Clearly then, M is directly indecomposable if and only if 0 and 1 are the only idempotents in E.

Clearly a criminal trial is a criminal proceeding since if convicted the defendant could be fined or imprisoned.

Tulane University Sports Law Program Director Gabe Feldman ( who attended the hearing in court ) said, " Clearly the judge, by her questions, indicated she thinks Goodell overstepped his authority, and this case was always going to be about if he executed his power fairly ...

Clearly, if both adrenals are removed, replacement with hydrocortisone or prednisolone is imperative.

Clearly if all states can be reached from the origin then any state can be reached from another state ( merely a shift in coordinates ).

Clearly, a complex is bounded above and below if and only if the complex is bounded.

Clearly, if a spark plug were to protrude into the Wankel's combustion chamber it would foul the rotating tip ; and if the plug were recessed to avoid this, the sunken spark might lead to poor combustion.

Clearly, if these two spheres do not intersect ( and that is very easy to test ), then neither do and.

Clearly if one does not have enough money to pay the price then they cannot buy any of that item.

Clearly, the British were penetrated by Philby, but it has never been determined, in any public forum, if there were other serious penetrations.

Clearly if we poured the entire GDP of the planet into protecting against this, we could minimise the risk, but might there be better things to spend it on?

Similar definitions apply to a Lie group G, a maximal commutative Lie subgroup H and any representation V of G. Clearly, if λ is a weight of the representation V of G, it is also a weight of V as a representation of the Lie algebra g of G.

Clearly, however, only good people can be friends to each other because of the other person himself ; for bad people find no enjoyment in one another if they get no benefit.

Clearly, the two statements contradict, but nevertheless, the " genius " has an urge to try to figure out which of the two statements ( if any ) is true.

Clearly, if then the poles are not located at the origin of the z-plane.

Clearly, this automaton recognizes L. Thus, a language L is recognizable if and only if the set is finite.

Clearly, each edge belongs to at most two such boundaries ; if an edge is a bridge of, it appears twice on a single face boundary and therefore has a zero coordinate in the corresponding vector.

Clearly if the lower end of the figures are both correct, the test is useless!

Trescothick stated that he would see how he progresses before committing to the international scene: " Of course I'd love to play for England again .... Clearly, if I want to continue my career I have to undertake another tour.

Clearly, P² = 1 ( the identity operator ), so the eigenvalues of P are + 1 and − 1.

Consider the theory obtained by adding a new constant symbol ε to the language and adjoining to Σ the axiom ε > 0 and the axioms ε < 1 / n for all positive integers n. Clearly, the standard real numbers R are a model for every finite subset of these axioms, because the real numbers satisfy everything in Σ and, by suitable choice of ε, can be made to satisfy any finite subset of the axioms about ε.

He continued to sell well in Jamaica and, to a lesser extent, the UK, returning to the mainstream pop charts in the US and elsewhere (# 1 in France ) with a version of Johnny Nash's " I Can See Clearly Now " on the Cool Runnings film soundtrack in 1993.

Clearly, the moving-average filter passes low frequencies with a gain near 1, and attenuates high frequencies.

Clearly I < sup > 1 </ sup > ƒ is an antiderivative of ƒ ( of first order ), and for positive integer values of α, I < sup > α </ sup > ƒ is an antiderivative of order α by Cauchy formula for repeated integration.

Clearly a frequency of just " 0. 1 " is insufficient to describe the true frequency of the discrete signal.

Other pop hits include " Sugar Sugar " by the Archies ( number 1 in 1969 ) and " I Can See Clearly Now " by Johnny Nash ( number 5 in 1972 ).

Clearly, π < sup > ab </ sup >/ tor = Z < sup > b </ sup >, where b = b < sub > 1 </ sub > ( M ).

Clearly any 3 lines perpendicular to the red ones in Fig 1, in particular those joining the centres of the circles, must also cut at angles of 60 ° and thereby form an equilateral triangle.

Clearly what the person brings to the reading is important.

Clearly, the transformation is involutorial.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

Clearly it is not.

Clearly, an evaluation of a user's abilities and requirements is necessary to match a user with the most appropriate AAC method, input approach, and vocabulary.

Clearly there is always at least one such string for any n, as otherwise all possible strings ( infinitely many ) could be generated by the ( finitely many ) programs with lower complexity, so GenerateComplexString must always return.

MSP Alex Johnstone wrote " Clearly, the Declaration of Arbroath is a literary work of outstanding universal significance by any stretch of the imagination " In 2008, the Campaign Group Chairman, Councillor Jim Millar launched a public petition to reinforce the bid explaining " We're simply asking people to, local people especially, to sign up to the campaign to have the Declaration of Arbroath and Arbroath Abbey recognised by the United Nations.

Clearly, the set of even numbers is infinitely large ; there is no requirement that a set be finite.

Clearly LIN-SPACE is a subset of NLIN-SPACE, but it is not known whether LIN-SPACE = NLIN-SPACE.

Clearly, as the number of trials is increased, one might expect the relative frequency to become a better approximation of a " true frequency ".

Clearly, is provable.

Clearly, instructing individuals about randomness is not sufficient in lessening the gambler's fallacy.

Clearly, this rule flies in the face of the first-user homesteading rule, arbitrarily and groundlessly overriding the very homesteading rule that is at the foundation of all property rights.

Clearly ( excluded middle ) this number is either rational or irrational.

Clearly, the conservators working for the Library of Congress believe that mass deacidification is vital to library collections, whatever the cosmetic effects

Clearly, replacing with either or gives a program with different meaning, and so the expression is not referentially transparent.

Clearly, its length is twice the length of the tree.

" Clearly, Vinson suggested, clear and present danger did not intimate " that before the Government may act, it must wait until the putsch is about to be executed, the plans have been laid and the signal is awaited.

Clearly it is not foolproof as there are input sequences that yield all-zeros, all-ones, or other undesirable periodic output sequences.

Clearly a group is both an I-semigroup and a *- semigroup.