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https://en.wikipedia.org/wiki/Cooperative%20Linux
Cooperative Linux, abbreviated as coLinux, is software which allows Microsoft Windows and the Linux kernel to run simultaneously in parallel on the same machine. Cooperative Linux utilizes the concept of a Cooperative Virtual Machine (CVM). In contrast to traditional virtual machines, the CVM shares resources that already exist in the host OS. In traditional VM hosts, resources are virtualized for every (guest) OS. The CVM gives both OSs complete control of the host machine while the traditional VM sets every guest OS in an unprivileged state to access the real machine. Overview The term "cooperative" is used to describe two entities working in parallel. In effect Cooperative Linux turns the two different operating system kernels into two big coroutines. Each kernel has its own complete CPU context and address space, and each kernel decides when to give control back to its partner. However, while both kernels theoretically have full access to the real hardware, modern PC hardware is not designed to be controlled by two different operating systems at the same time. Therefore, the host kernel is left in control of the real hardware and the guest kernel contains special drivers that communicate with the host and provide various important devices to the guest OS. The host can be any OS kernel that exports basic primitives that allow the Cooperative Linux portable driver to run in CPL0 mode (ring 0) and allocate memory. History Dan Aloni originally started the development of Cooperative Linux as a research project based on similar work with User-mode Linux. He announced the development on 25 Jan 2004. In July 2004 he presented a paper at the Linux Symposium. The source was released under the GNU General Public License. Other developers have since contributed various patches and additions to the software. Comparisons Cooperative Linux is significantly different from full x86 virtualization, which generally works by running the guest OS in a less privileged mode t
https://en.wikipedia.org/wiki/Cell%20proliferation
Cell proliferation is the process by which a cell grows and divides to produce two daughter cells. Cell proliferation leads to an exponential increase in cell number and is therefore a rapid mechanism of tissue growth. Cell proliferation requires both cell growth and cell division to occur at the same time, such that the average size of cells remains constant in the population. Cell division can occur without cell growth, producing many progressively smaller cells (as in cleavage of the zygote), while cell growth can occur without cell division to produce a single larger cell (as in growth of neurons). Thus, cell proliferation is not synonymous with either cell growth or cell division, despite these terms sometimes being used interchangeably. Stem cells undergo cell proliferation to produce proliferating "transit amplifying" daughter cells that later differentiate to construct tissues during normal development and tissue growth, during tissue regeneration after damage, or in cancer. The total number of cells in a population is determined by the rate of cell proliferation minus the rate of cell death. Cell size depends on both cell growth and cell division, with a disproportionate increase in the rate of cell growth leading to production of larger cells and a disproportionate increase in the rate of cell division leading to production of many smaller cells. Cell proliferation typically involves balanced cell growth and cell division rates that maintain a roughly constant cell size in the exponentially proliferating population of cells. Cell proliferation occurs by combining cell growth with regular "G1-S-M-G2" cell cycles to produce many diploid cell progeny. In single-celled organisms, cell proliferation is largely responsive to the availability of nutrients in the environment (or laboratory growth medium). In multicellular organisms, the process of cell proliferation is tightly controlled by gene regulatory networks encoded in the genome and executed mainly
https://en.wikipedia.org/wiki/Russian%20copulation
In cryptography, Russian copulation is a method of rearranging plaintext before encryption so as to conceal stereotyped headers, salutations, introductions, endings, signatures, etc. This obscures clues for a cryptanalyst, and can be used to increase cryptanalytic difficulty in naive cryptographic schemes (however, most modern schemes contain more rigorous defences; see ciphertext indistinguishability). This is of course desirable for those sending messages and wishing them to remain confidential. Padding is another technique for obscuring such clues. The technique is to break the starting plaintext message into two parts and then to invert the order of the parts (similar to circular shift). This puts all endings and beginnings (presumably the location of most boilerplate phrases) "somewhere in the middle" of the version of the plaintext that is actually encrypted. For some messages, mostly those not in a human language (e.g., images or tabular data), the decrypted version of the plaintext will present problems when reversing the inversion. For messages expressed in ordinary language, there is sufficient redundancy that the inversion can almost always be reversed by a human immediately on inspection. The English phrase suggests that it originally came from an observation about Russian cryptographic practice. However, the technique is generally useful and neither was, nor is, limited to use by Russians. References Classical cryptography
https://en.wikipedia.org/wiki/README
In software development, a README file contains information about the other files in a directory or archive of computer software. A form of documentation, it is usually a simple plain text file called README, Read Me, READ.ME, README.TXT, README.md (to indicate the use of Markdown), or README.1ST. The file's name is generally written in uppercase. On Unix-like systems in particular, this causes it to stand outboth because lowercase filenames are more common, and because the ls command commonly sorts and displays files in ASCII-code order, in which uppercase filenames will appear first. Contents A README file typically encompasses: Configuration instructions Installation instructions Operating instructions A file manifest (a list of files in the directory or archive) Copyright and licensing information Contact information for the distributor or author A list of known bugs Troubleshooting instructions Credits and acknowledgments A changelog (usually aimed at fellow programmers) A news section (usually aimed at end users) History It is unclear when the convention of including a README file began, but examples dating to the mid-1970s have been found. Early Macintosh system software installed a Read Me on the Startup Disk, and README files commonly accompanied third-party software. In particular, there is a long history of free software and open-source software including a README file; the GNU Coding Standards encourage including one to provide "a general overview of the package". Since the advent of the web as a de facto standard platform for software distribution, many software packages have moved (or occasionally, copied) some of the above ancillary files and pieces of information to a website or wiki, sometimes including the README itself, or sometimes leaving behind only a brief README file without all of the information required by a new user of the software. The popular source code hosting website GitHub strongly encourages the creation of a RE
https://en.wikipedia.org/wiki/Compactly%20generated%20group
In mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. This should not be confused with the unrelated notion (widely used in algebraic topology) of a compactly generated space -- one whose topology is generated (in a suitable sense) by its compact subspaces. Definition A topological group G is said to be compactly generated if there exists a compact subset K of G such that So if K is symmetric, i.e. K = K −1, then Locally compact case This property is interesting in the case of locally compact topological groups, since locally compact compactly generated topological groups can be approximated by locally compact, separable metric factor groups of G. More precisely, for a sequence Un of open identity neighborhoods, there exists a normal subgroup N contained in the intersection of that sequence, such that G/N is locally compact metric separable (the Kakutani-Kodaira-Montgomery-Zippin theorem). References Topological groups
https://en.wikipedia.org/wiki/IBM%205100
The IBM 5100 Portable Computer is one of the first portable computers, introduced in September 1975, six years before the IBM Personal Computer, and eight before the first successful IBM compatible portable computer, the Compaq Portable. It was the evolution of a prototype called the SCAMP (Special Computer APL Machine Portable) that was developed at the IBM Palo Alto Scientific Center in 1973. Whether considered evolutionary from SCAMP or revolutionary, it still needed to be plugged into an electric socket. When the IBM PC was introduced in 1981, it was originally designated as the IBM 5150, putting it in the "5100" series, though its architecture was unrelated to the IBM 5100's. The 5100 was IBM's second transportable computer. Previously, a truck-based IBM 1401 configured in 1960 for military use was designated a portable computer, and nicknamed a DataMobile. The IBM 5100 was withdrawn in March 1982, by which time IBM had announced its larger cousins, the IBM 5110 (January 1978) and the IBM 5120 (February 1980). SCAMP, the prototype In 1973, Bill Lowe was instrumental in fostering an engineering prototype called SCAMP (Special Computer APL Machine Portable) created by Dr. Paul Friedl and a team at the IBM Los Gatos Scientific Center. SCAMP has been dubbed in PC Magazine as "the world's first personal computer". The IBM Los Gatos engineering prototype and a design model by IBM Industrial designer Tom Hardy, were utilized internally by Lowe in his early efforts to demonstrate the viability of creating a single-user computer. SCAMP emulated an IBM 1130 minicomputer in order to run APL\1130. In 1973, APL was generally available only on mainframe computers, and most desktop sized microcomputers such as the Wang 2200 or HP 9800 offered only BASIC. Because SCAMP was the first to emulate APL\1130 performance on a portable, single user computer, PC Magazine in 1983 designated SCAMP a "revolutionary concept" and "the world's first personal computer". Description
https://en.wikipedia.org/wiki/Iomega
Iomega (later LenovoEMC) produced external, portable, and networked data storage products. Established in the 1980s in Roy, Utah, United States, Iomega sold more than 410 million digital storage drives and disks, including the Zip drive floppy disk system. Formerly a public company, it was acquired by EMC Corporation in 2008, and then by Lenovo, which rebranded the product line as LenovoEMC, until discontinuation in 2018. History Iomega started in Roy, Utah, U.S. in 1980 and moved its headquarters to San Diego, California in 2001. For many years, it was a significant name in the data storage industry. Iomega's most famous product, the Zip drive, offered relatively large amounts of storage on portable, high-capacity floppy disks. The original Zip disk's 100MB capacity was a huge improvement over the decades-long standard of 1.44MB standard floppy disks. The Zip drive became a common internal and external peripheral for IBM-compatible and Macintosh personal computers. However, Zip drives sometimes failed after a short period, which failure was commonly referred to as the "click of death." This problem, combined with competition from CD-RW drives, caused Zip drive sales to decline dramatically, even after introducing larger 250MB and 750MB versions. Iomega eventually launched a CD-RW drive. Without the revenue from its proprietary storage disks and drives, Iomega's sales and profits declined considerably. Iomega's stock price, which was over $100 at its height in the 1990s, fell to around $2 in the mid-2000s. Trying to find a niche, Iomega released devices such as the HipZip MP3 player, the FotoShow Digital Image Center, and numerous external hard drives, optical drives, and NAS products. None of these products were successful. In 2012, reporter Vincent Verweij of Dutch broadcaster Katholieke Radio Omroep revealed that at least 16,000 Iomega NAS devices were publicly exposing their users' files on the Internet. This was due to Iomega having disabled password securi
https://en.wikipedia.org/wiki/Calcium%20sulfate
Calcium sulfate (or calcium sulphate) is the inorganic compound with the formula CaSO4 and related hydrates. In the form of γ-anhydrite (the anhydrous form), it is used as a desiccant. One particular hydrate is better known as plaster of Paris, and another occurs naturally as the mineral gypsum. It has many uses in industry. All forms are white solids that are poorly soluble in water. Calcium sulfate causes permanent hardness in water. Hydration states and crystallographic structures The compound exists in three levels of hydration corresponding to different crystallographic structures and to minerals: (anhydrite): anhydrous state. The structure is related to that of zirconium orthosilicate (zircon): is 8-coordinate, is tetrahedral, O is 3-coordinate. (gypsum and selenite (mineral)): dihydrate. (bassanite): hemihydrate, also known as plaster of Paris. Specific hemihydrates are sometimes distinguished: α-hemihydrate and β-hemihydrate. Uses The main use of calcium sulfate is to produce plaster of Paris and stucco. These applications exploit the fact that calcium sulfate which has been powdered and calcined forms a moldable paste upon hydration and hardens as crystalline calcium sulfate dihydrate. It is also convenient that calcium sulfate is poorly soluble in water and does not readily dissolve in contact with water after its solidification. Hydration and dehydration reactions With judicious heating, gypsum converts to the partially dehydrated mineral called bassanite or plaster of Paris. This material has the formula CaSO4·(nH2O), where 0.5 ≤ n ≤ 0.8. Temperatures between are required to drive off the water within its structure. The details of the temperature and time depend on ambient humidity. Temperatures as high as are used in industrial calcination, but at these temperatures γ-anhydrite begins to form. The heat energy delivered to the gypsum at this time (the heat of hydration) tends to go into driving off water (as water vapor) rather than in
https://en.wikipedia.org/wiki/Nuclear%20Energy%20Agency
The Nuclear Energy Agency (NEA) is an intergovernmental agency that is organized under the Organisation for Economic Co-operation and Development (OECD). Originally formed on 1 February 1958 with the name European Nuclear Energy Agency (ENEA)—the United States participated as an Associate Member—the name was changed on 20 April 1972 to its current name after Japan became a member. The mission of the NEA is to "assist its member countries in maintaining and further developing, through international co-operation, the scientific, technological and legal bases required for the safe, environmentally friendly and economical use of nuclear energy for peaceful purposes." History The creation of the European Nuclear Energy Agency (ENEA) was agreed by the OEEC Council of Ministers on December 20, 1957. Members NEA currently consists of 34 countries from Europe, North America and the Asia-Pacific region. In 2021, Bulgaria accessioned to NEA as its most recent member. In 2022, following Russia's invasion of Ukraine, Russia's membership was suspended. (suspended) Together they account for approximately 85% of the world’s installed nuclear capacity. Nuclear power accounts for almost a quarter of the electricity produced in NEA Member countries. The NEA works closely with the International Atomic Energy Agency (IAEA) in Vienna and with the European Commission in Brussels. Within the OECD, there is close co-ordination with the International Energy Agency and the Environment Directorate, as well as contacts with other directorates, as appropriate. Areas of work Nuclear safety and regulation Nuclear energy development Radioactive waste management Radiation protection and public health Nuclear law and liability Nuclear science Data bank Information and communication European Nuclear Energy Tribunal Structure Since 1 September 2014, the Director-General of the NEA is William D Magwood, IV, who replaced Luis E. Echávarri on this post. The NEA Secretariat serves s
https://en.wikipedia.org/wiki/Functional%20equation%20%28L-function%29
In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations. There is an elaborate theory of what these equations should be, much of which is still conjectural. Introduction A prototypical example, the Riemann zeta function has a functional equation relating its value at the complex number s with its value at 1 − s. In every case this relates to some value ζ(s) that is only defined by analytic continuation from the infinite series definition. That is, writingas is conventionalσ for the real part of s, the functional equation relates the cases σ > 1 and σ < 0, and also changes a case with 0 < σ < 1 in the critical strip to another such case, reflected in the line σ = ½. Therefore, use of the functional equation is basic, in order to study the zeta-function in the whole complex plane. The functional equation in question for the Riemann zeta function takes the simple form where Z(s) is ζ(s) multiplied by a gamma-factor, involving the gamma function. This is now read as an 'extra' factor in the Euler product for the zeta-function, corresponding to the infinite prime. Just the same shape of functional equation holds for the Dedekind zeta function of a number field K, with an appropriate gamma-factor that depends only on the embeddings of K (in algebraic terms, on the tensor product of K with the real field). There is a similar equation for the Dirichlet L-functions, but this time relating them in pairs: with χ a primitive Dirichlet character, χ* its complex conjugate, Λ the L-function multiplied by a gamma-factor, and ε a complex number of absolute value 1, of shape where G(χ) is a Gauss sum formed from χ. This equation has the same function on both sides if and only if χ is a real character, taking values in {0,1,−1}. Then ε must be 1 or −1, and the case of the value −1 would imply a zero of Λ(s) at s = ½. According to the theory (of Gauss, in effect)
https://en.wikipedia.org/wiki/Linux%20kernel%20mailing%20list
The Linux kernel mailing list (LKML) is the main electronic mailing list for Linux kernel development, where the majority of the announcements, discussions, debates, and flame wars over the kernel take place. Many other mailing lists exist to discuss the different subsystems and ports of the Linux kernel, but LKML is the principal communication channel among Linux kernel developers. It is a very high-volume list, usually receiving about 1,000 messages each day, most of which are kernel code patches. Linux utilizes a workflow governed by LKML, which is the "bazaar" where kernel development takes place. In his book Linux Kernel Development, Robert Love notes: The LKML functions as the central place where Linux developers around the world share patches, argue about implementation details, and discuss other issues. The official releases of the Linux kernel are indicated by an email to LKML. New features are discussed and most code is posted to the list before any action is taken. It is also the official place for reporting bugs in the Linux kernel, in case one cannot find the maintainer to whom the bug should be reported. Author Michelle Delio suggests that it was on LKML that Tux, the official Linux mascot, was suggested and refined, although the accuracy of her reporting in other stories has been disputed. Many companies associated with Linux kernel make announcements and proposals on LKML; for example, Novell, Intel, VMware, and IBM. The list subscribers include all the Linux kernel maintainers as well as other known figures in Linux circles, such as Jeff V. Merkey and Eric S. Raymond. A 2000 study found that 14,535 people, from at least 30 countries, sent at least one email to LKML between 1995 and 2000 to participate in the discussion of Linux development. Authors of books such as The Linux Kernel Development As A Model of Open Source Knowledge Creation and Motivation of Software Developers in Open Source Projects, and Recovering Device Drivers have made use of
https://en.wikipedia.org/wiki/Tschirnhaus%20transformation
In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683. Simply, it is a method for transforming a polynomial equation of degree with some nonzero intermediate coefficients, , such that some or all of the transformed intermediate coefficients, , are exactly zero. For example, finding a substitutionfor a cubic equation of degree ,such that substituting yields a new equationsuch that , , or both. More generally, it may be defined conveniently by means of field theory, as the transformation on minimal polynomials implied by a different choice of primitive element. This is the most general transformation of an irreducible polynomial that takes a root to some rational function applied to that root. Definition For a generic degree reducible monic polynomial equation of the form , where and are polynomials and does not vanish at ,the Tschirnhaus transformation is the function:Such that the new equation in , , has certain special properties, most commonly such that some coefficients, , are identically zero. Example: Tschirnhaus' method for cubic equations In Tschirnhaus' 1683 paper, he solved the equationusing the Tschirnhaus transformationSubstituting yields the transformed equationorSetting yields,and finally the Tschirnhaus transformationWhich may be substituted into to yield an equation of the form: Tschirnhaus went on to describe how a Tschirnhaus transformation of the form: may be used to eliminate two coefficients in a similar way. Generalization In detail, let be a field, and a polynomial over . If is irreducible, then the quotient ring of the polynomial ring by the principal ideal generated by , , is a field extension of . We have where is modulo . That is, any element of is a polynomial in , which is thus a primitive element of . There will be other choices of primitive element in : for any such choice of we wi
https://en.wikipedia.org/wiki/Xerox%20Daybreak
Xerox Daybreak (also Xerox 6085 PCS, Xerox 1186) is a workstation computer marketed by Xerox from 1985 to 1989. Overview Daybreak is the final release in the D* (pronounced D-Star) series of machines, some of which share the Wildflower CPU design by Butler Lampson. Machines in this series include, in order, Dolphin, Dorado, Dicentra, Dandelion, Dandetiger, Daybreak, the never-manufactured Daisy, and Dragonfly "a 4-processor VLSI CPU developed at PARC and intended for a high-end printing system". It was sold as the Xerox 6085 PCS (Professional Computer System) or ViewPoint 6085 PCS when sold as an office workstation running the ViewPoint system. ViewPoint is based on the Star software originally developed for the Xerox Star. The 6085 ran the ViewPoint (later GlobalView) GUI and was used extensively throughout Xerox until being replaced by Suns and PCs. Although years ahead of its time, it was never a commercial success. The proprietary closed architecture and Xerox's reluctance to release the Mesa development environment for general use stifled any third-party development. A fully configured 6085 came with an 80 MB hard disk, 3.7 MB of RAM, a 5¼-inch floppy disk drive, an Ethernet controller, and a PC emulator card containing an 80186 CPU. The basic system comes with 1.1 MB of RAM and a 10 MB hard disk. It was introduced in 1985 at . The Daybreak was also sold as a Xerox 1186 workstation when configured as a Lisp machine. References External links OLD-COMPUTERS.COM: Museum: Xerox 6085 Daybreak Computer workstations Products introduced in 1985
