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Page "Born–Oppenheimer approximation" ¶ 18
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second and step
Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.
To accept the validity of the judgments of others is the second step.
This initiates the second step of glossary lookup -- connecting the information cell of forms in the text-form list to dictionary forms.
The second step in processing was to compare the responses from companies on the AIA list with those from companies on the TR list in order to determine whether it would be appropriate to merge the responses for the purposes of the study.
The second step is to recognize the substantial agreement -- frequently blurred by emotionalism and inaccurate newspaper reporting -- already existing between Catholics and Non-Catholics concerning the over-all objectives of family planning.
A recent report claims to have inhibited conjugation with chemicals that mimic an intermediate step of this second nicking event.
At the second step, the nucleophilic hydroperoxide or halogen anion attacks the boron atom.
In the second reaction step, a water molecule is activated by the basic histidine, and acts as a nucleophile.
Note that this expression indicates compositing C with all of the layers below it in one step and then blending all of the layers on top of it with the previous result to produce the final image in the second step.
Single-two steps in any direction closing feet on the second step ( the second step tends to be interpreted as a closing action in which weight usually stays on the same foot as before, consistent with descriptions from Renaissance sources ).
The second step is to assign a value, called planned value ( PV ), to each activity.
In this way, decisions made by the original designers of ephemeris time influenced the length of today's standard SI second, and in turn, this has a continuing influence on the number of leap seconds which have been needed for insertion into current broadcast time scales, to keep them approximately in step with mean solar time.
In the first step, the final nonzero remainder r < sub > N − 1 </ sub > is shown to divide both a and b. Since it is a common divisor, it must be less than or equal to the greatest common divisor g. In the second step, it is shown that any common divisor of a and b, including g, must divide r < sub > N − 1 </ sub >; therefore, g must be less than or equal to r < sub > N − 1 </ sub >.
In the second step, any natural number c that divides both a and b ( in other words, any common divisor of a and b ) divides the remainders r < sub > k </ sub >.
The second step uses back substitution to find the solution of the system above.
In Germany in the second half of the 17th century, diatonic single-row harps were fitted with manually turned hooks which fretted individual strings to raise their pitch by a half step.
The second step begins with removing the largest element from the heap.
In the second step, they were divided by 3.
The first step, which carried him to the outbreak of the schism, involves moderate recognition of the papal primacy ; the second, which carried him to 1381, is marked by an estrangement from the papacy ; and the third shows him in sharp contest.
The second step is to approximate the geoid by a mathematically simpler reference surface.

second and BO
In the second step of the BO approximation this function serves as a potential in a Schrödinger equation containing only the nuclei — for benzene an equation in 36 variables.
In the second step of the BO approximation the nuclear kinetic energy T < sub > n </ sub > ( containing partial derivatives with respect to the components of R ) is reintroduced and the Schrödinger equation for the nuclear motion
To that end the second step of the BO approximation is generalized to a set of coupled eigenvalue equations depending on nuclear coordinates only.
the BO approximation breaks down and a coupled set of nuclear motion equations must be considered, instead of the one equation appearing in the second step of the BO approximation.

second and approximation
For example, by using the above central difference formula for and and applying a central difference formula for the derivative of at x, we obtain the central difference approximation of the second derivative of f:
When an accuracy better than one second is not required, UTC can be used as an approximation of UT1.
Use the integer part, 2, as an approximation for the reciprocal, to get a second approximation of ;.
( The approximation in the second value of ε < sub > 0 </ sub > above stems from π being an irrational number.
This discovery proves that Hipparchus mathematics were much more advanced than Ptolemy describes in his books, as it is evident that he developed a good approximation of Kepler ΄ s second law.
At each iteration, the search takes a step s defined by solving Hs =-g for s, where s is the step, g is the gradient vector of the function's partial first derivatives with respect to the parameters, and H is an approximation to the Hessian matrix of partial second derivatives formed by repeated rank 1 updates at each iteration.
As you see, the approximation between two points on a given function gets worse with the second derivative of the function that is approximated.
The second approximation in Eq.
Pullin's early work on the subject ( including his second most cited paper, from 1994 ) involves the " close approximation " in which a pair of nearby black holes is treated mathematically as a single non-spherical black hole ; since joining LSU his work on this area has been based instead on supercomputer simulation.
In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth order approximation, a first order approximation, a second order approximation, and so forth.
A theorem of Kronecker from diophantine approximation can be used to show that any particular configuration that occurs once, will recur to within any specified accuracy: if we wait long enough we can observe the planets all return to within a second of arc to the positions they once were in.
The first spelling is derived from the French spelling " Acadien " and the second is an approximation, using French phonetics, of the pronunciation of the group name in Cajun French.
Vanderplaats initiated a second generation of high quality approximations when he developed the force approximation as an intermediate response approximation to improve the approximation of stress constraints.

