This classical statement, as well as the classical Divergence theorem and Green's Theorem, are simply special cases of the general formulation stated above.

* Green's Theorem on MathWorld

Then by Green's Theorem,

* O. Knill and D. Winter: ;; Green's Theorem and the Planimeter

Green's Theorem states that for any H-class H of a semigroup S either ( i ) or ( ii ) and H is a subgroup of S. An important corollary is that the equivalence class H < sub > e </ sub >, where e is an idempotent, is a subgroup of S ( its identity is e, and all elements have inverses ), and indeed is the largest subgroup of S containing e. No H-class can contain more than one idempotent, thus H is idempotent separating.

Much culture has arisen around Bowling Green's hills with an old reservoir, hospital and civil war fort on one, much of Western Kentucky Universities campus on another, Hobson Grove, a historic Italian Renaissance style civil war era plantation estate on another and yet another civil war fort on another.

Plug's " Drum and Bass for Papa " included an extra disc of tracks from earlier EPs, and The Bowling Green's " One Pound Note " omitted one track from the UK release due to problems with sample clearance.

Though others had earlier used similar techniques, Thin Lizzy are widely recognised as one of the first hard rock bands to employ double lead guitar harmony sound – a technique pioneered by Peter Green's Fleetwood Mac and Wishbone Ash in the UK, whilst independently in the USA by Lynyrd Skynyrd and The Allman Brothers Band.

In 1967, after one record with the Bluesbreakers, Green, with the Bluesbreaker's rhythm section Mick Fleetwood and John McVie, formed Peter Green's Fleetwood Mac, produced by Mike Vernon on the Blue Horizon label.

A " Greatest Hits " album was also released at the same time, including 17 of Green's most popular songs and one more previously unreleased Christian song, " Your Love Came Over Me ".

Apparently Green's wife mailed one which, while recovered, is the only cancelled sample.

During Double Your Money Green kept up an occasional but good-natured feud with " rival " quiz show host Michael Miles, who compered Take Your Pick, Miles even appearing on one occasion with a huge bouquet of flowers for a guest, to Green's ( mock ) indignation.

The date of Andy Green's record came exactly a half century and one day after Chuck Yeager broke the sound barrier in Earth's atmosphere, with the Bell X-1 research rocket plane on 14 October 1947.

This library exists today, and was likely one of the only sources of Green's advanced mathematical knowledge.

By 1829, the time when Green's father died, the senior Green had become one of the gentry due to his considerable accumulated wealth and land owned, roughly half of which he left to his son and the other half to his daughter.

Green's work has otherwise received comparatively little critical attention from academics ; one of the few academics engaged with Green's work is Jeremy Treglown, author of Romancing: The Life and Work of Henry Green ( Faber and Faber, 2000 ).

If the problem is to solve a Dirichlet boundary value problem, the Green's function should be chosen such that vanishes when either x or x < nowiki >'</ nowiki > is on the bounding surface. Thus only one of the two terms in the surface integral remains.

In the Huygens-Fresnel or Stratton-Chu viewpoints, the electric field is represented as a superposition of point sources, each one of which gives rise to a Green's function field.

The latter was one of Green's first instrumentals, which would soon become a trademark.

In the same year they scored a hit with Green's " Black Magic Woman " ( later covered more successfully by Santana ), followed by the guitar instrumental " Albatross " ( 1969 ), which reached number one in the British singles charts.

Their friendship had its ups and downs for years until June 1902, when Lomax met Bess Baumann Brown from Dallas, one of Green's acquaintances.

Warner and Green's combined gross passing yard total was 5, 492, which, if held by just one player, would surpass the single-season record held by Drew Brees ( 5, 476 yards ).

Lucas became the Green's first party leader 5 September 2008 after their leadership election gaining 92. 4 % of the vote ( against one other candidate, Ashley Gunstock ) on a turnout of 37. 9 %.

In fact, Green's report placed the Palette in a different layer one or two yards away from the deposit, which is considered to be more accurate on the basis of the original excavation notes.

