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88,300 | In May 2015, the Robotic Kitchen won the "Best of the Best" CES Shanghai award in China. In January 2016, the prototype was finalist at the first edition of the UAE AI & Robotics Award in the international category, health sector.The Robotic Kitchen was launched on 6 December 2020, at GITEX technology week in Dubai. In... | Moley Robotics | 0.78172 |
88,301 | In 2015, Moley Robotics started working on a robotic kitchen, which made its debut at the Hannover Messe industrial robotics trade fair in Hannover, Germany in April 2015.In six years, Moley Robotics went from the robotic kitchen Proof of Concept to a market-ready robotic cooking platform. A cooking platform with a rob... | Moley Robotics | 0.78172 |
88,302 | Moley Robotics was named after its creator: M. Oleynik. It trades as Moley Services UK Ltd. Mark Oleynik, a computer scientist, founded the Moley Robotics as a way to have good food at home without the skills to make it. | Moley Robotics | 0.78172 |
88,303 | Moley Robotics is a robotics company headquartered in London, United Kingdom, that was developed, created and put in the market as the first robotic kitchen based on a multifunctional cooking platform. Moley Robotics was founded by Russian and British mathematician, computer scientist and entrepreneur Mark Oleynik in 2... | Moley Robotics | 0.78172 |
88,304 | Later, The Robotic Kitchen reproduces the whole sequence of actions to cook an identical meal from scratch.Moley Robotics introduced a recipe creator tool to add new meals to its culinary library. The first recipe learned by Moley Robotic Kitchen was a crab bisque created by the renowned chef Tim Anderson, the winner o... | Moley Robotics | 0.78172 |
88,305 | X-kitchen can be upgraded to a fully automated robotic R model on client's request.Moley Robotic Kitchen facilitates limited human contact during food preparation and the integrated safe UV-disinfection of the worktop and the air in the cooking zone to minimize the risk of contamination. Moley Robotics captures, with a... | Moley Robotics | 0.78172 |
88,306 | In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after German mathematician Herbert Grötzsch, who used it as an example in connection with his 1959 theorem that planar triangle-free graphs are 3-colo... | Grötzsch graph | 0.781718 |
88,307 | The existence of the Grötzsch graph demonstrates that the assumption of planarity is necessary in Grötzsch's theorem that every triangle-free planar graph is 3-colorable. It has odd girth five but girth four, and does not have any graph homomorphism to a graph whose girth is five or more, so it forms an example that di... | Grötzsch graph | 0.781718 |
88,308 | Although harsh by modern standards, HI was commonly employed as a reducing agent early on in the history of organic chemistry. Chemists in the 19th century attempted to prepare cyclohexane by HI reduction of benzene at high temperatures, but instead isolated the rearranged product, methylcyclopentane (see the article o... | Hydrogen iodide | 0.781718 |
88,309 | Solutions of hydrogen iodide are easily oxidized by air: 4 HI + O2 → 2 H2O + 2 I2 HI + I2 ⇌ HI3HI3 is dark brown in color, which makes aged solutions of HI often appear dark brown. Like HBr and HCl, HI adds to alkenes: HI + H2C=CH2 → H3CCH2IHI is also used in organic chemistry to convert primary alcohols into alkyl iod... | Hydrogen iodide | 0.781718 |
88,310 | In general, a larger fraction of molecules in the first state means a higher number of transitions to the second state. This gives a stronger spectral line. However, there are other factors that influence the intensity of a spectral line, such as whether it is caused by an allowed or a forbidden transition. The softmax... | Boltzmann population | 0.781717 |
88,311 | In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation where ∇2 is the Laplace operator, k2 is the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number. The Helmholtz ... | Paraxial Helmholtz equation | 0.781717 |
88,312 | A Lie group G with the Lie algebra g is said to be in Harish-Chandra's class if it satisfies the following conditions: g is a reductive Lie algebra (the product of a semisimple and abelian Lie algebra). The Lie group G has only a finite number of connected components. The adjoint action of any element of G on g is give... | Harish-Chandra class | 0.781716 |
