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The mean value theorem proves that this must be true: The slope between any two points on the graph of f must equal the slope of one of the tangent lines of f. All of those slopes are zero, so any line from one point on the graph to another point will also have slope zero.
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mean and value
Field shifts were derived from the mean value of the resonance line, defined as the field about which the first moment is zero.
This does not necessarily mean that such teachers will favor vocational education, as contrasted with liberal education, but they are likely to favor an approach to liberal education which has a maximal vocational-advancement value, as against a kind of `` pure '' liberal education that is not designed to help people get better jobs.
These losses depend on fiber diameter and length, absorption coefficient, the mean value of the loss per internal reflection and last, but not least, on the angular distribution of the incident light.
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
In modern quantum mechanics however, n determines the mean distance of the electron from the nucleus ; all electrons with the same value of n lie at the same average distance.
The root mean square value of the thermal noise in a resistor is given by
) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is
* In statistics, spatial autocorrelation between sample locations also helps one estimate mean value uncertainties when sampling a heterogeneous population.
Small could mean less than 3 dB below ( i. e., power output < 1 / 2 or voltage output < 0. 707 of ) the maximum value, or more rarely 10 dB below, or it could mean below a certain absolute value.
then this expression gives the expectation value, or mean or average value, of the observable represented by operator A for the physical system in the state.
The astronomer's mean tropical year which is averaged over equinoxes and solstices is currently 365. 24219 days, slightly shorter than the average length of the year in most calendars, but the astronomer's value changes over time, so William Herschel's suggested correction to the Gregorian calendar may become unnecessary by the year 4000.
and this is its Cauchy principal value, which is zero, but we could also take ( 1 ) to mean, for example,
Although the sample values x < sub > i </ sub > will be concentrated about the central value x < sub > 0 </ sub >, the sample mean will become increasingly variable as more samples are taken, because of the increased likelihood of encountering sample points with a large absolute value.
* The mean value for the Soviet Union was: 5. 935 % ( 1974 )
( The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time.
In probability theory, the expected value ( or expectation, or mathematical expectation, or mean, or the first moment ) of a random variable is the weighted average of all possible values that this random variable can take on.
The expected value may be intuitively understood by the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity.
The value may not be expected in the ordinary sense — the " expected value " itself may be unlikely or even impossible ( such as having 2. 5 children ), just like the sample mean.
mean and theorem
For a certain class of Green functions coming from solutions of integral equations, Schmidt had shown that a property analogous to the Arzelà – Ascoli theorem held in the sense of mean convergence — or convergence in what would later be dubbed a Hilbert space.
It improves Dirichlet's theorem on prime numbers in arithmetic progressions, by showing that by averaging over the modulus over a range, the mean error is much less than can be proved in a given case.
This can be seen easily from the fact that the sequences do converge to a common limit ( which can be shown by Bolzano – Weierstrass theorem ) and the fact that geometric mean is preserved:
By " satisfactory " one would mean at least the equivalent of Plancherel theorem.
These order-theoretic properties lead to a number of important results in real analysis, such as the monotone convergence theorem, the intermediate value theorem and the mean value theorem.
Important results include the Bolzano – Weierstrass and Heine – Borel theorems, the intermediate value theorem and mean value theorem, the fundamental theorem of calculus, and the monotone convergence theorem.
" Here, the central limit theorem states that the distribution of the sample mean " for very large samples " is approximately normally distributed, if the distribution is not heavy tailed.
With finite samples, approximation results measure how close a limiting distribution approaches the statistic's sample distribution: For example, with 10, 000 independent samples the normal distribution approximates ( to two digits of accuracy ) the distribution of the sample mean for many population distributions, by the Berry – Esseen theorem.
However, it is standard practice to assume that the sample mean from a random sample is normal, because of the central-limit theorem.
( The slope of the tangent at is also 3 — a consequence of the mean value theorem.
The Gauss – Markov theorem states that the estimate of the mean having minimum variance is given by:
In probability theory, the central limit theorem ( CLT ) states that, given certain conditions, the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.
The mean value theorem gives a relationship between values of the derivative and values of the original function.
If f ( x ) is a real-valued function and a and b are numbers with, then the mean value theorem says that under mild hypotheses, the slope between the two points ( a, f ( a )) and ( b, f ( b )) is equal to the slope of the tangent line to f at some point c between a and b. In other words,
In practice, what the mean value theorem does is control a function in terms of its derivative.