https://en.wikipedia.org/wiki/Cell%20envelope
The cell envelope comprises the inner cell membrane and the cell wall of a bacterium. In gram-negative bacteria an outer membrane is also included. This envelope is not present in the Mollicutes where the cell wall is absent. Bacterial cell envelopes fall into two major categories: a gram-positive type which stains purple during gram staining and a gram-negative type which stains pink during gram staining. Either type may have an enclosing capsule of polysaccharides for extra protection. As a group these are known as polysaccharide encapsulated bacteria. Function As in other organisms, the bacterial cell wall provides structural integrity to the cell. In prokaryotes, the primary function of the cell wall is to protect the cell from internal turgor pressure caused by the much higher concentrations of proteins and other molecules inside the cell compared to its external environment. The bacterial cell wall differs from that of all other organisms by the presence of peptidoglycan (poly-N-acetylglucosamine and N-acetylmuramic acid), which is located immediately outside of the cytoplasmic membrane. Peptidoglycan is responsible for the rigidity of the bacterial cell wall and for the determination of cell shape. It is relatively porous and is not considered to be a permeability barrier for small substrates. While all bacterial cell walls (with a few exceptions e.g. intracellular parasites such as Mycoplasma) contain peptidoglycan, not all cell walls have the same overall structures. This is notably expressed through the classification into gram positive and gram negative bacteria. Types of bacterial cell envelopes The gram-positive cell wall The gram-positive cell wall is characterized by the presence of a very thick peptidoglycan layer, which is responsible for the retention of the crystal violet dyes during the Gram staining procedure. It is found exclusively in organisms belonging to the Actinomycetota (or high %G+C gram-positive organisms) and the Bacillota (or l
https://en.wikipedia.org/wiki/GeForce%206%20series
The GeForce 6 series (codename NV40) is Nvidia's sixth generation of GeForce graphic processing units. Launched on April 14, 2004, the GeForce 6 family introduced PureVideo post-processing for video, SLI technology, and Shader Model 3.0 support (compliant with Microsoft DirectX 9.0c specification and OpenGL 2.0). GeForce 6 series features SLI The Scalable Link Interface (SLI) allows two GeForce 6 cards of the same type to be connected in tandem. The driver software balances the workload between the cards. SLI-capability is limited to select members of the GeForce 6 family; 6500 and above. SLI is only available for cards utilizing the PCI-Express bus. Nvidia PureVideo Technology Nvidia PureVideo technology is the combination of a dedicated video processing core and software which decodes H.264, VC-1, WMV, and MPEG-2 videos with reduced CPU utilization. Shader Model 3.0 Nvidia was the first to deliver Shader Model 3.0 (SM3) capability in its GPUs. SM3 extends SM2 in a number of ways: standard FP32 (32-bit floating-point) precision, dynamic branching, increased efficiency and longer shader lengths are the main additions. Shader Model 3.0 was quickly adopted by game developers because it was quite simple to convert existing shaders coded with SM 2.0/2.0A/2.0B to version 3.0, and it offered noticeable performance improvements across the entire GeForce 6 line. Caveats PureVideo functionality varies by model, with some models lacking WMV9 and/or H.264 acceleration. In addition, motherboards with some VIA and SIS chipsets and an AMD Athlon XP processor seemingly have compatibility problems with the GeForce 6600 and 6800 GPUs. Problems that have been known to arise are freezing, artifacts, reboots, and other issues that make gaming and use of 3D applications almost impossible. These problems seem to happen only on Direct3D based applications and do not affect OpenGL. Geforce 6 series comparison Here is how the released versions of the "GeForce 6" series family comp
https://en.wikipedia.org/wiki/Brad%20Templeton
Brad Templeton (born June 1960 near Toronto) is a Canadian software developer, internet entrepreneur, online community pioneer, publisher of news, comedy, science fiction and e-books, writer, photographer, civil rights advocate, futurist, public speaker, educator and self-driving car consultant. He graduated from the University of Waterloo. Notable projects ClariNet Most notably, Templeton was founder and CEO in 1989 of ClariNet Communications, the first company founded to engage in commercial activity over the early Internet. Electronic Frontier Foundation Templeton has been involved with the Electronic Frontier Foundation since 1997, including being chairman from 2000 to 2010. His involvement in online civil rights also includes being the subject of one of the first major internet bans and being a plaintiff before the Supreme Court of the United States in Reno v. ACLU Templeton's strongest efforts have been in the areas of free speech, computer security, privacy and intellectual property. rec.humor.funny and USENET Templeton played an active role over the life of Usenet, including the development of software tools for it. His most notable activities involved the creation and moderation of the newsgroup "rec.humor.funny", a moderated newsgroup devoted to comedy. USENET statistics reported by Brian Reid reported rec.humor.funny as the most widely read online publication starting in 1989, continuing in that position into the mid-1990s, with an estimated 440,000 readers. Software career Templeton began as the first employee of VisiCorp (then called Personal Software Inc.) the first PC applications software company, where he published several games and tools and assisted on Visicalc the first spreadsheet and personal computing productivity tool. He also developed the IBM-PC version of the VisiPlot companion before release of the PC. He was CEO and Founder of Looking Glass Software Ltd. in Ontario. His software specialty has been languages, tools and spr
https://en.wikipedia.org/wiki/Rotations%20and%20reflections%20in%20two%20dimensions
In Euclidean geometry, two-dimensional rotations and reflections are two kinds of Euclidean plane isometries which are related to one another. Process A rotation in the plane can be formed by composing a pair of reflections. First reflect a point to its image on the other side of line . Then reflect to its image on the other side of line . If lines and make an angle with one another, then points and will make an angle around point , the intersection of and . I.e., angle will measure . A pair of rotations about the same point will be equivalent to another rotation about point . On the other hand, the composition of a reflection and a rotation, or of a rotation and a reflection (composition is not commutative), will be equivalent to a reflection. Mathematical expression The statements above can be expressed more mathematically. Let a rotation about the origin by an angle be denoted as . Let a reflection about a line through the origin which makes an angle with the -axis be denoted as . Let these rotations and reflections operate on all points on the plane, and let these points be represented by position vectors. Then a rotation can be represented as a matrix, and likewise for a reflection, With these definitions of coordinate rotation and reflection, the following four identities hold: Proof These equations can be proved through straightforward matrix multiplication and application of trigonometric identities, specifically the sum and difference identities. The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: . Every rotation has an inverse . Every reflection is its own inverse. Composition has closure and is associative, since matrix multiplication is associative. Notice that both and have been represented with orthogonal matrices. These matrices all have a determinant whose ab
https://en.wikipedia.org/wiki/Class%20number%20problem
In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields (for negative integers d) having class number n. It is named after Carl Friedrich Gauss. It can also be stated in terms of discriminants. There are related questions for real quadratic fields and for the behavior as . The difficulty is in effective computation of bounds: for a given discriminant, it is easy to compute the class number, and there are several ineffective lower bounds on class number (meaning that they involve a constant that is not computed), but effective bounds (and explicit proofs of completeness of lists) are harder. Gauss's original conjectures The problems are posed in Gauss's Disquisitiones Arithmeticae of 1801 (Section V, Articles 303 and 304). Gauss discusses imaginary quadratic fields in Article 303, stating the first two conjectures, and discusses real quadratic fields in Article 304, stating the third conjecture. Gauss conjecture (class number tends to infinity) Gauss class number problem (low class number lists) For given low class number (such as 1, 2, and 3), Gauss gives lists of imaginary quadratic fields with the given class number and believes them to be complete. Infinitely many real quadratic fields with class number one Gauss conjectures that there are infinitely many real quadratic fields with class number one. The original Gauss class number problem for imaginary quadratic fields is significantly different and easier than the modern statement: he restricted to even discriminants, and allowed non-fundamental discriminants. Status Gauss conjecture solved, Heilbronn, 1934. Low class number lists class number 1: solved, Baker (1966), Stark (1967), Heegner (1952). Class number 2: solved, Baker (1971), Stark (1971) Class number 3: solved, Oesterlé (1985) Class numbers h up to 100: solved, Watkins 2004 Infinitely many real quadratic fields with class nu
https://en.wikipedia.org/wiki/Omega%20%28TeX%29
Omega is an extension of the TeX typesetting system that uses the Basic Multilingual Plane of Unicode. It was authored by John Plaice and Yannis Haralambous after TeX development was frozen in 1991, primarily to enhance TeX's multilingual typesetting abilities. It includes a new 16-bit font encoding for TeX, as well as fonts (omlgc and omah) covering a wide range of alphabets. At the 2004 TeX Users Group conference, Plaice announced his decision to split off a new project (not yet public), while Haralambous continued to work on Omega proper. LaTeX for Omega is invoked as lambda. Aleph and LuaTeX Although the project seemed very promising from the beginning, the development has been slow and the functionality rather unstable. A separate project was started with the goal of stabilizing the code and extending it with e-TeX functionality, known as Aleph, and led by Giuseppe Bilotta. The LaTeX for Aleph is known as Lamed. Aleph alone is not being developed any more, but most of its functionality has been integrated into LuaTeX, a new project initially funded by Colorado State University (through the Oriental TeX Project by Idris Samawi Hamid) and NTG. LuaTeX started in 2006 and released the first beta version in Summer 2007. It will be a successor of both Aleph and pdfTeX, using Lua as an integrated lightweight programming language. It is developed primarily by Taco Hoekwater. See also XeTeX and LuaTeX for recent Unicode capable TeX extensions. List of TeX extensions External links Omega home page TeX FAQ entry on Aleph and Omega Mailing list for Omega Mailing list for Aleph TeX Unicode
https://en.wikipedia.org/wiki/Fat%20tree
The fat tree network is a universal network for provably efficient communication. It was invented by Charles E. Leiserson of the Massachusetts Institute of Technology in 1985. k-ary n-trees, the type of fat-trees commonly used in most high-performance networks, were initially formalized in 1997. In a tree data structure, every branch has the same thickness (bandwidth), regardless of their place in the hierarchy—they are all "skinny" (skinny in this context means low-bandwidth). In a fat tree, branches nearer the top of the hierarchy are "fatter" (thicker) than branches further down the hierarchy. In a telecommunications network, the branches are data links; the varied thickness (bandwidth) of the data links allows for more efficient and technology-specific use. Mesh and hypercube topologies have communication requirements that follow a rigid algorithm, and cannot be tailored to specific packaging technologies. Applications in supercomputers Supercomputers that use a fat tree network include the two fastest as of late 2018, Summit and Sierra, as well as Tianhe-2, the Meiko Scientific CS-2, Yellowstone, the Earth Simulator, the Cray X2, the Connection Machine CM-5, and various Altix supercomputers. Mercury Computer Systems applied a variant of the fat tree topology—the hypertree network—to their multicomputers. In this architecture, 2 to 360 compute nodes are arranged in a circuit-switched fat tree network. Each node has local memory that can be mapped by any other node. Each node in this heterogeneous system could be an Intel i860, a PowerPC, or a group of three SHARC digital signal processors. The fat tree network was particularly well suited to fast Fourier transform computations, which customers used for such signal processing tasks as radar, sonar, and medical imaging. Related topologies In August 2008, a team of computer scientists at UCSD published a scalable design for network architecture that uses a topology inspired by the fat tree topology to realize
https://en.wikipedia.org/wiki/Arzel%C3%A0%E2%80%93Ascoli%20theorem
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is the basis of many proofs in mathematics, including that of the Peano existence theorem in the theory of ordinary differential equations, Montel's theorem in complex analysis, and the Peter–Weyl theorem in harmonic analysis and various results concerning compactness of integral operators. The notion of equicontinuity was introduced in the late 19th century by the Italian mathematicians Cesare Arzelà and Giulio Ascoli. A weak form of the theorem was proven by , who established the sufficient condition for compactness, and by , who established the necessary condition and gave the first clear presentation of the result. A further generalization of the theorem was proven by , to sets of real-valued continuous functions with domain a compact metric space . Modern formulations of the theorem allow for the domain to be compact Hausdorff and for the range to be an arbitrary metric space. More general formulations of the theorem exist that give necessary and sufficient conditions for a family of functions from a compactly generated Hausdorff space into a uniform space to be compact in the compact-open topology; see . Statement and first consequences By definition, a sequence of continuous functions on an interval is uniformly bounded if there is a number such that for every function belonging to the sequence, and every . (Here, must be independent of and .) The sequence is said to be uniformly equicontinuous if, for every , there exists a such that whenever for all functions in the sequence. (Here, may depend on , but not , or .) One version of the theorem can be stated as follows: Conside
https://en.wikipedia.org/wiki/Integrated%20Windows%20Authentication
Integrated Windows Authentication (IWA) is a term associated with Microsoft products that refers to the SPNEGO, Kerberos, and NTLMSSP authentication protocols with respect to SSPI functionality introduced with Microsoft Windows 2000 and included with later Windows NT-based operating systems. The term is used more commonly for the automatically authenticated connections between Microsoft Internet Information Services, Internet Explorer, and other Active Directory aware applications. IWA is also known by several names like HTTP Negotiate authentication, NT Authentication, NTLM Authentication, Domain authentication, Windows Integrated Authentication, Windows NT Challenge/Response authentication, or simply Windows Authentication. Overview Integrated Windows Authentication uses the security features of Windows clients and servers. Unlike Basic Authentication or Digest Authentication, initially, it does not prompt users for a user name and password. The current Windows user information on the client computer is supplied by the web browser through a cryptographic exchange involving hashing with the Web server. If the authentication exchange initially fails to identify the user, the web browser will prompt the user for a Windows user account user name and password. Integrated Windows Authentication itself is not a standard or an authentication protocol. When IWA is selected as an option of a program (e.g. within the Directory Security tab of the IIS site properties dialog) this implies that underlying security mechanisms should be used in a preferential order. If the Kerberos provider is functional and a Kerberos ticket can be obtained for the target, and any associated settings permit Kerberos authentication to occur (e.g. Intranet sites settings in Internet Explorer), the Kerberos 5 protocol will be attempted. Otherwise NTLMSSP authentication is attempted. Similarly, if Kerberos authentication is attempted, yet it fails, then NTLMSSP is attempted. IWA uses SPNEGO to a
https://en.wikipedia.org/wiki/Particle-in-cell
In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points. PIC methods were already in use as early as 1955, even before the first Fortran compilers were available. The method gained popularity for plasma simulation in the late 1950s and early 1960s by Buneman, Dawson, Hockney, Birdsall, Morse and others. In plasma physics applications, the method amounts to following the trajectories of charged particles in self-consistent electromagnetic (or electrostatic) fields computed on a fixed mesh. Technical aspects For many types of problems, the classical PIC method invented by Buneman, Dawson, Hockney, Birdsall, Morse and others is relatively intuitive and straightforward to implement. This probably accounts for much of its success, particularly for plasma simulation, for which the method typically includes the following procedures: Integration of the equations of motion. Interpolation of charge and current source terms to the field mesh. Computation of the fields on mesh points. Interpolation of the fields from the mesh to the particle locations. Models which include interactions of particles only through the average fields are called PM (particle-mesh). Those which include direct binary interactions are PP (particle-particle). Models with both types of interactions are called PP-PM or P3M. Since the early days, it has been recognized that the PIC method is susceptible to error from so-called discrete particle noise. This error is statistical in nature, and today it remains less-well understood than for traditional fixed-grid methods, such as Eulerian or semi-Lagrangian schemes. Modern geometric PIC algorithms are based on a very
https://en.wikipedia.org/wiki/Xanthan%20gum
Xanthan gum () is a polysaccharide with many industrial uses, including as a common food additive. It is an effective thickening agent, emulsifier, and stabilizer that prevents ingredients from separating. It can be produced from simple sugars by fermentation and derives its name from the species of bacteria used, Xanthomonas campestris. History Xanthan gum was discovered by Allene Rosalind Jeanes and her research team at the United States Department of Agriculture, and brought into commercial production by CP Kelco under the trade name Kelzan in the early 1960s. It was approved for use in foods in 1968 and is accepted as a safe food additive in the US, Canada, European countries, and many other countries, with E number E415, and CAS number 11138-66-2. Xanthan gum derives its name from the species of bacteria used during the fermentation process, Xanthomonas campestris. Uses Xanthan gum, 1%, can produce a significant increase in the viscosity of a liquid. In foods, xanthan gum is common in salad dressings and sauces. It helps to prevent oil separation by stabilizing the emulsion, although it is not an emulsifier. Xanthan gum also helps suspend solid particles, such as spices. Xanthan gum helps create the desired texture in many ice creams. Toothpaste often contains xanthan gum as a binder to keep the product uniform. Xanthan gum also helps thicken commercial egg substitutes made from egg whites, to replace the fat and emulsifiers found in yolks. It is also a preferred method of thickening liquids for those with swallowing disorders, since it does not change the color or flavor of foods or beverages at typical use levels. In gluten-free baking, xanthan gum is used to give the dough or batter the stickiness that would otherwise be achieved with gluten. In most foods, it is used at concentrations of 0.5% or less. Xanthan gum is used in a wide range of food products, such as sauces, dressings, meat and poultry products, bakery products, confectionery products, bev
https://en.wikipedia.org/wiki/Tree%20traversal
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well. Types Unlike linked lists, one-dimensional arrays and other linear data structures, which are canonically traversed in linear order, trees may be traversed in multiple ways. They may be traversed in depth-first or breadth-first order. There are three common ways to traverse them in depth-first order: in-order, pre-order and post-order. Beyond these basic traversals, various more complex or hybrid schemes are possible, such as depth-limited searches like iterative deepening depth-first search. The latter, as well as breadth-first search, can also be used to traverse infinite trees, see below. Data structures for tree traversal Traversing a tree involves iterating over all nodes in some manner. Because from a given node there is more than one possible next node (it is not a linear data structure), then, assuming sequential computation (not parallel), some nodes must be deferred—stored in some way for later visiting. This is often done via a stack (LIFO) or queue (FIFO). As a tree is a self-referential (recursively defined) data structure, traversal can be defined by recursion or, more subtly, corecursion, in a natural and clear fashion; in these cases the deferred nodes are stored implicitly in the call stack. Depth-first search is easily implemented via a stack, including recursively (via the call stack), while breadth-first search is easily implemented via a queue, including corecursively. Depth-first search In depth-first search (DFS), the search tree is deepened as much as possible before going to the next sibling. To traverse binary tre
https://en.wikipedia.org/wiki/Sex%20segregation
