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ISO 31-0

ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It is intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of ISO 80000.


ISO 31 covers only physical quantities used for the quantitative description of physical phenomena. It does not cover conventional scales (e.g., Beaufort scale, Richter scale, colour intensity scales), results of conventional tests, currencies, or information content. The presentation here is only a brief summary of some of the detailed guidelines and examples given in the standard.

Quantities and units

Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all quantities of the same kind. One particular example of such a quantity can be chosen as a reference quantity, called the unit, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the numerical value. For example, if we write

then "λ" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10−7 " is the numerical value of the wavelength in metres.

More generally, we can write

where A is the symbol for the quantity, {A} symbolizes the numerical value of A, and [A] represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 ⋅ m = 0.3 ⋅ km = ...). This ambiguity makes the {A} and [A] notations useless, unless they are used together.

The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in {λ} = 6.982 × 10−7 or equivalently {λ} = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in

or equivalently

This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.

Typographic conventions
Symbols for quantities
  • Quantities are generally represented by a symbol formed from single letters of the Latin or Greek alphabet.
  • Symbols for quantities are set in italic type, independent of the type used in the rest of the text.
  • If in a text different quantities use the same letter symbol, they can be distinguished via subscripts.
  • A subscript is only set in italic type if it consists of a symbol for a quantity or a variable. Other subscripts are set in upright (roman) type. For example, write V for a "nominal volume" (where "n" is just an abbreviation for the word "nominal"), but write V if n is a running index number.
Names and symbols for units
  • If an internationally standardized symbol exists for a unit, then only that symbol should be used. See the SI articles for the list of standard symbols defined by the International System of Units. Note that the distinction between uppercase and lowercase letters is significant for SI unit symbols. For example, "k" is the prefix kilo and "K" stands for the unit kelvin. The symbols of all SI units named after a person or a place start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase; the only exception is litre, where both l and L are allowed. However, it is stated that the CIPM will examine whether one of the two may be suppressed.
  • Symbols for units should be printed in an upright (roman) typeface.

See Sect. 3.3 of the Standard text.

  • Numbers should be printed in upright (roman) type.
  • ISO 31-0 (after Amendment 2) specifies that "the decimal sign is either the comma on the line or the point on the line". This follows resolution 10[1] of the 22nd CGPM, 2003.[2]
  • Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. For this reason, ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use as the decimal sign.
  • For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
  • The multiplication sign is either a cross or a half-height dot, though the latter should not be used when the dot is the decimal separator.
  • Unit symbols follow the numerical value in the expression of a quantity.
  • Numerical value and unit symbol are separated by a space. This rule also applies to the symbol "°C" for degrees Celsius, as in "25 °C". The only exception are the symbols for the units of plane angle degree, minute and second, which follow the numerical value without a space in between (for example "30°").
  • Where quantities are added or subtracted, parenthesis can be used to distribute a unit symbol over several numerical values, as in
P = 100 kW ± 5 kW = (100 ± 5) kW
(but not: 100 ± 5 kW)
d = 12 × (1 ± 10−4 ) m
  • Products can be written as ab, a b, a⋅b, or a×b. The sign for multiplying numbers is a cross (×) or a half-height dot (⋅). The cross should be used adjacent to numbers if a dot on the line is used as the decimal separator, to avoid confusion between a decimal dot and a multiplication dot.
  • Division can be written as a b {\displaystyle {\frac {a}{b}}} , a/b, or by writing the product of a and b−1 , for example a⋅b−1 . Numerator or denominator can themselves be products or quotients, but in this case, a solidus (/) should not be followed by a multiplication sign or division sign on the same line, unless parentheses are used to avoid ambiguity.
Mathematical signs and symbols

A comprehensive list of internationally standardized mathematical symbols and notations can be found in ISO 31-11.

