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Traditionally, educators and administrators have to wait until students actually withdraw from school or nearly fail their courses to accurately predict when the drop out will occur. Learning engineers are now able to use data on off-task behavior or wheel spinning to better understand student engagement and predict wh... | Wikipedia - Learning engineering | null | null | null |
Proponents of Learning Engineering posit that data analytics will contribute to higher success rates and lower drop-out rates.Learning Engineering can also assist students by providing automatic and individualized feedback. Carnegie Learning’s tool LiveLab, for instance, employs big data to create a learning experience... | Wikipedia - Learning engineering | null | null | null |
Learning augmented algorithms are known for: The ski rental problem The maximum weight matching problem The weighted paging problem | Wikipedia - Learning augmented algorithm | null | null | null |
Learning how to calculate with the abacus may improve capacity for mental calculation. Abacus-based mental calculation (AMC), which was derived from the abacus, is the act of performing calculations, including addition, subtraction, multiplication, and division, in the mind by manipulating an imagined abacus. It is a h... | Wikipedia - Abacus | null | null | null |
They are able to retrieve memory to deal with complex processes. AMC involves both visuospatial and visuomotor processing that generate the visual abacus and move the imaginary beads. Since it only requires that the final position of beads be remembered, it takes less memory and less computation time. | Wikipedia - Abacus | null | null | null |
Learning is often more efficient in children and takes longer or is more difficult with age. A study using neuroimaging identified rapid neurotransmitter GABA boosting as a major potential explanation-component for why that is.Behavioral flexibility can refer to efficiently and appropriately adapting to different situa... | Wikipedia - Brain aging | null | null | null |
Learning problem P can be generalized to admit learning task matrix A as follows: Choice of F: S + T → R + {\displaystyle F:S_{+}^{T}\rightarrow \mathbb {R} _{+}} must be designed to learn matrices A of a given type. See "Special cases" below. | Wikipedia - Multi-task learning | null | null | null |
Learning systems are programs that have no given knowledge of the genre of music they are working with. Instead, they collect the learning material by themselves from the example material supplied by the user or programmer. The material is then processed into a piece of music similar to the example material. This metho... | Wikipedia - Algorithmic composition | null | null | null |
Learning techniques employ statistical methods to perform categorization and analysis without explicit programming. Supervised learning, unsupervised learning, reinforcement learning, and deep learning techniques are included in this category. | Wikipedia - Algorithmic technique | null | null | null |
Learning theorists have investigated other learning criteria, such as the following. Efficiency: minimizing the number of data points required before convergence to a correct hypothesis. Mind Changes: minimizing the number of hypothesis changes that occur before convergence.Mind change bounds are closely related to mis... | Wikipedia - Algorithmic learning theory | null | null | null |
Learning through play is not new, but the themes of computer and mobile games are relatively more modern. Most teachers now use games in elementary classrooms, and most children in developed countries play learning games at home. Computer games with intrinsically mathematical game mechanics can help children learn nove... | Wikipedia - Modern elementary mathematics | null | null | null |
Sometimes it's not obvious what mathematics children learn by "just playing," but basic spatial and numerical skills gained in free play help with mathematical concepts.Some abstract games such as chess can benefit learning mathematics by developing systems thinking, logic, and reasoning. Roleplaying games invite child... | Wikipedia - Modern elementary mathematics | null | null | null |
Board games can have all of the above aspects, and also promote communication about mathematics in small groups. Teachers working with disadvantaged kids note especially large mathematical skill gains after using games in the classroom, possibly because kids don't play such games at home.Many teachers, parents and stud... | Wikipedia - Modern elementary mathematics | null | null | null |
Least fixed point based logics of graphs extend the first-order logic of graphs by allowing predicates (properties of vertices or tuples of vertices) defined by special fixed-point operators. This kind of definition begins with an implication, a formula stating that when certain values of the predicate are true, then o... | Wikipedia - Logic of graphs | null | null | null |