Sex segregation, sex separation, gender segregation or gender separation is the physical, legal, or cultural separation of people according to their biological sex at any age. Sex segregation can refer simply to the physical and spatial separation by sex without any connotation of illegal discrimination. In other circumstances, sex segregation can be controversial. Depending on the circumstances, it can be a violation of capabilities and human rights and can create economic inefficiencies; on the other hand, some supporters argue that it is central to certain religious laws and social and cultural histories and traditions. Definitions The term "sex" in "sex segregation" refers to the biological distinctions between men and women, used in contrast to "gender". The term "segregation" refers to separation of the sexes, which can be enforced by rules, laws, and policies, or be a de facto outcome in which people are separated by sex. Even as a de facto outcome, sex segregation taken as a whole can be caused by societal pressures, historical practices, socialized preferences and “fundamental biological differences”. Sex segregation can refer to literal physical and spatial separation by sex. The term is also used for the exclusion of one sex from participation in an occupation, institution, or group. Sex segregation can be complete or partial, as when members of one sex predominate within, but do not exclusively constitute, a group or organization. In the United States some scholars use the term sex separation and not sex segregation. The term gender apartheid (or sexual apartheid) also has been applied to segregation of people by gender, implying that it is sexual discrimination. If sex segregation is a form of sex discrimination, its effects have important consequences for gender equality and equity. Types Sex segregation can occur in both public and private contexts, and be classified in many ways. Legal and gender studies scholar David S. Cohen offers one taxono
https://en.wikipedia.org/wiki/Multinomial%20theorem
In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from binomials to multinomials. Theorem For any positive integer and any non-negative integer , the multinomial formula describes how a sum with terms expands when raised to an arbitrary power : where is a multinomial coefficient. The sum is taken over all combinations of nonnegative integer indices through such that the sum of all is . That is, for each term in the expansion, the exponents of the must add up to . Also, as with the binomial theorem, quantities of the form that appear are taken to equal 1 (even when equals zero). In the case , this statement reduces to that of the binomial theorem. Example The third power of the trinomial is given by This can be computed by hand using the distributive property of multiplication over addition, but it can also be done (perhaps more easily) with the multinomial theorem. It is possible to "read off" the multinomial coefficients from the terms by using the multinomial coefficient formula. For example: has the coefficient has the coefficient Alternate expression The statement of the theorem can be written concisely using multiindices: where and Proof This proof of the multinomial theorem uses the binomial theorem and induction on . First, for , both sides equal since there is only one term in the sum. For the induction step, suppose the multinomial theorem holds for . Then by the induction hypothesis. Applying the binomial theorem to the last factor, which completes the induction. The last step follows because as can easily be seen by writing the three coefficients using factorials as follows: Multinomial coefficients The numbers appearing in the theorem are the multinomial coefficients. They can be expressed in numerous ways, including as a product of binomial coefficients or of factorials: Sum of all multino
https://en.wikipedia.org/wiki/Independent%20component%20analysis
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room. Introduction Independent component analysis attempts to decompose a multivariate signal into independent non-Gaussian signals. As an example, sound is usually a signal that is composed of the numerical addition, at each time t, of signals from several sources. The question then is whether it is possible to separate these contributing sources from the observed total signal. When the statistical independence assumption is correct, blind ICA separation of a mixed signal gives very good results. It is also used for signals that are not supposed to be generated by mixing for analysis purposes. A simple application of ICA is the "cocktail party problem", where the underlying speech signals are separated from a sample data consisting of people talking simultaneously in a room. Usually the problem is simplified by assuming no time delays or echoes. Note that a filtered and delayed signal is a copy of a dependent component, and thus the statistical independence assumption is not violated. Mixing weights for constructing the observed signals from the components can be placed in an matrix. An important thing to consider is that if sources are present, at least observations (e.g. microphones if the observed signal is audio) are needed to recover the original signals. When there are an equal number of observations and source signals, the mixing matrix is square (). Other cases of underdetermined () and overdetermined () have been investigated. The success of ICA separation of mixed signals relies on two assumptions an
https://en.wikipedia.org/wiki/DIBOL
DIBOL or Digital's Business Oriented Language is a general-purpose, procedural, imperative programming language that was designed for use in Management Information Systems (MIS) software development. It was developed from 1970 to 1993. DIBOL has a syntax similar to FORTRAN and BASIC, along with BCD arithmetic. It shares the COBOL program structure of separate data and procedure divisions. Unlike Fortran's numeric labels (for GOTO), DIBOL's were alphanumeric; the language supported a counterpart to computed goto. History DIBOL was originally marketed by Digital Equipment Corporation (DEC) in 1970. The original version, DIBOL-8, was produced for PDP-8 systems running COS-300. The PDP-8-like DECmate II, supports the COS-310 Commercial Operating System, featuring DIBOL. DIBOL-11 was developed for the PDP-11 running COS-350 operating system. It also ran on RSX-11, RT-11, and from 1978 on RSTS/E. DIBOL-32 runs on VMS systems, although it can also be used on other systems through emulators. ANSI Standards were released in 1983, 1988 and 1992 (ANSI X3.165-1992). The 1992 standard was revised in 2002. DIBOL compilers were developed by several other companies, including DBL from DISC (later Synergex), Softbol from Omtool, and Unibol from Software Ireland, Ltd. Development of DIBOL effectively ceased after 1993, when an agreement between DEC and DISC replaced DIBOL with DBL on OpenVMS, Digital UNIX, and SCO Unix. See also Timeline of programming languages References Reading Procedural programming languages OpenVMS software Programming languages created in 1970 Programming languages Digital Equipment Corporation
https://en.wikipedia.org/wiki/Pathophysiology
Pathophysiology (or physiopathology) is a branch of study, at the intersection of pathology and physiology, concerning disordered physiological processes that cause, result from, or are otherwise associated with a disease or injury. Pathology is the medical discipline that describes conditions typically observed during a disease state, whereas physiology is the biological discipline that describes processes or mechanisms operating within an organism. Pathology describes the abnormal or undesired condition, whereas pathophysiology seeks to explain the functional changes that are occurring within an individual due to a disease or pathologic state. Etymology The term pathophysiology comes from the Ancient Greek πάθος (pathos) and φυσιολογία (phisiologia). History Nineteenth century Reductionism In Germany in the 1830s, Johannes Müller led the establishment of physiology research autonomous from medical research. In 1843, the Berlin Physical Society was founded in part to purge biology and medicine of vitalism, and in 1847 Hermann von Helmholtz, who joined the Society in 1845, published the paper "On the conservation of energy", highly influential to reduce physiology's research foundation to physical sciences. In the late 1850s, German anatomical pathologist Rudolf Virchow, a former student of Müller, directed focus to the cell, establishing cytology as the focus of physiological research, while Julius Cohnheim pioneered experimental pathology in medical schools' scientific laboratories. Germ theory By 1863, motivated by Louis Pasteur's report on fermentation to butyric acid, fellow Frenchman Casimir Davaine identified a microorganism as the crucial causal agent of the cattle disease anthrax, but its routinely vanishing from blood left other scientists inferring it a mere byproduct of putrefaction. In 1876, upon Ferdinand Cohn's report of a tiny spore stage of a bacterial species, the fellow German Robert Koch isolated Davaine's bacterides in pure culture —a
https://en.wikipedia.org/wiki/Cell%20site
A cell site, cell phone tower, cell base tower, or cellular base station is a cellular-enabled mobile device site where antennas and electronic communications equipment are placed (typically on a radio mast, tower, or other raised structure) to create a cell, or adjacent cells, in a cellular network. The raised structure typically supports antenna and one or more sets of transmitter/receivers transceivers, digital signal processors, control electronics, a GPS receiver for timing (for CDMA2000/IS-95 or GSM systems), primary and backup electrical power sources, and sheltering. Multiple cellular providers often save money by mounting their antennas on a common shared mast; since separate systems use different frequencies, antennas can be located close together without interfering with each other. Some provider companies operate multiple cellular networks and similarly use colocated base stations for two or more cellular networks, (CDMA2000 or GSM, for example). Cell sites are sometimes required to be inconspicuous; they can be blended with the surrounding area or mounted on buildings or advertising towers. Preserved treescapes can often hide cell towers inside an artificial or preserved tree. These installations are generally referred to as concealed cell sites or stealth cell sites. Overview A cellular network is a network of handheld mobile phones (cell phones) in which each phone communicates with the telephone network by radio waves through a local antenna at a cellular base station (cell site). The coverage area in which service is provided is divided into a mosaic of small geographical areas called "cells", each served by a separate low power multichannel transceiver and antenna at a base station. All the cell phones within a cell communicate with the system through that cell's antenna, on separate frequency channels assigned by the base station from a common pool of frequencies used by the system. The purpose of cellular organization is to conserve radi
https://en.wikipedia.org/wiki/Algebraic%20K-theory
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups of the integers. K-theory was discovered in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only K0, the zeroth K-group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Intersection theory is still a motivating force in the development of (higher) algebraic K-theory through its links with motivic cohomology and specifically Chow groups. The subject also includes classical number-theoretic topics like quadratic reciprocity and embeddings of number fields into the real numbers and complex numbers, as well as more modern concerns like the construction of higher regulators and special values of L-functions. The lower K-groups were discovered first, in the sense that adequate descriptions of these groups in terms of other algebraic structures were found. For example, if F is a field, then is isomorphic to the integers Z and is closely related to the notion of vector space dimension. For a commutative ring R, the group is related to the Picard group of R, and when R is the ring of integers in a number field, this generalizes the classical construction of the class group. The group K1(R) is closely related to the group of units , and if R is a field, it is exactly the group of units. For a number field F, the group K2(F) is related to class field theory, the Hilbert symbol, and the solvability of quadratic equations over completions. In contrast, finding the correct definition of the hi
https://en.wikipedia.org/wiki/Frank%E2%80%93Starling%20law
The Frank–Starling law of the heart (also known as Starling's law and the Frank–Starling mechanism) represents the relationship between stroke volume and end diastolic volume. The law states that the stroke volume of the heart increases in response to an increase in the volume of blood in the ventricles, before contraction (the end diastolic volume), when all other factors remain constant. As a larger volume of blood flows into the ventricle, the blood stretches cardiac muscle, leading to an increase in the force of contraction. The Frank-Starling mechanism allows the cardiac output to be synchronized with the venous return, arterial blood supply and humoral length, without depending upon external regulation to make alterations. The physiological importance of the mechanism lies mainly in maintaining left and right ventricular output equality. Physiology The Frank-Starling mechanism occurs as the result of the length-tension relationship observed in striated muscle, including for example skeletal muscles, arthropod muscle and cardiac (heart) muscle. As striated muscle is stretched, active tension is created by altering the overlap of thick and thin filaments. The greatest isometric active tension is developed when a muscle is at its optimal length. In most relaxed skeletal muscle fibers, passive elastic properties maintain the muscle fibers length near optimal, as determined usually by the fixed distance between the attachment points of tendons to the bones (or the exoskeleton of arthropods) at either end of the muscle. In contrast, the relaxed sarcomere length of cardiac muscle cells, in a resting ventricle, is lower than the optimal length for contraction. There is no bone to fix sarcomere length in the heart (of any animal) so sarcomere length is very variable and depends directly upon blood filling and thereby expanding the heart chambers. In the human heart, maximal force is generated with an initial sarcomere length of 2.2 micrometers, a length which is rare
https://en.wikipedia.org/wiki/Common%20Scrambling%20Algorithm
The Common Scrambling Algorithm (CSA) is the encryption algorithm used in the DVB digital television broadcasting for encrypting video streams. CSA was specified by ETSI and adopted by the DVB consortium in May 1994. It is being succeeded by CSA3, based on a combination of 128-bit AES and a confidential block cipher, XRC. However, CSA3 is not yet in any significant use, so CSA continues to be the dominant cipher for protecting DVB broadcasts. History CSA was largely kept secret until 2002. The patent papers gave some hints, but important details, like the layout of the so-called S-boxes, remained secret. Without these, free implementations of the algorithm was not possible. Initially, CSA was to remain implemented in hardware only, making it difficult to reverse engineer existing implementations. In 2002 FreeDec was released, implementing CSA in software. Though released as binary only, disassembly revealed the missing details and allowed reimplementation of the algorithm in higher-level programming languages. With CSA now publicly known in its entirety, cryptanalysts started looking for weaknesses. Description of the cipher The CSA algorithm is composed of two distinct ciphers: a block cipher and a stream cipher. When used in encryption mode the data are first encrypted using the 64-bit block cipher in CBC mode, starting from packet end. The stream cipher is then applied from packet start. Block cipher The block cipher process 64-bit blocks in 56 rounds. It uses 8 bits from an expanded key on each round. Stream cipher The first 32 round of the stream cipher are used for initialization and do not generate any output. The first 64 bits of data are used as initialization vector during this phase and are left unchanged. The stream cipher then generates 2 bits of pseudo-random stream on each round which are xored starting at bit 64 of the packet. Weaknesses Were CSA to be broken, encrypted DVB transmissions would be decipherable, which would compromise pai
https://en.wikipedia.org/wiki/Integrated%20circuit%20layout
In integrated circuit design, integrated circuit (IC) layout, also known IC mask layout or mask design, is the representation of an integrated circuit in terms of planar geometric shapes which correspond to the patterns of metal, oxide, or semiconductor layers that make up the components of the integrated circuit. Originally the overall process was called tapeout, as historically early ICs used graphical black crepe tape on mylar media for photo imaging (erroneously believed to reference magnetic data—the photo process greatly predated magnetic media). When using a standard process—where the interaction of the many chemical, thermal, and photographic variables is known and carefully controlled—the behaviour of the final integrated circuit depends largely on the positions and interconnections of the geometric shapes. Using a computer-aided layout tool, the layout engineer—or layout technician—places and connects all of the components that make up the chip such that they meet certain criteria—typically: performance, size, density, and manufacturability. This practice is often subdivided between two primary layout disciplines: analog and digital. The generated layout must pass a series of checks in a process known as physical verification. The most common checks in this verification process are Design rule checking (DRC), Layout versus schematic (LVS), parasitic extraction, antenna rule checking, and electrical rule checking (ERC). When all verification is complete, layout post processing is applied where the data is also translated into an industry-standard format, typically GDSII, and sent to a semiconductor foundry. The milestone completion of the layout process of sending this data to the foundry is now colloquially called "tapeout". The foundry converts the data into mask data and uses it to generate the photomasks used in a photolithographic process of semiconductor device fabrication. In the earlier, simpler, days of IC design, layout was done by
https://en.wikipedia.org/wiki/Fisher%20information
In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covariance of the posterior distribution, provided that the prior is sufficiently smooth (a result known as Bernstein–von Mises theorem, which was anticipated by Laplace for exponential families). The same result is used when approximating the posterior with Laplace's approximation, where the Fisher information appears as the covariance of the fitted Gaussian. Statistical systems of a scientific nature (physical, biological, etc.) whose likelihood functions obey shift invariance have been shown to obey maximum Fisher information. The level of the maximum depends upon the nature of the system constraints. Definition The Fisher information is a way of measuring the amount of information that an observable random variable carries about an unknown parameter upon which the probability of depends. Let be the probability density function (or probability mass function) for conditioned on the value of . It describes the probability that we observe a given outcome of , given a known value of . If is sharply peaked with respect to changes in , it is easy
https://en.wikipedia.org/wiki/Shotgun%20wedding
A shotgun wedding is a wedding arranged in response to pregnancy resulting from premarital sex. The phrase is a primarily U.S. colloquialism, termed as such based on a stereotypical scenario in which the father of the pregnant bride-to-be threatens the reluctant groom with a shotgun in order to ensure that he follows through with the wedding. Rationale One purpose of such a wedding can be to get recourse from the man for the act of impregnation; another reason is trying to ensure that the child is raised by both parents. In some cases, as in early U.S. and in the Middle East, a major objective was restoring the social honor of the mother. The practice is a loophole method of preventing the birth of illegitimate children, or if the marriage occurs early enough in the gestation period, to conceal the fact that conception had already occurred prior to marriage. In some societies, the stigma attached to pregnancy out of wedlock can be enormous, and coercive means (in spite of the legal defense of undue influence) for gaining recourse are often seen as the prospective father-in-law's "right". Often, a couple will arrange a shotgun wedding without explicit outside encouragement, and some religious groups consider it a moral imperative to marry in that situation. By culture Middle East Premarital sexual relations remain taboo across all social strata throughout the Arab world. In many cases, fornication is illegal and even a criminal offence under Sharia law. Even when it is not, the social response can be extreme, especially against women who have lost their virginity prior to marriage. In Arabic culture, shotgun weddings serve to obscure the fact that a baby was conceived prior to marriage. When that proves impossible, the social standing of the couple involved is irreparably damaged. Nevertheless, shotgun weddings help prevent the individuals involved, especially the women, from becoming social pariahs. Apart from instances of regional slang, there is no univ
https://en.wikipedia.org/wiki/American%20Society%20of%20Civil%20Engineers
The American Society of Civil Engineers (ASCE) is a tax-exempt professional body founded in 1852 to represent members of the civil engineering profession worldwide. Headquartered in Reston, Virginia, it is the oldest national engineering society in the United States. Its constitution was based on the older Boston Society of Civil Engineers from 1848. ASCE is dedicated to the advancement of the science and profession of civil engineering and the enhancement of human welfare through the activities of society members. It has more than 143,000 members in 177 countries. Its mission is to provide essential value to members, their careers, partners, and the public; facilitate the advancement of technology; encourage and provide the tools for lifelong learning; promote professionalism and the profession; develop and support civil engineers. History The first serious and documented attempts to organize civil engineers as a professional society in the newly created United States were in the early 19th century. In 1828, John Kilbourn of Ohio, managed a short-lived "Civil Engineering Journal", editorializing about the recent incorporation of the Institution of Civil Engineers in Great Britain that same year, Kilbourn suggested that the American corps of engineers could constitute an American society of civil engineers. Later, in 1834, an American trade periodical, the "American Railroad Journal" advocated for similar national organization of civil engineers. Institution of American Civil Engineers On December 17, 1838, a petition started circulating asking civil engineers to meet in 1839 in Baltimore, Maryland to organize a permanent society of civil engineers. Prior to that, thirteen notable civil engineers largely identifiable as being from New York, Pennsylvania, or Maryland met in Philadelphia. This group presented the Franklin Institute of Philadelphia with a formal proposal that an Institution of American Civil Engineers be established as an adjunct of the Franklin...