* An everywhere differentiable function g: R → R is Lipschitz continuous ( with K = sup | g ′( x )|) if and only if it has bounded first derivative ; one direction follows from the mean value theorem.
For any randomized trial, some variation from the mean is expected, of course, but the randomization ensures that the experimental groups have mean values that are close, due to the central limit theorem and Markov's inequality.
mean and proves
Alone, the Welsh element dy can mean ‘ thy, thine ’ or rather ‘ your ’ ( singular ) but there is no gloss of this word meaning ‘ great ,’ as the most cursory glance at the Welsh dictionary proves.
Jeannie's sister, mentioned in a second-season episode ( and also named Jeannie ), proves to have a mean streak starting in the third season ( demonstrated in her initial appearance in " Jeannie or the Tiger?
The above proves that phase speed is always westward relative to mean flow, but group speed can travel both ways depending on the wave number ; large zonal wave number waves ( short waves ) leads the mean flow, and small zonal wave number waves ( long wave ) retrogrades.
" While this would appear to be contrary to the principle of “ innocent until proven guilty ,” Shaw ’ s charge to the jury has been interpreted to mean that if the prosecutions evidence proves that a life was taken and does not produce any evidence of extenuating circumstances, the law will imply that malice existed.
mean and must
But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.
However, this does not mean that a child's teeth or jaws must necessarily resemble those of someone in his family.
When we say that a mythological mode of thought must be completely abandoned, we mean it must be abandoned as the sole or proper means for presenting the Christian understanding of existence.
This is what we mean when we say this demand must be accepted without condition.
" Identical vertices " are usually taken to mean that for any two vertices, there must be an isometry of the entire solid that takes one vertex to the other.
As nothing cannot be known by any means or method it must mean, in the context of the question, that a specific named object is present or not present in the observer's experience of a set of objects, conditions for which English uses " is " or " is not.
This does not mean that the episcopate, in the sense of the holder of the order or office of bishop, must have developed only later, or have been plural, because in each church the college or presbyter-overseers ( also called " presbyter-bishops ") did not exercise an independent supreme power ; it was subject to the Apostles or to their delegates.
Earth's rate of rotation must be integrated to obtain time, which is Earth's angular position ( specifically, the orientation of the meridian of Greenwich relative to the fictitious mean sun ).
The " equation of time ", for example, is a correction that must be applied to the reading of a sundial in order to obtain mean time, as would be shown by a clock.
Random does not mean haphazard, and great care must be taken that appropriate random methods are used.
This does not mean that there must be a linear relationship between the independent and dependent variables.
Moses I. Finley observes " this typical bit of fiction must mean that there was an old Theban hero Hector, a Greek, whose myths antedated the Homeric poems.
Heathers picks up 20 years later when Veronica returns home to Sherwood, Ohio with her teenage daughter, who must contend with the next generation of mean girls, all named " Ashley ".
He examines each of the three terms in the Berkeleian aphorism esse est percipi, " to be is to be perceived ", finding that it must mean that the object and the subject are necessarily connected so that " yellow " and " the sensation of yellow " are identical-" to be yellow " is " to be experienced as yellow ".
The serpent drips venom from above him that Sigyn collects into a bowl ; however, she must empty the bowl when it is full, and the venom that drips in the mean time causes Loki to writhe in pain, thereby causing earthquakes.
Disputes are still common when deciding appropriate action, and differences in opinion over what light is considered reasonable, and who should be responsible, mean that negotiation must sometimes take place between parties.
Scorsese changed the title from Season of the Witch to Mean Streets, a reference to Raymond Chandler's essay " The Simple Art of Murder ", where he writes, " But down these mean streets a man must go who is not himself mean, who is neither tarnished nor afraid.
They must understand that a bomb thrown at a Jewish bus is going to mean a bomb thrown at an Arab bus.
The International Narcotics Control Board typically interprets this provision to mean that states must prosecute drug possession offenses.
What did people mean when they said " A is B ", " A must be B ", " A was B "...?
The term is sometimes popularly taken to mean " knowledge meant only for certain people " or " knowledge that must be kept hidden ", but for most practicing occultists it is simply the study of a deeper spiritual reality that extends beyond pure reason and the physical sciences.
If a lower court judge disagrees with a higher court precedent on what the First Amendment should mean, the lower court judge must rule according to the binding precedent.
The programme was based on the view that " Socialism cannot mean only liberation of the working people from the domination of exploiting class relations, but must make more provisions for a fuller life of the personality than any bourgeois democracy.
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