MAGNETOHYDRODYNAMIC EQUILIBRIUM OF HELICITY-INJECTED SPHEROMAK BY COMBINATION OF FDM AND BEM

The sustainment of the spheromak has been successfully achieved by DC helicity injection in the FACT device at Himeji Institute of Technology. The flux conserver actually used in the experiments has the shielding wall to prevent the plasma from being in contact with the divertor bias coil. Equilibrium configurations of the spheromak in the flux conserver with the shielding wall and the divertor bias coil are numerically determined by using the combination of the finite difference and the boundary element method. Several results for equilibrium configurations and their equilibrium quantities are presented. On the basis of the results, the effects of the divertor bias coil on equilibrium configurations of the helicity-injected spheromak are investigated

Algebraic Numbers

This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to the polynomial ring of ℚ[x] turns to be a field.Suginami-ku Matsunoki 6, 3-21 Tokyo, JapanMichael Francis Atiyah and Ian Grant Macdonald. Introduction to Commutative Algebra, volume 2. Addison-Wesley Reading, 1969.Jonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. Formalized Mathematics, 9(3):565–582, 2001.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990.Hideyuki Matsumura. Commutative Ring Theory. Cambridge University Press, 2nd edition, 1989. Cambridge Studies in Advanced Mathematics.Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339–346, 2001.Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391–395, 2001.Masayoshi Nagata. Theory of Commutative Fields, volume 125. American Mathematical Society, 1985. Translations of Mathematical Monographs.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329–334, 1990.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990.Oscar Zariski and Pierre Samuel. Commutative Algebra I. Springer, 2nd edition, 1975

External iliac venous aneurysm in a pregnant woman: a case report

AbstractWe report an external iliac venous aneurysm in a young pregnant woman who was diagnosed incidentally by ultrasound scanning. The aneurysm was successfully treated by tangential aneurysmectomy and lateral venorrhaphy. Primary iliac venous aneurysm is a rare vascular abnormality. The clinical significance of the disease is unknown. However, embolism, rupture, and thrombosis might occur as they can occur with popliteal venous aneurysm. In fact, three of four reported patients with iliac venous aneurysms had a thromboembolic event. For those reasons, prophylactic treatment is indicated. This is the first patient with an iliac venous aneurysm to be diagnosed without complication