https://en.wikipedia.org/wiki/List%20of%20Historic%20Civil%20Engineering%20Landmarks
The following is a list of Historic Civil Engineering Landmarks as designated by the American Society of Civil Engineers since it began the program in 1964. The designation is granted to projects, structures, and sites in the United States (National Historic Civil Engineering Landmarks) and the rest of the world (International Historic Civil Engineering Landmarks). As of 2019, there are over 280 landmarks that have been approved by the ASCE Board of Direction. Sections or chapters of the American Society of Civil Engineers may also designate state or local landmarks within their areas; those landmarks are not listed here. See also List of Historic Mechanical Engineering Landmarks References External links American Society of Civil Engineers Historic Landmarks Civil engineering American Society of Civil Engineers Civil engineering
https://en.wikipedia.org/wiki/Oil%20rig
An oil rig is any kind of apparatus constructed for oil drilling. Kinds of oil rig include: Drilling rig, an apparatus for on-land oil drilling Drillship, a floating apparatus for offshore oil drilling Oil platform, an apparatus for offshore oil drilling Oil well, a boring from which oil is extracted Petroleum engineering
https://en.wikipedia.org/wiki/Voltage-controlled%20oscillator
A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform whose pitch can be adjusted by a voltage determined by a musical keyboard or other input. A voltage-to-frequency converter (VFC) is a special type of VCO designed to be very linear in frequency control over a wide range of input control voltages. Types VCOs can be generally categorized into two groups based on the type of waveform produced. Linear or harmonic oscillators generate a sinusoidal waveform. Harmonic oscillators in electronics usually consist of a resonator with an amplifier that replaces the resonator losses (to prevent the amplitude from decaying) and isolates the resonator from the output (so the load does not affect the resonator). Some examples of harmonic oscillators are LC oscillators and crystal oscillators. Relaxation oscillators can generate a sawtooth or triangular waveform. They are commonly used in integrated circuits (ICs). They can provide a wide range of operational frequencies with a minimal number of external components. Frequency control A voltage-controlled capacitor is one method of making an LC oscillator vary its frequency in response to a control voltage. Any reverse-biased semiconductor diode displays a measure of voltage-dependent capacitance and can be used to change the frequency of an oscillator by varying a control voltage applied to the diode. Special-purpose variable-capacitance varactor diodes are available with well-characterized wide-ranging values of capacitance. A varactor is used to change the capacitance (and hence the frequency) of an LC tank. A varactor can
https://en.wikipedia.org/wiki/PDF417
PDF417 is a stacked linear barcode format used in a variety of applications such as transport, identification cards, and inventory management. "PDF" stands for Portable Data File. The "417" signifies that each pattern in the code consists of 4 bars and spaces in a pattern that is 17 units (modules) long. The PDF417 symbology was invented by Dr. Ynjiun P. Wang at Symbol Technologies in 1991. It is defined in ISO 15438. Applications PDF417 is used in many applications by both commercial and government organizations. PDF417 is one of the formats (along with Data Matrix) that can be used to print postage accepted by the United States Postal Service. PDF417 is also used by the airline industry's Bar Coded Boarding Pass (BCBP) standard as the 2D bar code symbolism for paper boarding passes. PDF417 is the standard selected by the Department of Homeland Security as the machine readable zone technology for RealID compliant driver licenses and state issued identification cards. PDF417 barcodes are also included on visas and border crossing cards issued by the State of Israel (example). Features In addition to features typical of two dimensional bar codes, PDF417's capabilities include: Linking. PDF417 symbols can link to other symbols which are scanned in sequence allowing even more data to be stored. User-specified dimensions. The user can decide how wide the narrowest vertical bar (X dimension) is, and how tall the rows are (Y dimension). Public domain format. Anyone can implement systems using this format without any license. The introduction of the ISO/IEC document states: Manufacturers of bar code equipment and users of bar code technology require publicly available standard symbology specifications to which they can refer when developing equipment and application standards. It is the intent and understanding of ISO/IEC that the symbology presented in this International Standard is entirely in the public domain and free of all user restrictions, licences an
https://en.wikipedia.org/wiki/ROM%20image
A ROM image, or ROM file, is a computer file which contains a copy of the data from a read-only memory chip, often from a video game cartridge, or used to contain a computer's firmware, or from an arcade game's main board. The term is frequently used in the context of emulation, whereby older games or firmware are copied to ROM files on modern computers and can, using a piece of software known as an emulator, be run on a different device than which they were designed for. ROM burners are used to copy ROM images to hardware, such as ROM cartridges, or ROM chips, for debugging and QA testing. Creation ROMs can be copied from the read-only memory chips found in cartridge-based games and many arcade machines using a dedicated device in a process known as dumping. For most common home video game systems, these devices are widely available, examples being the Doctor V64, or the Retrode. Dumping ROMs from arcade machines, which are highly customized PCBs, often requires individual setups for each machine along with a large amount of expertise. Copy protection mechanisms While ROM images are often used as a means of preserving the history of computer games, they are also often used to facilitate the unauthorized copying and redistribution of modern games. Viewing this as potentially reducing sales of their products, many game companies have incorporated so-called features into newer games which are designed to prevent copying, while still allowing the original game to be played. For instance, the GameCube uses non-standard 8 cm DVD-like optical media, which for a long time prevented games stored on those discs from being copied. It was not until a security hole was found in Phantasy Star Online Episode I & II that GameCube games could be successfully copied, using the GameCube itself to read the discs. SNK also employed a method of copy prevention on their Neo Geo games, starting with The King of Fighters in 1999, which used an encryption algorithm on the graphics R
https://en.wikipedia.org/wiki/Karyogamy
Karyogamy is the final step in the process of fusing together two haploid eukaryotic cells, and refers specifically to the fusion of the two nuclei. Before karyogamy, each haploid cell has one complete copy of the organism's genome. In order for karyogamy to occur, the cell membrane and cytoplasm of each cell must fuse with the other in a process known as plasmogamy. Once within the joined cell membrane, the nuclei are referred to as pronuclei. Once the cell membranes, cytoplasm, and pronuclei fuse, the resulting single cell is diploid, containing two copies of the genome. This diploid cell, called a zygote or zygospore can then enter meiosis (a process of chromosome duplication, recombination, and division, to produce four new haploid cells), or continue to divide by mitosis. Mammalian fertilization uses a comparable process to combine haploid sperm and egg cells (gametes) to create a diploid fertilized egg. The term karyogamy comes from the Greek karyo- (from κάρυον karyon) 'nut' and γάμος gamos 'marriage'. Importance in haploid organisms Haploid organisms such as fungi, yeast, and algae can have complex cell cycles, in which the choice between sexual or asexual reproduction is fluid, and often influenced by the environment. Some organisms, in addition to their usual haploid state, can also exist as diploid for a short time, allowing genetic recombination to occur. Karyogamy can occur within either mode of reproduction: during the sexual cycle or in somatic (non-reproductive) cells. Thus, karyogamy is the key step in bringing together two sets of different genetic material which can recombine during meiosis. In haploid organisms that lack sexual cycles, karyogamy can also be an important source of genetic variation during the process of forming somatic diploid cells. Formation of somatic diploids circumvents the process of gamete formation during the sexual reproduction cycle and instead creates variation within the somatic cells of an already developed organ
https://en.wikipedia.org/wiki/Observer%20bias
Observer bias is one of the types of detection bias and is defined as any kind of systematic divergence from accurate facts during observation and the recording of data and information in studies. The definition can be further expanded upon to include the systematic difference between what is observed due to variation in observers, and what the true value is. Observer bias is the tendency of observers to not see what is there, but instead to see what they expect or want to see. This is a common occurrence in the everyday lives of many and is a significant problem that is sometimes encountered in scientific research and studies. Observation is critical to scientific research and activity, and as such, observer bias may be as well. When such biases exist, scientific studies can result in an over- or underestimation of what is true and accurate, which compromises the validity of the findings and results of the study, even if all other designs and procedures in the study were appropriate. Observational data forms the foundation of a significant body of knowledge. Observation is a method of data collection and falls into the category of qualitative research techniques. There are a number of benefits of observation, including its simplicity as a data collection method and its usefulness for hypotheses. Simultaneously, there are many limitations and disadvantages in the observation process, including the potential lack of reliability, poor validity, and faulty perception. Participants' observations are widely used in sociological and anthropological studies, while systematic observation is used where researchers need to collect data without participants direct interactions. The most common observation method is naturalistic observation, where subjects are observed in their natural environments with the goal to assess the behaviour in an intervention free and natural setting. Observer bias is especially probable when the investigator or researcher has vested interests in
https://en.wikipedia.org/wiki/List%20of%20lemmas
This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures. Algebra Abhyankar's lemma Aubin–Lions lemma Bergman's diamond lemma Fitting lemma Injective test lemma Hua's lemma (exponential sums) Krull's separation lemma Schanuel's lemma (projective modules) Schwartz–Zippel lemma Shapiro's lemma Stewart–Walker lemma (tensors) Whitehead's lemma (Lie algebras) Zariski's lemma Algebraic geometry Abhyankar's lemma Fundamental lemma (Langlands program) Category theory Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Linear algebra Matrix determinant lemma Matrix inversion lemma Group theory Burnside's lemma also known as the Cauchy–Frobenius lemma Frattini's lemma (finite groups) Goursat's lemma Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma Schur's lemma (representation theory) Zassenhaus lemma Polynomials Gauss's lemma (polynomials) Schwartz–Zippel lemma Ring theory and commutative algebra Artin–Rees lemma Hensel's lemma (commutative rings) Nakayama lemma Noether's normalization lemma Prime avoidance lemma Universal algebra Jónsson's lemma Analysis Fekete's lemma Fundamental lemma of calculus of variations Hopf lemma Sard's lemma (singularity theory) Stechkin's lemma (functional and numerical analysis) Vitali covering lemma (real analysis) Watson's lemma Complex analysis Estimation lemma (contour integrals) Hartogs's lemma (several complex variables) Jordan's lemma Lemma on the Logarithmic derivative Schwarz lemma Fourier analysis Riemann–Lebesgue lemma Differential equations Borel's lemma (partial differential equations) Grönwall's lemma Lax–Milgram lemma Pugh's closing lemma Weyl's lemma (Laplace equation) (partial differential equations) Differential forms Poincaré lemma of closed and exa
https://en.wikipedia.org/wiki/List%20of%20conjectures
This is a list of notable mathematical conjectures. Open problems The following conjectures remain open. The (incomplete) column "cites" lists the number of results for a Google Scholar search for the term, in double quotes . Conjectures now proved (theorems) The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names. Deligne's conjecture on 1-motives Goldbach's weak conjecture (proved in 2013) Sensitivity conjecture (proved in 2019) Disproved (no longer conjectures) The conjectures in following list were not necessarily generally accepted as true before being disproved. Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture Chinese hypothesis (not a conjecture to start with) Doomsday conjecture Euler's sum of powers conjecture Ganea conjecture Generalized Smith conjecture Hauptvermutung Hedetniemi's conjecture, counterexample announced 2019 Hirsch conjecture (disproved in 2010) Intersection graph conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved 1910) Tait's conjecture Von Neumann conjecture Weyl–Berry conjecture Williamson conjecture In mathematics, ideas are supposedly not accepted as fact until they have been rigorously proved. However, there have been some ideas that were fairly accepted in the past but which were subsequently shown to be false. The following list is meant to serve as a repository for compiling a list of such ideas. The idea of the Pythagoreans that all numbers can be expressed as a ratio of two whole numbers. This was disproved by one of Pythagoras' own disciples, Hippasus, who showed that the square root of two is what we today call an irrational number. One story claims that he was thrown off the ship in which he and some other Pythagoreans were sailing because his discovery was too heretical. Euclid's parallel
https://en.wikipedia.org/wiki/Status%20register
A status register, flag register, or condition code register (CCR) is a collection of status flag bits for a processor. Examples of such registers include FLAGS register in the x86 architecture, flags in the program status word (PSW) register in the IBM System/360 architecture through z/Architecture, and the application program status register (APSR) in the ARM Cortex-A architecture. The status register is a hardware register that contains information about the state of the processor. Individual bits are implicitly or explicitly read and/or written by the machine code instructions executing on the processor. The status register lets an instruction take action contingent on the outcome of a previous instruction. Typically, flags in the status register are modified as effects of arithmetic and bit manipulation operations. For example, a Z bit may be set if the result of the operation is zero and cleared if it is nonzero. Other classes of instructions may also modify the flags to indicate status. For example, a string instruction may do so to indicate whether the instruction terminated because it found a match/mismatch or because it found the end of the string. The flags are read by a subsequent conditional instruction so that the specified action (depending on the processor, a jump, call, return, or so on) occurs only if the flags indicate a specified result of the earlier instruction. Some CPU architectures, such as the MIPS and Alpha, do not use a dedicated flag register. Others do not implicitly set and/or read flags. Such machines either do not pass implicit status information between instructions at all, or they pass it in an explicitly selected general purpose register. A status register may often have other fields as well, such as more specialized flags, interrupt enable bits, and similar types of information. During an interrupt, the status of the thread currently executing can be preserved (and later recalled) by storing the current value of the status re
https://en.wikipedia.org/wiki/Shelf%20life
Shelf life is the length of time that a commodity may be stored without becoming unfit for use, consumption, or sale. In other words, it might refer to whether a commodity should no longer be on a pantry shelf (unfit for use), or no longer on a supermarket shelf (unfit for sale, but not yet unfit for use). It applies to cosmetics, foods and beverages, medical devices, medicines, explosives, pharmaceutical drugs, chemicals, tyres, batteries, and many other perishable items. In some regions, an advisory best before, mandatory use by or freshness date is required on packaged perishable foods. The concept of expiration date is related but legally distinct in some jurisdictions. Background Shelf life is the recommended maximum time for which products or fresh (harvested) produce can be stored, during which the defined quality of a specified proportion of the goods remains acceptable under expected (or specified) conditions of distribution, storage and display. According to the United States Department of Agriculture (USDA), "canned foods are safe indefinitely as long as they are not exposed to freezing temperatures, or temperatures above 90 °F (32.2 °C)". If the cans look okay, they are safe to use. Discard cans that are dented, rusted, or swollen. High-acid canned foods (tomatoes, fruits) will keep their best quality for 12 to 18 months; low-acid canned foods (meats, vegetables) for 2 to 5 years. "Sell by date" is a less ambiguous term for what is often referred to as an "expiration date". Most food is still edible after the expiration date. A product that has passed its shelf life might still be safe, but quality is no longer guaranteed. In most food stores, waste is minimized by using stock rotation, which involves moving products with the earliest sell by date from the warehouse to the sales area, and then to the front of the shelf, so that most shoppers will pick them up first and thus they are likely to be sold before the end of their shelf life. Some stores ca
https://en.wikipedia.org/wiki/Gradient%20conjecture
In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie, France), Tadeusz Mostowski (Warsaw University, Poland) and Adam Parusiński (University of Angers, France). The conjecture states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the secant lines from x(t) to x0, as t tends to zero. The proof depends on a theorem due to Stanis%C5%82aw %C5%81ojasiewicz. References R. Thom (1989) "Problèmes rencontrés dans mon parcours mathématique: un bilan", Publications Math%C3%A9matiques de l%27IH%C3%89S 70: 200 to 214. (This gradient conjecture due to René Thom was in fact well-known among specialists by the early 70's, having been often discussed during that period by Thom during his weekly seminar on singularities at the IHES.) In 2000 the conjecture was proven correct in Annals of Mathematics 152: 763 to 792. The proof is available here. Theorems in analysis
https://en.wikipedia.org/wiki/Scenario%20planning
Scenario planning, scenario thinking, scenario analysis, scenario prediction and the scenario method all describe a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and generalization of classic methods used by military intelligence. In the most common application of the method, analysts generate simulation games for policy makers. The method combines known facts, such as demographics, geography and mineral reserves, with military, political, and industrial information, and key driving forces identified by considering social, technical, economic, environmental, and political ("STEEP") trends. In business applications, the emphasis on understanding the behavior of opponents has been reduced while more attention is now paid to changes in the natural environment. At Royal Dutch Shell for example, scenario planning has been described as changing mindsets about the exogenous part of the world prior to formulating specific strategies. Scenario planning may involve aspects of systems thinking, specifically the recognition that many factors may combine in complex ways to create sometimes surprising futures (due to non-linear feedback loops). The method also allows the inclusion of factors that are difficult to formalize, such as novel insights about the future, deep shifts in values, and unprecedented regulations or inventions. Systems thinking used in conjunction with scenario planning leads to plausible scenario storylines because the causal relationship between factors can be demonstrated. These cases, in which scenario planning is integrated with a systems thinking approach to scenario development, are sometimes referred to as "dynamic scenarios". Critics of using a subjective and heuristic methodology to deal with uncertainty and complexity argue that the technique has not been examined rigorously, nor influenced sufficiently by scientific evidence. They caution against using such methods to "
https://en.wikipedia.org/wiki/H-space
In mathematics, an H-space is a homotopy-theoretic version of a generalization of the notion of topological group, in which the axioms on associativity and inverses are removed. Definition An H-space consists of a topological space , together with an element of and a continuous map , such that and the maps and are both homotopic to the identity map through maps sending to . This may be thought of as a pointed topological space together with a continuous multiplication for which the basepoint is an identity element up to basepoint-preserving homotopy. One says that a topological space is an H-space if there exists and such that the triple is an H-space as in the above definition. Alternatively, an H-space may be defined without requiring homotopies to fix the basepoint , or by requiring to be an exact identity, without any consideration of homotopy. In the case of a CW complex, all three of these definitions are in fact equivalent. Examples and properties The standard definition of the fundamental group, together with the fact that it is a group, can be rephrased as saying that the loop space of a pointed topological space has the structure of an H-group, as equipped with the standard operations of concatenation and inversion. Furthermore a continuous basepoint preserving map of pointed topological space induces a H-homomorphism of the corresponding loop spaces; this reflects the group homomorphism on fundamental groups induced by a continuous map. It is straightforward to verify that, given a pointed homotopy equivalence from a H-space to a pointed topological space, there is a natural H-space structure on the latter space. As such, the existence of an H-space structure on a given space is only dependent on pointed homotopy type. The multiplicative structure of an H-space adds structure to its homology and cohomology groups. For example, the cohomology ring of a path-connected H-space with finitely generated and free cohomology groups is a Hopf alge