More precisely, its true values should be a subset of the true values of any other fixed point.For instance, define C ( u , v ) {\displaystyle C(u,v)} to be true when the two vertices u {\displaystyle u} and v {\displaystyle v} are connected by a path in a given graph, and false otherwise. Then every vertex is connecte... | Wikipedia - Logic of graphs | null | null | null |
Being the least fixed point, in this case, implies that no two vertices will be defined as connected unless their connectivity comes from repeated use of this implication.Several variations of fixed point logics have been studied. In least fixed point logic, the right hand side of the ← {\displaystyle \leftarrow } oper... | Wikipedia - Logic of graphs | null | null | null |
In another variant with equivalent logical power, inflationary fixed point logic, the formula need not be monotone but the resulting fixed point is defined as the one obtained by repeatedly applying implications derived from the defining formula starting from the all-false predicate. Other variants, allowing negative i... | Wikipedia - Logic of graphs | null | null | null |
The fixed point of a logical formula can be constructed in polynomial time, by an algorithm that repeatedly adds tuples to the set of values for which the predicate is true until reaching a fixed point, so deciding whether a graph models a sentence in this logic can always be decided in polynomial time. Not every polyn... | Wikipedia - Logic of graphs | null | null | null |
Least significant in terms of commercial uses and numbers are the organoarsenic(I) compounds. The anti-syphylic drugs Salvarsan and Neosalvarsan are representative of this class. These compounds typically feature three bonds to As, but only As-As single bonds. | Wikipedia - Organoarsenic compound | null | null | null |
Least-cost paths are calculated for instance to establish tracks of electricity lines or oil pipelines. The algorithm has also been used to calculate optimal long-distance footpaths in Ethiopia and contrast them with the situation on the ground. | Wikipedia - Uniform-cost search | null | null | null |
Least-to-most prompting prompts a model to first list the sub-problems to a problem, then solve them in sequence, such that later sub-problems can be solved with the help of answers to previous sub-problems. | Wikipedia - Few-shot learning (natural language processing) | null | null | null |
Leaves are the primary photosynthetic organs of a plant. Based on their structure, they are classified into two types - microphylls, that lack complex venation patterns and megaphylls, that are large and with a complex venation. It has been proposed that these structures arose independently. Megaphylls, according to th... | Wikipedia - Plant evolutionary developmental biology | null | null | null |
Studies have revealed that these three steps happened multiple times in the evolution of today's leaves.Contrary to the telome theory, developmental studies of compound leaves have shown that, unlike simple leaves, compound leaves branch in three dimensions. Consequently, they appear partially homologous with shoots as... | Wikipedia - Plant evolutionary developmental biology | null | null | null |
Molecular genetics confirmed these conclusions (see below). It has been proposed that the before the evolution of leaves, plants had the photosynthetic apparatus on the stems. Today's megaphyll leaves probably became commonplace some 360 mya, about 40 my after the simple leafless plants had colonized the land in the ea... | Wikipedia - Plant evolutionary developmental biology | null | null | null |
This spread has been linked to the fall in the atmospheric carbon dioxide concentrations in the late Paleozoic era associated with a rise in density of stomata on leaf surface. This must have allowed for better transpiration rates and gas exchange. Large leaves with less stomata would have heated up in the sun's rays, ... | Wikipedia - Plant evolutionary developmental biology | null | null | null |
Leaves contain the cyanogenic glucoside prunasin. == References == | Wikipedia - Olinia ventosa | null | null | null |
Leavitt path algebras has been computed for many graphs, and the following table shows some particular graphs and their Leavitt path algebras. We use the convention that a double arrow drawn from one vertex to another and labeled ∞ {\displaystyle \infty } indicates that there are a countably infinite number of edges fr... | Wikipedia - Leavitt path algebra | null | null | null |
Lebesgue integration In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis. The Lebesgue integral extends the integral to a larger class of functions. It also extends the domains on which these fu... | Wikipedia - Glossary of calculus | null | null | null |
Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be evaluated by substitution, allowing easier evaluation of the limit. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital. Although the contribution of the rule is often att... | Wikipedia - Glossary of calculus | null | null | null |
L'Hôpital's rule states that for functions f and g which are differentiable on an open interval I except possibly at a point c contained in I, if lim x → c f ( x ) = lim x → c g ( x ) = 0 or ± ∞ , {\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0{\text{ or }}\pm \infty ,} g ′ ( x ) ≠ 0 {\displaystyle g'(x)\neq 0} ... | Wikipedia - Glossary of calculus | null | null | null |
limit comparison test The limit comparison test allows one to determine the convergence of one series based on the convergence of another. limit of a function . limits of integration . | Wikipedia - Glossary of calculus | null | null | null |
linear combination In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is ce... | Wikipedia - Glossary of calculus | null | null | null |
list of integrals . logarithm . logarithmic differentiation . lower bound . | Wikipedia - Glossary of calculus | null | null | null |
Lebesgue's number lemma (dimension theory) | Wikipedia - List of lemmas | null | null | null |
The second rule is just a means of introducing assumptions into the derivation. The third and fourth rules just perform directional feature checking, combining the assumptions required to build the subparts that are being combined. The entropy rule presumably allows the ordered sequents to be broken up into unordered s... | Wikipedia - Minimalist grammar | null | null | null |
And finally, the last rule implements "movement" by means of assumption elimination. The last rule can be given a number of different interpretations in order to fully mimic movement of the normal sort found in the Minimalist Program. The account given by Lecomte and Retoré (2001) is that if one of the product types is... | Wikipedia - Minimalist grammar | null | null | null |
Lectins have these functions in animals: The regulation of cell adhesion The regulation of glycoprotein synthesis The regulation of blood protein levels The binding of soluble extracellular and intercellular glycoproteins As a receptor on the surface of mammalian liver cells for the recognition of galactose residues, w... | Wikipedia - Lectin | null | null | null |
Other immune lectins play a role in self-nonself discrimination and they likely modulate inflammatory and autoreactive processes. Intelectins (X-type lectins) bind microbial glycans and may function in the innate immune system as well. Lectins may be involved in pattern recognition and pathogen elimination in the innat... | Wikipedia - Lectin | null | null | null |
Lectins may bind to a soluble carbohydrate or to a carbohydrate moiety that is a part of a glycoprotein or glycolipid. They typically agglutinate certain animal cells and/or precipitate glycoconjugates. Most lectins do not possess enzymatic activity. | Wikipedia - Lectin | null | null | null |
Leduc, Steven A. (May 1, 1996), Linear Algebra (Cliffs Quick Review), Cliffs Notes, ISBN 978-0-8220-5331-6 Lipschutz, Seymour; Lipson, Marc (December 6, 2000), Schaum's Outline of Linear Algebra (3rd ed. ), McGraw-Hill, ISBN 978-0-07-136200-9 Lipschutz, Seymour (January 1, 1989), 3,000 Solved Problems in Linear Algebra... | Wikipedia - Linear Algebra | null | null | null |
Lee Cronbach and Paul Meehl (1955) proposed that the development of a nomological net was essential to the measurement of a test's construct validity. A nomological network defines a construct by illustrating its relation to other constructs and behaviors. It is a representation of the concepts (constructs) of interest... | Wikipedia - Construct validity | null | null | null |
A thorough observation of constructs relationships to each other it can generate new constructs. For example, intelligence and working memory are considered highly related constructs. | Wikipedia - Construct validity | null | null | null |
Through the observation of their underlying components psychologists developed new theoretical constructs such as: controlled attention and short term loading. Creating a nomological net can also make the observation and measurement of existing constructs more efficient by pinpointing errors. Researchers have found tha... | Wikipedia - Construct validity | null | null | null |
Removing the theory of phrenology from the nomological net of intelligence and adding the theory of brain mass evolution, constructs of intelligence are made more efficient and more powerful. The weaving of all of these interrelated concepts and their observable traits creates a "net" that supports their theoretical co... | Wikipedia - Construct validity | null | null | null |
