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Spectral density (physical science) Summary Spectrum A spectrum (PL: spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word spectrum was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. It thereby became a mapping of a range of magnitudes (wavelengths) to a range of qualities, which are the perceived "colors of the rainbow" and other properties which correspond to wavelengths that lie outside of the visible light spectrum. |
Ohms Law Hydraulic analogy Ohm's_Law > Hydraulic analogy A hydraulic analogy is sometimes used to describe Ohm's law. Water pressure, measured by pascals (or PSI), is the analog of voltage because establishing a water pressure difference between two points along a (horizontal) pipe causes water to flow. The water volume flow rate, as in liters per second, is the analog of current, as in coulombs per second. Finally, flow restrictors—such as apertures placed in pipes between points where the water pressure is measured—are the analog of resistors. |
281 (number) Summary 281_(number) 281 is the 60th prime, twin prime with 283, Sophie Germain prime, sum of the first fourteen primes, sum of seven consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53), Chen prime, Eisenstein prime with no imaginary part, centered decagonal number. 281 is the smallest prime p such that the decimal period length of the reciprocal of p is (p−1)/10, i.e. the period length of 1/281 is 28. However, in binary, it has period length 70. The generalized repunit number 281 p − 1 280 {\displaystyle {\frac {281^{p}-1}{280}}} is composite for all prime p < 60000. |
Temporal bone Postnatal development Temporal_bone > Structure > Postnatal development Apart from size increase, the chief changes from birth through puberty in the temporal bone are as follows: The tympanic ring extends outward and backward to form the tympanic part. This extension does not, however, take place at an equal rate all around the circumference of the ring, but occurs more at its anterior and posterior portions. As these outgrowths meet, they create a foramen in the floor of the meatus, the foramen of Huschke. This foramen is usually closed about the fifth year, but may persist throughout life. |
Gadget (computer science) Optimization of gadgets Gadget_(computer_science) > Optimization of gadgets They give as an example a reduction from 3-satisfiability to 2-satisfiability by Garey, Johnson & Stockmeyer (1976), in which the gadget representing a 3-SAT clause consists of ten 2-SAT clauses, and in which a truth assignment that satisfies 3-SAT clause also satisfies at least seven clauses in the gadget, while a truth assignment that fails to satisfy a 3-SAT clause also fails to satisfy more than six clauses of the gadget. Using this gadget, and the fact that (unless P = NP) there is no polynomial-time approximation scheme for maximizing the number of 3-SAT clauses that a truth assignment satisfies, it can be shown that there is similarly no approximation scheme for MAX 2-SAT. Trevisan et al. show that, in many cases of the constraint satisfaction problems they study, the gadgets leading to the strongest possible inapproximability results may be constructed automatically, as the solution to a linear programming problem. |
Audio fingerprinting Shazam Music_identification > Shazam Shazam's algorithm picks out points where there are peaks in the spectrogram which represent higher energy content. Focusing on peaks in the audio greatly reduces the impact that background noise has on audio identification. Shazam builds their fingerprint catalog out as a hash table, where the key is the frequency. They do not just mark a single point in the spectrogram, rather they mark a pair of points: the peak intensity plus a second anchor point. So their database key is not just a single frequency, it is a hash of the frequencies of both points. This leads to fewer hash collisions improving the performance of the hash table. |
D Line Extension Initial alternatives analysis D_Line_Extension > History > Environmental review process > Initial alternatives analysis The West Hollywood alignment (sometimes known as the "Pink Line") was proposed during the public scoping process. The route travels along Santa Monica Boulevard and San Vicente Boulevard, connecting Hollywood/Highland in the north to the Wilshire route in the south. The West Hollywood route generated considerable support from the public, transit advocates, and the City of West Hollywood.Other alignments studied involved various deviations from Wilshire Boulevard to allow service to destinations such as Beverly Center, Cedars-Sinai Medical Center, and Farmers Market. |
Deprotonation Summary Deprotonation Acid–base reactions typically occur faster than any other step which may determine the product of a reaction. The conjugate base is more electron-rich than the molecule which can alter the reactivity of the molecule. For example, deprotonation of an alcohol forms the negatively charged alkoxide, which is a much stronger nucleophile. |
Strong artificial intelligence Criticisms of simulation-based approaches Strong_artificial_intelligence > Brain simulation > Criticisms of simulation-based approaches Desktop computers using microprocessors capable of more than 109 cps (Kurzweil's non-standard unit "computations per second", see above) have been available since 2005. According to the brain power estimates used by Kurzweil (and Moravec), such a computer should be capable of supporting a simulation of a bee brain, but despite some interest no such simulation exists. There are several reasons for this: The neuron model seems to be oversimplified (see next section). |
Fatal exception error Summary Critical_error In computing, a fatal exception error or fatal error is an error that causes a program to abort and may therefore return the user to the operating system. When this happens, data that the program was processing may be lost. A fatal error is usually distinguished from a fatal system error (colloquially referred to in the MS Windows operating systems by the error message it produces as a "blue screen of death"). A fatal error occurs typically in any of the following cases: An illegal instruction has been attempted Invalid data or code has been accessed An operation is not allowed in the current ring or CPU mode A program attempts to divide by zero (only for integers; with the IEEE floating point standard, this creates an infinity instead).In some systems, such as macOS and Microsoft Windows, a fatal error causes the operating system to create a log entry or to save an image (core dump) of the process. |
Isotope ratio mass spectrometry Gas source mass spectrometry Isotope_ratio_mass_spectrometry > Gas source mass spectrometry Water incorporating a deuterium atom has a mass of 19, over 5% heavier. The energy to vaporise the heavy water molecule is higher than that to vaporize the normal water so isotope fractionation occurs during the process of evaporation. |
Thermo-mechanical fatigue Looking forward Thermo_mechanical_fatigue > Looking forward They are using a finite element method that accounts for the known microstructure. They have discovered that the large difference in the thermal expansion coefficient between the matrix and the fiber is the driving cause of failure, causing high internal stress. == References == |
