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Alternating Current Potential Drop Measurement
Alternating may refer to: Mathematics * Alternating algebra, an algebra in which odd-grade elements square to zero * Alternating form, a function formula in algebra * Alternating group, the group of even permutations of a finite set * Alternating knot, a knot or link diagram for which the crossings alternate under, over, under, over, as one travels along each component of the link * Alternating map, a multilinear map that is zero whenever any two of its arguments are equal * Alternating operator, a multilinear map in algebra * Alternating permutation, a type of permutation studied in combinatorics * Alternating series, an infinite series in which the signs of the general terms alternate between positive and negative Electronics * Alternating current Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Algebra
In mathematics, an alternating algebra is a -graded algebra for which for all nonzero homogeneous elements and (i.e. it is an Graded-commutative ring, anticommutative algebra) and has the further property that (Nilpotent, nilpotence) for every homogeneous element of odd degree. Examples * The Differential forms#Operations, differential forms on a differentiable manifold form an alternating algebra. * The exterior algebra is an alternating algebra. * The cohomology ring of a topological space is an alternating algebra. Properties * The algebra formed as the Direct sum of modules, direct sum of the homogeneous subspaces of even degree of an anticommutative algebra is a subalgebra contained in the Center (ring theory), centre of , and is thus Associative_algebra#Definition, commutative. * An anticommutative algebra over a (commutative) base Ring (mathematics), ring in which 2 is not a zero divisor is alternating. See also * Alternating multilinear map * Exterior algebra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Form
In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v=0 for every vector v in V. The exterior algebra is named after Hermann Grassmann, and the names of the product come from the "wedge" symbol \wedge and the fact that the product of two elements of V is "outside" V. The wedge product of k vectors v_1 \wedge v_2 \wedge \dots \wedge v_k is called a ''blade of degree k'' or ''k-blade''. The wedge product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude of a -blade v\wedge w is the area of the parallelogram defined by v and w, and, more generally, the magnitude of a k-blade is the (hyper)volume of the parallelotope defined by the constituent vectors. The alternating property that v\wedge v=0 implies a skew-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Group
In mathematics, an alternating group is the Group (mathematics), group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted by or Basic properties For , the group A''n'' is the commutator subgroup of the symmetric group S''n'' with Index of a subgroup, index 2 and has therefore factorial, ''n''!/2 elements. It is the kernel (algebra), kernel of the signature group homomorphism explained under symmetric group. The group A''n'' is abelian group, abelian if and only if and simple group, simple if and only if or . A5 is the smallest non-abelian simple group, having order of a group, order 60, and thus the smallest non-solvable group. The group A4 has the Klein four-group V as a proper normal subgroup, namely the identity and the double transpositions , that is the kernel of the surjection of A4 onto . We have the exact sequence . In Galois theory, this m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Knot
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. A link is alternating if it has an alternating diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating knots, such as the Tait conjectures, was what enabled early knot tabulators, such as Tait, to construct tables with relatively few mistakes or omissions. The simplest non-alternating prime knots have 8 crossings (and there are three such: 819, 820, 821). It is conjectured that as the crossing number increases, the percentage of knots that are alternating goes to 0 exponentially quickly. Alternating links end up having an important role in knot theory and 3-manifold theory, due to their complements having useful and interesting geometric and topological properties. This led Ralph Fox to ask, "What is an alternating knot?" By this he was asking what non-dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Map
In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a multilinear form) that is zero whenever any pair of its arguments is equal. This generalizes directly to a module over a commutative ring. The notion of alternatization (or alternatisation) is used to derive an alternating multilinear map from any multilinear map of which all arguments belong to the same space. Definition Let R be a commutative ring and , W be modules over R. A multilinear map of the form f: V^n \to W is said to be alternating if it satisfies the following equivalent conditions: # whenever there exists 1 \leq i \leq n-1 such that x_i = x_ then . # whenever there exists 1 \leq i \neq j \leq n such that x_i = x_j then . Vector spaces Let V, W be vector spaces over the same field. Then a multilinear map of the form f: V^n \to W is alternating if it satisfies the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Operator
In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v=0 for every vector v in V. The exterior algebra is named after Hermann Grassmann, and the names of the product come from the "wedge" symbol \wedge and the fact that the product of two elements of V is "outside" V. The wedge product of k vectors v_1 \wedge v_2 \wedge \dots \wedge v_k is called a ''blade of degree k'' or ''k-blade''. The wedge product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude of a -blade v\wedge w is the area of the parallelogram defined by v and w, and, more generally, the magnitude of a k-blade is the (hyper)volume of the parallelotope defined by the constituent vectors. The alternating property that v\wedge v=0 implies a skew-sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Permutation
In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry. For example, the five alternating permutations of are: * 1, 3, 2, 4 because 1 2 < 4, * 1, 4, 2, 3 because 1 < 4 > 2 < 3, * 2, 3, 1, 4 because 2 < 3 > 1 < 4, * 2, 4, 1, 3 because 2 < 4 > 1 < 3, and * 3, 4, 1, 2 because 3 < 4 > 1 < 2. This type of permutation was first studied by [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Series
In mathematics, an alternating series is an infinite series of terms that alternate between positive and negative signs. In capital-sigma notation this is expressed \sum_^\infty (-1)^n a_n or \sum_^\infty (-1)^ a_n with for all . Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit. The alternating series test guarantees that an alternating series is convergent if the terms converge to 0 monotonically, but this condition is not necessary for convergence. Examples The geometric series − + − + ⋯ sums to . The alternating harmonic series has a finite sum but the harmonic series does not. The series 1-\frac+\frac-\ldots=\sum_^\infty\frac converges to \frac, but is not absolutely convergent. The Mercator series provides an analytic power series expression of the natural logarithm, given by \sum_^\infty \frac x^n = \ln (1+x),\;\;\;, x, \le1, x\ne-1. The functions si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Current
Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, Fan (machine), fans and electric lamps into a wall socket. The abbreviations ''AC'' and ''DC'' are often used to mean simply ''alternating'' and ''direct'', respectively, as when they modify ''Electric current, current'' or ''voltage''. The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction of the current and vice versa (the full period is called a ''wave cycle, cycle''). "Alternating current" most commonly refers to power distribution, but a wide range of other appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Turns
Turn-taking is a type of organization in conversation and discourse where participants speak one at a time in alternating turns. In practice, it involves processes for constructing contributions, responding to previous comments, and transitioning to a different speaker, using a variety of linguistic and non-linguistic cues. While the structure is generally universal, that is, overlapping talk is generally avoided and silence between turns is minimized, turn-taking conventions vary by culture and community. Conventions vary in many ways, such as how turns are distributed, how transitions are signaled, or how long the average gap is between turns. In many contexts, conversation turns are a valuable means to participate in social life and have been subject to competition. It is often thought that turn-taking strategies differ by gender; consequently, turn-taking has been a topic of intense examination in gender studies. While early studies supported gendered stereotypes, such as men ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternate Bass
In music, alternate bass is a performance technique on many instruments where the bass alternates between two notes, most often the root and the fifth of a triad or chord. The perfect fifth is often, but not always, played below the root, transposed down an octave creating a fourth interval. The alternation between the root note and the fifth scale degree below it creates the characteristic sound of the alternate bass. On the guitar and bass guitar this is accomplished with the right hand alternating between two or more strings, often the bottom two on the guitar. In the following example in the C major chord C is located on the fifth string while G is located on the adjacent sixth (lowest) string and in the F major chord F is located on the adjacent fourth string: Alternate bass lines are also used on the double bass in country music, bluegrass music and related genres. On the Stradella bass system commonly found on accordions, the left-hand bass-note buttons are arrange ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