If they do not then there is a problem with measurement (of academic achievement or studiousness), or with the purported theory of achievement. If they are indicators of one another then the nomological network, and therefore the constructed theory, of academic achievement is strengthened. Although the nomological netw... | Wikipedia - Construct validity | null | null | null |
Left censoring – a data point is below a certain value but it is unknown by how much. Interval censoring – a data point is somewhere on an interval between two values. Right censoring – a data point is above a certain value but it is unknown by how much. Type I censoring occurs if an experiment has a set number of subj... | Wikipedia - Censoring (statistics) | null | null | null |
Type II censoring occurs if an experiment has a set number of subjects or items and stops the experiment when a predetermined number are observed to have failed; the remaining subjects are then right-censored. Random (or non-informative) censoring is when each subject has a censoring time that is statistically independ... | Wikipedia - Censoring (statistics) | null | null | null |
Left and right censoring are special cases of interval censoring, with the beginning of the interval at zero or the end at infinity, respectively. Estimation methods for using left-censored data vary, and not all methods of estimation may be applicable to, or the most reliable, for all data sets.A common misconception ... | Wikipedia - Censoring (statistics) | null | null | null |
Left eigenvectors Left and right group actions | Wikipedia - Left and right (algebra) | null | null | null |
Left-digit effect has also been shown to influence stock-market transactions. Bhattacharya, Holden, and Jacobsen (2011) examined the left-digit effect in stock market transactions. They found that there was excess buying at just-below prices ($1.99) versus round numbers ($2.00) right above them. This discrepancy in buy... | Wikipedia - Psychological pricing | null | null | null |
Left: hardening of Portland cement (P.C.) through hydration of calcium silicate into calcium silicate hydrate (C-S-H) and portlandite, Ca(OH)2. Right: hardening (setting) of geopolymer cement (GP) through poly-condensation of potassium oligo-(sialate-siloxo) into potassium poly(sialate-siloxo) cross linked network. | Wikipedia - Geopolymer concrete | null | null | null |
Left: setting and hardening of Portland cement through hydration of calcium silicate into calcium silicate hydrates (C-S-H) and portlandite, Ca(OH)2. Right: setting of geopolymer cement through poly-condensation of potassium oligo-(sialate-siloxo) into potassium poly(sialate-siloxo) cross linked network. If a geopolyme... | Wikipedia - Geopolymer cement | null | null | null |
Legacies of racism exist in Haiti, and affect the way that food grown by peasants domestically is viewed compared to foreign food. Racially coded hierarchies are associated with food that differs in origin – survey respondents reported that food such as millet and root crops are associated with negative connotations, w... | Wikipedia - Ecological racism | null | null | null |
Legacy systems need maintenance and replacement parts to operate past their intended life cycle. Demand for parts that are no longer being manufactured can lead to material shortages of parts, called DMS/DMSMS. There is much demand that entire government divisions have been created to regulate and plan the obsolescence... | Wikipedia - PCB reverse engineering | null | null | null |
There are many legacy systems developed in the 70s, 80s or 90s whose original manufacturer is no longer in business or no longer has the original design data, but whose original equipment is still in use. In many cases exact Form, fit and function is required, either that so parts can “handshake” properly with the exis... | Wikipedia - PCB reverse engineering | null | null | null |
Legal norms form the foundations of legal systems. Its structure can be presented using an ontological model that depicts how rules of conduct stipulated by legal norms influence the creation and use of legislation.The ontological model of legal norms is an important tool as it facilitates efficient research that enabl... | Wikipedia - Legal norms | null | null | null |
The norms themselves can be modelled by logic, rules or ontologies to ease the process of retrieving legal information and semantic browsing.Traditionally, legislation retrieval and browsing systems were based on text retrieval whereby a legal practitioner was required to enter specific words in order to acquire the se... | Wikipedia - Legal norms | null | null | null |
Legal time (PDF), ITU, 2015. The tz database home page, UCLA (deprecated, see Official IANA sources below) The tz mailing list archive, Gmane, archived from the original on 3 February 2008. tz (archive) (mailing list). tz mailing list at ICANN "A literary appreciation of the Olson/Zoneinfo/tz database" by Jon Udell | Wikipedia - Tz database | null | null | null |
