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 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, if 1 January is a Sunday, all the days marked by A will also be Sundays ; If 1 January is a Saturday, Sunday will fall on 2 January which is a B, and all the other days marked B will be Sundays ; if 1 January is a Monday, then Sunday will not come until 7 January, a G, and all the days marked G will be Sundays.

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 one of the main issues with nuclear propulsion would be safety, both during a launch for the passengers, but also in case of a failure during launch.

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

Clearly, Swift's idea of having another species domesticate mankind was anathema to Heinlein ( who did not hesitate to point out weaknesses of both human and alien characters in his works ), and this part of the book expresses his vociferous rebuttal.

Clearly the intense coverage by the NBC's television system has brought a closer look to the personalities, backgrounds, and history of both men and women in sports and opens a new source for comparison with pre-Title IX sports activity by women.

Clearly, in early Vedic religion, both the Asura and the Devas were deities who constantly competed with each other, some bearing both designations at the same time.

Clearly, both Daoism and Confucianism presume that human nature is basically good.

) Clearly a syncretism has occurred since Taylor's day, although its implementation has been uneven, as lean management in capable hands has produced good results for both managers and workers, but in incompetent hands has damaged enterprises.

The heavily advertised " See Clearly Method " ( of which sales were halted by a court order in November 2006, in response to what were found to be dishonest marketing practices ) included " palming " and " light therapy ", both adapted from Bates.

Clearly, their audience wanted to know both results.

Clearly, to Babai, Christ is both God and man.

Clearly, if an object were simultaneously subject to both a centripetal force and an equal and opposite centrifugal force, the resultant force would vanish and the object could not experience a circular motion.

Clearly both places were still mere hamlets.

Clearly Bob will not go on his own: he would not set off alone, but if he did then Alice would follow, and Alice's personal liberty means the joint preference must have both to go > Bob to go.

Clearly, there needed to be a scientific method where experiments can be repeated by other people, and results needed to be reported in a clear language that laid out both what is known and unknown.

Clearly, the two are overlapping concepts, with usability including pragmatic aspects ( getting a task done ) and user experience focusing on users ’ feelings stemming both from pragmatic and hedonic aspects of the system.

Clearly Maryland no longer had a claim to the Wedge, as it is east of the Mason – Dixon Line and as both Pennsylvania and Delaware were owned by the Penns, there was no particular incentive to determine which possession it was a part of, at least until they became separate states.

" Clearly Eno had been very impressed with both Musik von Harmonia and Zuckerzeit and had joined Harmonia once live in 1974, jamming with the group at The Fabrik in Hamburg.

Clearly the advantage of this is that both DRM and analogue radios can receive a signal they can discriminate and demodulate, with little disadvantage to either mode.

Clearly the phenomenon cannot be a property of the exact solution, since this is the same for both problems, and must be a property of the differential system itself.

* Clearly Defined Role: Defined roles and responsibilities for both clients, other stakeholders and consulting team

Clearly the most provocative plays are all imported originals -- A Taste Of Honey, by Britain's young ( 19 when she wrote it ) Shelagh Delaney ; ;

Clearly these are the Church ’ s agents of ministry and work of whom the body of Christ consists ; and God has ordained them.

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

Clearly, those who study folklore and literature are interested in them, but scholars from a variety of fields have found ways to profitably incorporate the study proverbs.

Clearly, no ethical rules apply, as they are all based on higher powers or on justification.

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

Clearly, there are some individuals, including non-humans such as a racehorse, which have economic value unique to their individual body and being that cannot be captured or defined as an " intellectual " asset nor as a set of " social " relationships ( because horses do not socialize in the sense humans do ).

Clearly the maximal right ideals of a ring R are exactly the maximal submodules of the module R < sub > R </ sub >.

Clearly recognisable examples are stands of E. platypus, E. vesiculosa and the unrelated E. stoatei.

Clearly, lethality, level of activity, and hippocampal plasticity are rescued, but are the animals free of any other RTT signs such as social behavior deficits, anxiety, and cognitive impairments?

Clearly visible, though, are the major and various subsequent minor alterations, giving an interesting insight into its architectural history.

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.

Clearly, such sets are not autonomous and are objects of human agency.

Clearly there are a great many kinds of trance.

Clearly, many more parameters are required to register every detail of the system down to the molecular or atomic scale than to simply specify, say, the temperature or the pressure of the system.

Clearly, there are some solutions to the equation.

Clearly, all Banach spaces and Fréchet spaces are F-spaces.

* " Some Reforms are Clearly Needed ", Constitutional Centenary Foundation ( Vic.

Clearly ' few experiences are more prominent in the lives of preadolescents than the onset of puberty '; so that ' at eleven or twelve you're just reaching the end of a long period during which change was steady and incremental ': Freud's latency years.

Clearly there are many ways this can be done.

Clearly today parliament tolerates only a very narrow exercise of the royal prerogative by issuance of letters patent, and such documents are issued with prior informal government approval, or indeed are now generated by government itself with the monarch's seal affixed as a mere formality.