Logarithmic space is sufficient to hold a constant number of pointers into the input and a logarithmic number of boolean flags and many basic logspace algorithms use the memory in this way.

** Logarithmic step size control for easier bit rate management by encoders and simplified inverse-quantization scaling

He invented market scoring rules like LMSR ( Logarithmic Market Scoring Rule ) used by prediction markets such as Knew The News, Inkling Markets and Consensus Point ( where Hanson is Chief Scientist ), and has conducted research on signaling.

In complexity theory, ZPL ( Zero-error Probabilistic Logarithmic space ) is the set of problems solvable by a probabilistic Turing machine which always yields the correct answer and uses logarithmic space on average.

Logarithmic chart of solar system objects by volumetric mean radius.

Logarithmic units are abstract mathematical units that can be used to express any quantities ( physical or mathematical ) that are defined on a logarithmic scale, that is, as being proportional to the value of a logarithm function.

The plot is Logarithmic scale | logarithmic, so the fitted line corresponds to exponential growth.

A groove on a record or the arms of a spiral galaxy ( a Logarithmic spiral ) are examples of a spiral.

Image: Logarithmic Spiral Pylab. svg | logarithmic spiral

Logarithmic taper potentiometers are often used in connection with audio amplifiers as human perception of audio volume is logarithmic.

Logarithmic scales are either defined for ratios of the underlying quantity, or one has to agree to measure the quantity in fixed units.

Logarithmic graph paper, before the advent of computer graphics, was a basic scientific tool.

Note the vertical axis is Logarithmic scale | logarithmic and represents millions of people.

* Logarithmic Hierarchy a complexity class used in computer theory.

Logarithmic derivatives can simplify the computation of derivatives requiring the product rule.

Logarithmic timelines have also been used in future studies to justify the idea of a technological singularity.

Logarithmic magnitudes can be negative.

* Chapter 16: Logarithmic space, pp. 395 – 408.

* Section 7. 5: Logarithmic Space, pp. 177 – 181.

* The Murderous Maths of Everything, ISBN 1-407-10367-9 ( prime numbers, Sieve of Eratosthenes, Pythagoras ' Theorem, triangle numbers, square numbers, the International Date Line, geometry, geometric constructions, topology, Mobius strips, curves ( conic sections and cycloids Golomb Rulers, 4 dimensional " Tic Tac Toe ", The Golden Ratio, Fibonacci sequence, Logarithmic spirals, musical ratios, Theorems ( including Ham sandwich theorem and Fixed point theorem ), probability ( cards, dice etc.

* Logarithmic converter circuit.

An advanced student has read a considerable number of descriptions of consonantal systems, including some of the more unusual types.

Tone systems are certainly more complex than the number of units would suggest, and often analytically more difficult than much larger consonantal systems.

As already noted in an earlier paragraph, the more familiar cost analyses of utility enterprises or utility systems divide the total costs among a number of major classes of service, such as residential, commercial, industrial power, street lighting, etc..

Although a large number of coatings systems, particularly at low thicknesses fail cohesively by the cutting mechanism, frequently a second type of cohesive failure may also take place.

The Proto-Sinatic or Proto Canaanite script and the Ugaritic script were the first scripts with limited number of signs, in contrast to the other widely used writing systems at the time, Cuneiform, Egyptian hieroglyphs, and Linear B.

Syllabaries typically contain 50 to 400 glyphs ( though the Múra-Pirahã language of Brazil would require only 24 if it did not denote tone, and Rotokas would require only 30 ), and the glyphs of logographic systems typically number from the many hundreds into the thousands.

Phoenician gave way to a number of new writing systems, including the Greek alphabet and Aramaic, a widely used abjad.

The acre is a unit of area in a number of different systems, including the imperial and U. S. customary systems.

Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world.

Armour is being supplemented with active protection systems on a number of vehicles, allowing the AFV to protect itself from incoming projectiles.

Although a number of different broadcast television systems were in use worldwide, the same principles of operation apply.

These show a number of systems of script employing either ideograms or syllabograms ( see Linear B ).

This significantly reduced the number of channels available at each site in real-world systems.

Early number systems that included positional notation were not decimal, including the sexagesimal ( base 60 ) system for Babylonian numerals and the vigesimal ( base 20 ) system that defined Maya numerals

The Smartmodem was not necessary for BBS use, other modems could be left in " answer mode ", but the Smartmodem made operation dramatically simpler on the user end by allowing the easy dialling of any number of BBS systems.

There are a number of systems of transport in Burundi, including road and water-based infrastructure, the latter of which makes use of Lake Tanganyika.

In computing and electronic systems, binary-coded decimal ( BCD ) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight, although other sizes ( such as six bits ) have been used historically.

* Cancer immunotherapy / cancer vaccine: A number of cancer vaccines use BCG as an adjuvant to provide an initial stimulation of the patients ' immune systems.

BRP is similar to other generic systems such as GURPS, Hero System or Savage Worlds in that it uses a simple resolution method which can be broadly applied, in this case an attempt to roll under a certain number with percentile dice.

Finite geometry is the study of geometric systems having only a finite number of points.

SMP systems are limited to a small number of CPUs while NUMA systems have been built with thousands of processors.

The need to support more writing systems for different languages, including the CJK family of East Asian scripts, required support for a far larger number of characters and demanded a systematic approach to character encoding rather than the previous ad hoc approaches.