See also
  1. "Resolution 10", 22nd General Conference on Weights and Measures, BIPM.
  2. Brief reference to the history, NIST.
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MPEG-4 Part 3


MPEG-4 Part 3 or MPEG-4 Audio (formally ISO/IEC 14496-3) is the third part of the ISO/IEC MPEG-4 international standard developed by Moving Picture Experts Group. It specifies audio coding methods. The first version of ISO/IEC 14496-3 was published in 1999. The MPEG-4 Part 3 consists of a variety of audio coding technologies – from lossy speech coding (HVXC, CELP), general audio coding (AAC, TwinVQ, BSAC), lossless audio compression (MPEG-4 SLS, Audio Lossless Coding, MPEG-4 DST), a Text-To-Speech Interface (TTSI), Structured Audio (using SAOL, SASL, MIDI) and many additional audio synthesis and coding techniques. MPEG-4 Audio does not target a single application such as real-time telephony or high-quality audio compression. It applies to every application which requires the use of advanced sound compression, synthesis, manipulation, or playback. MPEG-4 Audio is a new type of audio standard that integrates numerous different types of audio coding: natural sound and synthetic sound, low bitrate delivery and ...more...

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Office Open XML


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List of Wikipedias


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International Standard Book Number


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ISO 13567


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ISO/IEC 8859-16


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International Standard Atmosphere


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ISO 13849


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Ring size


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IEC 60027


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ISO 10303


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List of common physics notations


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.NET Framework


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Extended ASCII


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PDF/UA (PDF/Universal Accessibility) is the informal name for ISO 14289, the International Standard for accessible PDF technology. A technical specification intended for developers implementing PDF writing and processing software, PDF/UA provides definitive terms and requirements for accessibility in PDF documents and applications. For those equipped with appropriate software, conformance with PDF/UA ensures accessibility for people with disabilities who use assistive technology such as screen readers, screen magnifiers, joysticks and other technologies to navigate and read electronic content. On February 18, 2015 the US Access Board announced its Proposed Rule for US federal policy on accessibility, commonly known as Section 508. The proposed rule identifies PDF/UA as equivalent to WCAG 2.0 for "appropriate content". Description PDF/UA is not a separate file-format but simply a way to use the familiar PDF format invented by Adobe Systems and now standardized as ISO 32000. In general PDF/UA requires Tagg ...more...

Nominal Pipe Size


Nominal Pipe Size (NPS) is a North American set of standard sizes for pipes used for high or low pressures and temperatures. "Nominal" refers to pipe in non-specific terms and identifies the diameter of the hole with a non-dimensional number (for example – "2-inch nominal steel pipe" consists of many varieties of steel pipe with the only criterion being a 2.375-inch (60.3 mm) outside diameter). Specific pipe is identified by pipe diameter and another non-dimensional number for wall thickness referred to as the Schedule (Sched. or Sch., for example – "2 inch diameter pipe, Schedule 40"). NPS is often incorrectly called National Pipe Size, due to confusion with the American standard for pipe threads, "national pipe straight", which also abbreviates as "NPS". The European and international designation equivalent to NPS is DN (diamètre nominal/nominal diameter/Durchmesser nach Norm), in which sizes are measured in millimetres, see ISO 6708. The term NB (nominal bore) is also frequently used interchangeably with N ...more...

ISO 15924


ISO 15924, Codes for the representation of names of scripts, defines two sets of codes for a number of writing systems (scripts). Each script is given both a four-letter code and a numeric one. Script is defined as "set of graphic characters used for the written form of one or more languages". Where possible the codes are derived from ISO 639-2 where the name of a script and the name of a language using the script are identical (example: Gujarātī ISO 639 guj, ISO 15924 Gujr). Preference is given to the 639-2 Bibliographical codes, which is different from the otherwise often preferred use of the Terminological codes. 4-letter ISO 15924 codes are incorporated into the Language Subtag Registry for IETF language tags and so can be used in file formats that make use of such language tags. For example, they can be used in HTML and XML to help Web browsers determine which typeface to use for foreign text. This way one could differentiate, for example, between Serbian written in the Cyrillic (sr-Cyrl) or Latin (sr- ...more...



