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Expi (mathematics)
is a mathematical notation defined by , where is the cosine function, is the imaginary unit and is the sine function. The notation is less commonly used in mathematics than Euler's formula, which offers an even shorter notation for but cis(x) is widely used as a name for this function in software libraries. Overview The notation is a shorthand for the combination of functions on the right-hand side of Euler's formula: :e^ = \cos x + i\sin x, where . So, :\operatorname x = \cos x + i\sin x, i.e. "" is an acronym for "". The notation was first coined by William Rowan Hamilton in ''Elements of Quaternions'' (1866) and subsequently used by Irving Stringham in works such as ''Uniplanar Algebra'' (1893), or by James Harkness and Frank Morley in their ''Introduction to the Theory of Analytic Functions'' (1898). It connects trigonometric functions with exponential functions in the complex plane via Euler's formula. It is mostly used as a convenient shorthand not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous and accurate way. For example, Albert Einstein's equation E=mc^2 is the quantitative representation in mathematical notation of the mass–energy equivalence. Mathematical notation was first introduced by François Viète at the end of the 16th century, and largely expanded during the 17th and 18th century by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols The use of many symbols is the basis of mathematical notation. They play a similar role as words in natural languages. They may play different roles in mathematical notation similarly as verbs, adjective and nouns play different roles in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math Kernel Library
Intel oneAPI Math Kernel Library (Intel oneMKL; formerly Intel Math Kernel Library or Intel MKL) is a library of optimized math routines for science, engineering, and financial applications. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. The library supports Intel processors and is available for Windows, Linux and macOS operating systems. ''Intel oneAPI Math Kernel Library'' is not to be confused with ''oneAPI Math Kernel Library'' (oneMKL) Interfaces, a piece of open-source glue code that allows Intel MKL routines to be used from Data Parallel C++. History and licensing Intel launched the Math Kernel Library on May 9, 2003, and called it blas.lib. The project's development teams are located in Russia and the United States. The library was available in a standalone form, free of charge under the terms of Intel Simplified Software License which allow redistribution. Since April 2020, MKL has become part of oneAPI ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the 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. 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, and 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. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including (ε, δ)-definition of limit, codify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mnemonic
A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imagery as specific tools to encode information in a way that allows for efficient storage and retrieval. Mnemonics aid original information in becoming associated with something more accessible or meaningful—which, in turn, provides better retention of the information. Commonly encountered mnemonics are often used for lists and in auditory form, such as short poems, acronyms, initialisms, or memorable phrases, but mnemonics can also be used for other types of information and in visual or kinesthetic forms. Their use is based on the observation that the human mind more easily remembers spatial, personal, surprising, physical, sexual, humorous, or otherwise "relatable" information, rather than more abstract or impersonal forms of informa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HP-UX
HP-UX (from "Hewlett Packard Unix") is Hewlett Packard Enterprise's proprietary implementation of the Unix operating system, based on Unix System V (initially System III) and first released in 1984. Current versions support HPE Integrity Servers, based on Intel's Itanium architecture. Earlier versions of HP-UX supported the HP Integral PC and HP 9000 Series 200, 300, and 400 computer systems based on the Motorola 68000 series of processors, the HP 9000 Series 500 computers based on HP's proprietary FOCUS architecture, and later HP 9000 Series models based on HP's PA-RISC instruction set architecture. HP-UX was the first Unix to offer access control lists for file access permissions as an alternative to the standard Unix permissions system. HP-UX was also among the first Unix systems to include a built-in logical volume manager. HP has had a long partnership with Veritas Software, and uses VxFS as the primary file system. It is one of four commercial operating systems that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MacOS
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and laptop computers it is the second most widely used desktop OS, after Microsoft Windows and ahead of ChromeOS. macOS succeeded the classic Mac OS, a Mac operating system with nine releases from 1984 to 1999. During this time, Apple cofounder Steve Jobs had left Apple and started another company, NeXT, developing the NeXTSTEP platform that would later be acquired by Apple to form the basis of macOS. The first desktop version, Mac OS X 10.0, was released in March 2001, with its first update, 10.1, arriving later that year. All releases from Mac OS X 10.5 Leopard and after are UNIX 03 certified, with an exception for OS X 10.7 Lion. Apple's other operating systems (iOS, iPadOS, watchOS, tvOS, audioOS) are derivatives of macOS. A promi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linux
Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which includes the kernel and supporting system software and libraries, many of which are provided by the GNU Project. Many Linux distributions use the word "Linux" in their name, but the Free Software Foundation uses the name "GNU/Linux" to emphasize the importance of GNU software, causing some controversy. Popular Linux distributions include Debian, Fedora Linux, and Ubuntu, the latter of which itself consists of many different distributions and modifications, including Lubuntu and Xubuntu. Commercial distributions include Red Hat Enterprise Linux and SUSE Linux Enterprise. Desktop Linux distributions include a windowing system such as X11 or Wayland, and a desktop environment such as GNOME or KDE Plasma. Distributions intended for ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Windows
Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for servers, and Windows IoT for embedded systems. Defunct Windows families include Windows 9x, Windows Mobile, and Windows Phone. The first version of Windows was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs). Windows is the most popular desktop operating system in the world, with 75% market share , according to StatCounter. However, Windows is not the most used operating system when including both mobile and desktop OSes, due to Android's massive growth. , the most recent version of Windows is Windows 11 for consumer PCs and tablets, Windows 11 Enterprise for corporations, and Windows Server 2022 for servers. Genealogy By marketing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rust (programming Language)
Rust is a multi-paradigm, general-purpose programming language. Rust emphasizes performance, type safety, and concurrency. Rust enforces memory safety—that is, that all references point to valid memory—without requiring the use of a garbage collector or reference counting present in other memory-safe languages. To simultaneously enforce memory safety and prevent concurrent data races, Rust's "borrow checker" tracks the object lifetime of all references in a program during compilation. Rust is popular for systems programming but also offers high-level features including some functional programming constructs. Software developer Graydon Hoare created Rust as a personal project while working at Mozilla Research in 2006. Mozilla officially sponsored the project in 2009. Since the first stable release in May 2015, Rust has been adopted by companies including Amazon, Discord, Dropbox, Facebook ( Meta), Google (Alphabet), and Microsoft. Rust has been noted for its growth as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia (programming Language)
Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programming language; with multiple dispatch as its core programming paradigm. Julia supports concurrent, (composable) parallel and distributed computing (with or without using MPI or the built-in corresponding to "OpenMP-style" threads), and direct calling of C and Fortran libraries without glue code. Julia uses a just-in-time (JIT) compiler that is referred to as "just- ahead-of-time" (JAOT) in the Julia community, as Julia compiles all code (by default) to machine code before running it. Julia is garbage-collected, uses eager evaluation, and includes efficient libraries for floating-point calculations, linear algebra, random number generation, and regular expression matching. Many libraries are available, including some (e.g., for fast Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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