And then the application of the count rules to the width ( horizontally ) of the configuration gives us an intial estimate of the probable depth of the decline.

If Af denotes the net profit from stage R and Af, then the principle of optimality gives Af.

He gives this to the medium at the appointed time, and the reading then will be concerned with material about or messages from the communicator.

Nicomachus gives the example of 49 and 21: " I subtract the less from the greater ; 28 is left ; then again I subtract from this the same 21 ( for this is possible ); 7 is left ; I subtact this from 21, 14 is left ; from which I again subtract 7 ( for this is possible ); 7 will be left, but 7 cannot be subtracted from 7.

This R-bilinear mapping then gives A the structure of a ring and an associative R-algebra.

Existence is the principle that gives reality to an essence not the same in any way as the existence: " If things having essences are real, and it is not of their essence to be, then the reality of these things must be found in some principle other than ( really distinct from ) their essence.

Loki then gives a greeting to all gods and goddesses who are in the hall save to Bragi.

then the distribution correctly gives the Maxwell – Boltzmann distribution of gas molecule speeds, previously predicted by Maxwell in 1859.

( Chapter 1 is the first of three important moments in Joshua marked with major speeches and reflections by the main characters ; here first God and then Joshua make speeches about the goal of conquest of the Promised Land ; at chapter 12, Joshua looks back on the conquest ; and at chapter 23 Joshua gives a speech about what must be done if Israel is to live in peace in the land ).

then this expression gives the expectation value, or mean or average value, of the observable represented by operator A for the physical system in the state.

This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power one temporarily labels the term X with an index i ( running from 1 to n ), then each subset of k indices gives after expansion a contribution X < sup > k </ sup >, and the coefficient of that monomial in the result will be the number of such subsets.

In calculus, this picture also gives a geometric proof of the derivative if one sets and interpreting b as an infinitesimal change in a, then this picture shows the infinitesimal change in the volume of an n-dimensional hypercube, where the coefficient of the linear term ( in ) is the area of the n faces, each of dimension

It can be then seen that the simple molecular orbital approach gives too much weight to the ionic structures, while the simple valence bond approach gives too little.

The Bolzano – Weierstrass theorem gives an equivalent condition for sequential compactness when considering subsets of Euclidean space: a set then is compact if and only if it is closed and bounded.

Adding and subtracting the last two equations then gives the solution

Differentiation then gives

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

" Joseph ( 1989: IJDL 18. 2: 134-42 ) gives extensive references to the use of the term, dramila first as the name of a people, then of a country.

Since then it has been eroding, creating dramatic incised valleys, and providing the sediment that gives the Yellow River its yellow color and that causes the flooding of the river in the lower reaches ( hence the river's nickname ' China's sorrow ').

This oscillation at a given frequency gives rise to changing electric and magnetic fields, which then set the electromagnetic radiation in motion.

That organization then bundles donations and gives them to parents as vouchers to be used for private school tuition.

For example, if the last player to draw wants three replacements but there are only two cards remaining in the deck, the dealer gives the player the one top card he can give, then shuffles together the bottom card of the deck, the burn card, and the earlier players ' discards ( but not the player's own discards ), and finally deals two more replacements to the last player.

* If the entire language does not allow side-effects, then any evaluation strategy can be used ; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program ( for example, using deforestation ).

At the 1836 dedication of the Kirtland Temple the dedicatory prayer asks that God grant them the gift of tongues and at the end of the service Brigham Young speaks in tongues, another elder interprets it and then gives his own exhortation in tongues.

Alexandre Livshitz repeated a fantastic technical bit from the closing number, `` Taras Bulba '', but even then there was a substantial number of diehards who seemed determined not to go home at all.

To accomplish the UK / US mutual defense strategy, in November 1965, the UK purchased the Chagos Archipelago, which includes Diego Garcia, from the then self-governing colony of Mauritius for £ 3 million to create the British Indian Ocean Territory ( BIOT ), with the intent of ultimately closing the plantations to provide the uninhabited British territory from which the US would conduct its military activities in the region.

In 1956, after the 1954 closing of the U. S. immigration station, the then Mayor of Jersey City, Bernard J. Berry, commandeered a U. S. Coast Guard cutter and led a contingent of New Jersey officials on an expedition to claim the island.

Encyclopedia solves these cases by briefly closing his eyes while he thinks deeply, then asking a single question which directly leads to him finding the solution.

If the reloaded cartridges are going to be used in the same firearm in which they were previously fired, though, and if that firearm has a bolt action or other action with a strong camming action on closing, then full length resizing may not be needed.

The villanelle is a nineteen-line poem made up of five triplets with a closing quatrain ; the poem is characterized by having two refrains, initially used in the first and third lines of the first stanza, and then alternately used at the close of each subsequent stanza until the final quatrain, which is concluded by the two refrains.

* Approach the shrine ; if there is a bell, you may ring the bell first ( or after depositing a donation ); if there is a box for donations, leave a modest one in relation to your means ; then bow twice, clap twice, and hold the second clap with your hands held together in front of your heart for a closing bow after your prayers.

In the second edition of January 1860, Darwin quoted Kingsley as " a celebrated cleric ", and added the phrase " by the Creator " to the closing sentence, which from then on read " life, with its several powers, having been originally breathed by the Creator into a few forms or into one ".

In Goa and Dakshina Kannada ( Karnataka state, India ), turmeric plant leaf is used to prepare special sweet dishes, patoleo, by layering rice flour and coconut-jaggery mixture on the leaf, and then closing and steaming it in a special copper steamer ( goa ).

When closing a gate wrap the rope around the upturned post on the gate itself, then the latch post and the repeat three times then wrap around the tractor post such that it is pulled toward the latch post, once snug, pull the loose end under the wraps and tight against the post.

By far the most destructive method is to weld the weapon shut by inserting one or more armed thermite grenades into the breech and then quickly closing it.

* If a person pushes outwards with their hands against something for a while, then stops, it will feel as if there is something stopping the person's hands from closing together.

Timing of the monsoon strengthening of the Indian Monsoon of around 5 million years ago was suggested due to an interval of closing of the Indonesian Seaway to cold thermocline waters passage from the Pacific to the Indian Ocean which is believed to have resulted in an increased sea surface temperature in the Indian Ocean, which increased gyral circulation and then caused an increased intensity of the monsoon.

With the music reaching its grand climax Astaire and Rogers rush toward the camera, then away in a series of bold, dramatic manoeuvers culminating in three ballroom lifts which showcase Rogers ' dress before abruptly coming to a halt in a final, deepest backbend, maintained as the music approaches its closing bars.

" If one accepts this theory, then the Induction becomes vital to interpretation, as it serves to undermine any questions of the seriousness of Katherina's closing sentiments.

The local host receives the answer and the close signal, then proceeds closing its end of the connection.

The closest the Barrier has come to closing was on 27 November 2011, then the Closure Team was called out and started to close the gates, but was not fully closed since the surge subsided at the very last moment.

Other on-location scenes are also shown during the closing credits, including a rear shot of Mary holding hands with her date, played by Moore's then husband, Grant Tinker.

Final closing arguments are presented, and the judge then instructs the jury to decide whether the boy is guilty of murder.

Richmond leapt to third place and then in 1902, with Johnson dominating the ruck, Richmond entered the closing weeks of the season neck and neck with Port Melbourne at the head of the ladder.

Prospect Street School then became an elementary school until its closing in January 2008.

It was first settled in 1867 and had a post office from 1871 until 1875, and then reopened again six months later until closing in 1905.

It was then renovated into a triplex, after which it was converted to a single movie theater, closing its doors in the late 1980s.