ASTM F568M is an ASTM International standard for metric bolts, screws and studs that are used in general engineering applications. It is titled: Standard Specification for Carbon and Alloy Steel Externally Threaded Metric Fasteners. It defines mechanical properties for fasteners that range from M1.6 to 100 in diameter. The standard was withdrawn in 2012. and has been replaced by ISO 898-1 This standard defines property classes, the metric equivalent of a screw grade, that are almost identical to those defined by ISO 898-1, except for the addition of the 8.8.3 and 10.9.3 classes. These two additional standards are fasteners that have the same mechanical properties as their base property class (i.e. 8.8 and 10.9), but are made from weathering steel. This is a standard set by the standards organization ASTM International, a voluntary standards development organization that sets technical standards for materials, products, systems, and services. Mechanical properties Head markings and mechanical properties ...more...

Radio-frequency identification


Radio-frequency identification (RFID) uses electromagnetic fields to automatically identify and track tags attached to objects. The tags contain electronically stored information. Passive tags collect energy from a nearby RFID reader's interrogating radio waves. Active tags have a local power source (such as a battery) and may operate hundreds of meters from the RFID reader. Unlike a barcode, the tag need not be within the line of sight of the reader, so it may be embedded in the tracked object. RFID is one method for Automatic Identification and Data Capture (AIDC). RFID tags are used in many industries, for example, an RFID tag attached to an automobile during production can be used to track its progress through the assembly line; RFID-tagged pharmaceuticals can be tracked through warehouses; and implanting RFID microchips in livestock and pets allows for positive identification of animals. Since RFID tags can be attached to cash, clothing, and possessions, or implanted in animals and people, the possibil ...more...



Windows-1252, sometimes incorrectly called "ANSI" or "ASCII". Red indicates code points that are C1 control codes in ISO-8859-1. Blue dots indicate control codes or unused code points. Windows-1252 or CP-1252 (code page – 1252) is a 1 byte character encoding of the Latin alphabet, used by default in the legacy components of Microsoft Windows in English and some other Western languages (other languages use different default encodings). It is probably the most-used 8-bit character encoding in the world. As of February 2018, 0.7% of all web sites declared use of Windows-1252, but at the same time 4.2% used ISO 8859-1, which by HTML5 standards should be considered the same encoding, so that 4.9% of web sites effectively used Windows-1252. In addition most web browsers will correctly render it if encountered in text that claims to be UTF-8, so its actual usage may be higher. Details This character encoding is a superset of ISO 8859-1 in terms of printable characters, but differs from the IANA's ISO-8859-1 by ...more...

Ash (analytical chemistry)


In analytical chemistry , ashing or ash content determination is the process of mineralization for preconcentration of trace substances prior to a chemical analysis, such as chromatography , or optical analysis, such as spectroscopy . Overview A crucible and tongs, on a green mat. The residues after a sample is completely burnt - in contrast to the ash remaining after incomplete combustion - consist mostly of metal oxides . Ash is one of the components in the proximate analysis of biological materials, consisting mainly of salty, inorganic constituents. It includes metal salts which are important for processes requiring ions such as Na (Sodium), K (Potassium), and Ca (Calcium). It also includes trace minerals which are required for unique molecules, such as chlorophyll and hemoglobin . A crucible can be used to determine the percentage of ash contained in an otherwise burnable sample of material such as coal , wood , oil , rubber or plastics. The ISO mandates ash content determination for most foodstuffs. ...more...

Code page


In computing, a code page is a table of values that describes the character set used for encoding a particular set of characters, usually combined with a number of control characters. The term "code page" originated from IBM's EBCDIC-based mainframe systems, but Microsoft, SAP, and Oracle Corporation are among the few vendors which use this term. The majority of vendors identify their own character sets by a name. In the case when there is a plethora of character sets (like in IBM), identifying character sets through a number is a convenient way to distinguish them. Originally, the code page numbers referred to the page numbers in the IBM standard character set manual, a condition which has not held for a long time. Vendors that use a code page system allocate their own code page number to a character encoding, even if it is better known by another name; for example, UTF-8 has been assigned page numbers 1208 at IBM, 65001 at Microsoft, and 4110 at SAP. Hewlett-Packard uses a similar concept in its HP-UX ope ...more...

