The implication from ' exact ' to ' closed ' is then a consequence of the symmetry of second derivatives, with respect to x and y.

An implication graph must be a skew-symmetric graph, meaning that the undirected graph formed by forgetting the orientations of its edges has a symmetry that takes each variable to its negation and reverses the orientations of all of the edges.

The host of novel applications of electronics to medical problems is far more thrilling because of their implication in matters concerning our health and vitality.

And our question is, is such an implication consistent with what we meant??

it is only after he has involved her emotions in his scheme that he uses her given name, placing himself by implication in the position of a solicitous father.

The implication is that Paneloux's loss of faith is what lead to his death.

" Peter Heather agrees with Wood's implication in this instance: " I doubt that this is the full story, but the effects of Frankish intervention are clear enough.

The implication is that the entropy of a perfect crystal simply approaches a constant value.

But, there is " certainly no evidence for this view in the New Testament " and in the case of Clement of Rome and Ignatius of Antioch the implication is not that it cannot be celebrated by anyone else, but that it ought not.

The implication is that Bluetooth does the same with communications protocols, uniting them into one universal standard.

" The purpose is to drive out and dispossess the Canaanites, with the implication that there are to be no treaties with the enemy, no mercy, and no intermarriage.

The implication, seen in the closing scenes of the book, with the release of Jehoiachin and his restoration to a place of honour in Babylon, is the promise to David of an eternal dynasty is still in effect, and the Davidic line will be restored.

James Mays, however, says that the failure to mention Hosea's paternity this is " hardly an implication " of Gomer's adultery.

In fact, the concavity of the water clearly involves gravitational attraction, and by implication the Earth also is a participant.

Coming Home converts the huge problem of the returning injured Vietnam War soldier into the chance that the injured soldier will fall in love, and when he does, the strong implication is that the larger problem is also solved.

One implication of utilitarianism is that one's intention in performing an act may include all of its foreseen consequences.

The implication of this attack is that all data encrypted using current standards based security systems such as the ubiquitous SSL used to protect e-commerce and Internet banking and SSH used to protect access to sensitive computing systems is at risk.

An objection against the theist implication of the proposition is that even if one accepts the argument as a proof of a First Cause, it does not identify that First Cause with God.

Under the Curry – Howard correspondence, the existence of currying and uncurrying is equivalent to the logical theorem, as tuples ( product type ) corresponds to conjunction in logic, and function type corresponds to implication.

In a historical or geopolitical sense the term usually refers collectively to Christian majority countries or countries in which Christianity dominates or was a territorial phenomenon .“ Christendom is originally a medieval concept steadily to have evolved since the fall of the Western Roman Empire and the gradual rise of the Papacy more in religio-temporal implication practically during and after the reign of Charlemagne ; and the concept let itself to be lulled in the minds of the staunch believers to the archetype of a holy religious space inhabited by Christians, blessed by God, the Heavenly Father, ruled by Christ through the Church and protected by the Spirit-body of Christ ; no wonder, this concept, as included the whole of Europe and then the expanding Christian territories on earth, strengthened the roots of Romance of the greatness of Christianity in the world .”

The rabbis recognize a positive value to the yetzer hara: one tradition identifies it with the observation on the last day of creation that God's accomplishment was " very good " ( God's work on the preceding days was just described as " good ") and explain that without the yetzer ha ' ra there would be no marriage, children, commerce or other fruits of human labor ; the implication is that yetzer ha ' tov and yetzer ha ' ra are best understood not as moral categories of good and evil but as selfless versus selfish orientations, either of which used rightly can serve God's will.

Berlin's argument was partly grounded in Wittgenstein's later theory of language, which argued that inter-translatability was supervenient on a similarity in forms of life, with the inverse implication that our epistemic access to other cultures entails an ontologically contiguous value-structure.

* " Our foreign policy has always helped other countries, except of course when it is against our National Interest ..." ( The false implication is that our foreign policy always helps other countries ).

Kin agrees ; the implication being that the world she will build is in fact our own Earth.

She gave her last public speech, on May 25, 2011, at the Canadian Club of Ottawa, entitled Serving Parliament Through a Decade of Change, where she warned the government faces long-term fiscal pressures that will mean " very hard choices " between raising taxes or cutting programs and encouraged the government to publicize its long-term fiscal projections because " without them, we cannot begin to understand the scale and complexity of our financial challenges and the implication of policy choices .".

By implication previous intelligent entities may have generated our Universe.

