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Page "Numerical analysis" ¶ 5
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These and same
These are, of course, the same people whose support he has only now rejected to seek the independent vote.
These teams carried out the same operations successively in different areas.
From here they proceeded to ( 3 ) These same areas in relation to their own future family life stages, developing these to the extent of examining various crises which could be expected to confront them at some time or other.
These were the same subjects who were given the Rorschach test.
These are grouped into sections according to the crystal system, and within each section compounds are arranged in the same order as in Groth's Chemische Krystallographie.
These are substantially the same factors considered by Non-Catholics in family planning.
These 1750 cases were carted off in a one-night operation by the O'Banion men, who left in their stead the same number of barrels filled with water.
These things both express and, at the same time, continue contributing to, their identity diffusion in an area that could have become a source of developing dignity and self-certainty.
These were rejected in a referendum the following May at the same time as parliamentary elections which left Kocharyan's party in a very powerful position in parliament.
These praise songs are probably the same performed at Matilda's coronation, but might have been used at other court ceremonies before Ealdred's death.
These orchestral works are mainly in the galant style and though they show some development toward the late classical they reflect a general weakness in comparison to his operatic works of the same and later periods.
These use the same principles as a gas refrigerator.
These two sequences converge to the same number, which is the arithmetic – geometric mean of and ; it is denoted by, or sometimes by.
These are inherently more aerodynamic than upright versions, as the rider may lean back onto a support and operate pedals that are on about the same level as the seat.
These two styles ( K = 1024 and truncation ) were used loosely around the same time, sometimes by the same company.
These same compounds also increase secretion of macrophage colony-stimulating factor by osteoblasts, which promotes the differentiation of progenitor cells into osteoclasts, and decrease secretion of osteoprotegerin.
These are not the same as midplane backplanes.
These are often the same person, and the terms are sometimes used interchangeably.
These same bubbles also float for a time before bursting, and can be jumped on, allowing access to otherwise inaccessible areas.
These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field.
These changes may be made either by the same writer who made it, or more commonly by an author that has taken over the creative lead of a corporate owned show or publication.
( These rules are not intended to apply in case of differing episodes of the same series ; this difference may not always be communicated to distributors, although this is rather rare.
These superseded wrap-spring single-revolution clutches in page printers, such as teleprinters, including the Teletype Model 28 and its successors, using the same design principles.
These were developed as " companions " to the popular revolvers of the day, firing the same cartridge but allowing more velocity and accuracy than the revolver.

These and interpolation
These methods rely on constructing first a Newton interpolation of the polynomial and then converting it to the monomial form above.
These include Stein interpolation ( a variable-parameter version of complex interpolation ), the Stein maximal principle ( showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of
These also allow use of the average of the three readings ( 3-wire leveling ) as a check against blunders and for averaging out the error of interpolation between marks on the rod scale.
These showed that the book, as hitherto edited, had been thrown into disorder by the displacement of two pages near the end ; they also removed other difficulties upon which the theory of interpolation had been based.
These processes most often achieve a smooth transition through interpolation.

These and formulas
These formulas can even serve as the definition of the trigonometric functions for complex arguments x.
These results, however, are very sensitive to the accuracy of the twiddle factors used in the FFT ( i. e. the trigonometric function values ), and it is not unusual for incautious FFT implementations to have much worse accuracy, e. g. if they use inaccurate trigonometric recurrence formulas.
These simple formulas will not do if the input values are not equally likely, or are not independent.
These two researchers developed several formulas for mineral nutrient solutions, known as Hoagland solution.
These formulas provide the solution for the initial-value problem for the wave equation.
These changes can be represented in formulas by inserting appropriate electrons into each half-reaction:
These formulas however only provide the calculation for the τ = τ < sub > 0 </ sub > case.
These formulas may be used when h is much smaller than the radius of the Earth ( 6371 km ), including all views from any mountaintops, aeroplanes, or high-altitude balloons.
These formulas characterize the periapsis and apoapsis of an orbit:
These formulas are traditionally used in analog televisions and equipment ; digital equipment such as HDTV and digital video cameras use Y ' CbCr.
These formulas are connected to the Schubert decomposition of the Grassmannian, and are q-analogs of the Betti numbers of complex Grassmannians.
These formulas are the basis for comparing and investigating the nature of non-random patterns in the structure of food web networks among many different types of ecosystems.
These formulas are generalized by the Faà di Bruno's formula.
These formulas can also be written using Lagrange's notation.
These formulas contain the " slope " of the line connecting P and Q, hence involve divisions between residue classes modulo n, which can be performed using the extended Euclidean algorithm.
These operators are direct extensions of their complex analogs: if and are taken from the real subset of complex numbers, the appearance of the conjugate in the formulas has no effect, so the operators are the same as those for the complex numbers.
These ideas were regarded as dynamic forces that Herbart attempted to explain by means of mathematical formulas.
These formulas for denatured alcohol are found in 27 CFR part 21 of the Code of Federal Regulations.
These formulas are for single-frequency sine waves or narrowband signals.
These formulas only state in another form the assertions in the table of derivatives.
These formulas all provide a different view into the processes that generate longshore drift.
These five formulas are:
These formulas give the explicit numbers of rational curves of all degrees in a large class of Calabi – Yau manifolds, in terms of the Picard – Fuchs equations of the corresponding mirror manifolds.
These two formulas, added together, produce

0.221 seconds.