We cannot regard foreign policy as something left over after defense policy or trade policy or fiscal policy has been extracted.

`` We regard it as fair only when each party feels that what he has received is as valuable, or more valuable, than what he has given ''.

I regard myself as Left of Centre which … is where a Party Leader ought to be … It is no use asking, “ What would Keir Hardie have done ?” We must have at the top men brought up in the present age, not, as I was, in the Victorian Age .’

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

We can, therefore, regard ‘ suggestion ’ as the most simple form of a typical reflex in man.

In response to the claim in Whewell's treatise that " We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe ", Charles Babbage published what he called The Ninth Bridgewater Treatise, A Fragment.

Carlyle notes: " There is no change in political theory so startling in its completeness as the change from the theory of Aristotle to the later philosophical view represented by Cicero and Seneca .... We think that this cannot be better exemplified than with regard to the theory of the equality of human nature.

The book was rejected by publishers in Sweden prompting an open letter in 2003 defending Johnstone's book ( and her right to publish ) which was signed by, among others, Noam Chomsky, Arundhati Roy, Tariq Ali and John Pilger: " We regard Diana Johnstone ’ s Fools ’ Crusade as an outstanding work, dissenting from the mainstream view but doing so by an appeal to fact and reason, in a great tradition.

Bishop John Tong Hon of Hong Kong used it with regard merely to an openness to dialogue with others, saying: " We are guided by the spirit of Vatican II: only dialogue and negotiation can solve conflicts.

We can use the three-dimensional theory to solve this problem if we regard u as a function in three dimensions that is independent of the third dimension.

Other officers complained about the way in which Raeder sought to re-write history in the Official History in way that gloried Tirpitz with no regard to what actually happened with Admiral Assemann of the Historical Branch complaining to Raeder: " I am convinced that it makes no difference to you Herr Admiral, what we write ... We must only write in such a way that you have peace with the old admirals ".

We will not give even an inch of soil to anyone and we will not be dictated in our foreign policy will we accept anybody's orders in this regard.

" We regard ourselves as the custodians of an extremely interesting and controversial document ," said Yale librarian Alice Prochaska in 2002, " and we watch the scholarly work on it with great interest.

We will leave the matter undecided although, in the case of an indulgent nature ( remissum ingenium ), we regard as suspicious ( suspectum ) the association between persons of disparate age ( aestimantes societatem aevi longe imparilis ).

We regard both intranets and extranets as VPNs.

We find that history records very little about Frankfort with regard to the American Revolutionary War.

" McKenna found that the legislation was within the boundaries of Congress ' powers to regulate interstate commerce, and, in regard to the Fifth Amendment, a line was to be drawn between private and public business: " We are dealing with rights exercised in a quasi-public business, and therefore subject to control in the interest of the public.

The Lords still favoured a compromise, and suggested the addition of a paragraph to the petition reading " We humbly present this petition to your majesty, not only with a care of preserving our own liberties, but with due regard to leave entire that sovereign power, wherewith your majesty is trusted, for the protection, safety, and happiness of your people ".

Others are less complimentary and in the BBC series How We Used To Cook in an episode dedicated to Cradock and Graham Kerr, Keith Floyd and Hugh Fearnley-Whittingstall, amongst others, were very disparaging in regard to her method and cooking skill.

On the 15 November 1830, he expressed himself: “ We are preyed upon by our enemies, by those who regard us as hypocrites or as imbeciles, and by those who are persuaded that our life depends on money ... Freedom is not given, it is taken.

We might be tempted to regard this discourse as a fabrication of later date, were it not for the fact that a Latin hymn directed against the Albigenses, and certainly belonging to the early 13th century, speaks in exactly similar terms.

We also recommend that a strict and inviolable regard be paid to the wise and judicious councils of the late American Congress, and particularly considering that the experience of almost every day points out to us the danger arising from the collection and movements of bodies of men, who, notwithstanding, we willingly hope would promote the common cause and serve the interest of their country, yet are in danger of pursuing a track which may cross the general plan, and so disconcert those public measures which we view as of the greatest importance.

We further recommend a serious and steady regard to the rules of temperance, sobriety and righteousness, and that those Laws which have heretofore been our security and defense from the hand of violence may still answer all their former valuable purposes, though persons of vicious and corrupt minds would willingly take advantage from our present situation.

As Daniel Mudd, then President and CEO of Fannie Mae, testified in 2007, instead the agency's underwriting requirements drove business into the arms of the private mortgage industry who marketed aggressive products without regard to future consequences: " We also set conservative underwriting standards for loans we finance to ensure the homebuyers can afford their loans over the long term.

We may thus trace the notion of individual autonomy from its manifestation in religious practice and theological reflection through practical politics and political theory into literature and the arts.

In the rhyming catechism this doctrine is worded thus: `` In Adam's fall We sin-ned all ''.

We have chosen to give it at the end of the section since it deals with differential equations and thus is not purely linear algebra.

We thus have an optimal policy which maximizes the expected value of the objective function for a given Af.

We will make a few simplifying assumptions: that the uncompressed volume of the cylinder is 1000cc's ( one liter ), that the gas within is nearly pure nitrogen ( thus a diatomic gas with five degrees of freedom and so

We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:

Leary received an honorary doctorate and spoke briefly at his alma mater's undergraduate commencement ceremony on May 16, 2005 ; he is thus credited as " Dr. Denis Leary " on the cover of his 2009 book, Why We Suck.

We have explained that ' regularity ' must be understood to exclude all pseudo-initiatic organizations, which, regardless of pretention and outward appearance, in no way possess any spiritual influence and thus are incapable of transmitting anything .”

The EPR paper says: " We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

Here, we are told, ' We need to go beyond the pleasure principle, the reality principle, and repetition compulsion to ... the fantasy principle ' - ' not, as Freud did, reduce fantasies to wishes ... consider all other imaginable emotions '; and thus envisage emotional fantasies as a possible means of moving beyond stereotypes to more nuanced forms of personal and social relating.

We thus obtain a functor from the category of pointed topological spaces to the category of groups.

We have thus over-counted the actual number of states.

We thus say that dog and dogs are different forms of the same lexeme.

We sent it in, and Schopf reacted strongly against it — thus signaling the tenor of the reaction it has engendered, though for shifting reasons, down to the present day.

We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.

We are enabled thus to contrast Tacitus with Josephus, who warped his narrative to do honour to Titus.

We can thus understand the high importance of barriers, whether of land or water, which separate our several zoological and botanical provinces.

We can thus understand the localisation of sub-genera, genera, and families ; and how it is that under different latitudes, for instance in South America, the inhabitants of the plains and mountains, of the forests, marshes, and deserts, are in so mysterious a manner linked together by affinity, and are likewise linked to the extinct beings which formerly inhabited the same continent ... On these same principles, we can understand, as I have endeavoured to show, why oceanic islands should have few inhabitants, but of these a great number should be endemic or peculiar ; ...

We thus say that in order to solve this problem, the computer needs to perform a number of steps that grows linearly in the size of the problem.

i. e., z is a vector orthogonal to the vector v ( Indeed, z is the projection of u onto the plane orthogonal to v .) We can thus apply the Pythagorean theorem to

We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its " arrow " would be.

We recognize this genre ; thus, expectations are set.

We have also come to understand Harvey's somewhat unorthodox method of dealing with his gout, here cited completely: "... his ( Harvey's ) cure was thus: he would sit with his legs bare ... put them into a pail of water till he was almost dead with cold, then betake himself to his stove, and so ' twas gone ".