Exposure value


In photography, exposure value (EV) is a number that represents a combination of a camera's shutter speed and f-number, such that all combinations that yield the same exposure have the same EV (for any fixed scene luminance). Exposure value is also used to indicate an interval on the photographic exposure scale, with a difference of 1 EV corresponding to a standard power-of-2 exposure step, commonly referred to as a stop. The EV concept was developed by the German shutter manufacturer Friedrich Deckel in the 1950s (Gebele 1958; Ray 2000, 318). Its intent was to simplify choosing among equivalent camera exposure settings by replacing combinations of shutter speed and f-number (e.g., 1/125 s at f/16) with a single number (e.g., 15). On some lenses with leaf shutters, the process was further simplified by allowing the shutter and aperture controls to be linked such that when one was changed, the other was automatically adjusted to maintain the same exposure. This was especially helpful to beginners with limited ...more...

QR code


QR code for the URL of the English Wikipedia Mobile main page QR code (abbreviated from Quick Response Code) is the trademark for a type of matrix barcode (or two-dimensional barcode) first designed for the automotive industry in Japan. A barcode is a machine-readable optical label that contains information about the item to which it is attached. A QR code uses four standardized encoding modes (numeric, alphanumeric, byte/binary, and kanji) to efficiently store data; extensions may also be used. The QR code system became popular outside the automotive industry due to its fast readability and greater storage capacity compared to standard UPC barcodes. Applications include product tracking, item identification, time tracking, document management, and general marketing. A QR code consists of black squares arranged in a square grid on a white background, which can be read by an imaging device such as a camera, and processed using Reed–Solomon error correction until the image can be appropriately interpreted. ...more...

Hazard symbol


Skull and crossbones, a common symbol for poison and other sources of lethal danger (GHS hazard pictograms). Hazard symbols or warning symbols are recognisable symbols designed to warn about hazardous or dangerous materials, locations, or objects, including electric currents, poisons, and radioactivity. The use of hazard symbols is often regulated by law and directed by standards organisations. Hazard symbols may appear with different colors, backgrounds, borders and supplemental information in order to specify the type of hazard and the level of threat (for example, toxicity classes). Warning symbols are used in many places in lieu of or addition to written warnings as they are quickly recognized (faster than reading a written warning) and more commonly understood (the same symbol can be recognized as having the same meaning to speakers of different languages). List of common symbols Type of hazard Unicode glyph Unicode Image Generic caution ⚠ U+26A0 Poison ☠ U+2620 Ionizing radiation ☢ U+2622 Radiat ...more...

Preferred metric sizes


Preferred metric sizes are a set of international standards and de facto standards that are designed to make using the metric system easier and simpler, especially in engineering and construction practices. One of the methods used to arrive at these preferred sizes is the use of preferred numbers and convenient numbers such as the Renard series, the 1-2-5 series to limit the number of different sizes of components needed. One of the largest benefits of such limits is an ensuing multiplicative or exponential reduction in the number of parts, tools and other items needed to support the installation and maintenance of the items built using these techniques. This occurs because eliminating one diameter fastener will typically allow the elimination of a large number of variations on that diameter (multiple thread pitches, multiple lengths, multiple tip types, multiple head types, multiple drive types, and the tools needed for installing each, including multiple drill bits (one for each different thread pitch, mat ...more...



MPEG-1 is a standard for lossy compression of video and audio . It is designed to compress VHS -quality raw digital video and CD audio down to 1.5 Mbit/s (26:1 and 6:1 compression ratios respectively) without excessive quality loss, making video CDs , digital cable / satellite TV and digital audio broadcasting (DAB) possible. Today, MPEG-1 has become the most widely compatible lossy audio/video format in the world, and is used in a large number of products and technologies. Perhaps the best-known part of the MPEG-1 standard is the MP3 audio format it introduced. The MPEG-1 standard is published as ISO / IEC 11172 – Information technology—Coding of moving pictures and associated audio for digital storage media at up to about 1.5 Mbit/s. The standard consists of the following five Parts: Systems (storage and synchronization of video, audio, and other data together) Video (compressed video content) Audio (compressed audio content) Conformance testing (testing the correctness of implementations of the standard) ...more...

