusz Mikielewicz ◽  
Jarosław Mikielewicz
Keyword(s):  
Power Plant ◽  
Heat Source ◽  
Steam Turbine ◽  
Hybrid System ◽  
Heat Recovery ◽  
Reference Conditions ◽  
Hot Water ◽  
Operational Parameters ◽  
Reference Case ◽  
Unit Power

Abstract The objective of the paper is to analyse thermodynamical and operational parameters of the supercritical power plant with reference conditions as well as following the introduction of the hybrid system incorporating ORC. In ORC the upper heat source is a stream of hot water from the system of heat recovery having temperature of 90 °C, which is additionally aided by heat from the bleeds of the steam turbine. Thermodynamical analysis of the supercritical plant with and without incorporation of ORC was accomplished using computational flow mechanics numerical codes. Investigated were six working fluids such as propane, isobutane, pentane, ethanol, R236ea and R245fa. In the course of calculations determined were primarily the increase of the unit power and efficiency for the reference case and that with the ORC.

Reducing Functional Unit Power Consumption and its Variation Using Leakage Sensors

2010 ◽  
Vol 18 (6) ◽  
pp. 988-997 ◽  
Author(s):  
Aviral Shrivastava ◽  
Deepa Kannan ◽  
Sarvesh Bhardwaj ◽  
Sarma Vrudhula
Keyword(s):  
Power Consumption ◽  
Functional Unit ◽  
Unit Power

scholarly journals DOWNHOLE REACTIVE POWER COMPENSATION

2015 ◽  
pp. 29-33
Author(s):  
V. A. Kopyrin ◽  
V. A. Iordan ◽  
O. V. Smirnov
Keyword(s):  
Centrifugal Pump ◽  
Power Supply ◽  
Reactive Power ◽  
Reactive Power Compensation ◽  
Pump Unit ◽  
Unit Power ◽  
Transformer Substation ◽  
Electrical Centrifugal Pump

The authors provide a method for compensation of the reactive power inside a well. In the environment Matlab/ Simylink a model was developed of the site of the electrical centrifugal pump unit power supply from the transformer substation. A comparison is made of the proposed method of downhole reactive power compensation with the existing method.

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