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Dimensionless Numbers
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL). The number one is recognized as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios in limits or derivatives often involve dimensionless quantities. In differential geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Organization For Standardization
The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Article 3 of the ISO Statutes. ISO was founded on 23 February 1947, and () it has published over 25,000 international standards covering almost all aspects of technology and manufacturing. It has over 800 technical committees (TCs) and subcommittees (SCs) to take care of standards development. The organization develops and publishes international standards in technical and nontechnical fields, including everything from manufactured products and technology to food safety, transport, IT, agriculture, and healthcare. More specialized topics like electrical and electronic engineering are instead handled by the International Electrotechnical Commission.Editors of Encyclopedia Britannica. 3 June 2021.Inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable. Infinitesimal calculus was formulated separately ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concentration Ratio
In economics, concentration ratios are used to quantify market concentration and are based on companies' market shares in a given industry. A concentration ratio (CR) is the sum of the percentage market shares of (a pre-specified number of) the largest firms in an industry. An ''n''-firm concentration ratio is a common measure of market structure and shows the combined market share of the ''n'' largest firms in the market. For example, if ''n'' = 5, ''CR''5 defines the combined market share of the five largest firms in an industry. Calculation The concentration ratio is calculated as follows: \text_n = C_1 + C_2 + \cdots + C_n = \sum\limits_^n C_i where C_i defines the market share of the ith largest firm in an industry as a percentage of total industry market share, and n defines the number of firms included in the concentration ratio calculation. The \text_4 and \text_8 concentration ratios are commonly used. Concentration ratios show the extent of largest firms' mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mole Fraction
In chemistry, the mole fraction or molar fraction, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, ''ni'' (expressed in unit of moles, symbol mol), and the total amount of all constituents in a mixture, ''n''tot (also expressed in moles): :x_i = \frac It is denoted ''xi'' (lowercase Roman letter '' x''), sometimes (lowercase Greek letter chi). (For mixtures of gases, the letter ''y'' is recommended.) It is a dimensionless quantity with dimension of \mathsf/\mathsf and dimensionless unit of moles per mole (mol/mol or molmol−1) or simply 1; metric prefixes may also be used (e.g., nmol/mol for 10−9). When expressed in percent, it is known as the mole percent or molar percentage (unit symbol %, sometimes "mol%", equivalent to cmol/mol for 10−2). The mole fraction is called amount fraction by the International Union of Pure and Applied Chemistry (IUPAC) and amount-of-substance fractio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of State
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Though there are many equations of state, none accurately predicts properties of substances under all conditions. The quest for a universal equation of state has spanned three centuries. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during chemical reaction, reactions with other chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Electrodynamics of Moving Bodies", the theory is presented as being based on just Postulates of special relativity, two postulates: # The laws of physics are Invariant (physics), invariant (identical) in all Inertial frame of reference, inertial frames of reference (that is, Frame of reference, frames of reference with no acceleration). This is known as the principle of relativity. # The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance. The first postulate was first formulated by Galileo Galilei (see ''Galilean invariance''). Background Special relativity builds upon important physics ide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Factor
The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentz ether theory, Lorentzian electrodynamics – named after the Netherlands, Dutch physicist Hendrik Lorentz. It is generally denoted (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as (Greek uppercase-gamma) rather than . Definition The Lorentz factor is defined as \gamma = \frac = \frac = \frac , where: * is the relative velocity between inertial reference frames, * is the speed of light in vacuum, * is the ratio of to , * is coordinate time, * is the proper time for an observer (measuring time intervals in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