https://en.wikipedia.org/wiki/Duality%20%28order%20theory%29
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P. It is easy to see that this construction, which can be depicted by flipping the Hasse diagram for P upside down, will indeed yield a partially ordered set. In a broader sense, two partially ordered sets are also said to be duals if they are dually isomorphic, i.e. if one poset is order isomorphic to the dual of the other. The importance of this simple definition stems from the fact that every definition and theorem of order theory can readily be transferred to the dual order. Formally, this is captured by the Duality Principle for ordered sets: If a given statement is valid for all partially ordered sets, then its dual statement, obtained by inverting the direction of all order relations and by dualizing all order theoretic definitions involved, is also valid for all partially ordered sets. If a statement or definition is equivalent to its dual then it is said to be self-dual. Note that the consideration of dual orders is so fundamental that it often occurs implicitly when writing ≥ for the dual order of ≤ without giving any prior definition of this "new" symbol. Examples Naturally, there are a great number of examples for concepts that are dual: Greatest elements and least elements Maximal elements and minimal elements Least upper bounds (suprema, ∨) and greatest lower bounds (infima, ∧) Upper sets and lower sets Ideals and filters Closure operators and kernel operators. Examples of notions which are self-dual include: Being a (complete) lattice Monotonicity of functions Distributivity of lattices, i.e. the lattices for which ∀x,y,z: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z) holds are exactly those for which the dual statement ∀x,y,z: x ∨ (y ∧ z) = (x ∨ y) ∧ (x
https://en.wikipedia.org/wiki/Animals%20in%20space
Animals in space originally served to test the survivability of spaceflight, before human spaceflights were attempted. Later, other non-human animals were flown to investigate various biological processes and the effects microgravity and space flight might have on them. Bioastronautics is an area of bioengineering research that spans the study and support of life in space. To date, seven national space programs have flown animals into space: the United States, Soviet Union, France, Argentina, China, Japan and Iran. A wide variety of animals have been launched into space, including monkeys and apes, dogs, cats, tortoises, mice, rats, rabbits, fish, frogs, spiders, quail eggs (which hatched in 1990 on Mir), and insects. The US launched the first Earthlings into space - fruit flies in 1947 - and flights carrying primates primarily between 1949 and 1961, with one flight in 1969 and one in 1985. France launched two monkey-carrying flights in 1967. The Soviet Union and Russia launched monkeys between 1983 and 1996. During the 1950s and 1960s, the Soviet space program used a number of dogs for sub-orbital and orbital space flights. Two tortoises and several varieties of plants were the first inhabitants of Earth to circle the Moon, on the September 1968 Zond 5 mission. Turtles followed on the November 1968 Zond 6 circumlunar mission, and four turtles flew to the Moon on Zond 7 in August 1969. In 1972 five mice, Fe, Fi, Fo, Fum, and Phooey, orbited the Moon a record 75 times in Apollo 17's Command Module America, the last crewed voyage to the Moon. Background Animals had been used in aeronautic exploration since 1783 when the Montgolfier brothers sent a sheep, a duck, and a rooster aloft in a hot air balloon to see if ground-dwelling animals can survive (the duck serving as the experimental control). The limited supply of captured German V-2 rockets led to the U.S. use of high-altitude balloon launches carrying fruit flies, mice, hamsters, guinea pigs, cats, dogs, frogs,
https://en.wikipedia.org/wiki/IBM%20System/32
The IBM System/32 (IBM 5320) introduced in January 1975 was a midrange computer with built-in display screen, disk drives, printer, and database report software. It was used primarily by small to midsize businesses for accounting applications. RPG II was the primary programming language for the machine. Overview The 16-bit single-user System/32, also known as the IBM 5320, was introduced in 1975, and it was the successor to the IBM System/3 model 6 in the IBM midrange computer line. IBM described it as "the first system to incorporate hardware and comprehensive application software." The New York Times described the 32 as "a compact computer for first‐time users with little or no computer programming experience." Within 40 months, "the System/32 had surpassed the IBM System/3 as the most installed IBM computer." The computer looked like a large office desk with a very small six-line by forty-character display. Having the appearance of a computerized desk, the System/32 was nicknamed the "Bionic Desk" after The Six Million Dollar Man (bionic man), a popular U.S. TV program when the computer was introduced in 1975. The 32 had a built-in line printer, that directly faced the operator when seated, and could print reports, memos, billing statements, address labels, etc. It had been introduced January 7, 1975 and was withdrawn from marketing on October 17, 1984. Migration to the IBM System/34 was generally simple because source code was compatible and programs just needed recompilation. Processor The System/32 featured a 16-bit processor with a 200ns cycle time known as the Control Storage Processor (CSP). Whereas the System/3 used a hardwired processor, the System/32 implemented the System/3 instruction set in microcode. The System/32 processor utilized a vertical microcode format, with each microinstruction occupying 16 bits of control storage. There were 19 different microinstruction opcodes, however certain microinstructions could carry out different operation
https://en.wikipedia.org/wiki/Arbitrary-precision%20arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision. Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should not be confused with the symbolic computation provided by many computer algebra systems, which represent numbers by expressions such as , and can thus represent any computable number with infinite precision. Applications A common application is public-key cryptography, whose algorithms commonly employ arithmetic with integers having hundreds of digits. Another is in situations where artificial limits and overflows would be inappropriate. It is also useful for checking the results of fixed-precision calculations, and for determining optimal or near-optimal values for coefficients needed in formulae, for example the that appears in Gaussian integration. Arbitrary precision arithmetic is also used to compute fundamental mathematical constants such as π to millions or more digits and to analyze the properties of the digit strings or more generally to investigate the precise behaviour of functions such as the Riemann zeta function where certain questions are difficult to explore via analytical methods. A
https://en.wikipedia.org/wiki/Minkowski%E2%80%93Bouligand%20dimension
In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set in a Euclidean space , or more generally in a metric space . It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand. To calculate this dimension for a fractal , imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this number changes as we make the grid finer by applying a box-counting algorithm. Suppose that is the number of boxes of side length required to cover the set. Then the box-counting dimension is defined as Roughly speaking, this means that the dimension is the exponent such that , which is what one would expect in the trivial case where is a smooth space (a manifold) of integer dimension . If the above limit does not exist, one may still take the limit superior and limit inferior, which respectively define the upper box dimension and lower box dimension. The upper box dimension is sometimes called the entropy dimension, Kolmogorov dimension, Kolmogorov capacity, limit capacity or upper Minkowski dimension, while the lower box dimension is also called the lower Minkowski dimension. The upper and lower box dimensions are strongly related to the more popular Hausdorff dimension. Only in very special applications is it important to distinguish between the three (see below). Yet another measure of fractal dimension is the correlation dimension. Alternative definitions It is possible to define the box dimensions using balls, with either the covering number or the packing number. The covering number is the minimal number of open balls of radius ε required to cover the fractal, or in other words, such that their union contains the fractal. We can also consider the intrinsic covering number , which is defined the same
https://en.wikipedia.org/wiki/List%20of%20inequalities
This article lists Wikipedia articles about named mathematical inequalities. Inequalities in pure mathematics Analysis Agmon's inequality Askey–Gasper inequality Babenko–Beckner inequality Bernoulli's inequality Bernstein's inequality (mathematical analysis) Bessel's inequality Bihari–LaSalle inequality Bohnenblust–Hille inequality Borell–Brascamp–Lieb inequality Brezis–Gallouet inequality Carleman's inequality Chebyshev–Markov–Stieltjes inequalities Chebyshev's sum inequality Clarkson's inequalities Eilenberg's inequality Fekete–Szegő inequality Fenchel's inequality Friedrichs's inequality Gagliardo–Nirenberg interpolation inequality Gårding's inequality Grothendieck inequality Grunsky's inequalities Hanner's inequalities Hardy's inequality Hardy–Littlewood inequality Hardy–Littlewood–Sobolev inequality Harnack's inequality Hausdorff–Young inequality Hermite–Hadamard inequality Hilbert's inequality Hölder's inequality Jackson's inequality Jensen's inequality Khabibullin's conjecture on integral inequalities Kantorovich inequality Karamata's inequality Korn's inequality Ladyzhenskaya's inequality Landau–Kolmogorov inequality Lebedev–Milin inequality Lieb–Thirring inequality Littlewood's 4/3 inequality Markov brothers' inequality Mashreghi–Ransford inequality Max–min inequality Minkowski's inequality Poincaré inequality Popoviciu's inequality Prékopa–Leindler inequality Rayleigh–Faber–Krahn inequality Remez inequality Riesz rearrangement inequality Schur test Shapiro inequality Sobolev inequality Steffensen's inequality Szegő inequality Three spheres inequality Trace inequalities Trudinger's theorem Turán's inequalities Von Neumann's inequality Wirtinger's inequality for functions Young's convolution inequality Young's inequality for products Inequalities relating to means Hardy–Littlewood maximal inequality Inequality of arithmetic and geometric means Ky Fan inequality Levinson's inequality Mac
https://en.wikipedia.org/wiki/Chase%20H.Q.
is a vehicular combat racing game, originally released as an arcade video game by Taito in 1988. It is sometimes seen as a spiritual successor to Taito's earlier Full Throttle. The player assumes the role of a police officer named Tony Gibson, member of the "Chase Special Investigation Department". Along with his partner, Raymond Broady, he must stop fleeing criminals in high-speed pursuits in a black Porsche 928. Chase H.Q. was ported to many home computers by Ocean Software in 1989, including versions for the ZX Spectrum, Amstrad CPC, Commodore 64, MSX, Amiga and Atari ST. Taito produced versions for the Family Computer (1989), Game Boy (1990), Master System (1990), TurboGrafx-16 (1990), Game Gear (1991), and Saturn (1996). It was released for PlayStation 2 in Japan in 2007 as part of Taito Memories II Volume 2. The game was a commercial success, becoming Japan's highest-grossing dedicated arcade game of 1989 while also becoming a hit overseas for arcades and home systems. The game was also well received by critics. It was followed by three arcade-based sequels: Special Criminal Investigation (1989), Super Chase: Criminal Termination (1992) and Chase H.Q. 2 (2007). Two spin-offs were also released: Crime City (1989) and Quiz H.Q. (1990). Gameplay At the start of each level the player is informed who they are pursuing, a great distance away: They must apprehend the criminal before their time limit expires. The criminal's car is constantly moving away, so if the player repeatedly crashes or drives too slowly, the criminal will escape. At some points during the game the road splits, and the correct turn must be taken, otherwise it will take longer to catch the criminal. When their vehicle is reached, the time limit is extended; the vehicle must be rammed a number of times until the criminal is forced to stop, then is arrested. The game includes five levels. Both the initial time limit to reach the criminal and the time extension to ram the criminal are 60, 65, or
https://en.wikipedia.org/wiki/Semantic%20theory%20of%20truth
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot be defined within that language. Tarski's theory of truth To formulate linguistic theories without semantic paradoxes such as the liar paradox, it is generally necessary to distinguish the language that one is talking about (the object language) from the language that one is using to do the talking (the metalanguage). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "P") is always the metalanguage's name for a sentence, such that this name is simply the sentence P rendered in the object language. In this way, the metalanguage can be used to talk about the object language; Tarski's theory of truth (Alfred Tarski 1935) demanded that the object language be contained in the metalanguage. Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "P", a sentence of the following form (known as "form (T)"): (1) "P" is true if, and only if, P. For example, (2) 'snow is white' is true if and only if snow is white. These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the
https://en.wikipedia.org/wiki/Paul%20Erd%C5%91s
Paul Erdős ( ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. He was known both for his social practice of mathematics, working with more than 500 collaborators, and for his eccentric lifestyle; Time magazine called him "The Oddball's Oddball". He devoted his waking hours to mathematics, even into his later years—indeed, his death came at a mathematics conference in Warsaw. Erdős's prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships. Life Paul Erdős was born on 26 March 1913, in Budapest, Austria-Hungary, the only surviving child of Anna (née Wilhelm) and Lajos Erdős (né Engländer). His two sisters, aged three and five, both died of scarlet fever a few days before he was born. His parents, both Jewish, were high school mathematics teachers. His fascination with mathematics developed early—he was often left home by himself because his father was held captive in Siberia as an Austro-Hungarian prisoner of war during 1914–1920, causing his mot
https://en.wikipedia.org/wiki/Display%20resolution
The display resolution or display modes of a digital television, computer monitor or display device is the number of distinct pixels in each dimension that can be displayed. It can be an ambiguous term especially as the displayed resolution is controlled by different factors in cathode ray tube (CRT) displays, flat-panel displays (including liquid-crystal displays) and projection displays using fixed picture-element (pixel) arrays. It is usually quoted as , with the units in pixels: for example, means the width is 1024 pixels and the height is 768 pixels. This example would normally be spoken as "ten twenty-four by seven sixty-eight" or "ten twenty-four by seven six eight". One use of the term display resolution applies to fixed-pixel-array displays such as plasma display panels (PDP), liquid-crystal displays (LCD), Digital Light Processing (DLP) projectors, OLED displays, and similar technologies, and is simply the physical number of columns and rows of pixels creating the display (e.g. ). A consequence of having a fixed-grid display is that, for multi-format video inputs, all displays need a "scaling engine" (a digital video processor that includes a memory array) to match the incoming picture format to the display. For device displays such as phones, tablets, monitors and televisions, the use of the term display resolution as defined above is a misnomer, though common. The term display resolution is usually used to mean pixel dimensions, the maximum number of pixels in each dimension (e.g. ), which does not tell anything about the pixel density of the display on which the image is actually formed: resolution properly refers to the pixel density, the number of pixels per unit distance or area, not the total number of pixels. In digital measurement, the display resolution would be given in pixels per inch (PPI). In analog measurement, if the screen is 10 inches high, then the horizontal resolution is measured across a square 10 inches wide. For television stand
https://en.wikipedia.org/wiki/Network%20security%20policy
A network security policy (NSP) is a generic document that outlines rules for computer network access, determines how policies are enforced and lays out some of the basic architecture of the company security/ network security environment. The document itself is usually several pages long and written by a committee. A security policy is a complex document, meant to govern data access, web-browsing habits, use of passwords, encryption, email attachments and more. It specifies these rules for individuals or groups of individuals throughout the company. The policies could be expressed as a set of instructions that understood by special purpose network hardware dedicated for securing the network. Security policy should keep the malicious users out and also exert control over potential risky users within an organization. Understanding what information and services are available and to which users, as well as what the potential is for damage and whether any protection is already in place to prevent misuse are important when writing a network security policy. In addition, the security policy should dictate a hierarchy of access permissions, granting users access only to what is necessary for the completion of their work. The National Institute of Standards and Technology provides an example security-policy guideline. See also Internet security Security engineering Computer security Cybersecurity information technology list Network security Industrial espionage Information security Security policy References External links Computer Security Resource Center at National Institute of Standards and Technology Network Security Policy and Procedures document by the City of Madison, Wisconsin Computer security procedures Computer network security
https://en.wikipedia.org/wiki/Process%20engineering
Process engineering is the understanding and application of the fundamental principles and laws of nature that allow humans to transform raw material and energy into products that are useful to society, at an industrial level. By taking advantage of the driving forces of nature such as pressure, temperature and concentration gradients, as well as the law of conservation of mass, process engineers can develop methods to synthesize and purify large quantities of desired chemical products. Process engineering focuses on the design, operation, control, optimization and intensification of chemical, physical, and biological processes. Process engineering encompasses a vast range of industries, such as agriculture, automotive, biotechnical, chemical, food, material development, mining, nuclear, petrochemical, pharmaceutical, and software development. The application of systematic computer-based methods to process engineering is "process systems engineering". Overview Process engineering involves the utilization of multiple tools and methods. Depending on the exact nature of the system, processes need to be simulated and modeled using mathematics and computer science. Processes where phase change and phase equilibria are relevant require analysis using the principles and laws of thermodynamics to quantify changes in energy and efficiency. In contrast, processes that focus on the flow of material and energy as they approach equilibria are best analyzed using the disciplines of fluid mechanics and transport phenomena. Disciplines within the field of mechanics need to be applied in the presence of fluids or porous and dispersed media. Materials engineering principles also need to be applied, when relevant. Manufacturing in the field of process engineering involves an implementation of process synthesis steps. Regardless of the exact tools required, process engineering is then formatted through the use of a process flow diagram (PFD) where material flow paths, storage equipm
https://en.wikipedia.org/wiki/Discovery%20%28law%29
Discovery, in the law of common law jurisdictions, is a pre-trial procedure in a lawsuit in which each party, through the law of civil procedure, can obtain evidence from the other party or parties by means of discovery devices such as interrogatories, requests for production of documents, requests for admissions and depositions. Discovery can be obtained from non-parties using subpoenas. When a discovery request is objected to, the requesting party may seek the assistance of the court by filing a motion to compel discovery. History Discovery evolved out of a unique feature of early equitable pleading procedure before the English Court of Chancery: among various requirements, a plaintiff's bill in equity was required to plead "positions". These were statements of evidence that the plaintiff assumed to exist in support of his pleading and which he believed lay within the knowledge of the defendant. They strongly resembled modern requests for admissions, in that the defendant was required to plead only whether they were true or false. At some point between the reign of Elizabeth I (1558-1603) and the late seventeenth century, positions were gradually replaced by interrogatories: written questions which the defendant was required to truthfully respond to under oath in his answer to the bill, based on information within his own personal knowledge as well as documents in his possession. But back then, interrogatories could only elicit admissible evidence (not the broader modern standard of "reasonably calculated to lead to the discovery of admissible evidence") and could only request evidence in support of the plaintiff's case, not either side's case (that is, they could not ask for evidence which the defendant intended to use in support of his defenses and was otherwise entirely irrelevant to the plaintiff's case). Even worse, this was purely a one-way procedure, because interrogatories could only be pleaded as part of a bill (a pleading initiating a suit in equity).
