`` An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with respect to the state resulting from the first decision ''.

Augustine of Hippo marks the beginning of a system of thought that denies free will ( with respect to salvation ) and affirms that salvation needs an initial input by God in the life of every person.

Completely regularity and the Tychonoff property are well-behaved with respect to initial topologies.

The term is most commonly used for the initial topology of a topological vector space ( such as a normed vector space ) with respect to its continuous dual.

More generally, if F is a subset of the algebraic dual space, then the initial topology of X with respect to F, denoted by σ ( X, F ), is the weak topology with respect to F.

The film also depicts Kirk and Spock's initial clashes at Starfleet Academy, and the gradual development of their friendship based on shared mutual respect, what the elder Spock calls "... a friendship that will define both in ways cannot yet realize.

“ Seneca has been claimed as a forerunner of radio drama because his plays were performed by readers as sound plays, not by actors as stage plays ; but in this respect Seneca had no significant successors until 20th-century technology made possible the widespread dissemination of sound plays .” Radio drama achieved widespread popularity within a decade of its initial development in the 1920s.

A bloody and battered Rocky gives a victory speech, acknowledging the initial and mutual disdain between himself and the crowd as much as the disdain between Russians and Americans generally, and how they've come to respect and admire each other during the course of the fight which he also says is better than war between their two countries.

The first law is completely symmetrical with respect to the initial and final states of an evolving system.

Counterculture youth rejected the cultural standards of their parents, especially with respect to racial segregation and initial widespread support for the Vietnam War, and, less directly, the Cold War — with many young people fearing that America's nuclear arms race with the Soviet Union, coupled with its involvement in Vietnam, would lead to a nuclear holocaust.

The angular displacement ( rotational position ) of each axle is given by and respectively, which are the angles of the unit vectors and with respect to their initial positions along the x and y axes.

By squaring the initial generating function, or by finding the derivative of both sides with respect to x and making a change of running variable n → n-1, one sees that the coefficients form the sequence 1, 2, 3, 4, 5, ..., so one has

Robert Christgau wrote in his initial review of the album, " In every respect — composition, arrangement, production, performance — this is the finest record of the year, much more accessible than the great-but-weird album that preceded it.

' The Queen soon came to regard her young daughter-in-law with great respect and affection, notwithstanding her initial concerns upon hearing from the match-making Vicky that Helena was an " intellectual ", being unusually well-educated for a Princess.

Thus the uncertainty in the outcome of a coin toss is derived ( for the most part ) from the uncertainty with respect to initial conditions.

( Correction with respect to Grossman's text: From the formula below it follows that Grossman means by Ω the initial value of the organic composition of capital ':')

On December 6, 2010, ITU-R recognized that these two technologies, as well as other beyond-3G technologies that do not fulfill the IMT-Advanced requirements, could nevertheless be considered " 4G ", provided they represent forerunners to IMT-Advanced compliant versions and " a substantial level of improvement in performance and capabilities with respect to the initial third generation systems now deployed ".

He is best known among other things for his initial defense of Anne Hutchinson early in her trials during the Antinomian Controversy, during which she mentioned him with respect, though he turned strongly against her with the further course of the trial.

The angle of rotation of this plane at a time t with respect to the initial orientation is the anholonomy of the system.

If one considers a moving initial position, or equivalenty a moving origin ( e. g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track ), the velocity of P ( e. g. a point representing the position of a passenger walking on the train ) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be ' fixed in space ' ( such as, for instance, a point fixed on the floor of the train station ).

No doubt it is indeed unfortunate that Gone with the Wind perpetuates many myths about Reconstruction, particularly with respect to blacks.

With respect to Reconstruction, he thought Congress had been magnanimous in its offers to the South.

With United States v. Cruikshank ( 1876 ), a case which arose out of the Colfax Massacre of blacks contesting the results of a Reconstruction era election, the Fourteenth Amendment was held by the Supreme Court not to have applied the First Amendment or Second Amendment to state governments in respect to their own citizens, only acts of the federal government.

However, the monetary authorities will continue to be required to pay attention to the consequences of their actions with respect to our international balance of payments position and the outflow of gold, as well as with regard to avoiding the creation of excessive liquidity in the economy, which would delay the effectiveness of monetary policy measures in the next expansion phase of the business cycle.

He recognized that whatever transformation may be effected in the first stage of an R-stage process, the remaining stages must use an optimal Af-stage policy with respect to the state resulting from the first stage, if there is to be any chance of optimizing the complete process.

When it is necessary to be specific we say that the optimal policy is an optimal R-stage policy with respect to the feed state Af.

This is the feed state of the subsequent Af stages which, according to the principle of optimality, must use an optimal Af-stage policy with respect to this state.

To extract the optimal R-stage policy with respect to the feed state Af, we enter section R of this table at the state Af and find immediately from the last column the maximum value of the objective function.

Since by the principle of optimality the remaining stages use an optimal Af-stage policy with respect to Af, we may enter section Af of the table at this state Af and read off the optimal policy for stage Af and the resulting state Af.

If we consider a process in which the outcome of one stage is known before passage to the next, then the principle of optimality shows that the policy in subsequent stages should be optimal with respect to the outcome of the first.

1986 — In January 1986, following the rift between New Zealand and the USA in respect of the ANZUS security arrangements Prime Minister Tom Davis declared the Cook Islands a neutral country, because he considered that New Zealand ( which has control over the islands ' defence and foreign policy ) was no longer in a position to defend the islands.

On July 5, 2009, Colin Powell told CNN said that the policy was " correct for the time " but that " sixteen years have now gone by, and I think a lot has changed with respect to attitudes within our country, and therefore I think this is a policy and a law that should be reviewed.

The broad objectives of Ghana's foreign policy thus include maintaining friendly relations and cooperation with all countries that desire such cooperation, irrespective of ideological considerations, on the basis of mutual respect and noninterference in each other's internal affairs.

The protection offered by a liability insurance policy is twofold: a legal defense in the event of a lawsuit commenced against the policyholder and indemnification ( payment on behalf of the insured ) with respect to a settlement or court verdict.

While there have been specific cases in which FBI agents have Mirandized suspects overseas at both Bagram and in other situations, in order to preserve the quality of evidence obtained, there has been no overall policy change with respect to detainees.

The principles of the foreign policy are constitutionally recognized in the Article 89, Section 10, which include: respect for international law and legal equality of states, their sovereignty and independence, non-intervention in the domestic affairs of other countries, peaceful resolution of conflicts, and promotion of collective security through active participation in international organizations.

In this respect, policy decisions pertaining to topics like abortion, contraception, embryonic stem cell research, same-sex marriage, and sex education are prominently focused upon by American secularist organizations such as the Center for Inquiry.

Since the establishment of the United Arab Emirates in 2 December 1971, UAE adopted a balanced foreign policy based on adoption of dialogue, respect of international conventions, commitment to the United Nations Charter and non-interference of other country's internal affairs, and the settlement of disputes by peaceful means.

Venezuelan oil minister Alí Rodríguez Araque's announcement in 1999 that his country would respect OPEC production quotas marked " a historic turnaround from the nation's traditional pro-US oil policy.

Again displaying his inept administrative leadership, Taft, while not sharing any of Knox's respect for Wilson's ability, deferred to much of Wilson's policy making.

In Germany there was a rapid and general feeling in favor of Gregory, and the princes took the opportunity to carry out their anti-regal policy under the cloak of respect for the papal decision.