The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

The basic objectives in each instance are to make available supplies of food during the intervals between harvesting or slaughter, to minimize losses resulting from the action of microorganisms and insects, and to make it possible to transport foods from the area of harvest or production to areas of consumption.

The large pillars called " Kose (' Mile ') Minar ", erected at intervals of two miles ( 3 km ) along the entire way between Agra and Ajmer mark the places where the royal pilgrims halted every day.

Rounds were three minutes long with one minute rest intervals between rounds.

There were minimum intervals between holding successive offices and laws forbade repeating an office.

In its natural regime, chaparral is characterized by infrequent fires, with intervals ranging between 10 – 15 years to over a hundred years.

Mature chaparral ( stands that have been allowed greater intervals between fires ) is characterized by nearly impenetrable, dense thickets ( except the more open chaparral of the desert ).

When intervals between fires drop below 10 to 15 years, many chaparral species are eliminated and the system is typically replaced by non-native, invasive, weedy grassland.

In the past, surface-fires burned through these forests at intervals of anywhere between 4 and 36 years, clearing out the understory and creating a more ecologically balanced system.

The Rankine temperature scale was created to use degree intervals the same size as those of the Fahrenheit scale, such that a temperature difference of one degree Rankine ( 1 R ) is equal to a difference of 1 ° F, except that absolute zero is 0 R – the same way that the Kelvin temperature scale matches the Celsius scale, except that absolute zero is 0 K. The Fahrenheit scale uses ( in the same manner as the later Celsius scale ) the symbol ° to denote a point on the temperature scale and the letter F to indicate the use of the Fahrenheit scale ( e. g. " Gallium melts at 85. 5763 ° F "), as well as to denote a difference between temperatures or an uncertainty in temperature ( e. g. " The output of the heat exchanger experiences an increase of 72 ° F " and " Our standard uncertainty is ± 5 ° F ").

:" Guerrilla warfare is an inevitable form of struggle at a time when the mass movement has actually reached the point of an uprising and when fairly large intervals occur between the ' big engagements ' in the civil war.

Some parallels can be drawn between the general election in parliamentary systems and the biennial elections determining all House seats, although there is no analogue to " calling early elections " in the U. S., and the members of the elected U. S. Senate face elections of only one-third at a time at two year intervals including during a general election.

The shamal, another wind of some significance, comes from the north or northwest, generally at intervals between June and September.

His system, intended to be compatible with typography, is based on a single line, displaying numbers representing intervals between notes and dots and commas indicating rhythmic values.

The lengths of the parameter intervals which yield oscillations of a given length decrease rapidly ; the ratio between the lengths of two successive such bifurcation intervals approaches the Feigenbaum constant δ = 4. 669.

Unfortunately, there is no generally accepted worldwide criterion of difference definitively diagnostic, although a volume difference of 200 ml between limbs or a 4-cm difference ( at a single measurement site or set intervals along the limb ) is often used.

By this is meant switching from one opioid to another, usually at intervals of between a few weeks and, more commonly, several months.

In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals: in quality control one might demand that the probability of a " 500 g " package containing between 490 g and 510 g should be no less than 98 %.

The logic for this is believed to be that the prime number intervals between emergences make it very difficult for predators to evolve that could specialize as predators on Magicicadas.

Apparently the sea advanced and receded over the valley in conformance to an equilibrium between sedimentation and glacial advance or recession at 100, 000-year intervals and to fluctuation of sea level.

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the music intervals created by the division of a monochord.

Spaced repetition is a learning technique that incorporates increasing intervals of time between subsequent review of previously learned material in order to exploit the psychological spacing effect.

Certain types of world lines ( called geodesics of the spacetime ) are the shortest paths between any two events, with distance being defined in terms of spacetime intervals.

With his free hand he pulled a pad and pencil toward him and began to make notes as he listened, saying, `` Uh-huh '' and `` I see '' at intervals.

Its most noticeable feature is what appears to be its extreme discontinuity, often from note to note: there may be enormous intervals between consecutive notes, and rather than aspiring to the consistency of timbre typical of most guitar-playing, Bailey interrupts it as much as possible: four consecutive notes, for instance, may be played on an open string, a fretted string, via harmonics, and using a nonstandard technique such as scraping the string with the pick or plucking below the bridge.

The second code, consisting of unpredictable rhythms, irregular phrasing and based on long passages with many repeat notes, augmented and diminished intervals and extended melismas, depict sensual longing.

Each Gamelan is tuned to itself, and the intervals between notes on the scale vary between ensembles.

Further, an important difference between the music of the Border pipes and of the Great Highland Bagpipe is that many melodic figures in older Border pipe music typically move stepwise or in thirds rather than by wide intervals, and lack the multiple repeated notes found in many Highland pipe tunes.

Ethiopian music uses a distinct modal system that is pentatonic, with characteristically long intervals between some notes.

Typically, cents are used to measure extremely small finite intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes.

As memory became cheaper, it became possible to use multisampling ; instead of a single recording of an instrument being played back faster or slower to reproduce other pitches, the original instrument could be sampled at regular intervals to cover regions of several adjacent notes ( called " splits ") or for every note.

* Omnitonic – The final phase of tonality, and one embodied for Fétis by Wagner, where the alteration of the intervals of natural chords and modification by substitution of notes is so complex that it becomes impossible to identify the original chord.

Microtones are those intervals that are smaller than a semitone ; human voices and unfretted strings can easily produce them by going in between the " normal " notes, but other instruments will have more difficulty — the piano and organ have no way of producing them at all, aside from retuning and / or major reconstruction.

The typical contact call of the Goldcrest is a thin, high-pitched zee given at intervals of 1 – 4 seconds, with all the notes at the same pitch.

* Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings.

* Ability to read, recognize, and remember groups of notes ( directions, patterns, phrases, chords, rhythmic groupings, themes, inversions, intervals, etc.

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.

Since the function of pitch classes is a key element, the problem of compound intervals with interval recognition is not an issue — whether the notes in a melody are played within a single octave or over many octaves is irrelevant.

Interval recognition is also a useful skill for musicians: in order to determine the notes in a melody, a musician must have some ability to recognize intervals.

The technique of angling the bar so that the strings played are unequal in length and different intervals between the notes are played is called " slanting ".

The Tristan chord is a chord made up of the notes F, B, D and G. More generally, it can be any chord that consists of these same intervals: augmented fourth, augmented sixth, and augmented ninth above a root.

The notes ( svaras ) are separated by intervals, which are measured in terms of shrutis.

The simplest examples given by van der Merwe are fixed notes, definite intervals, and regular beats, while the most complex given are the Baroque fugue, Classical tonality, and Romantic chromaticism.

The bell's strongest overtones are tuned to be at octave intervals below the nominal note, but other notes also need to be brought into their proper relationship.