Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.

In the third category the function is double-valued in this interval.

In the neighborhood of an end point of an interval of tangent points in the f-plane the function is two-valued or no-valued on one side, and is a single-valued function consisting entirely of tangent points on the other side.

The graph of f has at least one component whose support is the entire interval Aj.

We have shown that the graph of F contains at least one component whose inverse is the entire interval {0,T}, and whose multiplicity is odd.

For example, the open interval ( 0, 1 ) does not have a least element: if x is in ( 0, 1 ), then so is x / 2, and x / 2 is always strictly smaller than x.

The front porch is the first component of the horizontal blanking interval which also contains the horizontal sync pulse

# VBR-Variable bit rate: an average or Sustainable Cell Rate ( SCR ) is specified, which can peak at a certain level, a PCR, for a maximum interval before being problematic.

Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.

Percentage of fluent speakers of Basque ( areas where Basque is not spoken are included within the 0-4 % interval ).

After a worrying interval she reveals that E. D. Wivens is a cat.

In electronic filter design, a filter specification may require that within the filter passband, the gain is nominally 0 dB +/- a small number of dB, for example within the +/- 1 dB interval.

Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

The marching step size ( interval ) is consistent, and usually at a " 6 to 5 " ( six steps per five yards ) or " 8 to 5 ".

The source – which was termed " pulsar " – emitted beams of electromagnetic radiation at a very short and consistent interval.

This definition includes both ends x = 0 and x = 1, which is consistent with definitions for other continuous distributions supported on a bounded interval which are special cases of the beta distribution, for example the arcsine distribution, and consistent with several authors, such as N. L. Johnson and S. Kotz.

Throughout this interval, the nerve has never had a consistent name among investigators and medical practitioners.

In this case the best estimate is taken to be the smallest interval consistent with the largest number of sources.

If instead the ranges are, and then there is no interval consistent with all these values but is consistent with the largest number of sources — namely, two of them.

While Marzullo's Algorithm will return the smallest interval consistent with the largest number of sources, the returned interval does not necessarily include the center point ( calculated offset ) of all the sources in the intersection.

Varro may have used the consular list with its mistakes, and called the year of the first consuls " 245 ab urbe condita ", accepting the 244-year interval from Dionysius of Halicarnassus for the kings after the foundation of Rome.

The interval O ' O ", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i. e. with the field of view.

Side-effects include a prolonged QT interval in the heart, which can be dangerous for patients with heart disease or those taking other drugs that prolong the QT interval.

Bouts consist of three rounds of three minutes in the Olympic and Commonwealth Games, and three rounds of three minutes in a national ABA ( Amateur Boxing Association ) bout, each with a one-minute interval between rounds.

By measuring the mean squared displacement over a time interval along with the universal gas constant, the temperature, the viscosity, and the particle radius, Avogadro's number can be determined.

Areas with high tidal ranges allow waves to reach farther up the shore, and areas with lower tidal ranges produce deposition at a smaller elevation interval.

This would present with a longer PR interval.

Intuitively, the process can be pictured as follows: first shrink the real line to the open interval (- π, π ) on the x-axis ; then bend the ends of this interval upwards ( in positive y-direction ) and move them towards each other, until you get a circle with one point ( the topmost one ) missing.

A strong indication of the reliability of Chandrasekhar's formula is that the absolute magnitudes of supernovae of Type Ia are all approximately the same ; at maximum luminosity, M < sub > V </ sub > is approximately-19. 3, with a standard deviation of no more than 0. 3 .< sup >, ( 1 )</ sup > A 1-sigma interval therefore represents a factor of less than 2 in luminosity.

The open interval ( 0, 1 ), again with the absolute value metric, is not complete either.

The space C of continuous real-valued functions on a closed and bounded interval is a Banach space, and so a complete metric space, with respect to the supremum norm.

This measure of sickness is contrasted with the mortality rate of a condition, which is the proportion of people dying during a given time interval.

* A " stable " filter produces an output that converges to a constant value with time, or remains bounded within a finite interval.

The agricultural export interests, centered in the coastal region near Guayaquil, became closely associated with the Liberals, whose political power also grew steadily during the interval.

So P < sub > n </ sub > agree with the Bernoulli polynomials on the interval ( 0, 1 ) and are periodic with period 1.

A histogram consists of tabular frequencies, shown as adjacent rectangles, erected over discrete intervals ( bins ), with an area equal to the frequency of the observations in the interval.

An example of an inner product which induces an incomplete metric occurs with the space C of continuous complex valued functions on the interval.

Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if f is a continuous real-valued function defined on a closed interval, then, once an antiderivative F of f is known, the definite integral of f over that interval is given by