Every non-inner automorphism yields a non-trivial element of Out ( G ), but different non-inner automorphisms may yield the same element of Out ( G ).

Every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincaré group and an internal group if there is a mass gap: no mixing between these two is possible.

Every hyperbolic Riemann surface has a non-trivial fundamental group.

Every single problem touched on thus far is related to good marketing planning.

This problem is encapsulated in the phrase " Every selection of one is a rejection of many ".

* Every finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem

Every human advance solves one problem but also engenders another.

Every three years the College also holds a ball, usually off site due to the problem of securing the college's perimeter sufficiently for insurance purposes. The most recent off-site ball was held was February 9, 2008 at Heythrop Park.

Every CSP can also be considered as a conjunctive query containment problem.

Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).

* Every positive integer can be written as the sum of 73 or fewer sixth powers ( see Waring's problem ).

Every positive integer is the sum of at most 37 fifth powers ( see Waring's problem ).

Every linear program has a dual problem with the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa.

Every positive integer can be expressed as the sum of at most 19 fourth powers ; every sufficiently large integer can be expressed as the sum of at most 16 fourth powers ( see Waring's problem ).

Every graph ( that is connected and not a tree ) has multiple spanning trees, so we once again have an example where the problem itself allows multiple possible outcomes, and the algorithm chosen can arrive at any one of them, but will never arrive at something else.

# Every solution to a wicked problem is a " one-shot operation "; because there is no opportunity to learn by trial and error, every attempt counts significantly.

# Every wicked problem is essentially unique.

# Every wicked problem can be considered to be a symptom of another problem.

# Every wicked problem is essentially novel and unique.

# Every solution to a wicked problem is a ' one shot operation.

Russell L. Ackoff wrote about complex problems as messes: " Every problem interacts with other problems and is therefore part of a set of interrelated problems, a system of problems ….

Every search problem has a corresponding decision problem, namely

Every car uses either a 5. 0 L Ford " Boss 302 " SVO or a 5. 0 L Chevrolet small block race-engine ( depending on the make )-capable of producing between 460 and 485 kW ( 620 — 650 bhp ) of power, but generally quoted as a little over 450 kW ( 600 bhp ) in race trim.

# " Every Little Bit o ' You " ( Irwin Levine, L. Russell Brown )

** L. A. Reid and Babyface for " Every Little Step " performed by Bobby Brown

Every year, usually around August, this marina hosts the R. N. L. I.

Every square-integrable vector field u ∈ ( L < sup > 2 </ sup >( Ω ))< sup > 3 </ sup > has an orthogonal decomposition:

Every musician in L. A. wanted to participate, but soon Lennon's drinking and Spector's erratic behavior ( which included his firing a gun in the studio control room ) caused the sessions to break down.

* Let K < sup > a </ sup > be an algebraic closure of K containing L. Every embedding σ of L in K < sup > a </ sup > which restricts to the identity on K, satisfies σ ( L ) = L. In other words, σ is an automorphism of L over K.

* Every irreducible polynomial in K which has a root in L factors into linear factors in L.

Every year CEI hosts an annual dinner gala and presents the Julian L. Simon Memorial Award.

** Every single member of the New Covenant " knows the L " in an intimate way.

Professor Herman Bondi, who gave the first J. L. Synge Public Lecture in 1992, had this to say: " Every one of the other 88 % has been deeply influenced by his geometric vision and the clarity of his expression ".

Every L. A. # 1 song would be played in chronological order ( utilizing the older KHJ radio charts and other local charts ) from 1955 through 1985.

Every commutative von Neumann algebra on a separable Hilbert space is isomorphic to L < sup >∞</ sup >( X ) for some standard measure space ( X, μ ) and conversely, for every standard measure space X, L < sup >∞</ sup >( X ) is a von Neumann algebra.

Every Data Matrix is composed of two solid adjacent borders in an " L " shape ( called the " finder pattern ") and two other borders consisting of alternating dark and light " cells " or modules ( called the " timing pattern ").

Every year since 1994, Lloydies have climbed onto the top of Millikan Library to construct the Lloyd Christmas Tree, a monumental structure of numerous Christmas lights strung together to resemble a 10-story Christmas tree topped with a 12-feet-tall " L ." The latest off-campus pranks have been the pranking of MIT's Campus Preview Weekend, which included many Lloydies.

* James Allen ’ s Book of Meditations for Every Day in the Year ( 1913 ) of earlier texts, compiled by his wife Lily L. Allen

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.