https://en.wikipedia.org/wiki/TreadMarks
TreadMarks is a distributed shared memory system created at Rice University in the 1990s. References External links TreadMarks official site Distributed computing architecture
https://en.wikipedia.org/wiki/LC%20circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency. LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal; this function is called a bandpass filter. They are key components in many electronic devices, particularly radio equipment, used in circuits such as oscillators, filters, tuners and frequency mixers. An LC circuit is an idealized model since it assumes there is no dissipation of energy due to resistance. Any practical implementation of an LC circuit will always include loss resulting from small but non-zero resistance within the components and connecting wires. The purpose of an LC circuit is usually to oscillate with minimal damping, so the resistance is made as low as possible. While no practical circuit is without losses, it is nonetheless instructive to study this ideal form of the circuit to gain understanding and physical intuition. For a circuit model incorporating resistance, see RLC circuit. Terminology The two-element LC circuit described above is the simplest type of inductor-capacitor network (or LC network). It is also referred to as a second order LC circuit to distinguish it from more complicated (higher order) LC networks with more inductors and capacitors. Such LC networks with more than two reactances may have more than one resonant frequency. The order of the network is the order of the rational function describing the network in the complex frequency variable . Generally, the order is equal to the number of L and C elements in the circuit and in any event cannot exceed this number. Operation An LC circuit, oscillatin
https://en.wikipedia.org/wiki/IMSAI%208080
The IMSAI 8080 was an early microcomputer released in late 1975, based on the Intel 8080 and later 8085 and S-100 bus. It was a clone of its main competitor, the earlier MITS Altair 8800. The IMSAI is largely regarded as the first "clone" microcomputer. The IMSAI machine ran a highly modified version of the CP/M operating system called IMDOS. It was developed, manufactured and sold by IMS Associates, Inc. (later renamed IMSAI Manufacturing Corp). In total, between 17,000 and 20,000 units were produced from 1975 to 1978. History In May 1972, William Millard started a business called IMS Associates (IMS) in the areas of computer consulting and engineering, using his home as an office. By 1973, Millard incorporated the business and soon found funding for it, receiving several contracts, all for software. IMS stood for "Information Management Services". In 1974, IMS was contacted by a client which wanted a "workstation system" that could complete jobs for any General Motors car dealership. IMS planned a system including a terminal, small computer, printer, and special software. Five of these workstations were to have common access to a hard disk drive, which would be controlled by a small computer. Eventually product development was stopped. Millard and his chief engineer Joe Killian turned to the microprocessor. Intel had announced the 8080 chip, and compared to the 4004 to which IMS Associates had been first introduced, it looked like a "real computer". Full-scale development of the IMSAI 8080 was put into action using the existing Altair 8800's S-100 bus, and by October 1975 an ad was placed in Popular Electronics, receiving positive reactions. IMS shipped the first IMSAI 8080 kits on 16 December 1975, before turning to fully assembled units. In 1976, IMS was renamed to IMSAI Manufacturing Corporation because by then, they were a manufacturing company, not a consulting firm. In 1977, IMSAI marketing director Seymour I. Rubinstein paid Gary Kildall $25,000 for
https://en.wikipedia.org/wiki/Gardening%20%28cryptanalysis%29
In cryptanalysis, gardening is the act of encouraging a target to use known plaintext in an encrypted message. It was a term used at the British Government Code and Cypher School at Bletchley Park, England, during World War II, for schemes to entice the Germans to include particular words, which the British called "cribs", in their encrypted messages. This term presumably came from RAF minelaying missions, or "gardening" sorties. "Gardening" was standard RAF slang for sowing mines in rivers, ports and oceans from low heights, possibly because each sea area around the European coasts was given a code-name of flowers or vegetables. The technique is claimed to have been most effective against messages produced by the German Navy's Enigma machines. If the Germans had recently swept a particular area for mines, and analysts at Bletchley Park were in need of some cribs, they might (and apparently did on several occasions) request that the area be mined again. This would hopefully evoke encrypted messages from the local command mentioning Minen (German for mines) and/or the location, and perhaps messages also from the headquarters with minesweeping ships to assign to that location, mentioning the same. It worked often enough to try several times. This crib-based decryption is an example of a chosen-plaintext attack, because plain text effectively chosen by the British was injected into the ciphertext. See also Cryptanalysis of the Enigma Known-plaintext attack Notes Cryptographic attacks Bletchley Park
https://en.wikipedia.org/wiki/Type%20safety
In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors. The behaviors classified as type errors by a given programming language are usually those that result from attempts to perform operations on values that are not of the appropriate data type, e.g., adding a string to an integer when there's no definition on how to handle this case. This classification is partly based on opinion. Type enforcement can be static, catching potential errors at compile time, or dynamic, associating type information with values at run-time and consulting them as needed to detect imminent errors, or a combination of both. Dynamic type enforcement often allows programs to run that would be invalid under static enforcement. In the context of static (compile-time) type systems, type safety usually involves (among other things) a guarantee that the eventual value of any expression will be a legitimate member of that expression's static type. The precise requirement is more subtle than this — see, for example, subtyping and polymorphism for complications. Definitions Intuitively, type soundness is captured by Robin Milner's pithy statement that Well-typed programs cannot "go wrong". In other words, if a type system is sound, then expressions accepted by that type system must evaluate to a value of the appropriate type (rather than produce a value of some other, unrelated type or crash with a type error). Vijay Saraswat provides the following, related definition: A language is type-safe if the only operations that can be performed on data in the language are those sanctioned by the type of the data. However,
https://en.wikipedia.org/wiki/Petrifaction
In geology, petrifaction or petrification () is the process by which organic material becomes a fossil through the replacement of the original material and the filling of the original pore spaces with minerals. Petrified wood typifies this process, but all organisms, from bacteria to vertebrates, can become petrified (although harder, more durable matter such as bone, beaks, and shells survive the process better than softer remains such as muscle tissue, feathers, or skin). Petrifaction takes place through a combination of two similar processes: permineralization and replacement. These processes create replicas of the original specimen that are similar down to the microscopic level. Processes Permineralization One of the processes involved in petrifaction is permineralization. The fossils created through this process tend to contain a large amount of the original material of the specimen. This process occurs when groundwater containing dissolved minerals (most commonly quartz, calcite, apatite (calcium phosphate), siderite (iron carbonate), and pyrite), fills pore spaces and cavities of specimens, particularly bone, shell or wood. The pores of the organisms' tissues are filled when these minerals precipitate out of the water. Two common types of permineralization are silicification and pyritization. Silicification Silicification is the process in which organic matter becomes saturated with silica. A common source of silica is volcanic material. Studies have shown that in this process, most of the original organic matter is destroyed. Silicification most often occurs in two environments—either the specimen is buried in sediments of deltas and floodplains or organisms are buried in volcanic ash. Water must be present for silicification to occur because it reduces the amount of oxygen present and therefore reduces the deterioration of the organism by fungi, maintains organism shape, and allows for the transportation and deposition of silica. The process begins
https://en.wikipedia.org/wiki/Food%20processing
Food processing is the transformation of agricultural products into food, or of one form of food into other forms. Food processing takes many forms, from grinding grain into raw flour, home cooking, and complex industrial methods used in the making of convenience foods. Some food processing methods play important roles in reducing food waste and improving food preservation, thus reducing the total environmental impact of agriculture and improving food security. The Nova classification groups food according to different food processing techniques. Primary food processing is necessary to make most foods edible while secondary food processing turns ingredients into familiar foods, such as bread. Tertiary food processing results in ultra-processed foods and has been widely criticized for promoting overnutrition and obesity, containing too much sugar and salt, too little fiber, and otherwise being unhealthful in respect to dietary needs of humans and farm animals. Processing levels Primary food processing Primary food processing turns agricultural products, such as raw wheat kernels or livestock, into something that can eventually be eaten. This category includes ingredients that are produced by ancient processes such as drying, threshing, winnowing and milling grain, shelling nuts, and butchering animals for meat. It also includes deboning and cutting meat, freezing and smoking fish and meat, extracting and filtering oils, canning food, preserving food through food irradiation, and candling eggs, as well as homogenizing and pasteurizing milk. Contamination and spoilage problems in primary food processing can lead to significant public health threats, as the resulting foods are used so widely. However, many forms of processing contribute to improved food safety and longer shelf life before the food spoils. Commercial food processing uses control systems such as hazard analysis and critical control points (HACCP) and failure mode and effects analysis (FMEA) to
https://en.wikipedia.org/wiki/Ray%20Dolby
Ray Milton Dolby Hon OBE, HonFREng (; January 18, 1933 – September 12, 2013) was an American engineer and inventor of the noise reduction system known as Dolby NR. He helped develop the video tape recorder while at Ampex and was the founder of Dolby Laboratories. Early life and education Dolby was born in Portland, Oregon, the son of Esther Eufemia (née Strand) and Earl Milton Dolby, an inventor. He attended Sequoia High School (class of 1951) in Redwood City, California. As a teenager in the decade following World War II, he held part-time and summer jobs at Ampex in Redwood City, working with their first audio tape recorder in 1949. While at San Jose State College and later at Stanford University (interrupted by two years of Army service), he worked on early prototypes of video tape recorder technologies for Alexander M. Poniatoff and Charlie Ginsburg. In 1957, Dolby received his B.Sc. in electrical engineering from Stanford. He subsequently won a Marshall Scholarship for a Ph.D (1961) in physics from the University of Cambridge, England, where he was a Research Fellow at Pembroke College. Career As a non degree-holding "consultant", Dolby played a key role in the effort that led Ampex to unveil their prototype Quadruplex videotape recorder in April 1956 which soon entered production. After Cambridge, Dolby acted as a technical advisor to the United Nations in India until 1965, when he returned to England, where he founded Dolby Laboratories in London with a staff of four. In that same year, 1965, he invented the Dolby noise-reduction system, a form of audio signal processing for analog tape recorders. His first U.S. patent application was made in 1969, four years later. The system was first used by Decca Records in the UK. The Dolby B consumer noise-reduction system works by compressing (boosting) low-level high-frequency sounds during recording and expanding (decreasing) them symmetrically during playback, which also decreases inherent tape noise. This re
https://en.wikipedia.org/wiki/Voltage%20clamp
The voltage clamp is an experimental method used by electrophysiologists to measure the ion currents through the membranes of excitable cells, such as neurons, while holding the membrane voltage at a set level. A basic voltage clamp will iteratively measure the membrane potential, and then change the membrane potential (voltage) to a desired value by adding the necessary current. This "clamps" the cell membrane at a desired constant voltage, allowing the voltage clamp to record what currents are delivered. Because the currents applied to the cell must be equal to (and opposite in charge to) the current going across the cell membrane at the set voltage, the recorded currents indicate how the cell reacts to changes in membrane potential. Cell membranes of excitable cells contain many different kinds of ion channels, some of which are voltage-gated. The voltage clamp allows the membrane voltage to be manipulated independently of the ionic currents, allowing the current–voltage relationships of membrane channels to be studied. History The concept of the voltage clamp is attributed to Kenneth Cole and George Marmont in the spring of 1947. They inserted an internal electrode into the giant axon of a squid and began to apply a current. Cole discovered that it was possible to use two electrodes and a feedback circuit to keep the cell's membrane potential at a level set by the experimenter. Cole developed the voltage clamp technique before the era of microelectrodes, so his two electrodes consisted of fine wires twisted around an insulating rod. Because this type of electrode could be inserted into only the largest cells, early electrophysiological experiments were conducted almost exclusively on squid axons. Squids squirt jets of water when they need to move quickly, as when escaping a predator. To make this escape as fast as possible, they have an axon that can reach 1 mm in diameter (signals propagate more quickly down large axons). The squid giant axon was the first
https://en.wikipedia.org/wiki/Coherent%20sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under operations such as taking kernels, images, and cokernels. The quasi-coherent sheaves are a generalization of coherent sheaves and include the locally free sheaves of infinite rank. Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf. Definitions A quasi-coherent sheaf on a ringed space is a sheaf of -modules which has a local presentation, that is, every point in has an open neighborhood in which there is an exact sequence for some (possibly infinite) sets and . A coherent sheaf on a ringed space is a sheaf satisfying the following two properties: is of finite type over , that is, every point in has an open neighborhood in such that there is a surjective morphism for some natural number ; for any open set , any natural number , and any morphism of -modules, the kernel of is of finite type. Morphisms between (quasi-)coherent sheaves are the same as morphisms of sheaves of -modules. The case of schemes When is a scheme, the general definitions above are equivalent to more explicit ones. A sheaf of -modules is quasi-coherent if and only if over each open affine subscheme the restriction is isomorphic to the sheaf associated to the module over . When is a locally Noetherian scheme, is coherent if and only if it is quasi-coherent and the modules above can be taken to be finitely generated. On an affine scheme , there is an equivalence of categories from -modules to quasi-coherent sheaves, taking a module to the as
https://en.wikipedia.org/wiki/Message%20forgery
In cryptography, message forgery is sending a message so to deceive the recipient about the actual sender's identity. A common example is sending a spam or prank e-mail as if it were originated from an address other than the one which was really used. See also Authentication Message authentication code Stream cipher attack Cryptographic attacks Practical jokes
https://en.wikipedia.org/wiki/K%C3%A4hler%20differential
In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. The notion was introduced by Erich Kähler in the 1930s. It was adopted as standard in commutative algebra and algebraic geometry somewhat later, once the need was felt to adapt methods from calculus and geometry over the complex numbers to contexts where such methods are not available. Definition Let and be commutative rings and be a ring homomorphism. An important example is for a field and a unital algebra over (such as the coordinate ring of an affine variety). Kähler differentials formalize the observation that the derivatives of polynomials are again polynomial. In this sense, differentiation is a notion which can be expressed in purely algebraic terms. This observation can be turned into a definition of the module of differentials in different, but equivalent ways. Definition using derivations An -linear derivation on is an -module homomorphism to an -module satisfying the Leibniz rule (it automatically follows from this definition that the image of is in the kernel of ). The module of Kähler differentials is defined as the -module for which there is a universal derivation . As with other universal properties, this means that is the best possible derivation in the sense that any other derivation may be obtained from it by composition with an -module homomorphism. In other words, the composition with provides, for every , an -module isomorphism One construction of and proceeds by constructing a free -module with one formal generator for each in , and imposing the relations , , , for all in and all and in . The universal derivation sends to . The relations imply that the universal derivation is a homomorphism of -modules. Definition using the augmentation ideal Another construction proceeds by letting be the ideal in the tensor product defined as the kernel of the multiplication map Then the module of Käh
https://en.wikipedia.org/wiki/RTAI
Real-time application interface (RTAI) is a real-time extension for the Linux kernel, which lets users write applications with strict timing constraints for Linux. Like Linux itself the RTAI software is a community effort. RTAI provides deterministic response to interrupts, POSIX-compliant and native RTAI real-time tasks. RTAI supports several architectures, including IA-32 (with and without FPU and TSC), x86-64, PowerPC, ARM (StrongARM and ARM7: clps711x-family, Cirrus Logic EP7xxx, CS89712, PXA25x), and MIPS. RTAI consists mainly of two parts: an Adeos-based patch to the Linux kernel which introduces a hardware abstraction layer, and a broad variety of services which make lives of real-time programmers easier. RTAI versions over 3.0 use an Adeos kernel patch, slightly modified in the x86 architecture case, providing additional abstraction and much lessened dependencies on the "patched" operating system. Adeos is a kernel patch comprising an Interrupt Pipeline where different operating system domains register interrupt handlers. This way, RTAI can transparently take over interrupts while leaving the processing of all others to Linux. Use of Adeos also frees RTAI from patent restrictions caused by RTLinux project. RTAI-XML RTAI-XML is a server component of RTAI, implementing a service-oriented way to design and develop real-time (RT) control applications. This project was born to fulfill the needs of a university group, mainly focused to have a flexible platform for learning control systems design, allowing the students to test their programs remotely, over the Internet. Leaving the first wishful thinking and going to the real implementation gave rise to the alpha version of RTAI-XML, that showed the potential impact of the basic idea of a net separation of hard and soft real-time tasks in the programmation logic. What was necessary to assure that students could not crash the RT process, is now becoming a new RTAI paradigm. RTAI-XML consists of a server compo
https://en.wikipedia.org/wiki/Adaptive%20Domain%20Environment%20for%20Operating%20Systems
Adeos (Adaptive Domain Environment for Operating Systems) is a nanokernel hardware abstraction layer (HAL), or hypervisor, that operates between computer hardware and the operating system (OS) that runs on it. It is distinct from other nanokernels in that it is not only a low level layer for an outer kernel. Instead, it is intended to run several kernels together, which makes it similar to full virtualization technologies. It is free and open-source software released under a GNU General Public License (GPL). Adeos provides a flexible environment for sharing hardware resources among multiple operating systems, or among multiple instances of one OS, thereby enabling multiple prioritized domains to exist simultaneously on the same hardware. Adeos has been successfully inserted beneath the Linux kernel, opening a range of possibilities, such as symmetric multiprocessing (SMP) clustering, more efficient virtualization, patchless kernel debugging, and real-time computing (RT) systems for Linux. Unusually among HALs, Adeos can be loaded as a Linux loadable kernel module to allow another OS to run along with it. Adeos was developed in the context of real-time application interface (RTAI) to modularize it and separate the HAL from the real-time kernel. Prior work Two categories of methods exist to enable multiple operating systems to run on the same system. The first is simulation-based and provides a virtual environment for which to run additional operating systems. The second suggests the use of a nanokernel layer to enable hardware sharing. In the simulation category, there are tools such as Xen, VMware, Plex86, VirtualPC and SimOS. There is also Kernel-based Virtual Machine (KVM) which is more similar to Adeos , but is not RT and requires specific virtualization hardware support. These methods are used for users who desire to run applications foreign to their base OS, they provide no control over the base OS to the user. Simulation was never meant to be used in a pr
https://en.wikipedia.org/wiki/Mosaic%20%28genetics%29