88,313 | A classical reference is the NBS Monograph 140 from 1974, which in chapter 8 has "Statistics of Time and Frequency Data Analysis". This is the extended variant of NBS Technical Note 394 and adds essentially in measurement techniques and practical processing of values. An important addition will be the Properties of sig... | Allan deviation | 0.781716 |
88,314 | Further developments have produced improved estimation methods for the same stability measure, the variance/deviation of frequency, but these are known by separate names such as the Hadamard variance, modified Hadamard variance, the total variance, modified total variance and the Theo variance. These distinguish themse... | Allan deviation | 0.781716 |
88,315 | The physics of crystal oscillators were analyzed by D. B. Leeson, and the result is now referred to as Leeson's equation. The feedback in the oscillator will make the white noise and flicker noise of the feedback amplifier and crystal become the power-law noises of f − 2 {\displaystyle f^{-2}} white frequency noise and... | Allan deviation | 0.781716 |
88,316 | A measurement system is expected to have a bandwidth at or below that of the Nyquist rate, as described within the Shannon–Hartley theorem. As can be seen in the power-law noise formulas, the white and flicker noise modulations both depends on the upper corner frequency f H {\displaystyle f_{H}} (these systems is assum... | Allan deviation | 0.781716 |
88,317 | Fleet and cargo tracking Internet disseminated AIS can be used by fleet or ship managers to keep track of the global location of their ships. Cargo dispatchers, or the owners of goods in transit can track the progress of cargo and anticipate arrival times in port. Statistics and economics the United Nations Statistics ... | Automatic Identification System | 0.781715 |
88,318 | This dedicated launch marked ORBCOMM's second and final OG2 mission to complete its next-generation satellite constellation. Compared to its current OG1 satellites, ORBCOMM's OG2 satellites are designed for faster message delivery, larger message sizes and better coverage at higher latitudes, while increasing network c... | Automatic Identification System | 0.781714 |
88,319 | Dematerialization is a phenomenon occurs simultaneously with technological advancement, especially in the Third Industrial revolution products. Miniaturization and optimization of products are enabled by the improvement of wafer fabrication and battery production. Internet supported the digitalization of products (Onli... | Dematerialization (economics) | 0.781714 |
88,320 | Dematerialization, on the other hand, is frequently hampered by the issue of reproduction rate. Renewable items will lose their price competitiveness in the market if their reproduction rate cannot exceed that of non-renewable products. Thus, Ecologists mostly suggest for government incentives for renewable energy deve... | Dematerialization (economics) | 0.781714 |
88,321 | Oxidative coupling in chemistry is a coupling reaction of two molecular entities through an oxidative process. Usually oxidative couplings are catalysed by a transition metal complex like in classical cross-coupling reactions, although the underlying mechanism is different due to the oxidation process that requires an ... | Oxidative coupling | 0.781713 |
88,322 | Coupling reactions involving methane are highly sought, related to C1 chemistry because C2 derivatives are far more valuable than methane. The oxidative coupling of methane gives ethylene: 2CH4 + O2 → C2H4 + 2H2O | Oxidative coupling | 0.781713 |
88,323 | To dampen this effect, CREAM uses a larger number of pixels with a smaller area, along with a very fast readout time to differentiate between events caused by the primary particle and events caused by back-scattering from the calorimeter. The relatively low density of the TRD allows for a larger detector geometry to de... | Cosmic Ray Energetics and Mass | 0.781713 |
88,324 | The dominating paradigm in this area of robust optimization is Wald's maximin model, namely max x ∈ X min u ∈ U ( x ) f ( x , u ) {\displaystyle \max _{x\in X}\min _{u\in U(x)}f(x,u)} where the max {\displaystyle \max } represents the decision maker, the min {\displaystyle \min } represents Nature, namely uncertainty, ... | Robust optimisation | 0.781712 |
88,325 | There are a number of classification criteria for robust optimization problems/models. In particular, one can distinguish between problems dealing with local and global models of robustness; and between probabilistic and non-probabilistic models of robustness. Modern robust optimization deals primarily with non-probabi... | Robust optimisation | 0.781712 |
88,326 | The origins of robust optimization date back to the establishment of modern decision theory in the 1950s and the use of worst case analysis and Wald's maximin model as a tool for the treatment of severe uncertainty. It became a discipline of its own in the 1970s with parallel developments in several scientific and tech... | Robust optimisation | 0.781712 |
88,327 | Thus, for β = 0 {\displaystyle \beta =0} the relaxed robustness constraint reduces back to the original robustness constraint. This yields the following (relaxed) robust optimization problem: z ( N , U ) := max x ∈ X { f ( x ): g ( x , u ) ≤ b + β ⋅ d i s t ( u , N ) , ∀ u ∈ U } {\displaystyle z({\mathcal {N}},U):=\max... | Robust optimisation | 0.781712 |
88,328 | Consider the following linear programming problem max x , y { 3 x + 2 y } s u b j e c t t o x , y ≥ 0 ; c x + d y ≤ 10 , ∀ ( c , d ) ∈ P {\displaystyle \max _{x,y}\ \{3x+2y\}\ \ \mathrm {subject\ to} \ \ x,y\geq 0;cx+dy\leq 10,\forall (c,d)\in P} where P {\displaystyle P} is a given subset of R 2 {\displaystyle \mathbb... | Robust optimisation | 0.781712 |
88,329 | Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution. It is related to,... | Robust optimisation | 0.781712 |
88,330 | In 1938 Bagley and other educators met together where Bagley gave a speech detailing the main points of the essentialism movement and attacking the public education in the United States. One point that Bagley noted was that students in the U.S. were not getting an education on the same levels as students in Europe who ... | Educational essentialism | 0.781712 |
88,331 | The term "meiosis" is derived from the Greek word μείωσις, meaning 'lessening'. It was introduced to biology by J.B. Farmer and J.E.S. Moore in 1905, using the idiosyncratic rendering "maiosis": We propose to apply the terms Maiosis or Maiotic phase to cover the whole series of nuclear changes included in the two divis... | Tetrad (chromosomal formation) | 0.781711 |
88,332 | The RPIFs store and maintain a variety of planetary data and imagery, making them unique resources covering decades of planetary science. Among the offerings are: Digital and non-digital data and supporting documents from U.S. and foreign lunar and planetary missions flown since 1959 The Earth Impact Database at the Ca... | Regional Planetary Image Facility | 0.781711 |
88,333 | The complaint was not well received. Among the many responses, Bob Albrecht, another Homebrew member and founder of the People's Computer Company (PCC), felt the best response would be to produce their own BASIC that was completely free to use by anyone. He approached Dennis Allison, a member of the Computer Science fa... | Tiny BASIC | 0.781709 |
88,334 | An 8K version added string variables and trigonometry functions. Both the 4K and 8K versions were sold by SWTPC. In January, 1978, Uiterwyk sold the rights of the source code to Motorola.Thomas F. Waitman wrote a Tiny BASIC in 1976 for the Hewlett-Packard HP-2640 and HP-2645 terminals (which used the Intel 8008 and 808... | Tiny BASIC | 0.781709 |
88,335 | The first description of melt electrospinning was by Charles Norton in a patent approved in 1936. After this first discovery, it wasn't until 1981 that melt electrospinning was described as part of a three-paper series. A meeting abstract on melt electrospinning in a vacuum was published by Reneker and Rangkupan 20 yea... | Melt electrospinning | 0.781709 |
88,336 | Melt electrospinning writing has been performed using either a translating flat surface or a rotating cylinder/mandrel. Most polymers that can be melt-electrospun can also be written assuming the parameters can be tuned in such a way as to produce a stable jet. Piezoelectric polymers such as polyvinylidene difluoride (... | Melt electrospinning | 0.781709 |
88,337 | The electrified molten jet created via melt electrospinning has a more predictable path, and polymer fibers can be deposited accurately onto the collector. When the collector is moved at sufficient speed (referred to as the critical translation speed), straight melt electrospun fibers can be deposited in a layer upon l... | Melt electrospinning | 0.781709 |
88,338 | The same physics of electrostatic fiber drawing apply to melt electrospinning. What differs are the physical properties of the polymer melt, compared to a polymer solution. When comparing polymer melts and polymer solutions, the former are normally more viscous than polymer solutions, and elongated electrified jets hav... | Melt electrospinning | 0.781709 |
88,339 | Melt electrospinning is a processing technique to produce fibrous structures from polymer melts for applications that include tissue engineering, textiles and filtration. In general, electrospinning can be performed using either polymer melts or polymer solutions. However, melt electrospinning is distinct in that the c... | Melt electrospinning | 0.781709 |
88,340 | Divers who are prone to trait anxiety are more likely to mismanage a developing emergency by panicking and missing the opportunity to recover from the initial incident. Training can help a diver to recognize rising stress levels, and allow them to take corrective action before the situation deteriorates into an injury ... | Psychological fitness to dive | 0.781707 |
88,341 | Psychological fitness has been defined in a military context as "the integration and optimization of mental, emotional, and behavioral abilities and capacities to optimize performance and strengthen resilience". There are other definitions in a self-help/personal growth context, also referred to as emotional or mental ... | Psychological fitness to dive | 0.781707 |
88,342 | Descartes's publication of La Géométrie in 1637, which introduced the Cartesian coordinate system, is considered to be the establishment of mathematical analysis. It would be a few decades later that Newton and Leibniz independently developed infinitesimal calculus, which grew, with the stimulus of applied work that co... | Classical analysis | 0.781706 |
88,343 | The modern foundations of mathematical analysis were established in 17th century Europe. This began when Fermat and Descartes developed analytic geometry, which is the precursor to modern calculus. Fermat's method of adequality allowed him to determine the maxima and minima of functions and the tangents of curves. | Classical analysis | 0.781706 |
88,344 | Foundation of Analysis: The Arithmetic of Whole Rational, Irrational and Complex Numbers, by Edmund Landau Introductory Real Analysis, by Andrey Kolmogorov, Sergei Fomin Differential and Integral Calculus (3 volumes), by Grigorii Fichtenholz The Fundamentals of Mathematical Analysis (2 volumes), by Grigorii Fichtenholz... | Classical analysis | 0.781706 |
88,345 | A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, biology, and other disciplines. Differential equat... | Classical analysis | 0.781706 |
88,346 | Techniques from analysis are used in many areas of mathematics, including: Analytic number theory Analytic combinatorics Continuous probability Differential entropy in information theory Differential games Differential geometry, the application of calculus to specific mathematical spaces known as manifolds that possess... | Classical analysis | 0.781706 |
88,347 | Harmonic analysis is a branch of mathematical analysis concerned with the representation of functions and signals as the superposition of basic waves. This includes the study of the notions of Fourier series and Fourier transforms (Fourier analysis), and of their generalizations. Harmonic analysis has applications in a... | Classical analysis | 0.781706 |
88,348 | This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ {\displaystyle \sigma } -algebra. This means that the empty set, countable unions, countable intersections and complements of measurable subsets are measurable. Non-mea... | Classical analysis | 0.781706 |
88,349 | A measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the c... | Classical analysis | 0.781706 |
88,350 | The SCC is currently still being used for research purposes. It currently can run the GNU operating system on the chip, but cannot boot Windows. Some applications of the SCC are web servers, data informatics, bioinformatics, and financial analytics. | Single-chip Cloud Computer | 0.781702 |
88,351 | Protections for the rights of Indigenous cultures exist in varying degrees of strength. The right to practise and revitalise cultural traditions by Indigenous groups is protected by the United Nations Declaration on the Rights of Indigenous People (UNDRIP), which encompasses Indigenous astronomy, and their right to mai... | Indigenous astronomy | 0.781701 |
88,352 | The practice of observing space is currently threatened by increasing satellite traffic in the outer space environment. The crowding of Earth's orbit, particularly low-Earth orbit (LEO), by satellites poses a serious risk to practising astronomy due to satellite's visibility and disruption of the sky. Satellites are vi... | Indigenous astronomy | 0.781701 |
88,353 | Research into the development of Aboriginal astronomical knowledge was used to develop an educational program at the Sydney Observatory, called Dreamtime Astronomy. It includes activities such as creating a planisphere with both Western scientific and Boorong names for celestial objects.There is a perception that publi... | Indigenous astronomy | 0.781701 |
88,354 | In the US, the Bell Museum planetarium of Minnesota worked with native American astronomer, Annette Lee, to construct a best practices framework for sharing Indigenous Astronomy and create a live online programme on Indigenous Star Knowledge. Lee also received NASA funding to deliver a school educational programme on I... | Indigenous astronomy | 0.781701 |
88,355 | Some academic literature argues that all science is embedded with culture, and to acknowledge this is integral to create diverse learning environments and decolonise Western knowledge systems. To acknowledge other cultures is to affirm them, revealing valuable alternative scientific perspectives. This is considered imp... | Indigenous astronomy | 0.781701 |
88,356 | Indigenous astronomies are diverse in their specificities, but find commonality in some storytelling themes, practices, and functions.In Aboriginal Astronomy, Kamilaroi and Euahlayi elders reveal that the Emu in the Sky, a dark constellation, informs on emu behaviour and seasonal changes, with consequences for food eco... | Indigenous astronomy | 0.781701 |
88,357 | Indigenous astronomy is the name given to the use and study of astronomical subjects and their movements by indigenous groups. This field encompasses culture, traditional knowledge, and astronomy. Astronomy has been practised by indigenous groups to create astronomical calendars which inform on weather, navigation, mig... | Indigenous astronomy | 0.781701 |
88,358 | Indigenous astronomy is an aspect of indigenous knowledge systems, which are used to explain and predict nature. It involves the notion of a living relationship with the sky, celestial objects and processes. This living relationship is a product of long-held observation and participation traditions, recognising the spi... | Indigenous astronomy | 0.781701 |
88,359 | For example, the absence of bembé’ é, the goat (the Coalsack), forecast calm weather. Polynesian astronomy also utilised star-compasses like the Buganese, with the memorisation of specific “steering-stars” and their rising and setting directions on the horizon.Astronomy was used across many cultures to develop lunar ca... | Indigenous astronomy | 0.781701 |
88,360 | These cross-functional activities have increased significantly in number and importance, due to the growth of complexity and dependence. New methodologies include business process redesign, business process innovation, business process management, integrated business planning, among others, all "aiming at improving pro... | Business modeling | 0.781696 |
88,361 | The term 'business process modeling' was coined in the 1960s in the field of systems engineering by S. Williams in his 1967 article 'Business Process Modelling Improves Administrative Control'. His idea was that techniques for obtaining a better understanding of physical control systems could be used in a similar way f... | Business modeling | 0.781696 |
88,362 | Business process modeling (BPM) in business process management and systems engineering is the activity of representing processes of an enterprise, so that the current business processes may be analyzed, improved, and automated. BPM is typically performed by business analysts, who provide expertise in the modeling disci... | Business modeling | 0.781696 |
88,363 | During epidemics the incidence of meningococcal disease approaches 100 per 100,000. Meningococcal vaccines have sharply reduced the incidence of the disease in developed countries.The disease's pathogenesis is not fully understood. Neisseria meningitidis colonises a substantial proportion of the general population harm... | Meningococcal meningitis | 0.781696 |
88,364 | Recent advances have striven to combine the nanometer phase retrieval of coherent interferometry with the ranging capability of low-coherence interferometry. Phase contrast and differential interference contrast (DIC) microscopy are important tools in biology and medicine. Most animal cells and single-celled organisms ... | Double-path interferometer | 0.781694 |
88,365 | Optical interferometry, applied to biology and medicine, provides sensitive metrology capabilities for the measurement of biomolecules, subcellular components, cells and tissues. Many forms of label-free biosensors rely on interferometry because the direct interaction of electromagnetic fields with local molecular pola... | Double-path interferometer | 0.781694 |
88,366 | The basic characteristics distinguishing it from the Michelson configuration are the use of a monochromatic point light source and a collimator. Michelson (1918) criticized the Twyman–Green configuration as being unsuitable for the testing of large optical components, since the light sources available at the time had l... | Double-path interferometer | 0.781694 |
88,367 | This technique was developed to enable greater resolution in electron microscopy than is possible using conventional imaging techniques. The resolution of conventional electron microscopy is not limited by electron wavelength, but by the large aberrations of electron lenses.Neutron interferometry has been used to inves... | Double-path interferometer | 0.781694 |
88,368 | The first observation of gravitational waves occurred on September 14, 2015.The Mach–Zehnder interferometer's relatively large and freely accessible working space, and its flexibility in locating the fringes has made it the interferometer of choice for visualizing flow in wind tunnels, and for flow visualization studie... | Double-path interferometer | 0.781694 |
88,369 | In physics, one of the most important experiments of the late 19th century was the famous "failed experiment" of Michelson and Morley which provided evidence for special relativity. Recent repetitions of the Michelson–Morley experiment perform heterodyne measurements of beat frequencies of crossed cryogenic optical res... | Double-path interferometer | 0.781694 |
88,370 | Constrained geometry complexes are related to ansa-metallocenes except that one ligand is not Cp-related. | Cyclopentadienyl complex | 0.781694 |
88,371 | A pair of cyclopentadienyl ligands can be covalently linked giving rise to so-call ansa metallocenes. The angle between the two Cp rings is fixed. Rotation of the rings about the metal-centroid axis is stopped as well. A related class of derivatives give rise to the constrained geometry complexes. In these cases, a Cp ... | Cyclopentadienyl complex | 0.781694 |
88,372 | Robotic pixel assembly method for manufacturing vdW solids provides high-speed and controllable design (area, geometry, and angle). In this approach, robotic assembly of prepatterned ‘pixels’ made from atomically thin two-dimensional components forms heterojunction devices. In the first implementation of this approach,... | Graphene production techniques | 0.781693 |
88,373 | Metal single crystals are often used as substrates in graphene growth since they form a smooth and chemically uniform growth platform for graphene. Especially, the chemical uniformity is an important advantage of metal single crystal surfaces: for example in different oxide surfaces the oxidized component and the oxyge... | Graphene production techniques | 0.781693 |
88,374 | Transmission electron microscopy (TEM) uses electrons to generate high-resolution images as using electrons allows to overcome limitations of visible light wavelengths. TEM on graphene should be done with electron energy less than 80 keV to induce a smaller amount of defects, because this energy is the threshold electr... | Graphene production techniques | 0.781693 |
88,375 | Graphene sheets have been reported to be grown by dosing ethylene onto the clean, single platinum(111) substrate at temperatures above 1000 °C in ultra-high vacuum (UHV). Graphene monolayer interacts weakly with the Pt(111) surface below it confirmed by the local density of states which is a ‘V’ shape. Kim et al., repo... | Graphene production techniques | 0.781693 |
88,376 | In chemistry, a ladder polymer is a type of double stranded polymer with the connectivity of a ladder. In a typical one-dimensional polymer, e.g. polyethylene and polysiloxanes, the monomers form two bonds, giving a chain. In a ladder polymer the monomers are interconnected by four bonds. | Ladder polymer | 0.781692 |
88,377 | Illustrative is the polymer n. When the 2-picoline is replaced by a tertiary phosphine, it forms a tetrameric cubane-type cluster, ]4. In both cases, the Cu(I) centers adopt tetrahedral molecular geometry. == References == | Ladder polymer | 0.781692 |
88,378 | Some polysilicates are ladder polymers. One example is provided by the mineral tremolite. In the area of coordination chemistry, the ladder structure is seen in some coordination polymers. | Ladder polymer | 0.781692 |
88,379 | The automotive engineering group of the mechanical engineering department at Clemson University is developing a low energy loss airless tire with Michelin through the NIST ATP project. Resilient Technologies and the University of Wisconsin–Madison's Polymer Engineering Center are creating a "non-pneumatic tire", which ... | Airless tire | 0.781692 |
88,380 | 24-isopropyl cholestane is an organic molecule produced by specific sponges, protists and marine algae. The identification of this molecule at high abundances in Neoproterozoic rocks has been interpreted to reflect the presence of multicellular life prior to the rapid diversification and radiation of life during the Ca... | 24-Isopropylcholestane | 0.78169 |
88,381 | Another class of examples of Noetherian schemes are families of schemes X → S {\displaystyle X\to S} where the base S {\displaystyle S} is Noetherian and X {\displaystyle X} is of finite type over S {\displaystyle S} . This includes many examples, such as the connected components of a Hilbert scheme, i.e. with a fixed ... | Noetherian scheme | 0.78169 |
88,382 | One of the most important structure theorems about Noetherian rings and Noetherian schemes is the Dévissage theorem. This theorem makes it possible to decompose arguments about coherent sheaves into inductive arguments. It is because given a short exact sequence of coherent sheaves 0 → E ′ → E → E ″ → 0 {\displaystyle ... | Noetherian scheme | 0.78169 |
88,383 | In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets Spec A i {\displaystyle \operatorname {Spec} A_{i}} , A i {\displaystyle A_{i}} noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus, a scheme i... | Noetherian scheme | 0.78169 |
88,384 | One of the natural rings which are non-Noetherian are the Ring of adeles A K {\displaystyle \mathbb {A} _{K}} for an algebraic number field K {\displaystyle K} . In order to deal with such rings, a topology is considered, giving topological rings. There is a notion of algebraic geometry over such rings developed by Wei... | Noetherian scheme | 0.78169 |
88,385 | In particular, quasi-projective varieties are Noetherian schemes. This class includes algebraic curves, elliptic curves, abelian varieties, calabi-yau schemes, shimura varieties, K3 surfaces, and cubic surfaces. Basically all of the objects from classical algebraic geometry fit into this class of examples. | Noetherian scheme | 0.78169 |
88,386 | In physics, dynamic speckle is a result of the temporal evolution of a speckle pattern where variations in the scattering elements responsible for the formation of the interference pattern in the static situation produce the changes that are seen in the speckle pattern, where its grains change their intensity (grey lev... | Dynamic speckle | 0.781689 |
88,387 | In clinical trials (or more generally, longitudinal studies), a patient's state of health may be observed only at irregular time intervals, and different patients are usually observed at different points in time. Wireless sensors in the Internet of things often transmit information only when a state changes to conserve... | Unevenly spaced time series | 0.781688 |
88,388 | In statistics, signal processing, and econometrics, an unevenly (or unequally or irregularly) spaced time series is a sequence of observation time and value pairs (tn, Xn) in which the spacing of observation times is not constant. Unevenly spaced time series naturally occur in many industrial and scientific domains: na... | Unevenly spaced time series | 0.781688 |
88,389 | However, most of the basic theory for time series analysis was developed at a time when limitations in computing resources favored an analysis of equally spaced data, since in this case efficient linear algebra routines can be used and many problems have an explicit solution. As a result, fewer methods currently exist ... | Unevenly spaced time series | 0.781688 |
88,390 | With this remark the theorem takes the stronger form: Let f {\displaystyle f} be a monotone function defined on an interval I . {\displaystyle I.} Then the set of discontinuities is at most countable. | Discontinuities of monotone functions | 0.781688 |
88,391 | In the mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily jump discontinuities and there are at most countably many of them. Usually, this theorem appears in li... | Discontinuities of monotone functions | 0.781687 |
88,392 | Loeb's construction starts with a finitely additive map ν {\displaystyle \nu } from an internal algebra A {\displaystyle {\mathcal {A}}} of sets to the nonstandard reals. Define μ {\displaystyle \mu } to be given by the standard part of ν {\displaystyle \nu } , so that μ {\displaystyle \mu } is a finitely additive map ... | Loeb space | 0.781687 |
88,393 | Instead the algebra A {\displaystyle {\mathcal {A}}} has the property that if a set in it is the union of a countable family of elements of A {\displaystyle {\mathcal {A}}} , then the set is the union of a finite number of elements of the family, so in particular any finitely additive map (such as μ {\displaystyle \mu ... | Loeb space | 0.781687 |
88,394 | Alkenes bind to copper(I), although again generally weakly. The binding of ethylene to Cu in proteins is of broad significance in plant biology so much so that ethylene is classified as a plant hormone. Its presence, detected by the Cu-protein, affects ripening and many other developments.Although copper does not form ... | Organocopper chemistry | 0.781686 |
88,395 | Organocopper chemistry is the study of the physical properties, reactions, and synthesis of organocopper compounds, which are organometallic compounds containing a carbon to copper chemical bond. They are reagents in organic chemistry. The first organocopper compound, the explosive copper(I) acetylide Cu2C2 (Cu−C≡C−Cu)... | Organocopper chemistry | 0.781686 |
88,396 | ε ( X , X ′ ) {\displaystyle \varepsilon \left(X,X^{\prime }\right)} denotes the topology of uniform convergence on equicontinuous subsets of X ′ {\displaystyle X^{\prime }} and X ε ( X , X ′ ) {\displaystyle X_{\varepsilon \left(X,X^{\prime }\right)}} or X ε {\displaystyle X_{\varepsilon }} denotes X {\displaystyle X}... | Injective tensor product | 0.781685 |
88,397 | τ ( X , X ′ ) {\displaystyle \tau (X,X^{\prime })} is the finest locally convex TVS topology on X {\displaystyle X} whose continuous dual space is equal to X ′ . {\displaystyle X^{\prime }.} τ ( X ′ , X ) {\displaystyle \tau \left(X^{\prime },X\right)} denotes the Mackey topology on X ′ {\displaystyle X^{\prime }} or t... | Injective tensor product | 0.781685 |
88,398 | σ ( X , X ′ ) {\displaystyle \sigma \left(X,X^{\prime }\right)} denotes the coarsest topology on X {\displaystyle X} making every map in X ′ {\displaystyle X^{\prime }} continuous and X σ ( X , X ′ ) {\displaystyle X_{\sigma \left(X,X^{\prime }\right)}} or X σ {\displaystyle X_{\sigma }} denotes X {\displaystyle X} end... | Injective tensor product | 0.781685 |
88,399 | We will now generalize the Schwartz space to functions valued in a TVS. Let L ( R n ; Y ) {\displaystyle {\mathcal {L}}\left(\mathbb {R} ^{n};Y\right)} be the space of all f ∈ C ∞ ( R n ; Y ) {\displaystyle f\in C^{\infty }\left(\mathbb {R} ^{n};Y\right)} such that for all pairs of polynomials P {\displaystyle P} and Q... | Injective tensor product | 0.781685 |
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