In a different example, one could consider javelin throw lengths, where the events typically are intervals like " between 60 and 65 meters " and unions of such intervals, but not " irrational numbers between 60 and 65 meters "

and then, on considering the lengths of the intervals to decrease to zero,

Then, on considering the lengths of the intervals to decrease to zero, the likelihood function for an observation from the discrete component is

The ratio of the lengths of successive intervals between values of r for which bifurcation occurs converges to the first Feigenbaum constant.

Indeed the basic concept that is applied in the synthetic presentation of projective geometry, the cross-ratio of four points of a line, was introduced through consideration of the lengths of intervals.

The Hilbert cube is best defined as the topological product of the intervals for n = 1, 2, 3, 4, ... That is, it is a cuboid of countably infinite dimension, where the lengths of the edges in each orthogonal direction form the sequence.

Due to their malleable nature, there were no hard and fast rules for the lengths each note was supposed to last, or even how high or low the intervals between notes were to be.

Large linear features may be sectioned at intervals along their lengths.

It is sold in rolls of various widths, lengths, and thicknesses – rolls, long and " 15 lb " () and " 30 lb " () weights are common in the U. S. – often marked with chalk lines at certain intervals to aid in laying it out straight on roofs with the proper overlap ( more overlap for flatter roofs ).

b is a subdivision of the interval b, as the lengths of the subdivision intervals approach zero.

This conversion factor is the speed of light, which turns time intervals measured in seconds to lengths measured in meters.

The lengths of ON and OFF periods, sizes of the packets and intervals between them are defined separately in each model, so these models differ in the way their parameters are defined.

Thus, in order to establish the convergence of the finite-difference approximation, it is necessary to use other methods, which in turn could imply further limitations on the length of the time step and / or the lengths of the spatial intervals.

There is no correlation between the lengths of polarity intervals.

The lengths of wire were collected and bound at intervals to form thicker strands, which were later compressed together into the main cables.

The background, which is available in various widths and continuous lengths, is extruded with parallel undercut grooves which grip the flexible letters securely.

Observations of the radio emission of a planet which has an extensive atmosphere will probe the atmosphere to a greater extent than those using shorter wave lengths and should in some cases give otherwise unobtainable information about the characteristics of the solid surface.

The radio radiation of the sun which is reflected from the moon and planets should be negligible compared with their thermal emission at centimeter wave lengths, except possibly at times of exceptional outbursts of solar radio noise.

Limitations on the lengths of these sequences diminish the stability of the comparatively short crystallites which can be formed, and this is reflected in a broadening of the melting range.

An aardvark's length is usually between, and can reach lengths of when its tail ( which can be up to ) is taken into account.

One method of building a mooring is to use three or more conventional anchors laid out with short lengths of chain attached to a swivel, so no matter which direction the vessel moves one or more anchors will be aligned to resist the force.

The most important of these was the principle that came to be called Ampère ’ s law, which states that the mutual action of two lengths of current-carrying wire is proportional to their lengths and to the intensities of their currents.

Solomonoff used this algorithm, and the code lengths it allows, to define a " universal probability " of a string on which inductive inference of the subsequent digits of the string can be based.

Other formula-based calendars can have lengths which are further out of step with the solar cycle, for example, the Julian calendar has an average length of 365. 25 days, and the Hebrew calendar has an average length of 365. 2425

Gauss's method involved determining a conic section in space, given one focus ( the Sun ) and the conic's intersection with three given lines ( lines of sight from the Earth, which is itself moving on an ellipse, to the planet ) and given the time it takes the planet to traverse the arcs determined by these lines ( from which the lengths of the arcs can be calculated by Kepler's Second Law ).

The most observed geometries are listed below, but there are many cases that deviate from a regular geometry, e. g. due to the use of ligands of different types ( which results in irregular bond lengths ; the coordination atoms do not follow a points-on-a-sphere pattern ), due to the size of ligands, or due to electronic effects ( see, e. g., Jahn-Teller distortion ):

This highly publicized tournament included hula hoops as holes, published, rules, hole lengths, pars, penalties, Wham-O prizes and, an event in which Fred Morrison, the Frisbee inventor was in attendance ( see article published in the fall issue of Discgolfer Magazine " Disc Golf's Unknown Pioneer " www. omagdigital. com / display_article. php? id = 835174 ).

Such phase differences are caused by differences in the path lengths over which contributing rays reach the point from the slit.

Euclid's proofs depend upon assumptions perhaps not obvious in Euclid's fundamental axioms, in particular that certain movements of figures do not change their geometrical properties such as the lengths of sides and interior angles, the so-called Euclidean motions, which include translations and rotations of figures.

The maximum observed lengths of ruptures and mapped faults, which may break in one go are approximately 1000 km.

The largest species is probably the Collared Grosbeak ( Mycerobas affinis ) at up to and, although larger lengths, to in the Pine Grosbeak ( Pinicola enucleator ), and weights, to in the Evening Grosbeak ( Coccothraustes vespertinus ), have been recorded in species which are slightly smaller on average.

" Although quite complicated, this was a carefully conducted study in which the investigators went to great lengths to eliminate bias and to rigorously measure outcomes.

Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.

Restricted: This includes handguns with barrel lengths greater than 4 inches, and long guns which do not meet the length requirements for non-restricted, and are not prohibited.

Let now x ' and y ' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol which takes as many arguments as the sum of lengths of x and y ; we consider the formula

It is characteristic of early literature that the evolution of the thought, or the grammatical form of the sentence, is guided by the structure of the verse ; and the correspondence which consequently obtains between the rhythm and the syntax — the thought being given out in lengths, as it were, and these again divided by tolerably uniform pauses — produces a swift flowing movement such as is rarely found when periods are constructed without direct reference to the metre.

A sophisticated ( and comparatively recent ) example is the slide rule in which numbers are represented as lengths on a logarithmic scale and computation is performed by setting a cursor and aligning sliding scales, thus adding those lengths.

Since synthetic polymerization techniques typically yield a polymer product including a range of molecular weights, the weight is often expressed statistically to describe the distribution of chain lengths present in the same.

Nervous of the lengths to which Anne might go, James formally charged Mar in writing never to surrender Henry to anyone except on orders from his own mouth, " because in the surety of my son consists my surety ," nor to yield Henry to the Queen even in the event of his own death.

Red oak or white oak was generally used for planking on vessels, as those trees tended to grow straight and tall and thus would yield straight trunk sections of length suitable for milling into plank lengths.

In finance, the yield curve is a curve showing several yields or interest rates across different contract lengths ( 2 month, 2 year, 20 year, etc ...) for a similar debt contract.