second and involves
The second involves something deeper, but its characteristic form focuses on a shift in policy for the community, not in the truth on which the community rests.
Notice that the second condition in the definition itself refers to natural numbers, and hence involves self-reference.
However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Legendre canonical forms ( i. e. the elliptic integrals of the first, second and third kind ).
" This second case usually involves the town bully and mischief maker Bugs Meany, leader of a gang who call themselves the Tigers, who, after being foiled, will attempt revenge in the third mystery.
Faith involves more than outward obedience to this authority, but also must be based on a deep personal understanding of religious teachings. By faith is meant, first, conscious knowledge, and second, the practice of good deeds.
A second strategy, cracking, involves spreading out voters of a particular type among many districts in order to deny them a sufficiently large voting bloc in any particular district.
The second, more radical, adaptation involves the selective influx of potassium ( K < sup >+</ sup >) ions into the cytoplasm.
The second approach, a worker-oriented job analysis, involves an examination of the knowledge, skills, abilities, and other characteristics ( KSAOs ) required to successfully perform the work.
The Multiple Kick is usually done in the " second " style described in the Side Kick article which " involves shooting the leg forward as in a front kick and then pivoting and turning so " to actually deliver a side kick.
Money laundering often occurs in three steps: first, cash is introduced into the financial system by some means (" placement "), the second involves carrying out complex financial transactions in order to camouflage the illegal source (" layering "), and the final step entails acquiring wealth generated from the transactions of the illicit funds (" integration ").
The first is a ritual designed for the individual, which involves sacrificing a " Cake of Light " ( a type of bread that serves as the host ) to Ra ( i. e. the Sun ) and infusing a second Cake with the adept's own blood ( either real or symbolic, in a gesture reflecting the myth of the Pelican cutting its own breast to feed its young ) and then consuming it with the words, " There is no grace: there is no guilt: This is the Law: Do what thou wilt!
For example, is a polynomial, but is not, because its second term involves division by the variable x ( 4 / x ), and also because its third term contains an exponent that is not a non-negative integer ( 3 / 2 ).
" The second advantage involves a physiological reaction provoked by the large amount of muscle submerged.
The second involves a continuous record of population trends from the registration of births, marriages, and burials.
A second defense of vertebrates against viruses, cell-mediated immunity, involves immune cells known as T cells: the body's cells constantly display short fragments of their proteins on the cell's surface, and if a T cell recognizes a suspicious viral fragment there, the host cell is destroyed and the virus-specific T-cells proliferate.
The second method involves the reaction of benzophenone with sodium cyanide in the presence of ammonium carbonate, followed by the simultaneous cyclization of the resulting product ( carboxyaminonitrile ) and its rearrangement under the reaction conditions to form phenytoin.
A second category of tactics for fighting viruses involves encouraging the body's immune system to attack them, rather than attacking them directly.
Trace scheduling is such a technique, and involves scheduling the most likely path of basic blocks first, inserting compensation code to deal with speculative motions, scheduling the second most likely trace, and so on, until the schedule is complete.
The second exercise, " Falun Standing Stance ", involves holding four static poses — each of which resembles holding a wheel — for an extended period.
The second method involves construction of a vehicle frame from scratch ; formed and welded using steel tubing.
The second classification, chemical weathering, involves the direct effect of atmospheric chemicals or biologically produced chemicals ( also known as biological weathering ) in the breakdown of rocks, soils and minerals.
Most of its series also employ are produced in the videotaped multi-camera setup that involves filming before a studio audience or utilizing a laugh track ; its multi-camera series also utilize a simulated film look ( the FilmLook image processing for series that debuted between 2003 and 2008 ; the HD-compatible ' filmizing ' technique for all newly-commissioned and returning original series produced in high definition after 2009, which reduce the videotape frame rate to 24 frames per second ).
: The second process that is referred to as androgenesis or androclinesis involves ( artificial ) culture of haploid plants from anther tissue or microspores.

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