* Volterra's function

* The SVC is used in the construction of Volterra's function ( see external link ).

* Wrestling with the Fundamental Theorem of Calculus: Volterra's function, talk by David Marius Bressoud

In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination of properties:

Volterra's function is differentiable everywhere just as f ( as defined above ) is.

If one were to repeat the construction of Volterra's function with the ordinary measure-0 Cantor set C in place of the " fat " ( positive-measure ) Cantor set S, one would obtain a function with many similar properties, but the derivative would then be discontinuous on the measure-0 set C instead of the positive-measure set S, and so the resulting function would have an integrable derivative.

* Wrestling with the Fundamental Theorem of Calculus: Volterra's function, talk by David Marius Bressoud

* Volterra's function, a differentiable function whose derivative is not Riemann integrable.

* Volterra's example of a derivative that is not integrable ( PPT ), talk by David Marius Bressoud

* E. R. Leigh ( 1968 ) The ecological role of Volterra's equations, in Some Mathematical Problems in Biology – a modern discussion using Hudson's Bay Company data on lynx and hares in Canada from 1847 to 1903.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

How, then, do the kinesthetic sensations function in all this??

If a union cannot perform this function, then collective bargaining is being palmed off by organizers as a gigantic fraud.

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.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

In general, if y = f ( x ), then it can be transformed into y = af ( b ( x − k )) + h. In the new transformed function, a is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative a values, the function is reflected in the x-axis.

Antiderivatives are important because they can be used to compute definite integrals, using the fundamental theorem of calculus: if F is an antiderivative of the integrable function f, then:

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.

Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function.

Although those of many marine species function first as males and then as females, their colonies always contain a combination of zooids that are in their male and female stages.

Division of whole numbers can be thought of as a function ; if Z is the set of integers, N < sup >+</ sup > is the set of natural numbers ( except for zero ), and Q is the set of rational numbers, then division is a binary function from Z and N < sup >+</ sup > to Q.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

In this case, the second linearly independent solution is then found to be the Bessel function of the second kind, as discussed below.

The Bessel function of the second kind then can be thought to naturally appear as the imaginary part of the Hankel functions.

This orthogonality relation can then be used to extract the coefficients in the Fourier – Bessel series, where a function is expanded in the basis of the functions J < sub > α </ sub >( x u < sub > α, m </ sub >) for fixed α and varying m.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

Caloric reflex test also evaluates both cortical and brainstem function ; cold water is injected into one ear and the patient is observed for eye movement ; if the patient's eyes slowly deviate toward the ear where the water was injected, then the brainstem is intact, however failure to deviate toward the injected ear indicates damage of the brainstem on that side.

Thyroid function tests yielded normal results.

If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results.

Dropping the principle that the wave function is a complete description results in a hidden variable theory.

Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field electron emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum.

Sporadic and genetic cretinism results from abnormal development or function of the foetal thyroid gland.

On some processors the control unit may be further broken down into other units, such as a scheduling unit to handle scheduling and a retirement unit to deal with results coming from the pipeline ; It is the main function of CPU.

Each replacement results in a function taking exactly one argument.

The following function returns the value of the “ if ” statement ( statements, too, produce results ), which evaluates to the value of either “ 1 ” or “ n * factorial ( n-1 )”:

The point estimators yield single-valued results, although this includes the possibility of single vector-valued results and results that can be expressed as a single function.

A production function has constant returns to scale if increasing all inputs by some proportion results in output increasing by that same proportion.

These results, however, are very sensitive to the accuracy of the twiddle factors used in the FFT ( i. e. the trigonometric function values ), and it is not unusual for incautious FFT implementations to have much worse accuracy, e. g. if they use inaccurate trigonometric recurrence formulas.

The G protein activates a cascade of further signaling events that finally results in a change in cell function.

Specifically, the results of this study suggest that this phenomenon occurs in a manner similar to the way that light passes through fiber optic tubes ( which do not function as effectively when kinked or sharply curved or coiled ).

Within the parlance of Icon, the evaluation of an expression or function results in a result sequence.

There is an isomorphism from X to Y if the bijective function happens to produce results, that sets up a correspondence between the operator and the operator.

Population-based studies ( e. g. Michael, et al., 2000 ) using the SF-36 have found significant decrease in QoL dimensions, including role / physical, bodily pain, vitality and social function, results that were supported by Rothrock's ( et al., 2002 ) cross-sectional study of IC patients showing decreased physical functioning, decreased ability to function in one's normal role, decreased vitality, and depression.

Zeleny ( 1944 ) confirmed these results and observed the corona charge transfer. In capacitors generally, the charge is not stored in the dielectric, but on the inside surfaces of the plates, as can be observed from capacitors that can function with a vacuum between their plates.

" These results suggest that riluzole might indeed have antidepressant efficacy in subjects with bipolar depression ," say the team. Safety monitoring includes regular liver function tests and people with liver disease such as hepatitis should be monitored especially carefully.

Simplified schema of basic nervous system function: signals are picked up by sensory receptors and sent to the spinal cord and brain, where processing occurs that results in signals sent back to the spinal cord and then out to motor neurons

The number of electrons also changes because the probability that each photon results in an emitted electron is a function of photon energy.

In particular, the dopamine hypothesis of psychosis has been influential and states that psychosis results from an overactivity of dopamine function in the brain, particularly in the mesolimbic pathway.

A more subtle example is that of a function that uses a global variable ( or a dynamically scoped variable, or a lexical closure ) to help it compute its results.