Orders of magnitude (numbers)


The logarithmic scale can compactly represent the relationship among variously sized numbers. This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language. Smaller than 10−100 (one googolth) Mathematics – Numbers: The number zero is a natural, even number which quantifies a count or an amount of null size. Mathematics – Writing: Approximately 10 is a rough first estimate of the probability that a monkey, placed in front of a typewriter, will perfectly type out William Shakespeare's play Hamlet on its first try. However, taking punctuation, capitalization, and spacing into account, the actual probability is far lower: around 10 . Computing: The number 1×10 is equal to the smallest positive non-zero value that ca ...more...

List of countries and dependencies by population


A map of world population in 2014 World population percentage by country This is a list of countries and dependent territories by population . It includes sovereign states , inhabited dependent territories and, in some cases, constituent countries of sovereign states, with inclusion within the list being primarily based on the ISO standard ISO 3166-1 . For instance, the United Kingdom is considered as a single entity while the constituent countries of the Kingdom of the Netherlands are considered separately. In addition, this list includes certain states with limited recognition not found in ISO 3166-1. The population figures do not reflect the practice of countries that report significantly different populations of citizens domestically and overall. Some countries, notably Thailand , do not report total population, exclusively counting citizens; for total populations an international agency must issue an estimate. Also given in percent is each country's population compared with the population of the world , ...more...

Character encoding


In computing character encoding is used to represent a repertoire of characters by some kind of encoding system. Depending on the abstraction level and context, corresponding code points and the resulting code space may be regarded as bit patterns, octets, natural numbers, electrical pulses, etc. A character encoding is used in computation, data storage, and transmission of textual data. "Character set", "character map", "codeset" and "code page" are related, but not identical, terms. Early character codes associated with the optical or electrical telegraph could only represent a subset of the characters used in written languages, sometimes restricted to upper case letters, numerals and some punctuation only. The low cost of digital representation of data in modern computer systems allows more elaborate character codes (such as Unicode) which represent most of the characters used in many written languages. Character encoding using internationally accepted standards permits worldwide interchange of text in el ...more...



Hypertext Markup Language (HTML) is the standard markup language for creating web pages and web applications. With Cascading Style Sheets (CSS) and JavaScript, it forms a triad of cornerstone technologies for the World Wide Web. Web browsers receive HTML documents from a web server or from local storage and render them into multimedia web pages. HTML describes the structure of a web page semantically and originally included cues for the appearance of the document. HTML elements are the building blocks of HTML pages. With HTML constructs, images and other objects, such as interactive forms, may be embedded into the rendered page. It provides a means to create structured documents by denoting structural semantics for text such as headings, paragraphs, lists, links, quotes and other items. HTML elements are delineated by tags, written using angle brackets. Tags such as and introduce content into the page directly. Others such as ... surround and provide information about document text and may include other t ...more...

Machine-readable passport


A machine-readable passport (MRP) is a machine-readable travel document (MRTD) with the data on the identity page encoded in optical character recognition format. Many countries began to issue machine-readable travel documents in the 1980s. Most travel passports worldwide are MRPs. They are standardized by the ICAO Document 9303 (endorsed by the International Organization for Standardization and the International Electrotechnical Commission as ISO/IEC 7501-1) and have a special machine-readable zone (MRZ), which is usually at the bottom of the identity page at the beginning of a passport. The ICAO Document 9303 describes three types of documents. Usually passport booklets are issued in "Type 3" format, while identity cards and passport cards typically use the "Type 1" format. The machine-readable zone of a Type 3 travel document spans two lines, and each line is 44 characters long. The following information must be provided in the zone: name, passport number, nationality, date of birth, sex, and passport exp ...more...