Wearable electronics Applications Wearable_electronics > Applications Wearable computers are not only limited to computers such as fitness trackers that are worn on wrists; they also include wearables such as heart pacemakers and other prosthetics. They are used most often in research that focuses on behavioral modeling, health monitoring systems, IT and media development, where the person wearing the computer actually moves or is otherwise engaged with his or her surroundings. Wearable computers have been used for the following: general-purpose computing (e.g. smartphones and smartwatches) sensory integration, e.g. to help people see better or understand the world better (whether in task-specific applications like camera-based welding helmets or for everyday use like Google Glass behavioral modeling health care monitoring systems service management electronic textiles and fashion design, e.g. Microsoft's 2011 prototype "The Printing Dress".Wearable computing is the subject of active research, especially the form-factor and location on the body, with areas of study including user interface design, augmented reality, and pattern recognition. The use of wearables for specific applications, for compensating disabilities or supporting elderly people steadily increases. |
COVID-19 pandemic Data and graphs COVID-19_pandemic > External links > Data and graphs Coronavirus disease (COVID-19) situation reports and map by the World Health Organization (WHO) COVID-19 Resource Center, map, and historical data by Johns Hopkins University COVID-19 data sets published by the European Centre for Disease Prevention and Control (ECDC) COVID-19 Observer based on Johns Hopkins University data COVID-19 Statistics and Research published by Our World in Data COVID-19 Tracker from Stat News COVID-19 Projections for many countries published by Institute for Health Metrics and Evaluation |
Ozone monitor Summary Ozone_monitor A photodiode at the other end of the tube detects the changes of brightness from the light. The onboard electronics process the values obtained and display the value on the screen and can also output an electrical signal in volts or a 4-20 mA current that can be read by an electronic data logger. Other options for output are RS232 serial port or ethernet or internal data storage on flash memory. |
Definite Integrals Summary Integral_over_time Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integrals with differentiation and provides a method to compute the definite integral of a function when its antiderivative is known; differentiation and integration are inverse operations. Although methods of calculating areas and volumes dated from ancient Greek mathematics, the principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width. |
Casimir vacuum Derivation of Casimir effect assuming zeta-regularization Casimir–Polder_force > Derivation of Casimir effect assuming zeta-regularization The presence of ħ shows that the Casimir force per unit area Fc/A is very small, and that furthermore, the force is inherently of quantum-mechanical origin. By integrating the equation above it is possible to calculate the energy required to separate to infinity the two plates as: where ħ is the reduced Planck constant, c is the speed of light, A is the area of one of the plates, a is the distance between the two platesIn Casimir's original derivation, a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). The zero-point energy on both sides of the plate is considered. Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler–Maclaurin summation with a regularizing function (e.g., exponential regularization) not so anomalous as |ωn|−s in the above. |
Mobile robots Line-following Car Mobile_robots > Mobile robot navigation > Line-following Car Some of the earliest Automated Guided Vehicles (AGVs) were line following mobile robots. They might follow a visual line painted or embedded in the floor or ceiling or an electrical wire in the floor. Most of these robots operated a simple "keep the line in the center sensor" algorithm. |
Scientific breakthrough Geometry and trigonometry Scientific_breakthrough > Bronze Age > Mathematics > Geometry and trigonometry 2100 BC: The concept of area is first recognised in Babylonian clay tablets, and 3-dimensional volume is discussed in an Egyptian papyrus. This begins the study of geometry. Early 2nd millennium BC: Similar triangles and side-ratios are studied in Egypt (e.g. in the Rhind Mathematical Papyrus, a copy of an older Middle Kingdom text) for the construction of pyramids, paving the way for the field of trigonometry. |
Davenport–Schinzel Sequences and Their Geometric Applications Summary Davenport–Schinzel_Sequences_and_Their_Geometric_Applications Davenport–Schinzel Sequences and Their Geometric Applications is a book in discrete geometry. It was written by Micha Sharir and Pankaj K. Agarwal, and published by Cambridge University Press in 1995, with a paperback reprint in 2010. |
Digital reformatting Process Digital_reformatting > Process The term digitization is often used when diverse forms of information, such as an object, text, sound, image, or voice, are converted into a single binary code. The core of the process is the compromise between the capturing device and the player device so that the rendered result represents the original source with the most possible fidelity, and the advantage of digitization is the speed and accuracy in which this form of information can be transmitted with no degradation compared with analog information. Digital information exists as one of two digits, either 0 or 1. These are known as bits (a contraction of binary digits) and the sequences of 0s and 1s that constitute information are called bytes.Analog signals are continuously variable, both in the number of possible values of the signal at a given time, as well as in the number of points in the signal in a given period of time. |
Zermelo–Fraenkel set theory Summary Zermelo-Fraenkel_axioms In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated ZFC, where C stands for "choice", and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. Informally, Zermelo–Fraenkel set theory is intended to formalize a single primitive notion, that of a hereditary well-founded set, so that all entities in the universe of discourse are such sets. |
Mechanical processes Early modern age Mechanics > History > Early modern age Two central figures in the early modern age are Galileo Galilei and Isaac Newton. Galileo's final statement of his mechanics, particularly of falling bodies, is his Two New Sciences (1638). Newton's 1687 Philosophiæ Naturalis Principia Mathematica provided a detailed mathematical account of mechanics, using the newly developed mathematics of calculus and providing the basis of Newtonian mechanics.There is some dispute over priority of various ideas: Newton's Principia is certainly the seminal work and has been tremendously influential, and many of the mathematics results therein could not have been stated earlier without the development of the calculus. However, many of the ideas, particularly as pertain to inertia and falling bodies, had been developed by prior scholars such as Christiaan Huygens and the less-known medieval predecessors. Precise credit is at times difficult or contentious because scientific language and standards of proof changed, so whether medieval statements are equivalent to modern statements or sufficient proof, or instead similar to modern statements and hypotheses is often debatable. |
