When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.

When he plotted the spectral types of these stars against their absolute magnitude, he found that dwarf stars followed a distinct relationship.

When a Hertzsprung-Russell diagram is plotted for an open cluster, most stars lie on the main sequence.

When plotted correctly, this model of analysis creates for a meaningful quantitative classification of sandstones.

When plotted on the CIE chromaticity diagram, it can be seen that this is a hue corresponding to that of a visual stimulus of approximately 380 nm on the spectrum.

When Schleicher brought down Groener in May 1932, Groener made a point in his resignation speech of praising Raeder for his " correct " behaviour as opposed to Army officers like former protégé Schleicher who had undermined his leadership and plotted against him.

When the royal family plotted to abscond from Versailles to Metz, Louis Stanislas advised the King not to leave, to which the latter duly agreed.

When analyzing a weather map, a station model is plotted at each point of observation.

When Agamemnon left Mycenae for the Trojan War, Aegisthus seduced his wife, Clytemnestra, and the couple plotted to kill her husband upon his return.

When the town site was surveyed and plotted by John Ball, United States deputy surveyor, it was given the name of " Montezuma ", as requested by Johnson and Smith.

When plotted computationally, one needs to be careful to cover all frequencies of interest.

When values that span large ranges need to be plotted, a logarithmic scale can provide a means of viewing the data that allows the values to be determined from the graph.

When police located and searched the house from which the attack had been plotted, they found the corpse of Robert Sheldon Harte.

When plotted, they form a tube with the orbit around the point at one end, a view which traces back to mathematicians Charles C. Conley and Richard P. McGehee in the 1960s.

When the Emperor Kōmei died the next year, there was a rumor Iwakura had plotted to murder the emperor with poison, but he escaped arrest.

When authorities learned that this was plotted under the cover of gatherings for slave funerals, they prohibited slave funerals.

When accused of engaging in sex acts with minors, Alan successfully sued The Times newspaper ; when he plotted to get his hands on the stolen millions of Robert Maxwell who was hiding in Bosnia he was hailed as a humanitarian hero.

When the absolute magnitude for a group of stars is plotted against the spectral classification of the star, in a Hertzsprung-Russell diagram, evolutionary patterns are found that relate to the mass, age and composition of the star.

When epicenters of modern earthquakes are plotted on a map, three trends become apparent.

When plotted on a chart, the collection of possible locations for any given time difference forms a hyperbolic curve.

When epicenters of modern earthquakes are plotted on a map, three trends become apparent.

When Mordo plotted to kill his teacher, the Ancient One's visitor, Dr. Stephen Strange learned of the plot, forcing Mordo to cast restraining spells to prevent him from warning his master or attacking him.

When the orbital elements of main belt asteroids are plotted ( typically inclination vs. eccentricity, or vs. semi-major axis ), a number of distinct concentrations are seen against the rather uniform background distribution of generic asteroids.

When Josie finds the ball again, she assumes that Vaughn and Victor had plotted to use it.

: When comparing the above illustration to the below text, please note that the above x: y aspect ratio values are shown as vertical orientation rectangles to better demonstrate visual differences, whereas the aspect ratio values of the text below are written as rotated horizontal orientation rectangles ( e. g. compare 3: 4 vertical orientation illustration to 4: 3 horizontal orientation text ).

When the boot loader detected a CP / M floppy, the Aster would reconfigure its internal memory architecture on the fly to optimally support CP / M with 60 KB free RAM for programs ( TPA ) and an 80 x 25 display.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

When α is an integer, the Bessel functions J are entire functions of x.

When g oscillates near a, then it might happen that no matter how close one gets to a, there is always an even closer x such that g ( x ) equals g ( a ).

When g ( x ) equals g ( a ), then the difference quotient for is zero because f ( g ( x )) equals f ( g ( a )), and the above product is zero because it equals f ′( g ( a )) times zero.

When Newton's method is used to find the solution for the maximum likelihood estimate, the middle 24 % order statistics can be used as an initial solution for x < sub > 0 </ sub >.

When a switch is pressed, it connects the corresponding x and y lines together.

When b is zero and A ≠ 0 the origin is an equilibrium ( or singular ) point of the flow, that is, if x < sub > 0 </ sub > = 0, then the orbit remains there.

When the eigenvalues of J are not in the unit circle, the dynamics near the fixed point x < sub > 0 </ sub > of F is called hyperbolic and when the eigenvalues are on the unit circle and complex, the dynamics is called elliptic.

When dealing with three or fewer variables, it is common to replace x < sub > 1 </ sub > with just x, x < sub > 2 </ sub > with y, and x < sub > 3 </ sub > with z, as appropriate.

When this is the case, and x < sub > 0 </ sub > is one solution of ( 1 ), then the set of all solutions is given by

When Mach was first being seriously used in the 2. x versions, performance was slower than traditional monolithic operating systems, perhaps as much as 25 %.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

When some thirteen records of newly and recently born individuals are collated, little or no correlation between length and distribution can be detected.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

When this happens the distribution of lift changes dramatically, typically causing a powerful nose-down trim.

When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers.

When metadata is not present in a distribution, the PAUSE's software will usually try to analyze the code in the distribution to look for the same information ; this is not necessarily very reliable.

When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U / V has the standard Cauchy distribution.

When zone heater is moving from the top to the bottom of the container then solid condensate with irregular impurity distribution is forming.

) When Thomas Young first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of wavefronts.

When the distribution company Elite Entertainment released the film on DVD in 1999, they retained the NC-17 version.

When reefs become environmentally stressed, this distribution of symbionts is related to the observed pattern of coral bleaching and recovery.

When testing a hash function, the uniformity of the distribution of hash values can be evaluated by the chi-squared test.

When this approach is used, the hash function must be chosen so that the result has fairly uniform distribution between 0 and n − 1, for any value of n that may occur in the application.

When the data values are long ( or variable-length ) character strings — such as personal names, web page addresses, or mail messages — their distribution is usually very uneven, with complicated dependencies.

When Ice split amicably with Sire / Warner Bros. Records after a dispute over the artwork of the album Home Invasion, he reactivated Rhyme Syndicate and formed a deal with Priority Records for distribution.

; Quantum mechanics or Particle physics: When a spinless particle ( or even an unpolarized particle with spin ) decays, the resulting decay distribution must be isotropic in the rest frame of the decaying particle regardless of the detailed physics of the decay.

When deciding to use lossy conversion without keeping the original, one should remember that format conversion may be needed in the future to achieve compatibility with software or devices ( format shifting ), or to avoid paying patent royalties for decoding or distribution of compressed files.

When is a conditional probability distribution and the loss function is the negative log likelihood:, then empirical risk minimization is equivalent to maximum likelihood estimation.

When a phoneme has more than one allophone, the one actually heard at a given occurrence of that phoneme may be dependent on the phonetic environment ( surrounding sounds ) – allophones which normally cannot appear in the same environment are said to be in complementary distribution.

When a postmaster is responsible for an entire mail distribution organization ( usually sponsored by a national government ), the title of Postmaster General is commonly used.

When the third protection level key scheme is used it affects the distribution of a message through the container ( see figure The Third Protection Level Scheme, where F ( P, L ) – distribution function of a message within a container ; P – minimum number of container samples that are needed to embed one message sample ; L – step of a message distribution within a container ).

When the term emerged within the Anglo-American tradition during the 1960s, it was basically applied as a synonym for the search for patterns in the distribution of social groups, thus being closely connected to urban geography and urban sociology.

When they employed them in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces.