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A curve (top) is filled according to two rules: the even-odd rule (left), and the non-zero winding rule (right). In each case an arrow shows a ray from a point P heading out of the curve. In the even-odd case, the ray is intersected by two lines, an even number; therefore P is concluded to be 'outside' the curve.
Field lines depicting the electric field created by a positive charge (left), negative charge (center), and uncharged object (right). A field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary integral curve which is tangent to the field vector at each point along its length.
Zero-field splitting (ZFS) describes various interactions of the energy levels of a molecule or ion resulting from the presence of more than one unpaired electron. In quantum mechanics , an energy level is called degenerate if it corresponds to two or more different measurable states of a quantum system.
Description: A training booket prepared for an edit-a-thon. The source odt is available by emailing the author. This booklet fulfills the need of students, who attend the course but need extensive notes to take home.
A field is a commutative ring (F, +, *) in which 0 ≠ 1 and every nonzero element has a multiplicative inverse. In a field we thus can perform the operations addition, subtraction, multiplication, and division. The non-zero elements of a field F form an abelian group under multiplication; this group is typically denoted by F ×;
A field of non-zero characteristic is called a field of finite characteristic or positive characteristic or prime characteristic. The characteristic exponent is defined similarly, except that it is equal to 1 when the characteristic is 0; otherwise it has the same value as the characteristic. [2]
A field F is perfect if and only if all irreducible polynomials are separable. It follows that F is perfect if and only if either F has characteristic zero, or F has (non-zero) prime characteristic p and the Frobenius endomorphism of F is an automorphism. This includes every finite field.
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