Legend 1st – Champions 2nd – Runners-up 3rd/4th/5th/SF/QF/GS – Semi-finals/Quarter-finals/Group Stage GS/10th – Relegated AI – All-Ireland Senior Hurling Championship JM – Joe McDonagh Cup NR – Nicky Rackard CupFor each year, the number of counties (in brackets) are shown. | Wikipedia - Christy Ring Cup | null | null | null |
Legend As of 1 July 2023 (After 2023 Christy Ring Cup). | Wikipedia - Christy Ring Cup | null | null | null |
Legend User Interface: Browser based - executes on a computer server and is accessed via a network using a web browser desktop - executes on a personal computer Create/alter table: Yes - can create table, alter its definition and data, and add new rows Some - can only create/alter table definition, not data Browse tabl... | Wikipedia - Comparison of database tools | null | null | null |
Legend: (s) – solid; (l) – liquid; (g) – gas; (aq) – aqueous (default for all charged species); (Hg) – amalgam; bold – water electrolysis equations. | Wikipedia - Electrochemical series | null | null | null |
Legend: + = Router − or | = Link (X) = Metric of link A (2) B (1) C + - - - - - + - - - - - + | | (2)| | (3) | | + - - - - - + D (1) E Now a client on router E wants to talk to a client on router A. That means a route between router A and router E must be available. This route is calculated as follows: The immediate ne... | Wikipedia - Diffusing Update Algorithm | null | null | null |
Legend: User manager: Yes - user manager with support for database and schema permissions as well as for individual object (table, view, functions) permissions Some - simple user manager with support for database and schema permissions No - no user manager, or read-only user manager | Wikipedia - Comparison of database administration tools | null | null | null |
Legend: Visual schema/E-R design: the ability to draw entity-relationship diagrams for the database. If missing, the following two features will also be missing Reverse engineering - the ability to produce an ER diagram from a database, complete with foreign key relationships Yes - supports incremental reverse engineer... | Wikipedia - Comparison of database tools | null | null | null |
Legendre proved the following identity: K ( cos θ ) E ( sin θ ) + K ( sin θ ) E ( cos θ ) − K ( cos θ ) K ( sin θ ) = π 2 , for all θ . {\displaystyle K(\cos \theta )E(\sin \theta )+K(\sin \theta )E(\cos \theta )-K(\cos \theta )K(\sin \theta )={\pi \over 2},{\text{ for all }}\theta .} | Wikipedia - Gauss–Legendre algorithm | null | null | null |
Legged robots may have one, two, four, six, or many legs depending on the application. One of the main advantages of using legs instead of wheels is moving on uneven environment more effectively. Bipedal, quadrupedal, and hexapedal locomotion are among the most favorite types of legged locomotion in the field of bio-in... | Wikipedia - Bio-inspired robotics | null | null | null |
Rhex, a Reliable Hexapedal robot and Cheetah are the two fastest running robots so far. iSprawl is another hexapedal robot inspired by cockroach locomotion that has been developed at Stanford University. This robot can run up to 15 body length per second and can achieve speeds of up to 2.3 m/s. The original version of ... | Wikipedia - Bio-inspired robotics | null | null | null |
Legibility is different from salience, discussed above. Legibility is related to clearly and distinctly seeing edges, shapes and spatial details, and therefore to reading. Legibility of a symbol depends upon luminance difference (not color difference) between the symbol and the background upon which the symbol is prese... | Wikipedia - Color coding in data visualization | null | null | null |
For this reason, yellow (a high-luminance color) is less legible on a bright white background, and conversely so are white symbols less legible on a yellow background. Dark blue (a low-luminance color) symbols are less legible on a black background, and conversely black letters are less legible on a dark blue backgroun... | Wikipedia - Color coding in data visualization | null | null | null |
Legislative metadata has been the subject of some discussion in law.gov forums such as workshops held by the Legal Information Institute at the Cornell Law School on 22 and 23 March 2010. The documentation for these forums is titled, "Suggested metadata practices for legislation and regulations".A handful of key points... | Wikipedia - Meta data | null | null | null |
Lego also initiated a robotics line of toys called 'Mindstorms' in 1999, and has continued to expand and update this range ever since. The roots of the product originate from a programmable brick developed at the MIT Media Lab, and the name is taken from a paper by Seymour Papert, a computer scientist and educator who ... | Wikipedia - Lego bricks | null | null | null |
