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Nondimensionalization
Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis. In some physical systems, the term ''scaling'' is used interchangeably with ''nondimensionalization'', in order to suggest that certain quantities are better measured relative to some appropriate unit. These units refer to quantities intrinsic to the system, rather than units such as SI units. Nondimensionalization is not the same as converting extensive quantities in an equation to intensive quantities, since the latter procedure results in variables that still carry units. Nondimensionalization can also recover characteristic properties of a system. For example, if a system has an intrinsic resonance frequency, length, or time constant, nondimensionalization can recover these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-life
Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: A Parable for the Nuclear Age'', a 1985 Australian documentary film Literature * Half Life (Jackson novel), ''Half Life'' (Jackson novel), a 2006 novel by Shelley Jackson * Half-Life (Krach novel), ''Half-Life'' (Krach novel), a 2004 novel by Aaron Krach * Halflife (Michalowski novel), ''Halflife'' (Michalowski novel), a 2004 novel by Mark Michalowski * ''Rozpad połowiczny'' (), a 1988 award-winning dystopia novel by Edmund Wnuk-Lipiński Music *Half Life (3 album), ''Half Life'' (3 album) (2001) *Halflife (EP), ''Halflife'' (EP), an EP by Lacuna Coil and the title track *''Half-Life E.P.'', an EP by Local H * "Half Life", a song by 10 Years from ''The Autumn Effect'' * "Half Life", a song by Come from ''Near-Life Experience'' * "Ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant Coefficients
In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written in the form a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) where and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable . Such an equation is an ordinary differential equation (ODE). A ''linear differential equation'' may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives. Types of solution A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients may be solved by quadrature, which means that the solutions may be expressed in terms of integrals. This is also true for a linear equation of order one, with non-constant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Units
In physics, natural unit systems are measurement systems for which selected physical constants have been set to 1 through nondimensionalization of physical units. For example, the speed of light may be set to 1, and it may then be omitted, equating mass and energy directly rather than using as a conversion factor in the typical mass–energy equivalence equation . A purely natural system of units has all of its dimensions collapsed, such that the physical constants completely define the system of units and the relevant physical laws contain no conversion constants. While natural unit systems simplify the form of each equation, it is still necessary to keep track of the non-collapsed dimensions of each quantity or expression in order to reinsert physical constants (such dimensions uniquely determine the full formula). Systems of natural units Summary table where: * is the fine-structure constant ( ≈ 0.007297) * ≈ * ≈ * A dash (—) indicates where the system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second. Special definitions of frequency are used in certain contexts, such as the angular frequency in rotational or cyclical properties, when the rate of angular progress is measured. Spatial frequency is defined for properties that vary or cccur repeatedly in geometry or space. The unit of measurement of frequency in the International System of Units (SI) is the hertz, having the symbol Hz. Definitions and units For cyclical phenomena such as oscillations, waves, or for examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pendulum
A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. Pendulums were widely used in early mechanical clocks for timekeeping. The regular motion of pendulums was used for timekeeping and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1656 became the world's standard timekeeper, used in homes and offices for 270 years, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measuring Instrument
Instrumentation is a collective term for measuring instruments, used for indicating, measuring, and recording physical quantities. It is also a field of study about the art and science about making measurement instruments, involving the related areas of metrology, automation, and control theory. The term has its origins in the art and science of scientific instrument-making. Instrumentation can refer to devices as simple as direct-reading thermometers, or as complex as multi- sensor components of industrial control systems. Instruments can be found in laboratories, refineries, factories and vehicles, as well as in everyday household use (e.g., smoke detectors and thermostats). Measurement parameters Instrumentation is used to measure many parameters (physical values), including: *Pressure, either differential or static * Flow *Temperature * Levels of liquids, etc. *Moisture or humidity *Density *Viscosity * ionising radiation * Frequency * Current *Voltage * Induct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalization (statistics)
In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment. In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Partial Differential Equation Topics
{{Short description, none This is a list of partial differential equation topics. General topics *Partial differential equation ** Nonlinear partial differential equation *** list of nonlinear partial differential equations * Boundary condition * Boundary value problem ** Dirichlet problem, Dirichlet boundary condition ** Neumann boundary condition ** Stefan problem ** Wiener–Hopf problem *Separation of variables * Green's function * Elliptic partial differential equation * Singular perturbation * Cauchy–Kovalevskaya theorem * H-principle * Atiyah–Singer index theorem * Bäcklund transform * Viscosity solution * Weak solution * Loewy decomposition of linear differential equations Specific partial differential equations * Broer–Kaup equations * Burgers' equation *Euler equations *Fokker–Planck equation *Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation *Heat equation *Laplace's equation **Laplace operator **Harmonic function ** Spherical harmonic ** Poiss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