Mosaicism or genetic mosaicism is a condition in which a multicellular organism possesses more than one genetic line as the result of genetic mutation. This means that various genetic lines resulted from a single fertilized egg. Mosaicism is one of several possible causes of chimerism, wherein a single organism is composed of cells with more than one distinct genotype. Genetic mosaicism can result from many different mechanisms including chromosome nondisjunction, anaphase lag, and endoreplication. Anaphase lagging is the most common way by which mosaicism arises in the preimplantation embryo. Mosaicism can also result from a mutation in one cell during development, in which case the mutation will be passed on only to its daughter cells (and will be present only in certain adult cells). Somatic mosaicism is not generally inheritable as it does not generally affect germ cells. History In 1929, Alfred Sturtevant studied mosaicism in Drosophila, a genus of fruit fly. Muller in 1930 demonstrated that mosaicism in Drosophila is always associated with chromosomal rearrangements and Schultz in 1936 showed that in all cases studied these rearrangements were associated with heterochromatic inert regions, several hypotheses on the nature of such mosaicism were proposed. One hypothesis assumed that mosaicism appears as the result of a break and loss of chromosome segments. Curt Stern in 1935 assumed that the structural changes in the chromosomes took place as a result of somatic crossing, as a result of which mutations or small chromosomal rearrangements in somatic cells. Thus the inert region causes an increase in mutation frequency or small chromosomal rearrangements in active segments adjacent to inert regions. In the 1930s, Stern demonstrated that genetic recombination, normal in meiosis, can also take place in mitosis. When it does, it results in somatic (body) mosaics. These organisms contain two or more genetically distinct types of tissue. The term somatic mosaicism
https://en.wikipedia.org/wiki/Stone%27s%20representation%20theorem%20for%20Boolean%20algebras
In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Marshall H. Stone. Stone was led to it by his study of the spectral theory of operators on a Hilbert space. Stone spaces Each Boolean algebra B has an associated topological space, denoted here S(B), called its Stone space. The points in S(B) are the ultrafilters on B, or equivalently the homomorphisms from B to the two-element Boolean algebra. The topology on S(B) is generated by a (closed) basis consisting of all sets of the form where b is an element of B. This is the topology of pointwise convergence of nets of homomorphisms into the two-element Boolean algebra. For every Boolean algebra B, S(B) is a compact totally disconnected Hausdorff space; such spaces are called Stone spaces (also profinite spaces). Conversely, given any topological space X, the collection of subsets of X that are clopen (both closed and open) is a Boolean algebra. Representation theorem A simple version of Stone's representation theorem states that every Boolean algebra B is isomorphic to the algebra of clopen subsets of its Stone space S(B). The isomorphism sends an element to the set of all ultrafilters that contain b. This is a clopen set because of the choice of topology on S(B) and because B is a Boolean algebra. Restating the theorem using the language of category theory; the theorem states that there is a duality between the category of Boolean algebras and the category of Stone spaces. This duality means that in addition to the correspondence between Boolean algebras and their Stone spaces, each homomorphism from a Boolean algebra A to a Boolean algebra B corresponds in a natural way to a continuous function from S(B) to S(A). In other words, there is a contravariant functor
https://en.wikipedia.org/wiki/Data%20Protection%20Act%201998
The Data Protection Act 1998 (DPA, c. 29) was an Act of Parliament of the United Kingdom designed to protect personal data stored on computers or in an organised paper filing system. It enacted provisions from the European Union (EU) Data Protection Directive 1995 on the protection, processing, and movement of data. Under the 1998 DPA, individuals had legal rights to control information about themselves. Most of the Act did not apply to domestic use, such as keeping a personal address book. Anyone holding personal data for other purposes was legally obliged to comply with this Act, subject to some exemptions. The Act defined eight data protection principles to ensure that information was processed lawfully. It was superseded by the Data Protection Act 2018 (DPA 2018) on 23 May 2018. The DPA 2018 supplements the EU General Data Protection Regulation (GDPR), which came into effect on 25 May 2018. The GDPR regulates the collection, storage, and use of personal data significantly more strictly. Background The 1998 Act replaced the Data Protection Act of 1984 and the Access to Personal Files Act of 1987. Additionally, the 1998 Act implemented the EU Data Protection Directive 1995. The Privacy and Electronic Communications (EC Directive) Regulations 2003 altered the consent requirement for most electronic marketing to "positive consent" such as an opt-in box. Exemptions remain for the marketing of "similar products and services" to existing customers and enquirers, which can still be permitted on an opt-out basis. The Jersey data protection law was modelled on the United Kingdom's law. Contents Scope of protection Section 1 of DPA 1998 defined "personal data" as any data that could have been used to identify a living individual. Anonymised or aggregated data was less regulated by the Act, provided the anonymisation or aggregation had not been done reversibly. Individuals could have been identified by various means including name and address, telephone number, or em
https://en.wikipedia.org/wiki/Multi-index%20notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices. Definition and basic properties An n-dimensional multi-index is an -tuple of non-negative integers (i.e. an element of the -dimensional set of natural numbers, denoted ). For multi-indices and , one defines: Componentwise sum and difference Partial order Sum of components (absolute value) Factorial Binomial coefficient Multinomial coefficient where . Power . Higher-order partial derivative where (see also 4-gradient). Sometimes the notation is also used. Some applications The multi-index notation allows the extension of many formulae from elementary calculus to the corresponding multi-variable case. Below are some examples. In all the following, (or ), , and (or ). Multinomial theorem Multi-binomial theorem Note that, since is a vector and is a multi-index, the expression on the left is short for . Leibniz formula For smooth functions and , Taylor series For an analytic function in variables one has In fact, for a smooth enough function, we have the similar Taylor expansion where the last term (the remainder) depends on the exact version of Taylor's formula. For instance, for the Cauchy formula (with integral remainder), one gets General linear partial differential operator A formal linear -th order partial differential operator in variables is written as Integration by parts For smooth functions with compact support in a bounded domain one has This formula is used for the definition of distributions and weak derivatives. An example theorem If are multi-indices and , then Proof The proof follows from the power rule for the ordinary derivative; if α and β are in , then Suppose , , and . Then we have that For each in , the function only depends on . In the above, each partial differe
https://en.wikipedia.org/wiki/X/Open
X/Open group (also known as the Open Group for Unix Systems and incorporated in 1987 as X/Open Company, Ltd.) was a consortium founded by several European UNIX systems manufacturers in 1984 to identify and promote open standards in the field of information technology. More specifically, the original aim was to define a single specification for operating systems derived from UNIX, to increase the interoperability of applications and reduce the cost of porting software. Its original members were Bull, ICL, Siemens, Olivetti, and Nixdorf—a group sometimes referred to as BISON. Philips and Ericsson joined in 1985, at which point the name X/Open was adopted. The group published its specifications as X/Open Portability Guide, starting with Issue 1 in 1985, and later as X/Open CAE Specification. In 1987, X/Open was incorporated as X/Open Company, Ltd. By March 1988, X/Open grew to 13 members: AT&T, Digital, Hewlett-Packard, Sun Microsystems, Unisys, NCR, Olivetti, Bull, Ericsson, Nixdorf, Philips, ICL, and Siemens. By 1990 the group had expanded to 21 members: in addition to the original five, Philips and Nokia from Europe; AT&T, Digital, Unisys, Hewlett-Packard, IBM, NCR, Sun, Prime Computer, Apollo Computer from North America; Fujitsu, Hitachi, and NEC from Japan; plus the Open Software Foundation and Unix International. In October 1993, a planned transfer of UNIX trademark from Novell to X/Open was announced; it was finalized in 2nd quarter of 1994. In 1994, X/Open published the Single UNIX Specification, which was drawn from XPG4 Base and other sources. In 1996, X/Open merged with the Open Software Foundation to form The Open Group. X/Open was also responsible for the XA protocol for heterogeneous distributed transaction processing, which was released in 1991. X/Open Portability Guide X/Open published its specifications under the name X/Open Portability Guide (or XPG). Based on the AT&T System V Interface Definition, the guide has a wider scope than POSIX, wh
https://en.wikipedia.org/wiki/TICOM
TICOM (Target Intelligence Committee) was a secret Allied project formed in World War II to find and seize German intelligence assets, particularly in the field of cryptology and signals intelligence. It operated alongside other Western Allied efforts to extract German scientific and technological information and personnel during and after the war, including Operation Paperclip (for rocketry), Operation Alsos (for nuclear information) and Operation Surgeon (for avionics). Competition with the Soviet Union for these same spoils of war was intense, with direct payoffs including missile technology that led both to a heightened Cold War stalemate and landing a man on the Moon. History The project was initiated by the British, but when the US Army Chief of Staff General George Marshall learnt of it, it soon became Anglo-American. The aim was to seek out and capture the cryptologic secrets of Germany. The concept was for teams of cryptologic experts, mainly drawn from the code-breaking center at Bletchley Park, to enter Germany with the front-line troops and capture the documents, technology and personnel of the various German signal intelligence organizations before these precious secrets could be destroyed, looted, or captured by the Soviets. There were six such teams. Team 1 was tasked to capture German Geheimschreiber (secret writer) machines whose enciphered traffic was code named Fish Team 2 was to assist Team 1 with transporting Field Marshal Kesselring's communications train to Britain (the so-called "Jellyfish Convoy") Team 3 was to investigate an intact German Signals intelligence unit called "Pers Z S" Team 4 was to investigate in more detail the places in southern Germany that the Team 1 search had passed over quickly Team 5: Following the serendipitous discovery of a waterproof box containing some of the archives of the Cipher Department of the High Command of the Wehrmacht (OKW/Chi) on the bed of Lake Schliersee, this team was tasked with recovering
https://en.wikipedia.org/wiki/Structured%20systems%20analysis%20and%20design%20method
Structured Systems Analysis and Design Method (SSADM) is a systems approach to the analysis and design of information systems. SSADM was produced for the Central Computer and Telecommunications Agency, a UK government office concerned with the use of technology in government, from 1980 onwards. Overview SSADM is a waterfall method for the analysis and design of information systems. SSADM can be thought to represent a pinnacle of the rigorous document-led approach to system design, and contrasts with more contemporary agile methods such as DSDM or Scrum. SSADM is one particular implementation and builds on the work of different schools of structured analysis and development methods, such as Peter Checkland's soft systems methodology, Larry Constantine's structured design, Edward Yourdon's Yourdon Structured Method, Michael A. Jackson's Jackson Structured Programming, and Tom DeMarco's structured analysis. The names "Structured Systems Analysis and Design Method" and "SSADM" are registered trademarks of the Office of Government Commerce (OGC), which is an office of the United Kingdom's Treasury. History The principal stages of the development of Structured System Analysing And Design Method were: 1980: Central Computer and Telecommunications Agency (CCTA) evaluate analysis and design methods. 1981: Consultants working for Learmonth & Burchett Management Systems, led by John Hall, chosen to develop SSADM v1. 1982: John Hall and Keith Robinson left to found Model Systems Ltd, LBMS later developed LSDM, their proprietary version. 1983: SSADM made mandatory for all new information system developments 1984: Version 2 of SSADM released 1986: Version 3 of SSADM released, adopted by NCC 1988: SSADM Certificate of Proficiency launched, SSADM promoted as ‘open’ standard 1989: Moves towards Euromethod, launch of CASE products certification scheme 1990: Version 4 launched 1993: SSADM V4 Standard and Tools Conformance Scheme 1995: SSADM V4+ announced, V4.2 laun
https://en.wikipedia.org/wiki/Truth%20function
In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly one truth value; and inputting the same truth value(s) will always output the same truth value. The typical example is in propositional logic, wherein a compound statement is constructed using individual statements connected by logical connectives; if the truth value of the compound statement is entirely determined by the truth value(s) of the constituent statement(s), the compound statement is called a truth function, and any logical connectives used are said to be truth functional. Classical propositional logic is a truth-functional logic, in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function. On the other hand, modal logic is non-truth-functional. Overview A logical connective is truth-functional if the truth-value of a compound sentence is a function of the truth-value of its sub-sentences. A class of connectives is truth-functional if each of its members is. For example, the connective "and" is truth-functional since a sentence like "Apples are fruits and carrots are vegetables" is true if, and only if each of its sub-sentences "apples are fruits" and "carrots are vegetables" is true, and it is false otherwise. Some connectives of a natural language, such as English, are not truth-functional. Connectives of the form "x believes that ..." are typical examples of connectives that are not truth-functional. If e.g. Mary mistakenly believes that Al Gore was President of the USA on April 20, 2000, but she does not believe that the moon is made of green cheese, then the sentence "Mary believes that Al Gore was President of the USA on April 20, 2000" is true w
https://en.wikipedia.org/wiki/Bluejacking
Bluejacking is the sending of unsolicited messages over Bluetooth to Bluetooth-enabled devices such as mobile phones, PDAs or laptop computers, sending a vCard which typically contains a message in the name field (i.e., for bluedating) to another Bluetooth-enabled device via the OBEX protocol. Bluetooth has a very limited range, usually around on mobile phones, but laptops can reach up to with powerful (Class 1) transmitters. Origins Bluejacking was reportedly first carried out between 2001 and 2003 by a Malaysian IT consultant who used his phone to advertise Ericsson to a single Nokia 7650 phone owner in a Malaysian bank. He also invented the name, which he claims is an amalgam of Bluetooth and ajack, his username on Esato, a Sony Ericsson fan online forum. Jacking is, however, an extremely common shortening of "hijack', the act of taking over something. Ajack's original posts are hard to find, but references to the exploit are common in 2003 posts. Another user on the forum claims earlier discovery, reporting a near-identical story to that attributed to Ajack, except they describe bluejacking 44 Nokia 7650 phones instead of one, and the location is a garage, seemingly in Denmark, rather than a Malaysian Bank. Also, the message was an insult to Nokia owners rather than a Sony Ericsson advertisement. Usage Bluejacking is usually not very harmful, except that bluejacked people generally don't know what has happened, and so may think that their phone is malfunctioning. Usually, a bluejacker will only send a text message, but with modern phones it's possible to send images or sounds as well. Bluejacking has been used in guerrilla marketing campaigns to promote advergames. Bluejacking is also confused with Bluesnarfing, which is the way in which mobile phones are illegally hacked via Bluetooth. Companies BluejackQ BlueJackQ is a website dedicated to bluejacking. The website contains a few bluejacking stories taken from the site's forum. The website also in
https://en.wikipedia.org/wiki/Joule%20heating
Joule heating (also known as resistive, resistance, or Ohmic heating) is the process by which the passage of an electric current through a conductor produces heat. Joule's first law (also just Joule's law), also known in countries of the former USSR as the Joule–Lenz law, states that the power of heating generated by an electrical conductor equals the product of its resistance and the square of the current. Joule heating affects the whole electric conductor, unlike the Peltier effect which transfers heat from one electrical junction to another. Joule-heating or resistive-heating is used in multiple devices and industrial process. The part that converts electricity into heat is called a heating element. Among the many practical uses are: An incandescent light bulb glows when the filament is heated by Joule heating, due to thermal radiation (also called blackbody radiation). Electric fuses are used as a safety, breaking the circuit by melting if enough current flows to melt them. Electronic cigarettes vaporize propylene glycol and vegetable glycerine by Joule heating. Multiple heating devices use Joule heating, such as electric stoves, electric heaters, soldering irons, cartridge heaters. Some food processing equipment may make use of Joule heating: running current through food material (which behave as an electrical resistor) causes heat release inside the food. The alternating electrical current coupled with the resistance of the food causes the generation of heat. A higher resistance increases the heat generated. Ohmic heating allows for fast and uniform heating of food products, which maintains quality. Products with particulates heat up faster (compared to conventional heat processing) due to higher resistance. History James Prescott Joule first published in December 1840, an abstract in the Proceedings of the Royal Society, suggesting that heat could be generated by an electrical current. Joule immersed a length of wire in a fixed mass of water and me
https://en.wikipedia.org/wiki/Store%20and%20forward
Store and forward is a telecommunications technique in which information is sent to an intermediate station where it is kept and sent at a later time to the final destination or to another intermediate station. The intermediate station, or node in a networking context, verifies the integrity of the message before forwarding it. In general, this technique is used in networks with intermittent connectivity, especially in the wilderness or environments requiring high mobility. It may also be preferable in situations when there are long delays in transmission and error rates are variable and high, or if a direct, end-to-end connection is not available. Modern store and forward networking Store and forward originates with delay-tolerant networks. No real-time services are available for these kinds of networks. Logistical Networking is a scalable form of store and forward networking that exposes network-embedded buffers on intermediate nodes and allows flexible creation of services by higher-level managers including caching, point-to-multipoint communication (or multicast), content delivery and many other stateful distributed services. Real time services can be created using logistical networking when data transfer connectivity permits. A store-and-forward switching center is a message switching center in which a message is accepted from the originating user, i.e., sender, when it is offered, held in a physical storage, and forwarded to the destination user, i.e., receiver, in accordance with the priority placed upon the message by the originating user and the availability of an outgoing channel. Store and forward switching centers are usually implemented in mobile service stations where the messages that are sent from the sender is first sent to these centers. If the destination address isn't available, then the center stores this message and tries sending it later. This improves the probability of the message to be delivered. In the other case, if the destinatio
https://en.wikipedia.org/wiki/OS-tan
OS-tan is an Internet meme consisting of moe anthropomorphs of popular operating systems, originating on the Japanese imageboard Futaba Channel. The designs of OS-tan, which were created by various amateur Japanese artists, are typically female; for example, the personifications of Microsoft Windows operating systems are often depicted as sisters of varying ages. The -tan element in the term is a hypocoristic suffix in Japanese that implies extremely youthful endearment. Though initially appearing only in fan works, the OS-tan proved popular enough that Microsoft branches in Singapore and Taiwan used the OS-tan concept as the basis for ad campaigns for Internet Explorer and Microsoft Silverlight, respectively. History The concept of the OS-tan is reported to have begun as a personification of the common perception of Windows Me (Released in 2000 by Microsoft as the 9x counterpart to Windows 2000) as unstable and prone to frequent crashes. Discussions on Futaba Channel likened this to the stereotype of a fickle, troublesome girl and as this personification expanded Me-tan was created and followed by the other characters. One of the early works to predominantly feature the OS-tan was an interactive Flash animation showing a possible intro to an imaginary anime show known as Trouble Windows. It was first published on April 2004 and appears to have quickly spread worldwide. Commercial products Ohzora Publishing produced one book based on OS-tan characters, titled . It includes illustrations by over 25 contributors. It also includes 95-tan, ME-tan, XP-tan figures, titled OS Girl 95, OS Girl me, OS Girl XP respectively, but include a molded space for 2k-tan (named OS Girl 2K). ME-tan, 2K-tan, XP-tan were designed by GUHICO of Stranger Workshop, while 95-tan was designed by Fujisaki Shiro from H.B.Company. Parthenon Production Limited, company had commercialized Pink Company's OS-tan products. MALINO from Deja Vu ArtWorks produced the Me Document and Shared Folder!
