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Page "Measure (mathematics)" ¶ 5
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function and from
`` Mr. Gross, your report says that ' our function is investigative and advisory and does not in any way derogate from or prejudice Mr. Bang-Jensen's rights as a staff member.
A primary function is the operation of a Government Bid Center, which receives bids daily from the Federal Government's principal purchasing agencies.
During the period from 1 July 1960 through 31 January 1961, additional research affiliations were effected with the U. S. Army Medical Research and Development Command to conduct research in procedures for quantitative electron microscopy, and for the study of biophysical and biological studies of the structure and function of ocular tissue.
The concept of the strain energy as a Gibbs function difference Af and exerting a force normal to the shearing face is compatible with the information obtained from optical birefringence studies of fluids undergoing shear.
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.
We are abstracting from the fact of strikes here, but it should be obvious that the extent to which the public-limit price is raised by a given increase in the basic wage rate is also a function of the show of resistance put up by the industry.
271 - 307 ) indicate, that the concept of function in sociology has been built up from physiological and biological models, in which the notions of teleology, i.e., metaphysical purpose, are central.
Its function is to separate from the base ruled mass, among whom private ownership prevails, the governing warrior elite.
Extreme caution should be used, however, to avoid the conflicting usage of an index word or electronic switch which may result from the assignment of more than one name or function to the same address.
In the second-order theory, one of the normal stress differences can be calculated from the first-order stress relaxation function.
In finding the optimal R-stage policy from that of Af stages, only the function Af is needed.
To extract the optimal R-stage policy with respect to the feed state Af, we enter section R of this table at the state Af and find immediately from the last column the maximum value of the objective function.
As retinal images are conceded to be an integral function of the brain it seems logical to suppose that the nerves, between the inner brain and the eyes, carry the direct drive for cooperation from the various brain centers -- rather than to theorize on the transmission of an image which is already in required location.
Her brain and intelligence controlled every function from navigation to such loading as a scout ship of her class needed.
These stateless societies are not less evolved than societies with states, but chose to conjure the institution of authority as a separate function from society.
The function of Apollo as a " healer " is connected with Paean ( Παιών-Παιήων ), the physician of the Gods in the Iliad, who seems to come from a more primitive religion.
In Iliad, his priest prays to Apollo Smintheus, the mouse god who retains an older agricultural function as the protector from field rats.
They differ from other related families by often being pachycauline ( i. e. with a thickened trunk, usually wider at the base, which has a water storage function ), by usually having succulent leaves, and by possessing a trimerous flower with a superior ovary and seeds with an aryl.
If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.
* There exists a model of ZF ¬ C in which there is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i. e., for any sequence
Axons are distinguished from dendrites by several features, including shape ( dendrites often taper while axons usually maintain a constant radius ), length ( dendrites are restricted to a small region around the cell body while axons can be much longer ), and function ( dendrites usually receive signals while axons usually transmit them ).
It differs from a digital signal, in which a continuous quantity is represented by a discrete function which can only take on one of a finite number of values.
Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy.
# The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron.
The part of the function that depends on the distance from the nucleus has nodes ( radial nodes ) and decays as e < sup >(- distance )</ sup > from the nucleus.

function and extended
* Applesoft could be extended by two means: the ampersand (&) command and the USR () function.
The notion of a directional derivative of a function from multivariable calculus is extended in Riemannian geometry to the notion of a covariant derivative of a tensor.
This integral function is extended by analytic continuation to all complex numbers except the non-positive integers ( where the function has simple poles ), yielding the meromorphic function we call the gamma function.
Schrödinger himself initially did not understand the fundamental probabilistic nature of quantum mechanics, as he thought that the absolute square of the wave function of an electron should be interpreted as the charge density of an object smeared out over an extended, possibly infinite, volume of space.
The exponential function can be extended to a function which gives a complex number as e < sup > x </ sup > for any arbitrary complex number x ; simply use the infinite series with x complex.
The main changes are: explicit numeric conversion functions ( e. g. FLOOR and FLT ) must be used, the LOOP and EXIT statements have been eliminated, WHILE statements have been extended, RETURN statements can only be connected to the end of a function, imported variables and structured value parameters are read-only and arrays can be assigned without using COPY.
Riemann introduced revolutionary ideas into the subject, the chief of them being that the distribution of prime numbers is intimately connected with the zeros of the analytically extended Riemann zeta function of a complex variable.
An " extensional stance " and restriction to a second-order predicate logic means that a propositional function extended to all individuals such as " All ' x ' are blue " now has to list all of the ' x ' that satisfy ( are true in ) the proposition, listing them in a possibly infinite conjunction: e. g. x < sub > 1 </ sub > V x < sub > 2 </ sub > V.
In the early 1920s Rolf Nevanlinna, partly in collaboration with his brother Frithiof, extended the theory to cover meromorphic functions, i. e. functions analytic in the plane except for isolated points in which the Laurent series of the function has a finite number of terms with a negative power of the variable.
A rigorous interpretation of the exponential form and the various limitations upon the function ƒ necessary for its application extended over several centuries.
The sovereign function ( embodied by Jupiter ) entailed omnipotence ; thence, a domain extended over every aspect of nature and life.
In telecommunication, endurability is the property of a system, subsystem, equipment, or process that enables it to continue to function within specified performance limits for an extended period of time, usually months, despite a severe natural or man-made disturbance, such as a nuclear attack, or a loss of external logistic or utility support.
From an extended source the Arago spot is only affected marginally, since one can interpret the Arago spot as a point-spread function.
And so the image of the extended source only becomes washed out due to the convolution with the point-spread function, but it does not decrease in over all intensity.
Dumézil elaborates that in Rome the whole site of the city itself was considered as an extended sacrificial ground, with the temple of Vesta performing the function of hearth of the landlord and other temples that of sacrificial fires.
Shape, for example, is a function of in what way the object is extended in space, as is color, since it is determined by how light bounces off a surface, which is in turn determined by how that object is extended in space.
if in the construction above we take the smallest possible ball, we see that the sup norm of the extended sequence does not grow ( although the image of the extended function can be bigger ).
Animals, including humans, kept in total darkness for extended periods eventually function with a freerunning rhythm.

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