The earliest is Botball, a national U.S. middle- and high-school competition stemming from the MIT 6.270 Lego robotics tournament. Other Lego robotics competitions include FIRST LEGO League Discover for children ages 4–6, FIRST LEGO League Explore for students ages 6–9 and FIRST Lego League Challenge for students ages ... | Wikipedia - Lego bricks | null | null | null |
These programs offer real-world engineering challenges to participants. FIRST LEGO League Challenge uses LEGO-based robots to complete tasks, FIRST LEGO League Explore participants build models out of Lego elements, and FIRST LEGO League Discover participants use Duplo. In its 2019–2020 season, there were 38,609 FIRST ... | Wikipedia - Lego bricks | null | null | null |
The international RoboCup Junior football competition involves extensive use of Lego Mindstorms equipment which is often pushed to its extreme limits.The capabilities of the Mindstorms range have now been harnessed for use in Iko Creative Prosthetic System, a prosthetic limbs system designed for children. Designs for t... | Wikipedia - Lego bricks | null | null | null |
Lego also released a blue computer called the Scout, which has 2 sensor ports, 2 motor ports (plus one extra if linked with a Micro Scout using a fiber optic cable), and a built-in light sensor, but no PC interface. It comes with the Robotics Discovery Set. The Scout can be programmed from a collection of built-in prog... | Wikipedia - Lego Mindstorms | null | null | null |
The Scout can store one program. The Scout is based on a Toshiba microcontroller with 32 KB of ROM and 1 KB of RAM, where about 400 bytes are available for user programs. Due to the extremely limited amount of RAM, many predefined subroutines were provided in ROM. | Wikipedia - Lego Mindstorms | null | null | null |
The Scout only supports passive external sensors, which means that only touch, temperature and other unpowered sensors can be used. The analog-to-digital converters used in the Scout only have a resolution of 8 bits, in contrast to the 10-bit converters of the RCX.There was a plan for Lego to create a booster set that ... | Wikipedia - Lego Mindstorms | null | null | null |
The RCX can control the Scout brick using the "Send IR Message" program block. The RCX does all of the controlling, and therefore can be programmed with the PC, while the Scout accepts commands. The Scout brick must have all of its options set to "off" during this process. | Wikipedia - Lego Mindstorms | null | null | null |
Legrand is present in the data center sector, notably with the following products: VDI (Virtual desktop infrastructure), PDUs (Power distribution unit), etc. | Wikipedia - Legrand (company) | null | null | null |
Lehmer noted that most of the quotients from each step of the division part of the standard algorithm are small. (For example, Knuth observed that the quotients 1, 2, and 3 comprise 67.7% of all quotients.) Those small quotients can be identified from only a few leading digits. Thus the algorithm starts by splitting of... | Wikipedia - Lehmer's GCD algorithm | null | null | null |
Say we want to obtain the GCD of the two integers a and b. Let a ≥ b. If b contains only one digit (in the chosen base, say β = 1000 or β = 232), use some other method, such as the Euclidean algorithm, to obtain the result. If a and b differ in the length of digits, perform a division so that a and b are equal in lengt... | Wikipedia - Lehmer's GCD algorithm | null | null | null |
That is, iterate as an inner loop: Compute the quotients w1 of the long divisions of (x + A) by (y + C) and w2 of (x + B) by (y + D) respectively. Also let w be the (not computed) quotient from the current long division in the chain of long divisions of the euclidean algorithm.If w1 ≠ w2, then break out of the inner it... | Wikipedia - Lehmer's GCD algorithm | null | null | null |
Replace the current matrix {\displaystyle \textstyle {\begin{bmatrix}A&B&x\\C&D&y\end{bmatrix}}} with the matrix product ⋅ = {\displaystyle \textstyle {\begin{bmatrix}0&1\\1&-w\end{bmatrix}}\cdot {\begin{bmatrix}A&B&x\\C&D&y\end{bmatrix}}={\begin{bmatrix}C&D&y\\A-wC&B-wD&x-wy\end{bmatrix}}} according to the matrix ... | Wikipedia - Lehmer's GCD algorithm | null | null | null |
Lehmer's algorithm is based on the observation that the initial quotients produced by Euclid's algorithm can be determined based on only the first few digits; this is useful for numbers that are larger than a computer word. In essence, one extracts initial digits, typically forming one or two computer words, and runs E... | Wikipedia - Common divisor | null | null | null |
This algorithm improves speed, because it reduces the number of operations on very large numbers, and can use hardware arithmetic for most operations. In fact, most of the quotients are very small, so a fair number of steps of the Euclidean algorithm can be collected in a 2-by-2 matrix of single-word integers. When Leh... | Wikipedia - Common divisor | null | null | null |