Critical point (mathematics) Examples Critical_number > Critical point of a single variable function > Examples This point is a global minimum of f. The corresponding critical value is f ( − 1 ) = 2. {\displaystyle f(-1)=2.} The graph of f is a concave up parabola, the critical point is the abscissa of the vertex, where the tangent line is horizontal, and the critical value is the ordinate of the vertex and may be represented by the intersection of this tangent line and the y-axis. |
Photosynthetic reaction centre protein family In bacteria Photosynthetic_reaction_centre_protein_family > In bacteria The Type II photosynthetic apparatus in non-oxygenic bacteria consists of light-harvesting protein-pigment complexes LH1 and LH2, which use carotenoid and bacteriochlorophyll as primary donors. LH1 acts as the energy collection hub, temporarily storing it before its transfer to the photosynthetic reaction centre (RC). Electrons are transferred from the primary donor via an intermediate acceptor (bacteriophaeophytin) to the primary acceptor (quinine Qa), and finally to the secondary acceptor (quinone Qb), resulting in the formation of ubiquinol QbH2. RC uses the excitation energy to shuffle electrons across the membrane, transferring them via ubiquinol to the cytochrome bc1 complex in order to establish a proton gradient across the membrane, which is used by ATP synthetase to form ATP.The core complex is anchored in the cell membrane, consisting of one unit of RC surrounded by LH1; in some species there may be additional subunits. |
SI defining constants Defining constants SI_defining_constants > Defining constants The Avogadro constant NA is exactly 6.02214076×1023 reciprocal mole (mol−1).The redefinition retains unchanged the numerical values associated with the following constants of nature: The speed of light c is exactly 299792458 metres per second (m⋅s−1); The ground state hyperfine structure transition frequency of the caesium-133 atom ΔνCs is exactly 9192631770 hertz (Hz); The luminous efficacy of monochromatic radiation of frequency 540×1012 Hz (540 THz) – a frequency of green-colored light at approximately the peak sensitivity of the human eye – Kcd (where the subscript "cd" is the symbol for candela) is exactly 683 lumens per watt (lm⋅W−1).The seven SI defining constants above, expressed in terms of derived units (joule, coulomb, hertz, lumen, and watt), are rewritten below in terms of the seven base units (second, metre, kilogram, ampere, kelvin, mole, and candela); the dimensionless unit steradian (symbol sr) is also used: ΔνCs = Δν(133Cs)hfs = 9192631770 s−1 c = 299792458 m⋅s−1 h = 6.62607015×10−34 kg⋅m2⋅s−1 e = 1.602176634×10−19 A⋅s k = 1.380649×10−23 kg⋅m2⋅K−1⋅s−2 NA = 6.02214076×1023 mol−1 Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2As part of the redefinition, the International Prototype of the Kilogram was retired and definitions of the kilogram, the ampere, and the kelvin were replaced. The definition of the mole was revised. These changes have the effect of redefining the SI base units, though the definitions of the SI derived units in terms of the base units remain the same. |
Two-body problem in general relativity General relativity, special relativity and geometry Kepler_problem_in_general_relativity > General relativity, special relativity and geometry In general relativity, however, space and time may have curvature, so this distance formula must be modified to a more general form c 2 d τ 2 = g μ ν d x μ d x ν {\displaystyle c^{2}\,d\tau ^{2}=g_{\mu \nu }dx^{\mu }\,dx^{\nu }\,\!} just as we generalized the formula to measure distance on the surface of the Earth. The exact form of the metric gμν depends on the gravitating mass, momentum and energy, as described by the Einstein field equations. Einstein developed those field equations to match the then known laws of Nature; however, they predicted never-before-seen phenomena (such as the bending of light by gravity) that were confirmed later. |
Throttle Summary Throttle_body A throttle is the mechanism by which fluid flow is managed by constriction or obstruction. An engine's power can be increased or decreased by the restriction of inlet gases (by the use of a throttle), but usually decreased. The term throttle has come to refer, informally, to any mechanism by which the power or speed of an engine is regulated, such as a car's accelerator pedal. What is often termed a throttle (in an aviation context) is also called a thrust lever, particularly for jet engine powered aircraft. For a steam locomotive, the valve which controls the steam is known as the regulator. |
Conditional assembly language Support for structured programming Macro_Assembler > Language design > Support for structured programming IBM's High Level Assembler Toolkit includes such a macro package. A curious design was A-Natural, a "stream-oriented" assembler for 8080/Z80, processors from Whitesmiths Ltd. (developers of the Unix-like Idris operating system, and what was reported to be the first commercial C compiler). |
Macdonald River railway bridge, Woolbrook Heritage listing Macdonald_River_railway_bridge,_Woolbrook > Heritage listing This bridge is one of Whitton's major 1870s wrought iron bridges and is an excellent example of early bridge construction. The lattice girder is one of Whitton's original 12 bridges of that design and they represent the third stage of bridge construction in NSW following the stone viaduct and iron tubular bridges.This bridge is a member of the most significant group of colonial bridges in New South Wales. Collectively, as items of railway infrastructure, they contributed significantly to the history and development of New South Wales. Each bridge is an imposing structure at its site. |
Georg Cantor Mathematical work Georg_Cantor > Mathematical work Cantor's work between 1874 and 1884 is the origin of set theory. Prior to this work, the concept of a set was a rather elementary one that had been used implicitly since the beginning of mathematics, dating back to the ideas of Aristotle. No one had realized that set theory had any nontrivial content. Before Cantor, there were only finite sets (which are easy to understand) and "the infinite" (which was considered a topic for philosophical, rather than mathematical, discussion). |
Measurement in quantum mechanics Laboratory implementations Measurement_in_quantum_mechanics > Laboratory implementations The range of physical procedures to which the mathematics of quantum measurement can be applied is very broad. In the early years of the subject, laboratory procedures involved the recording of spectral lines, the darkening of photographic film, the observation of scintillations, finding tracks in cloud chambers, and hearing clicks from Geiger counters. Language from this era persists, such as the description of measurement outcomes in the abstract as "detector clicks".The double-slit experiment is a prototypical illustration of quantum interference, typically described using electrons or photons. The first interference experiment to be carried out in a regime where both wave-like and particle-like aspects of photon behavior are significant was G. I. Taylor's test in 1909. |
Quantum logic gate Measurement Quantum_logic_gates > Measurement The number of dimensions (defined by the basis vectors, and thus also the possible outcomes from measurement) is then often implied by the operands, for example as the required state space for solving a problem. In Grover's algorithm, Lov named this generic basis vector set "the database". |
