When values of temperature derived with this instrument were compared with the accepted values associated with liquid helium-4 vapor pressures, differences of about 10 and 7 millidegrees respectively were found.

: 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 reconstructing the data, owing to the evaporation of successive layers of material from the sample, the lateral and in-depth reconstruction values are highly anisotropic.

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 the circuit is solved, the circuit element currents may have positive or negative values.

When other methods of calculation are used, it is conventional ( although not obligatory ) to quote the results on a scale that covers the same range of numerical values: this is known as an electronegativity in Pauling units.

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

When the hash function is used to store values in a hash table that outlives the run of the program, and the hash table needs to be expanded or shrunk, the hash table is referred to as a dynamic hash table.

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 changing moral behavior, one is said to be " internalized " when a new set of beliefs, attitudes, and values replaces or habituates the desired behavior.

When the result sequence is exhausted ( e. g. there are no more values within the result sequence ), the expression or function fails.

When it acts on a tensor product of two state vectors, it exchanges the values of the state vectors:

When transaction costs are low and parties involved are perfectly informed, a mutually beneficial agreement will occur: whoever values the property the highest will end up with it.

When many values have to be searched in the same list, it often pays to pre-process the list in order to use a faster method.

When comparing periodic trends in the size of atoms it is often desirable to apply so-called Goldschmidt correction, which converts the radii to the values the atoms would have if they were 12-coordinated.

When interpreting the results of a test, it is important to consider the morphine usage history of the individual, since a chronic user can develop tolerance to doses that would incapacitate an opiate-naive individual, and the chronic user often has high baseline values of these metabolites in his system.

When more than two buffer solutions are used the electrode is calibrated by fitting observed pH values to a straight line with respect to standard buffer values.

When parameters are present, the definition actually defines a whole family of functions, one for every valid set of values of the parameters.

When two geometrically similar flow patterns, in perhaps different fluids with possibly different flow rates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.

When properly managed, these values are converted into intensities or voltages via gamma correction to correct the inherent nonlinearity of some devices, such that the intended intensities are reproduced on the display.

When sulfide minerals are precipitated, isotopic equilibration among solids and liquid may cause small differences in the δS-34 values of co-genetic minerals.

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 there are only two means to compare, the t-test and the ANOVA F-test are equivalent ; the relation between ANOVA and t is given by F = t < sup > 2 </ sup >.

When the volume of an alcoholic drink is shown in centilitres, determining the number of units in a drink is as simple as < var > volume </ var > × < var > percentage </ var > ( converted into a fraction of 1 ).

( When measured in decibels it is logarithmically related to the power ratio: G ( dB )= 10 log ( P < sub > out </ sub > /( P < sub > in </ sub >)).

When fully implemented, CAIR will reduce SO < sub > 2 </ sub > emissions in 28 eastern states and the District of Columbia by over 70 percent and NOx emissions by over 60 percent from 2003 levels.

When clouds are present, the loss rate of SO < sub > 2 </ sub > is faster than can be explained by gas phase chemistry alone.

When certain ionic compounds containing bromine are mixed with potassium permanganate ( KMnO < sub > 4 </ sub >) and an acidic substance, they will form a pale brown cloud of bromine gas.

When the rate of bone formation exceeds the rate of bone resorption, soft tissue < sup > 44 </ sup > Ca /< sup > 40 </ sup > Ca rises.

When the partial pressure of is reduced, for example when a can of soda is opened, the equilibrium for each of the forms of carbonate ( carbonate, bicarbonate, carbon dioxide, and carbonic acid ) shifts until the concentration of in the solution is equal to the solubility of CO < sub > 2 </ sub > at that temperature and pressure.

When pH is too high, the concentration of hydrogen ions in the blood is too low, so the kidneys excrete bicarbonate ( HCO < sub > 3 </ sub >< sup >−</ sup >).

When applied to the simplest two-electron molecule, H < sub > 2 </ sub >, valence bond theory, even at the simplest Heitler-London approach, gives a much closer approximation to the bond energy, and it provides a much more accurate representation of the behavior of the electrons as chemical bonds are formed and broken.

When this is done, the model radius still decreases with mass, but becomes zero at M < sub > limit </ sub >.

When the critical stress, F < sub > cr </ sub > ( F < sub > cr </ sub > =

When s < sup > 2 </ sup >− v < sup > 2 </ sup > is expanded using these expressions the result is

When the trajectory r ( t ) rotates an amount dθ, u < sub > ρ </ sub >, which points in the same direction as r ( t ), also rotates by dθ.

When Yellowstone Caldera last erupted some 650, 000 years ago, it released about 1, 000 km < sup > 3 </ sup > of material ( as measured in dense rock equivalent ( DRE )), covering a substantial part of North America in up to two metres of debris.

* When the metal atoms are hexagonal close packed, ( hcp ), as the octahedral interstices lie directly opposite each other on either side of the layer of metal atoms, filling only one of these with carbon achieves 2: 1 stoichiometry with the CdI < sub > 2 </ sub > structure.

When the DNS resolver gets a PTR ( reverse-lookup ) request, it begins by querying the root servers ( which point to The American Registry For Internet Numbers ' ( ARIN's ) servers for the < tt > 208. in-addr. arpa </ tt > zone ).