However the amortized access cost of this worst case is logarithmic, O ( log n ).

The links may also be added in a non-probabilistic way so as to guarantee amortized ( rather than merely expected ) logarithmic cost.

Also, a statistician may specify that logarithmic transforms be applied to the responses, which are believed to follow a multiplicative model.

An improved Scheutzian calculation engine was sold to the British government and a later model was sold to the American government and these were used successfully in the production of logarithmic tables.

A common utility model, suggested by Bernoulli himself, is the logarithmic function U ( w ) = ln ( w ) ( known as “ log utility ”).

An algorithm's key length is distinct from its cryptographic security, which is a logarithmic measure of the fastest known computational attack on the algorithm, also measured in bits.

The intercept may also be biased if there is a logarithmic transformation.

Moog also established standards for analog synthesizer control interfacing, with a logarithmic one volt-per-octave pitch control and a separate pulse triggering signal.

In telecommunication, a log-periodic antenna ( LP, also known as a log-periodic array or log periodic beam antenna / aerial ) is a broadband, multi-element, directional, narrow-beam antenna that has impedance and radiation characteristics that are regularly repetitive as a logarithmic function of the excitation frequency.

It may also be defined on a logarithmic scale, in terms of the decimal logarithm of the same ratio (" dB gain ").

It is suspected that L ≠ P ; that is, that some problems that can be solved in polynomial time also require more than logarithmic space.

The logarithmic constant, pK < sub > a </ sub >, which is equal to − log < sub > 10 </ sub > K < sub > a </ sub >, is sometimes also ( but incorrectly ) referred to as an acid dissociation constant:

A logarithmic potentiometer can also be simulated ( not very accurately ) with a linear one and an external resistor.

The ' log pot ' is used as the volume control in audio amplifiers, where it is also called an " audio taper pot ", because the amplitude response of the human ear is approximately logarithmic.

There is also an anti-log pot or reverse audio taper which is simply the reverse of a logarithmic potentiometer.

The base of the logarithm also has to be specified, unless the scale's value is considered to be a dimensional quantity expressed in generic ( indefinite-base ) logarithmic units.

Examples of logarithmic units include common units of information and entropy, such as the bit and the byte 8 =, also the nat and the ban ; units of relative signal strength magnitude such as the decibel 0. 1 and bel, neper, and other logarithmic-scale units such as the Richter scale point or ( more generally ) the corresponding order-of-magnitude unit sometimes referred to as a factor of ten or decade ( here meaning, not 10 years ).

A logarithmic scale is also a graphical scale on one or both sides of a graph where a number x is printed at a distance c · log ( x ) from the point marked with the number 1.

The plot on the right uses logarithmic ( or log, as it is also referred to ) scaling on the vertical axis.

Decade lines, those values that denote powers of the log base, are also important in logarithmic interpolation.

It is indicated by log < sub > 10 </ sub >( x ), or sometimes Log ( x ) with a capital L ( however, this notation is ambiguous since it can also mean the complex natural logarithmic multi-valued function ).

He also completed a table of logarithmic sines and tangents for the hundredth part of every degree to fourteen decimal places, with a table of natural sines to fifteen places, and the tangents and secants for the same to ten places ; all of which were printed at Gouda in 1631 and published in 1633 under the title of Trigonometria Britannica ; this work was probably a successor to his 1617 Logarithmorum Chilias Prima (" The First Thousand Logarithms "), which gave a brief account of logarithms and a long table of the first 1000 integers calculated to the 14th decimal place.

Researchers have also studied algorithms for finding connected components in more limited models of computation, such as programs in which the working memory is limited to a logarithmic number of bits ( defined by the complexity class L ).

The 17th century saw also the invention of some very powerful calculating tools like Napier's bones, logarithmic tables and the slide rule which, for their ease of use by scientists in multiplying and dividing, ruled over and impeded the use and development of mechanical calculators until the production release of the arithmometer in the mid 19th century.

He also created a music replay routine for the Amiga called TFMX -- " The Final Musicsystem eXtended ", which featured far more musically-oriented features than rival Soundtracker, such as logarithmic pitch-bends, sound macros and individual tempos for each track.

In mathematics, the Ramanujan – Soldner constant ( also called the Soldner constant ) is a mathematical constant defined as the unique positive zero of the logarithmic integral function.

Many properties of the real logarithm also apply to the logarithmic derivative, even when the function does not take values in the positive reals.

In spectroscopy, the absorbance ( also called optical density ) of a material is a logarithmic ratio of the radiation falling upon a material, to the radiation transmitted through a material.

The loudness of these disturbances is called the sound pressure level ( SPL ), and is measured on a logarithmic scale in decibels.

Order-of-magnitude differences are called decades when measured on a logarithmic scale.

# Exponential phase ( sometimes called the log phase or the logarithmic phase ) is a period characterized by cell doubling.

Since both axes use logarithmic units, the slope of the linear section of the curve is called the gamma of the film.

On a logarithmic scale, μ and σ can be called the location parameter and the scale parameter, respectively.

During the late 1930s he developed and exhibited a style of painting based on a logarithmic form of anamorphic projection which he called " siderealism ".

This reduces the computation of the antiderivative of a rational function to the integration of the last sum, with is called the logarithmic part, because its antiderivative is a linear combination of logarithms.

By contrast, the point z < sub > 0 </ sub > is called a logarithmic branch point if it is impossible to return to the original function element by analytic continuation along a curve with nonzero winding number about z < sub > 0 </ sub >.

In applications involving sound, the particle velocity is usually measured using a logarithmic decibel scale called particle velocity level.

In 1730, Daniel Bernoulli studied " moral probability " in his book Mensura Sortis, where he introduced what would today be called " logarithmic utility of money " and applied it to gambling and insurance problems, including a solution of the paradoxical Saint Petersburg problem.

The logarithmic or continuously compounded return, sometimes called force of interest, is a function of time defined as follows:

The Weierstrass zeta function was called an integral of the second kind in elliptic function theory ; it is a logarithmic derivative of a theta function, and therefore has simple poles, with integer residues.

In computational complexity theory, RL ( Randomized Logarithmic-space ), sometimes called RLP ( Randomized Logarithmic-space Polynomial-time ), is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machines with one-sided error.

Pearson ( 1895, p. 362 ) called this the " logarithmic case ", because the integral