H2 antagonists Summary H2_receptor_antagonist They have been surpassed by proton pump inhibitors (PPIs); the PPI omeprazole was found to be more effective at both healing and alleviating symptoms of ulcers and reflux oesophagitis than the H2 blockers ranitidine and cimetidine.H2 antagonists are a type of antihistamine, although in common use the term "antihistamine" is often reserved for H1 antagonists, which relieve allergic reactions. Like the H1 antagonists, some H2 antagonists function as inverse agonists rather than receptor antagonists, due to the constitutive activity of these receptors.The prototypical H2 antagonist, called cimetidine, was developed by Sir James Black at Smith, Kline & French – now GlaxoSmithKline – in the mid-to-late 1960s. It was first marketed in 1976 and sold under the trade name Tagamet, which became the first blockbuster drug. The use of quantitative structure-activity relationships (QSAR) led to the development of other agents – starting with ranitidine, first sold as Zantac, which has fewer adverse effects and drug interactions and is more potent. H2 blockers, which all end in "-tidine", are not the same as H1 receptor antagonists, which relieve allergy symptoms. |
History of the International System of Units Changes to the SI History_of_the_International_System_of_Units > Evolution of the SI > Changes to the SI The International Bureau of Weights and Measures (BIPM) has described SI as "the modern form of metric system". : 95 Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself, and clarification of how to use units of measure that are not part of SI but are still nevertheless used on a worldwide basis. Since 1960 the CGPM has made a number of changes to the SI to meet the needs of specific fields, notably chemistry and radiometry. These are mostly additions to the list of named derived units, and include the mole (symbol mol) for an amount of substance, the pascal (symbol Pa) for pressure, the siemens (symbol S) for electrical conductance, the becquerel (symbol Bq) for "activity referred to a radionuclide", the gray (symbol Gy) for ionising radiation, the sievert (symbol Sv) as the unit of dose equivalent radiation, and the katal (symbol kat) for catalytic activity. |
Quantum Bayesianism Reception and criticism Quantum_Bayesian > Reception and criticism A critical article by Nauenberg in the American Journal of Physics prompted a reply by Fuchs, Mermin, and Schack. Some assert that there may be inconsistencies; for example, Stairs argues that when a probability assignment equals one, it cannot be a degree of belief as QBists say. Further, while also raising concerns about the treatment of probability-one assignments, Timpson suggests that QBism may result in a reduction of explanatory power as compared to other interpretations. |
Formation constant Theory Formation_constant > Theory In dilute solutions the concentration of water is effectively constant. The expression becomes β = . {\displaystyle \beta =\mathrm {\frac {}{}} .} |
Gamma function Main definition Euler_Gamma_Function > Definition > Main definition Specifically, the base case is that Γ ( 1 ) = 1 = 0 ! {\displaystyle \Gamma (1)=1=0!} , and the induction step is that Γ ( n + 1 ) = n Γ ( n ) = n ( n − 1 ) ! |
Complete homogeneous symmetric polynomial Relation with the elementary symmetric polynomials Complete_homogeneous_symmetric_polynomial > Properties > Relation with the elementary symmetric polynomials It has a ring automorphism that interchanges the sequences of the n elementary and first n complete homogeneous symmetric functions. The set of complete homogeneous symmetric polynomials of degree 1 to n in n variables generates the ring of symmetric polynomials in n variables. More specifically, the ring of symmetric polynomials with integer coefficients equals the integral polynomial ring Z . |
Technology of television Elements of a television system Technology_of_television > Elements of a television system A receiver (also called a tuner), which decodes the picture and sound information from the broadcast signals, and whose input is coupled to the antenna of the television set. A display device, which turns the electrical signals into visual images. An audio amplifier and loudspeaker, which turns electrical signals into sound waves (speech, music, and other sounds) to accompany the images.Practical television systems include equipment for selecting different image sources, mixing images from several sources at once, insertion of pre-recorded video signals, synchronizing signals from many sources, and direct image generation by computer for such purposes as station identification. |
Community education Youth participation Community_education > Participatory democracy > Youth participation In countries where democratic governments exist, people are encouraged to vote for someone to represent them. In today's society there is a dwindling interest in politics from our younger generation and this could have a negative effect on our democracy and political system in years to come. Community learning and development has the potential to encourage young people to become more interested in politics and helping them influence decisions that affect their lives. In many parts of the world, youth parliament-style organisations have been set up to allow young people to debate issues that affect them and others in their community. |
Sulfurous oxide Structure and bonding Vitriolic_acid_air > Structure and bonding SO2 is a bent molecule with C2v symmetry point group. A valence bond theory approach considering just s and p orbitals would describe the bonding in terms of resonance between two resonance structures. The sulfur–oxygen bond has a bond order of 1.5. There is support for this simple approach that does not invoke d orbital participation. In terms of electron-counting formalism, the sulfur atom has an oxidation state of +4 and a formal charge of +1. |
Nuclear power generation Economics Fission_power > Economics Nuclear power was found to be the least-cost option among dispatchable technologies. Variable renewables can generate cheaper electricity: the median cost of onshore wind power was estimated to be 50 USD/MWh, and utility-scale solar power 56 USD/MWh. At the assumed CO2 emission cost of 30 USD/ton, power from coal (88 USD/MWh) and gas (71 USD/MWh) is more expensive than low-carbon technologies. |
Turing Machine simulator Small Turing machines Deterministic_Turing_machine > References > Small Turing machines Rogozhin, Yurii, 1998, "A Universal Turing Machine with 22 States and 2 Symbols", Romanian Journal of Information Science and Technology, 1(3), 259–265, 1998. (surveys known results about small universal Turing machines) Stephen Wolfram, 2002, A New Kind of Science, Wolfram Media, ISBN 1-57955-008-8 Brunfiel, Geoff, Student snags maths prize, Nature, October 24. 2007. Jim Giles (2007), Simplest 'universal computer' wins student $25,000, New Scientist, October 24, 2007. |
Mycosporine-like amino acid Salt stress Mycosporine-like_amino_acid > Functions > Environmental stress responses > Salt stress Osmotic stress is defined as difficulty maintaining proper fluids in the cell within a hypertonic or hypotonic environment. MAAs accumulate within a cell’s cytoplasm and contribute to the osmotic pressure within a cell, thus relieving pressure from salt stress in a hypertonic environment. As evidence of this, MAAs are seldom found in large quantities in cyanobacteria living in freshwater environments. However, in saline and hypertonic environments, cyanobacteria often contain high concentrations of MAAs. |
