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Quantity Calculus
Quantity calculus is the formal method for describing the mathematical relations between ''abstract'' physical quantities. (Here the term ''calculus'' should be understood in its broader sense of "a system of computation", rather than in the sense of differential calculus and integral calculus.) Its roots can be traced to Fourier's concept of dimensional analysis (1822). The basic axiom of quantity calculus is Maxwell's description of a physical quantity as the product of a "numerical value" and a "reference quantity" (i.e. a "unit quantity" or a "unit of measurement"). De Boer summarized the multiplication, division, addition, association and commutation rules of quantity calculus and proposed that a full axiomatization has yet to be completed. Such axiomatization needs to begin from a definition of ''quantity'' in terms of ''physical dimension'' (see dimensional analysis) which is indeed a more fundamental concept than of ''unit'' or ''unit quantity'' or ''unit of measurement''. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Quantity
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For example, the physical quantity of mass can be quantified as '32.3 kg ', where '32.3' is the numerical value and 'kg' is the Unit. A physical quantity possesses at least two characteristics in common. # Numerical magnitude. # Units Symbols and nomenclature International recommendations for the use of symbols for quantities are set out in ISO/IEC 80000, the IUPAP red book and the IUPAC green book. For example, the recommended symbol for the physical quantity ''mass'' is ''m'', and the recommended symbol for the quantity ''electric charge'' is ''Q''. Subscripts and indices Subscripts are used for two reasons, to simply attach a name to the quantity or associate it with another quantity, or index a specific component (e.g., row or colum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (mathematics)
In mathematics, a variable (from Latin '' variabilis'', "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set. Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. In mathematical logic, a ''variable'' is either a symbol representing an unspecified term of the theory (a meta-variable), or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation. History In ancient works such as Euclid's ''Elements'', single letters refer to geometric points and shapes. In the 7th century, Brahmagupta used different colours to represent the u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantities, Units And Symbols In Physical Chemistry
''Quantities, Units and Symbols in Physical Chemistry'', also known as the ''Green Book'', is a compilation of terms and symbols widely used in the field of physical chemistry. It also includes a table of physical constants, tables listing the properties of elementary particles, chemical elements, and nuclides, and information about conversion factors that are commonly used in physical chemistry. The ''Green Book'' is published by the International Union of Pure and Applied Chemistry (IUPAC) and is based on published, citeable sources. Information in the ''Green Book'' is synthesized from recommendations made by IUPAC, the International Union of Pure and Applied Physics (IUPAP) and the International Organization for Standardization (ISO), including recommendations listed in the IUPAP Red Book ''Symbols, Units, Nomenclature and Fundamental Constants in Physics'' and in the ISO 31 standards. History, list of editions, and translations to non-English languages The third edition of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steradian
The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a ''length'' on the circumference, a solid angle in steradians, projected onto a sphere, gives an ''area'' on the surface. The name is derived from the Greek 'solid' + radian. The steradian, like the radian, is a dimensionless unit, the quotient of the area subtended and the square of its distance from the centre. Both the numerator and denominator of this ratio have dimension length squared (i.e. , dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr−1). The steradian was formerly an SI supplementary unit, but this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Derived Unit
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg⋅m−3), the SI derived unit of density. The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m". Special names The International System of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Base Unit
The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre (sometimes spelled meter) for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. The names and symbols of SI base units are written in lowercase, except the symbols of those named after a person, which are written with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measured Quantity
In a physical setting a measurement instrument may be gauged to measuring substances of a specific physical quantity. In such a context the specific physical quantity is called a measured quantity. The synonymous notion "observable" often is used in the context of quantum mechanics. Scientific model Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted ...s and ensuing mathematical models of a physical setting permit to calculate expected values of related non-measured physical quantities. See also * Physical property Physical quantities Measurement Metrology {{measurement-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Quantity
Abstract may refer to: * ''Abstract'' (album), 1962 album by Joe Harriott * Abstract of title a summary of the documents affecting title to parcel of land * Abstract (law), a summary of a legal document * Abstract (summary), in academic publishing * Abstract art, artistic works that do not attempt to represent reality or concrete subjects * '' Abstract: The Art of Design'', 2017 Netflix documentary series * Abstract music, music that is non-representational * Abstract object in philosophy * Abstract structure in mathematics * Abstract type in computer science * The property of an abstraction * Q-Tip (musician), also known as "The Abstract" * Abstract and concrete In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, hum ... See also * Abstraction (other) {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiomatization
In mathematics and logic, an axiomatic system is any Set (mathematics), set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A Theory (mathematical logic), theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication. A formal proof is a complete rendition of a mathematical proof within a formal system. Properties An axiomatic system is said to be ''Consistency, consistent'' if it lacks contradiction. That is, it is impossible to derive both a statement and its negation from the system's axioms. Consistency is a key requirement for most axiomatic systems, as the presence of contradiction would allow any statement to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metrologia
''Metrologia'' is a bimonthly journal dealing with the scientific aspects of metrology. It has been running since 1965 and has been published by the International Bureau of Weights and Measures since 1991. Since 2003 the journal has been published by IOP Publishing on behalf of the bureau. The journal covers the fundamentals of measurements, in particular those dealing with the seven base units of the International System of Units (metre, kilogram, second, ampere, kelvin, candela, mole) or proposals to replace them. The editors-in-chief are Sten Bergstrand (RISE Research Institutes of Sweden) and Janet Miles (International Bureau of Weights and Measures). Abstracting and indexing This journal is indexed by the following databases: *Science Citation Index Expanded *Scopus * Inspec *Chemical Abstracts Service *Compendex *GeoRef *MathSciNet *Astrophysics Data System *VINITI Abstracts Journal VINITI Database RAS is a database provided by the All-Russian Institute for Scientif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
