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Page "Probabilistic method" ¶ 11
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Note and number
Note that, because a name translated to an address, which included a socket number as well as a node number, a name in AppleTalk mapped directly to a service being provided by a machine, which was entirely separate from the name of the machine itself.
Note that the number of points used in braille computing is not 6, but 8, as this allows the user, among other things, to distinguish between small and capital letters, as well as identify the position of the cursor.
Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number ( as with " 2 " and " 2. 0 ", or when scientific notation is used, " 2e3 " and " 2000 ").
Note derivative is positive number | positive where green line appears, negative number | negative where red line appears, and zero ( number ) | zero where black line appears.
Note that the first element in a sequence has the index one and that $ refers to the length ( i. e. total number of elements ) of the sequence.
Note that reflection by a window is from the front side as well as the back side, and that some of the light bounces back and forth a number of times between the two sides.
It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.
Note that due to the reduced number of colors in the image, there are obvious display issues. GIF is palette-based: the colors used in an image ( a frame ) in the file have their RGB values defined in a palette table that can hold up to 256 entries, and the data for the image refer to the colors by their indexes ( 0 – 255 ) in the palette table.
Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J < sup > PC </ sup >( m ), where J is the spin quantum number, P the intrinsic parity ( or P-parity ), and C, the charge conjugation ( or C-parity ), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks ; rather, due to mass – energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.
Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i. e..
Note that the ICF and ZAAP are essentially identical to CP, but distinguished for software cost control: they are slightly restricted such they cannot be used to run arbitrary operating systems, and thus do not count in software licensing costs ( which are typically based on the number of CPs ).
Note: if the product resulting from the labor process is homogeneous ( all similar in quality and traits, for example, all cups of coffee ) then the value of the period ’ s product can be divided by the total number of items ( use-values ) produced to derive the unit value of each item.
Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.
Note that the vertical scale, the number of digits, is a double logarithmic scale of the value of the prime.
Note: A number of other plants have been suggested by biblical scholars, e. g., Most notably Ginseng which looks similar to the mandrake root and has fertility enhancing properties, for which it was picked by Reuben in the Bible.
Note that using a hierarchical system like this ( assuming it is done carefully ) changes the intersection computational time from a linear dependence on the number of objects to something between linear and a logarithmic dependence.
Note that the tensor rank of a matrix can also mean the minimum number of simple tensors necessary to express the matrix as a linear combination, and that this definition does agree with matrix rank as here discussed.
Note that s < sub > 0 </ sub > is now the sum of the weights and not the number of samples N.
Note that these statistics only show officially registered residents, and that the actual number of foreign citizens living in Shanghai is likely much higher.
Note derivative is positive number | positive where green, negative number | negative where red, and zero ( number ) | zero where black

Note and is
( Note: So far as State Police cars are concerned, only their replacement is under this division ).
Note, however, that it is six inches shorter at the forward end.
Note another piece of wood six inches wide is fastened to the transom between these pieces.
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large.
Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;
Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.
Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.
Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by
Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.
Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.
Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.
Note that there is no directly corresponding concept in the German language.
Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.
Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.
Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.
Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.
Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.
Note that this is subtly different to the ' thanks ' list in the original BBC Model B.

Note and sum
Note that we have to restrict the sum to ordered values of m < sub > 1 </ sub >, ..., m < sub > N </ sub > to ensure that we do not count each multi-particle state more than once.
Note that opportunity cost is not the sum of the available alternatives, but rather the benefit of the single, best alternative.
Note that the sum of the two sideband signals is:
** Note: The sum of the individual digits is usually compared with a previously computed value.
Note that opportunity cost is not the sum of the available alternatives when those alternatives are, in turn, mutually exclusive to each other – it is the value of the next best use.
Note that unlike the other two formulae ( the Euler product and the divisor sum ) this one does not require knowing the factors of n.
Note that commutativity is crucial here ; it ensures that the sum of two group homomorphisms is again a homomorphism.
With this choice of a hyperplane, the points in the feature space that are mapped into the hyperplane are defined by the relation: Note that if becomes small as grows further away from, each element in the sum measures the degree of closeness of the test point to the corresponding data base point.
Note that although potstickers are sometimes served in dim sum restaurants, they are not considered traditional Cantonese dim sum.
Note the Kroneker sum is also denoted ⊕; the context should make the usage clear.
Note that the equality holds only when the square root of the sum of the squared imaginary terms takes the same sign as.
Note that the invariant mass of a system of particles may be more than the sum of the particles ' rest masses, since kinetic energy in the system center-of-mass frame and potential energy from forces between the particles contribute to the invariant mass.
Note that the above examples show that the sum of diagonalizable matrices need not be diagonalizable.
Note that π ( x ) is a bounded linear operator since it is the direct sum of a family of operators, each one having norm ≤ || x ||.
Note also that the function A ( θ ) or equivalently g ( θ ) is automatically determined once the other functions have been chosen, and assumes a form that causes the distribution to be normalized ( sum or integrate to one over the entire domain ).
Note also that a factor consisting of a sum where both types of variables are involved ( e. g. a factor of the form ) cannot be factorized in this fashion ( except in some cases where occurring directly in an exponent ); this is why, for example, the Cauchy distribution and Student's t distribution are not exponential families.
Note that because of the second condition, power series are used here only to allow infinitely many terms of a fixed degree, rather than to sum terms of all possible degrees.
Note, however, that if the sum can be performed in twice the precision, then ε is replaced by ε < sup > 2 </ sup > and naive summation has a worst-case error comparable to the O ( nε < sup > 2 </ sup >) term in compensated summation at the original precision.
Note that if A and B are disjoint subsets of some weighted set ( U, w ), then the Dirichlet series for their ( disjoint ) union is equal to the sum of their Dirichlet series:
Note that any element in the direct sum of two vector spaces of matrices could be represented as a direct sum of two matrices.
Note that the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent.

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