Exergy Exergy Analysis involving Radiative Heat Transfer Exergy > Mathematical description > Exergy Analysis involving Radiative Heat Transfer However, for decades this result was contested in terms of its relevance to the conversion of radiation fluxes, and in particular, solar radiation. For example, Bejan stated that “Petela’s efficiency is no more than a convenient, albeit artificial way, of non-dimensionalizing the calculated work output” and that Petela’s efficiency “is not a ‘conversion efficiency.’ ” However, it has been shown that Petela’s result represents the exergy of blackbody radiation. This was done by resolving a number of issues, including that of inherent irreversibility, defining the environment in terms of radiation, the effect of inherent emission by the conversion device and the effect of concentrating source radiation. |
Machine Learning (journal) Selected articles Machine_Learning_(journal) > Selected articles "Clausal Discovery". Machine Learning. 26 (2/3): 99–146. |
Lebesgue integrable Measure theory Lebesgue-integrable_function > Introduction > Measure theory Riemann could only use planar rectangles to approximate the area under the curve, because there was no adequate theory for measuring more general sets. In the development of the theory in most modern textbooks (after 1950), the approach to measure and integration is axiomatic. This means that a measure is any function μ defined on a certain class X of subsets of a set E, which satisfies a certain list of properties. These properties can be shown to hold in many different cases. |
Induction cooking Efficiency Induction_burner > Cooking properties > Efficiency Such a test, using two power levels, is intended to mimic real life use. Wasted energy terms such as residual unused heat (retained by solid hot-plates, ceramic or coil at the end of the test), and losses from convection and radiation by hot surfaces (including the ones of the block itself) are disregarded. In typical cooking, the energy delivered by the cooker is only partly used to heat the food; once that has occurred, all the subsequent energy input is delivered to the air as loss through steam or convection and radiation. |
Meningococcal vaccine Summary Meningococcal_vaccines In countries with a low risk of disease, they recommend that high risk groups should be immunized. In the African meningitis belt efforts to immunize all people between the ages of one and thirty with the meningococcal A conjugate vaccine are ongoing. In Canada and the United States the vaccines effective against four types of meningococcus (A, C, W, and Y) are recommended routinely for teenagers and others who are at high risk. |
Knowledge distillation Concept of distillation Knowledge_distillation > Concept of distillation Compression was achieved by training a smaller model on large amounts of pseudo-data labelled by a higher-performing ensemble, optimising to match the logit of the compressed model to the logit of the ensemble. Knowledge distillation is a generalisation of such approach, introduced by Geoffrey Hinton et al. in 2015, in a preprint that formulated the concept and showed some results achieved in the task of image classification. Knowledge distillation is also related to the concept of behavioral cloning discussed by Faraz Torabi et. al. |
Payment Card Industry Data Security Standard Self-Assessment Questionnaire Payment_Card_Industry_Data_Security_Standard > Compliance validation > Self-Assessment Questionnaire The PCI DSS Self-Assessment Questionnaire (SAQ) is a validation tool intended for small to medium sized merchants and service providers to assess their own PCI DSS compliance status. There are multiple types of SAQ, each with a different length depending on the entity type and payment model used. Each SAQ question has a yes-or-no answer, and any "no" response requires the entity to indicate its future implementation. As with ROCs, an attestation of compliance (AOC) based on the SAQ is also completed. |
Macromolecular Chemistry RNA is multifunctional Macromolecule > Linear biopolymers > Structural features > RNA is multifunctional RNA is multifunctional, its primary function is to encode proteins, according to the instructions within a cell's DNA. : 5 They control and regulate many aspects of protein synthesis in eukaryotes. RNA encodes genetic information that can be translated into the amino acid sequence of proteins, as evidenced by the messenger RNA molecules present within every cell, and the RNA genomes of a large number of viruses. The single-stranded nature of RNA, together with tendency for rapid breakdown and a lack of repair systems means that RNA is not so well suited for the long-term storage of genetic information as is DNA. |
Games and learning Research Games_and_learning > Research Digital games are a medium with certain affordances and constraints, just as physical labs and virtual simulations are media with certain affordances and constraints. Simulations and digital games actually share many similarities in this regard. Although there are multiple definitions for games, the key characteristics differentiating games from simulations involve the explicit inclusion of (a) rules for engaging with the simulation, (b) goals for players to pursue, and (c) means for indicating players' progress toward those goals. |
Non-contact magnetic charging Summary Induction_charger The moving electric charge creates a magnetic field, which fluctuates in strength because the electric current's amplitude is fluctuating. This changing magnetic field creates an alternating electric current in the portable device's induction coil, which in turn passes through a rectifier to convert it to direct current. Finally, the direct current charges a battery or provides operating power.Greater distances between sender and receiver coils can be achieved when the inductive charging system uses resonant inductive coupling, where a capacitor is added to each induction coil to create two LC circuits with a specific resonance frequency. The frequency of the alternating current is matched with the resonance frequency, and the frequency is chosen depending on the distance desired for peak efficiency. Recent improvements to this resonant system include using a movable transmission coil (i.e., mounted on an elevating platform or arm) and the use of other materials for the receiver coil such as silver-plated copper or sometimes aluminum to minimize weight and decrease resistance due to the skin effect. |
Kinetic temperature Kinetic theory of gases Temperature > Theoretical foundation > Kinetic theory of gases Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases. This theory also explains the ideal gas law and the observed heat capacity of monatomic (or 'noble') gases. The ideal gas law is based on observed empirical relationships between pressure (p), volume (V), and temperature (T), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws). The ideal gas law states: p V = n R T , {\displaystyle pV=nRT,} where n is the number of moles of gas and R = 8.314462618... J⋅mol−1⋅K−1 is the gas constant. |
P-form electrodynamics Summary P-form_electrodynamics In theoretical physics, p-form electrodynamics is a generalization of Maxwell's theory of electromagnetism. |