Clothing sizes


In clothing, clothing size refers to the label sizes used for garments sold off-the-shelf. There are a large number of standard sizing systems around the world for various garments, such as dresses, tops, skirts, and trousers. Made-to-order garments require measurements to be taken, but these do not need to be converted into national standard form. History of standard clothing sizes Before the invention of clothing sizes in the early 1800s, all clothing was made to fit individuals by either tailors or makers of clothing in their homes. Then garment makers noticed that the range of human body dimensions was relatively small. Therefore, sizes were invented to Horizontal torso measurements include the neck circumference, the shoulder width, the bustline measurements – over-bust circumference, the full bust circumference, the bust-point separation, and the under-bust (rib-cage) circumference – the natural waist circumference, the upper hip circumference and the lower hip circumference. Vertical torso measure ...more...

C standard library


The C standard library or libc is the standard library for the C programming language, as specified in the ANSI C standard. It was developed at the same time as the C library POSIX specification, which is a superset of it. Since ANSI C was adopted by the International Organization for Standardization, the C standard library is also called the ISO C library. The C standard library provides macros, type definitions and functions for tasks such as string handling, mathematical computations, input/output processing, memory management, and several other operating system services. Application programming interface Header files The application programming interface (API) of the C standard library is declared in a number of header files. Each header file contains one or more function declarations, data type definitions, and macros. After a long period of stability, three new header files (iso646.h, wchar.h, and wctype.h) were added with Normative Addendum 1 (NA1), an addition to the C Standard ratified in 1995 ...more...



Cover of the C99 standards document C99 (previously known as C9X ) is an informal name for ''' ISO/IEC 9899:1999 , a past version of the C programming language standard. It extends the previous version ( C90 ) with new features for the language and the standard library , and helps implementations make better use of available computer hardware, such as the IEEE 754-1985 arithmetic, and compiler technology. The C11 version of the C programming language standard, published in 2011, replaces C99. History After ANSI produced the official standard for the C programming language in 1989, which became an international standard in 1990, the C language specification remained relatively static for some time, while C++ continued to evolve, largely during its own standardization effort. Normative Amendment 1 created a new standard for C in 1995, but only to correct some details of the 1989 standard and to add more extensive support for international character sets. The standard underwent further revision in the late 1990 ...more...

H.262/MPEG-2 Part 2


H.262 or MPEG-2 Part 2 (formally known as ITU-T Recommendation H.262 and ISO/IEC 13818-2, also known as MPEG-2 Video) is a video coding format developed and maintained jointly by ITU-T Video Coding Experts Group (VCEG) and ISO/IEC Moving Picture Experts Group (MPEG). It is the second part of the ISO/IEC MPEG-2 standard. The ITU-T Recommendation H.262 and ISO/IEC 13818-2 documents are identical. The standard is available for a fee from the ITU-T and ISO. MPEG-2 Video is similar to MPEG-1, but also provides support for interlaced video (an encoding technique used in analog NTSC, PAL and SECAM television systems). MPEG-2 video is not optimized for low bit-rates (less than 1 Mbit/s), but outperforms MPEG-1 at 3 Mbit/s and above. All standards-conforming MPEG-2 Video decoders are fully capable of playing back MPEG-1 Video streams. History The ISO/IEC approval process was completed in November 1994. The first edition was approved in July 1995 and published by ITU-T and ISO/IEC in 1996. Didier LeGall of Bellcore ...more...

Grain size


Wentworth grain size chart from United States Geological Survey Open-File Report 2006-1195 Beach cobbles at Nash Point, South Wales. Grain size (or particle size) refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain. A single grain can be composed of several crystals. Granular material can range from very small colloidal particles, through clay, silt, sand, gravel, and cobbles, to boulders. Krumbein phi scale Size ranges define limits of classes that are given names in the Wentworth scale (or Udden–Wentworth scale) used in the United States. The Krumbein phi (φ) scale, a modification of the Wentworth scale created by W. C. Krumbein in 1937, is a logarithmic scale computed by the equation where D {\displaystyle D} is the diameter of the particle or grain in millimeters ...more...

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