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Faddeeva Function
The Faddeeva function or Kramp function is a scaled complex complementary error function, :w(z):=e^\operatorname(-iz) = \operatorname(-iz) =e^\left(1+\frac\int_0^z e^\textt\right). It is related to the Fresnel integral, to Dawson's integral, and to the Voigt function. The function arises in various physical problems, typically relating to electromagnetic responses in complicated media. * problems involving small-amplitude waves propagating through Maxwellian plasmas, and in particular appears in the plasma's permittivity from which dispersion relations are derived, hence it is sometimes referred to as the plasma dispersion function (although this name is sometimes used instead for the rescaled function defined by ''Fried and Conte'', 1961). * the infrared permittivity functions of amorphous oxides have resonances (due to phonons) that are sometimes too complicated to fit using simple harmonic oscillators. The Brendel–Bormann oscillator model uses an infinite superposition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faddeeva
In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non- elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real. In statistics, for non-negative values of , the error function has the following interpretation: for a random variable that is normally distributed with mean 0 and standard deviation , is the probability that falls in the range . Two closely related functions are the complementary error function () defined as :\operatorname z = 1 - \operatorname z, and the imaginary error function () defined as :\operatorname z = -i\operatorname iz, where is the imaginary unit Name The name "error function" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for z=f(x, y, \ldots), the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: :f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language. As part of the GNU Project, it is free software under the terms of the GNU General Public License. History The project was conceived around 1988. At first it was intended to be a companion to a chemical reactor design course. Full development was started by John W. Eaton in 1992. The first alpha release dates back to 4 January 1993 and on 17 February 1994 version 1.0 was released. Version 7.1.0 was released on Apr 6, 2022. The program is named after Octave Levenspiel, a former professor of the principal author. Levenspiel was known for his ability to perform quick back-of-the-envelope calculations. Development history Developments In addition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plug-in (computing)
In computing, a plug-in (or plugin, add-in, addin, add-on, or addon) is a software component that adds a specific feature to an existing computer program. When a program supports plug-ins, it enables customization. A theme or skin is a preset package containing additional or changed graphical appearance details, achieved by the use of a graphical user interface (GUI) that can be applied to specific software and websites to suit the purpose, topic, or tastes of different users to customize the look and feel of a piece of computer software or an operating system front-end GUI (and window managers). Purpose and examples Applications may support plug-ins to: * enable third-party developers to extend an application * support easily adding new features * reduce the size of an application by not loading unused features * separate source code from an application because of incompatible software licenses. Types of applications and why they use plug-ins: * Digital audio workstation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT License
The MIT License is a permissive free software license originating at the Massachusetts Institute of Technology (MIT) in the late 1980s. As a permissive license, it puts only very limited restriction on reuse and has, therefore, high license compatibility. Unlike copyleft software licenses, the MIT License also permits reuse within proprietary software, provided that all copies of the software or its substantial portions include a copy of the terms of the MIT License and also a copyright notice. , the MIT License was the most popular software license found in one analysis, continuing from reports in 2015 that the MIT License was the most popular software license on GitHub. Notable projects that use the MIT License include the X Window System, Ruby on Rails, Nim, Node.js, Lua, and jQuery. Notable companies using the MIT License include Microsoft ( .NET), Google ( Angular), and Meta (React). License terms The MIT License has the identifier MIT in the SPDX License List. It is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free And Open Source
Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source code is openly shared so that people are encouraged to voluntarily improve the design of the software. This is in contrast to proprietary software, where the software is under restrictive copyright licensing and the source code is usually hidden from the users. FOSS maintains the software user's civil liberty rights (see the Four Essential Freedoms, below). Other benefits of using FOSS can include decreased software costs, increased security and stability (especially in regard to malware), protecting privacy, education, and giving users more control over their own hardware. Free and open-source operating systems such as Linux and descendants of BSD are widely utilized today, powering millions of servers, desktops, smartphones (e.g., A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free And Open-source Software
Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source code is openly shared so that people are encouraged to voluntarily improve the design of the software. This is in contrast to proprietary software, where the software is under restrictive copyright licensing and the source code is usually hidden from the users. FOSS maintains the software user's civil liberty rights (see the Four Essential Freedoms, below). Other benefits of using FOSS can include decreased software costs, increased security and stability (especially in regard to malware), protecting privacy, education, and giving users more control over their own hardware. Free and open-source operating systems such as Linux and descendants of BSD are widely utilized today, powering millions of servers, desktops, smartphones (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ACM Transactions On Mathematical Software
''ACM Transactions on Mathematical Software'' (''TOMS'') is a quarterly scientific journal that aims to disseminate the latest findings of note in the field of numeric, symbolic, algebraic, and geometric computing applications. It is one of the oldest scientific journals specifically dedicated to mathematical algorithms and their implementation in software, and has been published since March 1975 by the Association for Computing Machinery (ACM). The journal is described as follows on thTOMS Homepage of the ACM Digital Librarypage: The purpose of the journal was laid out by its founding editor, John Rice, in the inaugural issue. The decision to found the journal came out of the 1970 Mathematical Software Symposium at Purdue University, also organized by Rice, who then negotiated with both SIAM Thailand ( ), historically known as Siam () and officially the Kingdom of Thailand, is a country in Southeast Asia, located at the centre of the Mainland Southeast Asia, Indochi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter Gautschi
Walter Gautschi (born December 11, 1927) is a Swiss- American mathematician, known for his contributions to numerical analysis. He has authored over 200 papers in his area and published four books. Born in Basel, he has a Ph.D. in mathematics from the University of Basel on the thesis ''Analyse graphischer Integrationsmethoden'' advised by Alexander Ostrowski and Andreas Speiser (1953). Since then, he did postdoctoral work as a Janggen-Pöhn Research Fellow at the ''Istituto Nazionale per le Applicazioni del Calcolo'' in Rome (1954) and at the Harvard Computation Laboratory (1955). He had positions at the National Bureau of Standards (1956–59), the American University in Washington D.C., the Oak Ridge National Laboratory (1959–63) before joining Purdue University where he has worked from 1963 to 2000 and now being professor emeritus. He has been a Fulbright Scholar at the Technical University of Munich (1970) and held visiting appointments at the University of Wisconsin†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