Lehmers method is as follows. For a given complex polynomial p {\displaystyle p} , with the Schur-Cohn test a circular disk can be found large enough to contain all roots of p {\displaystyle p} . Next this disk can be covered with a set of overlapping smaller disks, one of them placed concentrically and the remaining o... | Wikipedia - Lehmer–Schur algorithm | null | null | null |
With each of the remaining disks this procedure of covering and removal can be repeated and so any number of times, resulting in a set of arbitrarily small disks that together contain all roots of p {\displaystyle p} . The merits of the method are that it consists of repetition of a single procedure and that all roots ... | Wikipedia - Lehmer–Schur algorithm | null | null | null |
And, remarkably, this polynomial has never to be evaluated. However, the smaller the disks become, the more the coefficients of the corresponding 'scaled' polynomials will differ in relative magnitude. This may cause overflow or underflow of computer computations, thus limiting the radii of the disks from below and the... | Wikipedia - Lehmer–Schur algorithm | null | null | null |
. To avoid extreme scaling, or just for the sake of efficiency, one may start with testing a number of concentric disks for the number of included roots and thus reduce the region where roots occur to a number of narrow , concentric annuli. | Wikipedia - Lehmer–Schur algorithm | null | null | null |
Repeating this procedure with another centre and combining the results, the said region becomes the union of intersections of such annuli. Finally, when a small disk is found that contains a single root, that root may be further approximated using other methods, e.g. Newton's method. == References == | Wikipedia - Lehmer–Schur algorithm | null | null | null |
Leibniz characterized the notion of equality as follows: Given any x and y, x = y if and only if, given any predicate P, P(x) if and only if P(y). | Wikipedia - Substitution property of equality | null | null | null |
Leibniz contributed a fair amount to the statics and dynamics emerging around him, often disagreeing with Descartes and Newton. He devised a new theory of motion (dynamics) based on kinetic energy and potential energy, which posited space as relative, whereas Newton was thoroughly convinced that space was absolute. An ... | Wikipedia - Algebra of concepts | null | null | null |
"Leibniz held a relationist notion of space and time, against Newton's substantivalist views. According to Newton's substantivalism, space and time are entities in their own right, existing independently of things. | Wikipedia - Algebra of concepts | null | null | null |
Leibniz's relationism, in contrast, describes space and time as systems of relations that exist between objects. The rise of general relativity and subsequent work in the history of physics has put Leibniz's stance in a more favorable light. One of Leibniz's projects was to recast Newton's theory as a vortex theory. Ho... | Wikipedia - Algebra of concepts | null | null | null |
Leibniz has been noted as one of the most important logicians between the times of Aristotle and Gottlob Frege. Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set. The principles of Leibniz's logic and, arguably, of his whole ph... | Wikipedia - Algebra of concepts | null | null | null |
Leibniz published nothing on formal logic in his lifetime; most of what he wrote on the subject consists of working drafts. In his History of Western Philosophy, Bertrand Russell went so far as to claim that Leibniz had developed logic in his unpublished writings to a level which was reached only 200 years later. Russe... | Wikipedia - Algebra of concepts | null | null | null |
He regarded such relations as (real) qualities of things (Leibniz admitted unary predicates only): For him, "Mary is the mother of John" describes separate qualities of Mary and of John. This view contrasts with the relational logic of De Morgan, Peirce, Schröder and Russell himself, now standard in predicate logic. No... | Wikipedia - Algebra of concepts | null | null | null |
Leibniz is credited, along with Sir Isaac Newton, with the discovery of calculus (differential and integral calculus). According to Leibniz's notebooks, a critical breakthrough occurred on 11 November 1675, when he employed integral calculus for the first time to find the area under the graph of a function y = f(x). He... | Wikipedia - Well-founded phenomenon | null | null | null |
Leibniz expressed the inverse relation of integration and differentiation, later called the fundamental theorem of calculus, by means of a figure in his 1693 paper Supplementum geometriae dimensoriae.... However, James Gregory is credited for the theorem's discovery in geometric form, Isaac Barrow proved a more general... | Wikipedia - Well-founded phenomenon | null | null | null |
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