Note that when they are considered within the complex plane the Gaussian integers may be seen to constitute the 2-dimensional integer lattice.

Note also that the X < sub > i </ sub > are in general not independent ; they can be seen as the result of applying the matrix A to a collection of independent Gaussian variables z.

Note that the denominator is one standard deviation of the Gaussian approximation, so can be written

( Note 33 is the 8th composite number to descend into the prime number 3, the others outside of this sequence being 30, 26, 16, 12 ) Since 33 is a semiprime with both its prime factors being Gaussian primes, 33 is a Blum integer.

Note that although this model is termed a " Gaussian chain ", the distribution function is not a gaussian ( normal ) distribution.

Note that the experimental variogram is an empirical estimate of the covariance of a Gaussian process.

Note that when N = R, the map dφ < sub > x </ sub >: T < sub > x </ sub > M → R coincides with the usual notion of the differential of the function φ.

Counter heat current exchange: Note the gradually declining differential and that the once hot and cold streams exit at the reversed temperature difference ; the hotter entering stream becomes the exiting cooler stream and vice versa.

Note: The Antikythera mechanism ( 150 BC – 100 BC ), discovered on an ancient shipwreck near the Greek island of Antikythera, was once suggested to have employed a differential gear.

Note that the coefficients attached to the dummy variables are called differential intercept coefficients.

Note that in any given coordinate patch, ( 1 ) defines an ordinary differential equation, with the initial condition given by ( 2 ).

Note that a differential amplifier is a more general form of amplifier than one with a single input ; by grounding one input of a differential amplifier, a single-ended amplifier results.

Note that since we divided by and we must check to see whether the solutions and solve the differential equation ( in this case they are both solutions ).

A property called the relativistic mass is defined as the ratio of the momentum of an object to its velocity .< ref > Note that the relativistic mass, in contrast to the rest mass m < sub > 0 </ sub >, is not a relativistic invariant, and that the velocity is not a Minkowski four-vector, in contrast to the quantity, where is the differential of the proper time.

:: Note: Vendors have standardized on the meaning of the terms " incremental backup " and " differential backup ".

Note: The Electronic Differential Lock ( EDL ) employed by Volkswagen is not-as the name suggests-a differential lock at all.

Note that the partial differential equation in the unconfined case is non-linear, whereas it is linear in the confined case.

Note that this algebraic function can be regarded as analytical solution for the function's differential:

Note that the RGB color may be premultiplied, hence saving the additional multiplication before RGB in the equation above.

Note that by reversing the equation, we can swap < math > < </ math > and, for example:

Note: The above equation applies only to incompressible fluid.

Note that in this equation, both force and displacement are vector quantities.

Note that, with the opposite sign convention ( used in Physics ), this is the potential generated by a point particle, for an inverse-square law force, arising in the solution of Poisson equation.

Note that in, the equation holds, and therefore

Note how the equation above reduces to that of the univariate normal distribution if is a matrix ( i. e. a real number ).

( Note that the same equation applies for recoil energy losses in x-rays, but the photon energy is much less, resulting in a lower energy loss, which is why gas-phase resonance could be observed with x-rays.

Note that this equation only holds when the density operator is taken to be in the Schrödinger picture, even though this equation seems at first look to emulate the Heisenberg equation of motion in the Heisenberg picture, with a crucial sign difference:

Note that the above equation is flawed — as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics.

Note that this equation reduces to that of the volume of a sphere when all three elliptic radii are equal, and to that of an oblate or prolate spheroid when two of them are equal.

Note that the integrand above ( uv ) differs from the previous equation.

Note that the above construction of the Galois group for a fifth degree polynomial only applies to the general polynomial, specific polynomials of the fifth degree may have different Galois groups with quite different properties, e. g. has a splitting field generated by a primitive 5th root of unity, and hence its Galois group is abelian and the equation itself solvable by radicals.

Note that this equation indicates that when expectations of future inflation ( or, more correctly, the future price level ) are totally accurate, the last term drops out, so that actual output equals the so-called " natural " level of real GDP.

Note in the second equation that if instead of planck masses the electron mass were used, the equation would no longer be unitary and instead equal a gravitational coupling constant, analogous to how the equation of the fine-structure constant operates with respect to the elementary charge and the Planck charge.

Note that the above equation describes the Earth's gravitational potential, not the geoid itself, at location the co-ordinate being the geocentric radius, i. e., distance from the Earth's centre.

Note: In the following examples the multiplier is the right-hand-side equation without the first component.

Treating free charges separately from bound charges, Ampère's equation including Maxwell's correction in terms of the H-field is ( the H-field is used because it includes the magnetization currents, so J < sub > M </ sub > does not appear explicitly, see H-field and also Note ):

Note that the right-hand side of the equation is also the price of buying a forward contract on the stock with delivery price K. Thus one way to read the equation is that a portfolio that is long a call and short a put is the same as being long a forward.

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 acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.

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, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.

Note that wav files can also be encoded with the gsm codec.

Note that arrows between categories are called functors, subject to specific defining commutativity conditions ; moreover, categorical diagrams and sequences can be defined as functors ( viz.

Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

Note that the chocolate pictured here is soft, can easily be crumbled by hand, and already has sugar added.

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 ").

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

Note that completeness is a property of the metric and not of the topology, meaning that a complete metric space can be homeomorphic to a non-complete one.

Note that this document type declaration can only appear after the optional XML declaration, and before the document body, if the document syntax conforms to XML.

Note that a dominatrix does not necessarily dominate a male partner ; a dominatrix may well have female submissives, nor must the role of a dominatrix involve pain toward the submissive ; her domination can be verbal, involving humiliating tasks and servitude.

Note that if the operations are performed in a colour space where γ is not equal to 1 then the operation will lead to non-linear effects which can potentially be seen as aliasing artifacts ( or ' jaggies ') along sharp edges in the matte.

: Note that the equivalence relation generated in this manner can be trivial.

Note that one can also define a contravariant functor as a covariant functor on the dual category.

Note: Many of the essays found in these works have been individually translated and can be found in the English collections.

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.

Hunters use the clues to try to find the benchmark ; the benchmark can be logged as Found, Not Found, Note, or Destroyed.

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.

Note also that ' br ' is an empty element in that, while it may have attributes, it can take no content and it may not have an end tag.

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..