Tarski-Grothendieck set theory Axioms Tarski-Grothendieck_set_theory > Axioms What Tarski's axiom states (in the vernacular) is that for each set x {\displaystyle x} there is a Grothendieck universe it belongs to. That y {\displaystyle y} looks much like a “universal set” for x {\displaystyle x} – it not only has as members the powerset of x {\displaystyle x} , and all subsets of x {\displaystyle x} , it also has the powerset of that powerset and so on – its members are closed under the operations of taking powerset or taking a subset. It's like a “universal set” except that of course it is not a member of itself and is not a set of all sets. |
Variational Bayes Summary Variational_inference To derive a lower bound for the marginal likelihood (sometimes called the evidence) of the observed data (i.e. the marginal probability of the data given the model, with marginalization performed over unobserved variables). This is typically used for performing model selection, the general idea being that a higher marginal likelihood for a given model indicates a better fit of the data by that model and hence a greater probability that the model in question was the one that generated the data. (See also the Bayes factor article. |
Bituminous shale Geology Bituminous_shale > Geology Oil shale, an organic-rich sedimentary rock, belongs to the group of sapropel fuels. It does not have a definite geological definition nor a specific chemical formula, and its seams do not always have discrete boundaries. Oil shales vary considerably in their mineral content, chemical composition, age, type of kerogen, and depositional history, and not all oil shales would necessarily be classified as shales in the strict sense. According to the petrologist Adrian C. Hutton of the University of Wollongong, oil shales are not "geological nor geochemically distinctive rock but rather 'economic' term". |
GC376 COVID-19 GC376 > COVID-19 Since GC376 shows broad-spectrum activity against coronavirus, early on during the pandemic of 2020 it was suggested as a potential treatment for COVID-19. In response to the crisis, researchers at the University of Arizona published in vitro research indicating GC376 is highly active against 3CLpro in SARS-CoV-2 (the coronavirus which causes COVID-19). Another group of virologists at the University of Alberta lead by D. Lorne Tyrrell then released a separate publication confirming GC376's activity against 3CLpro in SARS-CoV-2 and also indicating GC376 had a potent antiviral effect. The next day, Columbia University's Zuckerman Institute hosted a COVID-19 Virtual Symposium which released research led by David Ho and characterized GC376 as "the most promising" protease inhibitor under investigation in Ho's lab because GC376 was the "most potent" and reached "complete viral inhibition" in a culture of cells infected with SARS-CoV-2. |
Concrete syntax Constituency-based parse trees Parse_tree > Constituency-based parse trees A branch node is a parent node that connects to two or more child nodes. A leaf node, however, is a terminal node that does not dominate other nodes in the tree. S is the root node, NP and VP are branch nodes, and John (N), hit (V), the (D), and ball (N) are all leaf nodes. |
Online complex processing Summary Online_complex_processing Online complex processing (OLCP) is a class of realtime data processing involving complex queries, lengthy queries and/or simultaneous reads and writes to the same records. |
Psychology of programming Research methods Psychology_of_programming > Research methods Some methods which one can use to study the psychological aspects of computer programming include introspection, observation, experiment, and qualitative research. |
Single Transferable Vote Summary Single_transferable_voting The use of a quota means that, for the most part, each successful candidate is elected with the same number of votes. This equality produces fairness – a party taking twice the votes than another party will take twice the seats compared to that other party. |
Multitarget stool DNA screening test Medical imaging Colorectal_carcinoma > Diagnosis > Medical imaging A colorectal cancer is sometimes initially discovered on CT scan.Presence of metastases is determined by a CT scan of the chest, abdomen and pelvis. Other potential imaging tests such as PET and MRI may be used in certain cases. MRI is particularly useful to determine local stage of the tumor and to plan the optimal surgical approach.MRI is also performed after completion of neoadjuvant chemoradiotherapy to identify patients who achieve complete response. |
Retrospective think aloud Summary Retrospective_think_aloud Retrospective think aloud protocol is a technique used in usability, and eye tracking in particular, to gather qualitative information on the user intents and reasoning during a test. It's a form of think aloud protocol performed after the user testing session activities, instead of during them. Fairly often the retrospective protocol is stimulated by using a visual reminder such as a video replay. In writing studies, the visual reminder may be the writing produced during the think-aloud session. |
Sigma factor Sigma cycle Sigma_factor > Sigma cycle It had long been thought that the sigma factor obligatorily leaves the core enzyme once it has initiated transcription, allowing it to link to another core enzyme and initiate transcription at another site. Thus, the sigma factor would cycle from one core to another. However, fluorescence resonance energy transfer was used to show that the sigma factor does not obligatorily leave the core. Instead, it changes its binding with the core during initiation and elongation. Therefore, the sigma factor cycles between a strongly bound state during initiation and a weakly bound state during elongation. |
Privacy rights An individual right Privacy_rights > History > An individual right For Lessig, privacy breaches online can be regulated through code and law. Lessig claims "the protection of privacy would be stronger if people conceived of the right as a property right", and that "individuals should be able to control information about themselves". Economic approaches to privacy make communal conceptions of privacy difficult to maintain. |
Unit-point atomism Medieval Christendom Classical_atomism > History > Middle Ages > Medieval Christendom In medieval universities there were expressions of atomism. For example, in the 14th century Nicholas of Autrecourt considered that matter, space, and time were all made up of indivisible atoms, points, and instants and that all generation and corruption took place by the rearrangement of material atoms. |
Fixed wing Lifting body Fixed_wing_aircraft > Characteristics > Wings vs. bodies > Lifting body A lifting body is a configuration in which the body itself produces lift. In contrast to a flying wing, which is a wing with minimal or no conventional fuselage, a lifting body can be thought of as a fuselage with little or no conventional wing. Whereas a flying wing seeks to maximize cruise efficiency at subsonic speeds by eliminating non-lifting surfaces, lifting bodies generally minimize the drag and structure of a wing for subsonic, supersonic, and hypersonic flight, or, spacecraft re-entry. All of these flight regimes pose challenges for proper flight stability. |
Autonomous bus Technology used in vehicular automation Automated_Driving > Technology used in vehicular automation The main purpose for the perception system is to constantly scan the surrounding environment and determine which objects in the environment pose a threat to vehicles. In a sense, the perception system's main goal is to act like human perception, allowing the system to sense hazards and to prepare or correct for these hazards. In terms of the detection part of the perception system, many solutions are being tested for accuracy and compatibility, such as radar, lidar, sonar and moving image processing.With the development of these autonomous subsystems of the car, autonomous vehicle manufacturers have already developed systems which act as assistance features on a vehicle. |