A further implication of his theory was that many stars out in the universe, with characteristics similar to the Sun, would have to be expected to possess planetary systems similar to our own.

If it's not an early step ( i. e. in our past ), then the implication is that the improbable step lies in our future and our prospects of reaching step 9 ( interstellar colonization ) are still bleak.

Their purpose is to corrupt our moral premises by corrupting non-political movies — by introducing small, casual bits of propaganda into innocent stories — thus making people absorb the basic principles of Collectivism by indirection and implication .</ p >

Despite the implication that Peterson had also murdered Elizabeth Ratliff, her daughters stood by him: " The DA is trying to say that our dad killed our birth mother and our mother.

A related implication of the cosmological principle is that the largest discrete structures in the universe are in mechanical equilibrium.

By making the various ships and devices to be of roughly the same visual design, the implication is that all of series take place in the same universe.

Morgenstern's diary is an important and usually reliable source for Gödel's later years, but the implication of the August 1970 diary entry — that Gödel did not believe in God — is not consistent with the other evidence.

Left-wing journalists opposed to Kaiser Wilhelm II's policies outed a number of prominent members of his cabinet and inner circle — and by implication the Kaiser — beginning with Maximilian Harden's indictment of the aristocratic diplomat Prince Eulenburg.

When combined with Hubble's law, the implication of the redshift is that the quasars are very distant — and thus, it follows, objects from much earlier in the universe's history.

It was suggested that the two houses first adopt a resolution indicating that they deem an amendment necessary, but this procedure has never been used — the U. S. Senate and the U. S. House of Representatives instead directly proceed to the adoption of a joint resolution, thereby proposing the amendment with the implication that both bodies " deem " the amendment to be " necessary.

However, if a plaintiff wished to avail himself of Royal — and by implication superior — justice in one of the King's courts, then he would need a writ, a command of the King, to enable him to do this.

* To refuse the " Queen's Consent ", where direct monarchical assent is required for a bill affecting, directly or by implication, the prerogative, hereditary revenues — including ultimus haeres, treasure trove, and bona vacantia — or the personal property or interests of the Crown to be heard in Parliament.

However, later, it was confirmed that layoffs were not heavily confined to one team or another, countering early rumors that the teams were specifically targeted — countering the implication that the under performance of certain games might have been the catalyst.

Likewise, when Fortuna is qualified " imperatrix mundi " in the Carmina Burana there's no implication of any type of consort — the term describes ( the Goddess or personified ) Fortune " ruling the world ".

" Holmes replies scathingly that Miss Adler is indeed on a much different level from the King ( by which he means higher — an implication lost on the King ).

This track, and its implication of a moving source, roughly mirrors the similar track of the Yellowstone Hotspot from the McDermitt Caldera on the Oregon — Nevada border, on which basis the Newberry volcanism has been attributed to a so-called hotspot ( a plume of hot material arising from the earth's mantle ).

Secondly the name derives from the Tellurometer South Africa's world first electronic surveying development — and by implication a commitment to ongoing electronic research and development.

But a thesis concerning the extent of effective methods — which is to say, concerning the extent of procedures of a certain sort that a human being unaided by machinery is capable of carrying out — carries no implication concerning the extent of the procedures that machines are capable of carrying out, even machines acting in accordance with ' explicitly stated rules.

With the consent of the nobility, the Third Estate, and a great part of the clergy, he appeals in the matter from Boniface VIII to a future general council — the implication being that the council is superior to the pope.

Mantegna then began speaking in a low, controlled voice to the little boy, telling him it was best to stay in the audience and respect his performance ; he warned the boy that if he ( Mantegna ) made a call, then Montana would not play in his next game — an implication that Mantegna's true personality equaled his gangster roles.

Hydrogen atoms bonded to carbon are not shown — they can be inferred by counting the number of bonds to a particular carbon atom — each carbon is assumed to have four bonds in total, so any bonds not shown are, by implication, to hydrogen atoms.

With this came, most importantly, the implication that acquired characteristics of an organism — for example, the state of being leafless as a result of having been plucked — could be inherited by that organism's descendants.

Though it has seemed " obvious " to mathematicians literally for centuries that proving B from A conjoined with a set of theorems is sufficient to proving the implication A → B based on those theorems alone, it was left to Herbrand and Tarski to show ( independently ) this was logically correct in the general case — another instance, perhaps, of modern logic " cleaning up " mathematical practice.