https://en.wikipedia.org/wiki/Not%20Another%20Completely%20Heuristic%20Operating%20System
Not Another Completely Heuristic Operating System, or Nachos, is instructional software for teaching undergraduate, and potentially graduate level operating systems courses. It was developed at the University of California, Berkeley, designed by Thomas Anderson, and is used by numerous schools around the world. Originally written in C++ for MIPS, Nachos runs as a user-process on a host operating system. A MIPS simulator executes the code for any user programs running on top of the Nachos operating system. Ports of the Nachos code exist for a variety of architectures. In addition to the Nachos code, a number of assignments are provided with the Nachos system. The goal of Nachos is to introduce students to concepts in operating system design and implementation by requiring them to implement significant pieces of functionality within the Nachos system. In Nachos' case, Operating System simulator simply means that you can run an OS (a guest OS) on top of another one (the host OS), similar to Bochs/VMware. It features emulation for: A CPU (a MIPS CPU) A hard drive An interrupt controller, timer, and misc. other components which are there to run the Nachos user space applications. That means that you can write programs for Nachos, compile them with a real compiler (an old gcc compiler that produces code for MIPS) and run them. The Nachos kernel instead is compiled to the platform of the Host OS and thus runs natively on the Host OS' CPU. Nachos version 3.4 has been the stable, commonly used version of Nachos for many years. Nachos version 4.0 has existed as a beta since approximately 1996. Implementation Nachos has various modules implementing the functionality of a basic operating system. The wrapper functions for various system calls of the OS kernel are generally implemented in a manner similar to that of the UNIX system calls . Various parts of the OS are instantiated as objects using the native code. For example, a class Machineis used as the master cla
https://en.wikipedia.org/wiki/EMWIN
The Emergency Managers Weather Information Network (EMWIN) is a system for distributing a live stream of weather information in the United States. The backbone of the system is operated via satellite by the U.S. National Weather Service (NWS), but data are transmitted over radio repeaters by the NWS, citizens, and other organizations in many regions, and information can also be downloaded via the Internet. Local VHF/UHF radio rebroadcasts and older-generation EMWIN satellite systems operate at the speeds of 1200 and 9600 baud. EMWIN data consists of textual observational and forecast information, including a limited number of cloud and radar images. The new EMWIN, labeled EMWIN-N, began being upgraded in 2009. The upgrade continues through 2011 to ready older GOES satellites to provide a higher speed of 19.2 kbit/s. The data broadcasts are monetarily free with both local rebroadcasts and satellite feeds. EMWIN via Twitter may be done by anyone to spread information on all types of emergencies to virtually unlimited numbers of people in real time also. EMWIN weather data is primarily transmitted over GOES satellites that observe the United States. The new satellites are the GOES-R series, and are designated GOES 16 and GOES 17. On February 13, 2017 it suffered a service disruption. References External links EMWIN homepage EMWIN-N (new system) Meteorological data and networks Disaster preparedness in the United States
https://en.wikipedia.org/wiki/Free-radical%20theory%20of%20aging
The free radical theory of aging states that organisms age because cells accumulate free radical damage over time. A free radical is any atom or molecule that has a single unpaired electron in an outer shell. While a few free radicals such as melanin are not chemically reactive, most biologically relevant free radicals are highly reactive. For most biological structures, free radical damage is closely associated with oxidative damage. Antioxidants are reducing agents, and limit oxidative damage to biological structures by passivating them from free radicals. Strictly speaking, the free radical theory is only concerned with free radicals such as superoxide ( O2− ), but it has since been expanded to encompass oxidative damage from other reactive oxygen species (ROS) such as hydrogen peroxide (H2O2), or peroxynitrite (OONO−). Denham Harman first proposed the free radical theory of aging in the 1950s, and in the 1970s extended the idea to implicate mitochondrial production of ROS. In some model organisms, such as yeast and Drosophila, there is evidence that reducing oxidative damage can extend lifespan. However, in mice, only 1 of the 18 genetic alterations (SOD-1 deletion) that block antioxidant defences, shortened lifespan. Similarly, in roundworms (Caenorhabditis elegans), blocking the production of the naturally occurring antioxidant superoxide dismutase has been shown to increase lifespan. Whether reducing oxidative damage below normal levels is sufficient to extend lifespan remains an open and controversial question. Background The free radical theory of aging was conceived by Denham Harman in the 1950s, when prevailing scientific opinion held that free radicals were too unstable to exist in biological systems. This was also before anyone invoked free radicals as a cause of degenerative diseases. Two sources inspired Harman: 1) the rate of living theory, which holds that lifespan is an inverse function of metabolic rate which in turn is proportional to oxy
https://en.wikipedia.org/wiki/Word%20clock
In digital audio electronics, a word clock or wordclock (sometimes sample clock, which can have a broader meaning) is a clock signal used to synchronise other devices, such as digital audio tape machines and compact disc players, which interconnect via digital audio signals. Word clock is so named because it clocks each audio sample. Samples are represented in data words. S/PDIF, AES/EBU, MADI, ADAT, and TDIF are some of the formats that use a word clock. Various audio over Ethernet systems use communication protocols to distribute word clock. The device which generates the word clock is the clock source for all the other audio devices. The signal is used for synchronizing digital audio signals between devices, such as CD players, audio I/O cards, etc. It allows all the components in the signal path to process the data and remain synchronized with each other. Comparison to timecode Word clock should not be confused with timecode; word clock is used entirely to keep a perfectly timed and constant bitrate to avoid timing errors that can cause data transmission errors. Timecode is metadata about the media data being transmitted. Time code can be used as an initial phase reference for jam sync using the word clock as the frequency reference. Over coax cable Professional digital audio equipment may have a word clock input or output to synchronize timing between multiple devices. Although the electrical characteristics of the word clock signal have not been completely standardized, some characteristics should always apply. Items that should remain consistent are TTL level, a 75ohm output impedance, 75ohm cables and a 75ohm terminating resistor at the end of a chain or cable. Proper termination of the word clock signal with a 75ohm resistor is important. It prevents the clock signal from reflecting back into the cable and causing false detection of extra 1's and 0's. Some digital equipment includes a switchable terminator, some include a hardwired terminator and ot
https://en.wikipedia.org/wiki/Espada%20Acequia
The Espada Acequia, or Piedras Creek Aqueduct, was built by Franciscan friars in 1731 in what is now San Antonio, Texas, United States. It was built to supply irrigation water to the lands near Mission San Francisco de la Espada, today part of San Antonio Missions National Historical Park. The acequia is still in use today and is an National Historic Civil Engineering Landmark and a National Historic Landmark. Irrigation system Mission Espada's acequia (irrigation) system can still be seen today. The main ditch, or acequia madre, continues to carry water to the mission and its former farmlands. This water is still used by residents living on these neighboring lands. The initial survival of a new mission depended upon the planting and harvesting of crops. In south central Texas, intermittent rainfall and the need for a reliable water source made the design and installation of an acequia system a high priority. Irrigation was so important to Spanish colonial settlers that they measured cropland in suertes -the amount of land that could be watered in one day. The use of acequias was originally brought to the arid regions of Spain by the Romans and the Moors. When Franciscan missionaries arrived in the desert Southwest they found the system worked well in the hot, dry environment. In some areas, like New Mexico, it blended in easily with the irrigation system already in use by the Puebloan Native Americans. In order to distribute water to the missions along the San Antonio River, Franciscan missionaries oversaw the construction of seven gravity-flow ditches, dams, and at least one aqueduct—a network that irrigated approximately of land. The acequia not only conducted potable water and irrigation, but also powered a mill. Mission Espada has survived from its beginnings to the present day as a community center that still supports a Catholic parish and religious education, however a school originally opened by the Sisters of the Incarnate Word and Blessed Sacramen
https://en.wikipedia.org/wiki/Media%20filter
A media filter is a type of filter that uses a bed of sand, peat, shredded tires, foam, crushed glass, geo-textile fabric, anthracite, crushed granite or other material to filter water for drinking, swimming pools, aquaculture, irrigation, stormwater management, oil and gas operations, and other applications. Each layer of media is designed to filter out specific types and sizes of particles, allowing for more efficient and effective removal of contaminants. Design One design brings the water in the top of a container through a "header" which distributes the water evenly. The filter "media" start with fine sand on the top and then becomes gradually coarser sand in a number of layers followed by gravel on the bottom, in gradually larger sizes. The top sand physically removes particles from the water. The job of the subsequent layers is to support the finer layer above and provide efficient drainage. As particles become trapped in the media, the differential pressure across the bed increases. Periodically, a backwash may be initiated to remove the solids trapped in the bed. During backwash, flow is directed in the opposite direction from normal flow. In multi-media filters, the layers in the media re-stratify due to density differences prior to resuming normal filtration. Multimedia filter can remove particles down to 10-25 microns. Advantages and disadvantages Advantages of multimedia filters Multimedia filters use multiple layers of different filter media to achieve more effective and efficient filtration than single-media filters like sand filters.     They can remove a wider range of particle sizes and types than single-media filters, resulting in more efficient filtration and longer filter life.   They are effective at removing suspended solids, turbidity, and other contaminants from water.     They can be used for a wide range of flow rates and particle sizes. They can be easily backwashed to clean the filter media and restore filtration efficiency.  
https://en.wikipedia.org/wiki/Off-side%20rule
A computer programming language is said to adhere to the off-side rule of syntax if blocks in that language are expressed by their indentation. The term was coined by Peter Landin, possibly as a pun on the offside rule in association football. This is contrasted with free-form languages, notably curly-bracket programming languages, where indentation has no computational meaning and indent style is only a matter of coding conventions and formatting. Off-side-rule languages are also described as having significant indentation. Definition Peter Landin, in his 1966 article "The Next 700 Programming Languages", defined the off-side rule thus: "Any non-whitespace token to the left of the first such token on the previous line is taken to be the start of a new declaration." Code examples The following is an example of indentation blocks in Python. The colons are part of the Python language syntax for readability; they are not needed to implement the off-side rule. In Python, the rule is taken to define the boundaries of statements rather than declarations. def is_even(a: int) -> bool: """Determine whether number 'a' is even.""" if a % 2 == 0: print('Even!') return True print('Odd!') return False Python also suspends the off-side rule within brackets. A statement within brackets continues until its brackets match (or mismatch): { "this": True, "that": False, "them": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] } In this dictionary, the keys are indented, and a list is split between four lines. Implementation The off-side rule can be implemented in the lexical analysis phase, as in Python, where increasing the indenting results in the lexer outputting an INDENT token, and decreasing the indenting results in the lexer outputting a DEDENT token. These tokens correspond to the opening brace { and closing brace } in languages that use braces for blocks, and means that the phrase grammar does not depend on whether braces or indentation
https://en.wikipedia.org/wiki/Indentation%20%28typesetting%29
In the written form of many languages, an indentation or indent is an empty space at the beginning of a line to signal the start of a new paragraph. Many computer languages have adopted this technique to designate "paragraphs" or other logical blocks in the program. For example, the following lines are indented, using between one and six spaces:  This paragraph is indented by 1 space.    This paragraph is indented by 3 spaces.       This paragraph is indented by 6 spaces. In computer programming, the neologisms outdent, unindent and dedent are used to describe the reversal of the indentation process, realigning text with the page margin (or with previous, lesser, levels of indentation). In right-to-left languages (e.g. Hebrew and Arabic), indentation is used just the same, but from the right margin of the paper, where the line begins. Indentation in typesetting There are three main types of indentation, illustrated below in relation to borders representing the page dimensions. Indentation in programming In computer programming languages, indentation is used to format program source code to improve readability. Indentation is generally only of use to programmers; compilers and interpreters rarely care how much whitespace is present in between programming statements. However, certain programming languages rely on the use of indentation to demarcate programming structure, often using a variation of the off-side rule. The Haskell, Occam, Python, MoonScript, and Ya programming languages rely on indentation in this way. Opinions about where to indent, whether to use spaces or tabs, and how many spaces to use are often hotly debated among programmers, leading some to describe indentation disputes as akin to a religious war. In 2006 a third method of indentation was proposed, called elastic tabstops. In addition to general indentation of statements, different bracket indentation styles are commonly used. References Typography Source code
https://en.wikipedia.org/wiki/WordPress
WordPress (also known as WP or WordPress.org) is a web content management system. It was originally created as a tool to publish blogs but has evolved to support publishing other web content, including more traditional websites, mailing lists and Internet forum, media galleries, membership sites, learning management systems and online stores. Available as free and open-source software, WordPress is among the most popular content management systems – it was used by 42.8% of the top 10 million websites . WordPress is written in PHP hypertext preprocessor language and paired with a MySQL or MariaDB database. Features include a plugin architecture and a template system, referred to within WordPress as "Themes". To function, WordPress has to be installed on a web server, either as part of an Internet hosting service or on a computer running the WordPress software package. WordPress was released on May 27, 2003, by its founders, American developer Matt Mullenweg and English developer Mike Little. WordPress Foundation owns WordPress, WordPress projects, and other related trademarks. Overview "WordPress is a factory that makes webpages" is a core analogy designed to clarify the functions of WordPress: it stores content and enables a user to create and publish webpages, requiring nothing beyond a domain and a hosting service. WordPress has a web template system using a template processor. Its architecture is a front controller, routing all requests for non-static URIs to a single PHP file that parses the URI and identifies the target page. This allows support for more human-readable permalinks. Themes WordPress users may install and switch among many different themes. Themes allow users to change the look and functionality of a WordPress website without altering the core code or site content. Custom code can be added to the website by using a child theme or through code editor. Every WordPress website requires at least one theme to be present. Themes may be directly