Factorial design Analysis Factorial_experiment > Analysis A factorial experiment can be analyzed using ANOVA or regression analysis. To compute the main effect of a factor "A" in a 2-level experiment, subtract the average response of all experimental runs for which A was at its low (or first) level from the average response of all experimental runs for which A was at its high (or second) level. Other useful exploratory analysis tools for factorial experiments include main effects plots, interaction plots, Pareto plots, and a normal probability plot of the estimated effects. When the factors are continuous, two-level factorial designs assume that the effects are linear. If a quadratic effect is expected for a factor, a more complicated experiment should be used, such as a central composite design. Optimization of factors that could have quadratic effects is the primary goal of response surface methodology. |
Norm (philosophy) Types of norms Norm_(philosophy) > Types of norms The girls also acted more violently to the male models. These findings relate to norms as they show the influence of social norms on behavior. The young children were more likely to observe and copy the norms and be influenced by the behavior of others, especially those they may see as “older” or a “role model.” |
Polarized capacitor Impedance Polarized_capacitor > Electrical characteristics > Impedance In this sense impedance is a measure of the ability of the capacitor to pass alternating currents and can be used like Ohm's law. Z = u ^ ı ^ = U e f f I e f f . |
Hardy–Weinberg principle Deviations from Hardy–Weinberg equilibrium Hardy–Weinberg_principle > Deviations from Hardy–Weinberg equilibrium Recurrent mutation will maintain alleles in the population, even if there is strong selection against them. Migration genetically links two or more populations together. In general, allele frequencies will become more homogeneous among the populations. |
RNA silencing Main challenge RNA_silencing > Practical applications > Main challenge As with conventional manufactured drugs, the main challenge in developing successful offshoots of the RNAi-based drugs is the precise delivery of the RNAi triggers to where they are needed in the body. The reason that the ocular macular degeneration antidote was successful sooner than the antidote with other diseases is that the eyeball is almost a closed system, and the serum can be injected with a needle exactly where it needs to be. The future successful drugs will be the ones who are able to land where needed, probably with the help of nanobots. Below is a rendition of a table that shows the existing means of delivery of the RNAi triggers. |
Anthropogenic greenhouse gases Deforestation Anthropogenic_greenhouse_gases > Emissions by sector > Agriculture, forestry and land use > Agriculture > Deforestation Deforestation is a major source of greenhouse gas emissions. A study shows annual carbon emissions (or carbon loss) from tropical deforestation have doubled during the last two decades and continue to increase. (0.97 ±0.16 PgC per year in 2001–2005 to 1.99 ±0.13 PgC per year in 2015–2019) |
Reduced Planck Constant Atomic structure Reduced_Planck’s_constant > Development and application > Atomic structure Bohr also introduced the quantity ℏ = h 2 π {\displaystyle \hbar ={\frac {h}{2\pi }}} , now known as the reduced Planck constant or Dirac constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J {\displaystyle J} is the total angular momentum of a system with rotational invariance, and J z {\displaystyle J_{z}} the angular momentum measured along any given direction, these quantities can only take on the values J 2 = j ( j + 1 ) ℏ 2 , j = 0 , 1 2 , 1 , 3 2 , … , J z = m ℏ , m = − j , − j + 1 , … , j . {\displaystyle {\begin{aligned}J^{2}=j(j+1)\hbar ^{2},\qquad &j=0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\ldots ,\\J_{z}=m\hbar ,\qquad \qquad \quad &m=-j,-j+1,\ldots ,j.\end{aligned}}} |
Learned industriousness Reinforcement Learned_industriousness > Antecedents of industriousness > Reinforcement According to Daniels & Daniels, reinforcement is any stimulus, event, or situation that fulfills the following two requirements: Follows a behavior Increases the frequency of that behaviorA stimulus, event, or situation is considered a reinforcer if it follows a targeted behavior and causes the increased occurrence of that behavior. Many confuse the terms "reward" and "reinforcer" because they often mean the same thing; a reward is given as a consequence of a desired behavior and often motivates an individual to perform that behavior again in order to receive another reward. However, individuals can receive rewards and not increase the behavior in question (e.g., receiving a prize for completing a marathon may not motivate an individual to run more marathons). In that case, the reward is not a reinforcer because it does not increase the frequency of the behavior. |
Color symmetry Quark and gluon fields Colour_charge > Quark and gluon fields The colour of a gluon is similarly given by A {\displaystyle \mathbf {A} } which corresponds to the particular Gell-Mann matrix it is associated with. This matrix has indices i and j. These are the colour labels on the gluon. At the interaction vertex one has qi → gi j + qj. |
Linear hashing Hash functions Linear_hashing > Algorithm details > Hash functions In order to access a record with key c {\displaystyle c} , a family of hash functions, called collectively a dynamic hash function is applied to the key c {\displaystyle c} . At any time, at most two hash functions h i {\displaystyle h_{i}} and h i + 1 {\displaystyle h_{i+1}} are used. A typical example uses the division modulo x operation. If the original number of buckets is N {\displaystyle N} , then the family of hash functions is h i ( c ) ↦ c ( mod N ⋅ 2 i ) {\displaystyle h_{i}(c)\mapsto c{\pmod {N\cdot 2^{i}}}} |
Space-time adaptive processing Summary Space-time_adaptive_processing Space-time adaptive processing (STAP) is a signal processing technique most commonly used in radar systems. It involves adaptive array processing algorithms to aid in target detection. Radar signal processing benefits from STAP in areas where interference is a problem (i.e. ground clutter, jamming, etc.). Through careful application of STAP, it is possible to achieve order-of-magnitude sensitivity improvements in target detection. |
Small nucleolar RNA snR48 Summary Small_nucleolar_RNA_snR48 In molecular biology, the snoRNA snR48 is a non-coding RNA (ncRNA) molecule which functions in the modification of other small nuclear RNAs (snRNAs). This type of modifying RNA is usually located in the nucleolus of the eukaryotic cell which is a major site of snRNA biogenesis. It is known as a small nucleolar RNA (snoRNA) and also often referred to as a guide RNA. |
Continuous current Automotive DC_voltage > Applications > Automotive To save weight and wire, often the metal frame of the vehicle is connected to one pole of the battery and used as the return conductor in a circuit. Often the negative pole is the chassis "ground" connection, but positive ground may be used in some wheeled or marine vehicles. In a battery electric vehicle, there are usually two separate DC systems. |
EM algorithm Summary Expectation–maximization_algorithm In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. |
Glossary of computer science W Glossary_of_computer_science > W waterfall model A breakdown of project activities into linear sequential phases, where each phase depends on the deliverables of the previous one and corresponds to a specialisation of tasks. The approach is typical for certain areas of engineering design. In software development, it tends to be among the less iterative and flexible approaches, as progress flows in largely one direction ("downwards" like a waterfall) through the phases of conception, initiation, analysis, design, construction, testing, deployment and maintenance. Waveform Audio File Format Also WAVE or WAV due to its filename extension. |
Origin and function of meiosis DNA repair Origin_and_function_of_meiosis > Function > DNA repair Prokaryotes do have DNA repair mechanism enriched with recombinational repair, and the existence of prokaryotic life in severe environment indicates the extreme efficiency of this mechanism to help them survive many DNA damages related to the environment. This implies that an extra costly repair in the form of meiosis would be unnecessary. However, most of these mechanisms cannot be as accurate as meiosis and are possibly more mutagenic than the repair mechanism provided by meiosis. |
Industrial catalysts Summary Industrial_catalysts To achieve the best understanding and development of a catalyst it is important that different special fields work together. These fields can be: organic chemistry, analytic chemistry, inorganic chemistry, chemical engineers and surface chemistry. |
Mean error In univariate distributions Statistical_error > In univariate distributions The sum of squares of the statistical errors, divided by σ2, has a chi-squared distribution with n degrees of freedom: 1 σ 2 ∑ i = 1 n e i 2 ∼ χ n 2 . {\displaystyle {\frac {1}{\sigma ^{2}}}\sum _{i=1}^{n}e_{i}^{2}\sim \chi _{n}^{2}.} However, this quantity is not observable as the population mean is unknown. |
Concept drift Synthetic Concept_drift > External links > Datasets > Synthetic 22 (5): 730–742. doi:10.1109/TKDE.2009.156. S2CID 16592739. |
Wallerian degeneration Clearance in PNS Wallerian_degeneration > Myelin clearance > Clearance in PNS The response of Schwann cells to axonal injury is rapid. The time period of response is estimated to be prior to the onset of axonal degeneration. Neuregulins are believed to be responsible for the rapid activation. They activate ErbB2 receptors in the Schwann cell microvilli, which results in the activation of the mitogen-activated protein kinase (MAPK). |
Pleiotropy History Pleiotropy > History Natural selection favors genes that are more beneficial prior to reproduction than after (leading to an increase in reproductive success). Knowing this, Williams argued that if only close linkage was present, then beneficial traits will occur both before and after reproduction due to natural selection. This, however, is not observed in nature, and thus antagonistic pleiotropy contributes to the slow deterioration with age (senescence). |
Ectonucleotide pyrophosphatase/phosphodiesterase 1 Interactions Ectonucleotide_pyrophosphatase/phosphodiesterase_1 > Interactions Ectonucleotide pyrophosphatase/phosphodiesterase 1 has been shown to interact with Insulin receptor. |
Brandolini's law Similar concepts Brandolini's_law > Similar concepts In 1845, Frédéric Bastiat expressed an early notion of this law: We must confess that our adversaries have a marked advantage over us in the discussion. In very few words they can announce a half-truth; and in order to demonstrate that it is incomplete, we are obliged to have recourse to long and dry dissertations. |
Hamilton–Jacobi–Einstein equation Summary Hamilton–Jacobi–Einstein_equation In general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation of geometrodynamics in superspace, cast in the "geometrodynamics era" around the 1960s, by Asher Peres in 1962 and others. It is an attempt to reformulate general relativity in such a way that it resembles quantum theory within a semiclassical approximation, much like the correspondence between quantum mechanics and classical mechanics. It is named for Albert Einstein, Carl Gustav Jacob Jacobi, and William Rowan Hamilton. The EHJE contains as much information as all ten Einstein field equations (EFEs). It is a modification of the Hamilton–Jacobi equation (HJE) from classical mechanics, and can be derived from the Einstein–Hilbert action using the principle of least action in the ADM formalism. |
Barycentric subdivision Lefschetz's fixed-point theorem Barycentric_subdivision > Applications > Simplicial approximation > Lefschetz's fixed-point theorem The Lefschetz number is a useful tool to find out whether a continuous function admits fixed-points. This data is computed as follows: Suppose that X {\displaystyle X} and Y {\displaystyle Y} are topological spaces that admit finite triangulations. A continuous map f: X → Y {\displaystyle f:X\rightarrow Y} induces homomorphisms f i: H i ( X , K ) → H i ( Y , K ) {\displaystyle f_{i}:H_{i}(X,K)\rightarrow H_{i}(Y,K)} between its simplicial homology groups with coefficients in a field K {\displaystyle K} . These are linear maps between K {\displaystyle K} - vectorspaces, so their trace t r i {\displaystyle tr_{i}} can be determined and their alternating sum L K ( f ) = ∑ i ( − 1 ) i t r i ( f ) ∈ K {\displaystyle L_{K}(f)=\sum _{i}(-1)^{i}tr_{i}(f)\in K} is called the Lefschetz number of f {\displaystyle f} . |
Electrical charge History Negatively_charged > History Through these experiments, Gray discovered the importance of different materials, which facilitated or hindered the conduction of electrical effluvia. John Theophilus Desaguliers, who repeated many of Gray's experiments, is credited with coining the terms conductors and insulators to refer to the effects of different materials in these experiments. Gray also discovered electrical induction (i.e., where charge could be transmitted from one object to another without any direct physical contact). |
Classical three-dimensional momentum Relation to force Linear_Momentum > Newtonian > Relation to force If the net force F applied to a particle is constant, and is applied for a time interval Δt, the momentum of the particle changes by an amount In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force F acting on it, If the net force experienced by a particle changes as a function of time, F(t), the change in momentum (or impulse J) between times t1 and t2 is Impulse is measured in the derived units of the newton second (1 N⋅s = 1 kg⋅m/s) or dyne second (1 dyne⋅s = 1 g⋅cm/s) Under the assumption of constant mass m, it is equivalent to write hence the net force is equal to the mass of the particle times its acceleration.Example: A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3 newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which is numerically equivalent to 3 newtons. |
Metric power Concept of metric power Metric_power > Concept of metric power : 8 To have metric power is to both enable and constrain the possibilities of individuals. These possibilities can be situated in a range of areas, including "our behaviour, our cultural and social practices, and our material reality. ": 1774 |
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