These areas additionally house one of the region's most sought after toboggan hills at Green's Creek, a series of outdoor soccer fields, known collectively as the Hornet's Nest, which host international soccer tournaments and a cooperative garden maintained by residents for over 25 years.

In Tom Green's interview on The Opie and Anthony Show, host Opie noted the film had begun to be regarded as ' one of the funniest movies ever made '.

The Green's function to be used in the above integral is one which vanishes on the boundary:

Green's writing exerted a strong influence on Southern's early work, and Green became one of Southern's most ardent early supporters.

The acquisition of Central made Carlton one of the largest television producers in the UK, when include Action Time and Planet 24 were added to Green's empire.

In 1992, several artists joined together to re-record many of Green's best-known songs for a tribute album called No Compromise: Remembering the Music of Keith Green under the Sparrow Records label.

They targeted Green's home because of the presence of Fox, but stole several other things belonging to Green during their raid.

The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions.

There are several other methods for finding Green's functions, including the method of images, separation of variables, and Laplace transforms ( Cole 2011 ).

The consolidation movement was the work of several progressive politicians, most prominently Andrew Haswell Green so some opponents derided the effort as " Andy Green's hobby.

MP3. com in conjunction with tomgreen. com ran a remix competition where several remixes of " The Bum Bum Song " were profiled on Tom Green's website, promising the winner ( who was to be chosen by total number of downloads and song plays ) a flight to New York to see a taping of The Tom Green Show.

Newington Green's history is marked by several streets in the area taking their name from this period, such as King Henry ’ s Walk, Boleyn Road ( formerly Ann Boleyn ’ s Walk ), Wolsey Road and Queen Elizabeth ’ s Walk.

* ( Includes Green's annotations to the libretti of eleven G & S shows as well as his introductions to them and several song selections from each show, often in lower keys than the originals.

Green's widow, Linda Green, subsequently filed a lawsuit against several US drug manufacturers and retailers, including Leiner.

Reciprocity is also a basic lemma that is used to prove other theorems about electromagnetic systems, such as the symmetry of the impedance matrix and scattering matrix, symmetries of Green's functions for use in boundary-element and transfer-matrix computational methods, as well as orthogonality properties of harmonic modes in waveguide systems ( as an alternative to proving those properties directly from the symmetries of the eigen-operators ).

Whereas the above reciprocity theorems were for oscillating fields, Green's reciprocity is an analogous theorem for electrostatics with a fixed distribution of electric charge ( Panofsky and Phillips, 1962 ).

where R denotes the distance to the source point P and R ' denotes the distance to the reflected point P. A consequence of this expression for the Green's function is the Poisson integral formula.

In addition ( and in contrast to the quasiparticle Green's function ), its weight ( integral over frequency ) is suppressed by a quasiparticle weight factor < math > 0 < Z < 1 </ math >.

In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green, and is the two-dimensional special case of the more general Stokes ' theorem.

Green's theorem can be used to compute area by line integral.

A Green's function can also be thought of as a right inverse of L. Aside from the difficulties of finding a Green's function for a particular operator, the integral in equation ( 3 ), may be quite difficult to evaluate.

where the integral is performed over all possible values of the 3-vector momentum k. In this form, the fraction is seen to be the propagator or Green's function of the Klein-Gordon equation.

The second term in the integral above can be eliminated if we choose G to be the Green's function that vanishes on the boundary of region U ( Dirichlet boundary condition ):

The connection with Green's theorem can be understood in terms of integration in polar coordinates: in polar coordinates, area is computed by the integral where the form being integrated is quadratic in r, meaning that the rate at which area changes with respect to change in angle varies quadratically with the radius.

This last integrand can be recognized as the derivative of the earlier integrand ( with respect to r ) shows that a planimeter computes the area integral in terms of the derivative, which is reflected in Green's theorem, which equates a line integral of a function on a ( 1-dimensional ) contour to the ( 2-dimensional ) integral of the derivative.