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Comparing entries then gives the desired result.
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Comparing and then
Comparing the cat and the mousetrap, then, one sees that the mousetrap ( which is not alive ) offers better evidence, in terms of irreducible complexity, for intelligent design than the cat.
Comparing the recordings of Schnabel, from the beginning of modern recording, with those of Barenboim and then Pratt shows a distinct shift in how the structure of the sonata form is presented to the listener over time.
Comparing Richards to Lemon, Bannister said, " He'd post the lineups 10 minutes before the game, and only then we'd find out who was playing and where.
" Comparing it to David Lynch's Twin Peaks, he decided that " unlike Peaks, which started out brilliantly lucid and then rambled into incoherence, Palms sustains its length and adds layers of complexity to its characters.
Comparing signal strengths around the nine crystals, and front-to-back, then gives a coarse, two-dimensional position in space.
Comparing and gives
Comparing this with the latter equation gives V < sub > 1 </ sub >• V < sub > 2 </ sub >
Comparing with the domestic networks of the 1960s and 1980s gives reason to assume that the situation during the 1970s should have been more or less the same, though.
Comparing these is rough, and only gives an idea of the relative difficulty ; the reason different systems exist in the first place is because it's difficult to compare grades between climbing media.
Comparing this pattern as received to the known standard gives video engineers an indication of how an NTSC video signal has been altered by recording or transmission and what adjustments must be made to bring it back to specification.
Comparing and contrasting the material in the reading to the PQA and the story gives extra repetitions of the target structures.
Comparing the 2700 inhabitants to the 5000 beds for tourists with a number of 90. 000 tourists per year gives an impression of the formative influence of tourism for the village.
Comparing this distance to the redshift of the supernovae gives a measure of the rate at which the universe has been expanding at different points in history.
Comparing the bones in the upper forelimb gives a similar result.
Comparing the forms of the metric on this hypersurface gives:
Comparing radii and arguments gives
Comparing and .
Comparing card games are those where hand values are compared to determine the winner, also known as " vying " or " showdown " games.
Comparing the two formulae it can be seen that for a given compression ratio (), the ideal Otto cycle will be more efficient.
Comparing different embryonic stages of different animals is a tool that can be used to infer relationships between species, and thus biological evolution.
Comparing this data with the 2001 census shows that the number of permanent residents born on the island has increased by just 3, 000.
Comparing this to a color image of the visible light spectrum will show that " Indigo " corresponds to dark blue, while " Blue " corresponds to cyan.
Comparing motherhood to playing chess, Polgár has said that a chess tournament now " feels like a vacation.
( 1998 ) Comparing measures of sample skewness and kurtosis.
Comparing this yield to the observed damage produced a rule of thumb called the 5 psi lethal area rule.
Comparing the food to the waste can help determine the specific compounds and elements absorbed and metabolized in the body.
Emotional sweating across the body: Comparing 16 different skin conductance measurement locations.
Comparing the available records with especially the Gest and also other ballads, Hunter developed a fairly detailed theory according to which Robin Hood was an adherent of the rebel Earl of Lancaster, defeated at the Battle of Boroughbridge in 1322.
Comparing the recovery from the 1981 – 82 recession ( 1983 – 1990 ) with the years between 1971 ( end of a recession ) and 1980 shows that the rate of growth of real GDP per capita averaged 2. 77 under Reagan and 2. 50 % under Nixon, Ford and Carter.
Comparing throughput values is also dependent on each bit carrying the same amount of information.
Comparing engines on the dynamometer, a typical even-fire V6 shows instantaneous torque peaks of 150 % above mean torque and valleys of 125 % below mean torque, with a small amount of negative torque ( engine torque reversals ) between power strokes.
" Comparing Global History to World History ," Journal of Interdisciplinary History, Vol.
Comparing measured vapor pressures to predicted values from Raoult's law provides information about the true relative strength of intermolecular forces.
Comparing the angular expansion with the derived velocity of expansion will reveal the distance to the nebula.
" Defining Moments and Recurring Myths: Comparing Canadians and Americans after the American Revolution " in The Canadian Review of Sociology and Anthropology, Vol.
Comparing these basis functions with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals.
Comparing and Contrasting Classical Realism and Neorealism: A Re-examination of Hans Morgenthau ’ s and Kenneth Waltz ’ s Theories of International Relations.
Comparing this to the definition of the Fourier transform, it follows that c < sub > n </ sub > = ƒ ̂( n / T ) since ƒ ( x ) is zero outside.
Comparing the two respective climates, it would appear that Vulcan is identified as Gamma Vega.
entries and then
In an N-dimensional Hilbert space, can be written as an N × 1 column vector, and then A is an N × N matrix with complex entries.
Under each letter, the entries are organized first by the book they are found in, and then by their place in that book.
This is often followed by a connecting passage, or episode, developed from previously heard material ; further " entries " of the subject then are heard in related keys.
As entries began to be revised for the OED3 in sequence starting from M, the longest entry became make in 2000, then put in 2007.
In some models, if there is no entry in the table for the current combination of symbol and state then the machine will halt ; other models require all entries to be filled .</ li >
Winning entries are awarded with a category, such as " Worst Abuse of the C preprocessor " or " Most Erratic Behavior ", and then announced on the official IOCCC website.
< li > If M = ( m < sub > ij </ sub >) ≥ 0 then the diagonal entries m < sub > ii </ sub > are real and non-negative.
The binary-reflected Gray code list for n bits can be generated recursively from the list for n − 1 bits by reflecting the list ( i. e. listing the entries in reverse order ), concatenating the original list with the reversed list, prefixing the entries in the original list with a binary 0, and then prefixing the entries in the reflected list with a binary 1.
In one round of the board game Derivation, players describe or fabricate a word's etymology ; players who provide a correct etymology receive one point for doing so, but their entries are then removed from play, and they lose their chance to receive multiple points by drawing multiple votes from other players.
Rising costs coupled with declining entries led to the death of this class, and it was replaced by what was then GT2 ( FIA, which evolved into the current GT1 ) and Le Mans Prototype ( LMP, by the ACO ).
If we denote the-fold product of with itself by, then morphisms from to are m-by-n matrices with entries from the ring.
The initial dictionary, then, will consist of the following entries:
If these dates are accurate, then it is unlikely that the earlier entries in the chronicle, starting with his arrival in Britain with his father Cerdic in 495, are correct.
The crowd then read silently from books of their own, earning the city dual entries in the Guinness Book of World Records for the most people reading together in one place as well as the most reading together silently.
for some constants a < sub > jk </ sub > in F ; the matrix corresponding to T is then just the matrix with entries given by the a < sub > jk </ sub >.
If the entries of the matrix are real or complex numbers ( or from any other commutative ring ), then all four quantities are equal.
If A and B have complex entries, then
So if the entries are written as A = ( a < sub > ij </ sub >), then
If A has real entries and is symmetric ( or more generally, has complex-valued entries and is Hermitian ) and positive definite, then A can be decomposed as
In the special but common case in which M is just an m × m square matrix with positive determinant whose entries are plain real numbers, then U, V *, and Σ are m × m matrices of real numbers as well, Σ can be regarded as a scaling matrix, and U and V * can be viewed as rotation matrices.
In mathematics, the dot product, or scalar product ( or sometimes inner product in the context of Euclidean space ), is an algebraic operation that takes two equal-length sequences of numbers ( usually coordinate vectors ) and returns a single number obtained by multiplying corresponding entries and then summing those products.
< li > If A has only real entries, then A < sup > T </ sup > A is a positive-semidefinite matrix.
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