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Theories about religion Methodologies Theories_about_religions > Methodologies When explaining religion they reject divine or supernatural explanations for the status or origins of religions because they are not scientifically testable. In fact, theorists such as Marett (an Anglican) excluded scientific results altogether, defining religion as the domain of the unpredictable and unexplainable; that is, comparative religion is the rational (and scientific) study of the irrational. The dichotomy between the two classifications is not bridgeable, even though they have the same methods, because each excludes the data of the other.The functionalists and some of the later essentialists (among others E. E. Evans-Pritchard) have criticized the substantive view as neglecting social aspects of religion.
Hybrid capacitor Measurement Supercapacitor > Electrical parameters > Capacitance > Measurement The IEC standard defines four classes: Memory backup, discharge current in mA = 1 • C (F) Energy storage, discharge current in mA = 0,4 • C (F) • V (V) Power, discharge current in mA = 4 • C (F) • V (V) Instantaneous power, discharge current in mA = 40 • C (F) • V (V)The measurement methods employed by individual manufacturers are mainly comparable to the standardized methods.The standardized measuring method is too time consuming for manufacturers to use during production for each individual component. For industrial-produced capacitors, the capacitance value is instead measured with a faster, low-frequency AC voltage, and a correlation factor is used to compute the rated capacitance. This frequency dependence affects capacitor operation. Rapid charge and discharge cycles mean that neither the rated capacitance value nor specific energy are available. In this case the rated capacitance value is recalculated for each application condition.
Vectorizing compiler Techniques Automatic_vectorization > Techniques An example would be a program to multiply two vectors of numeric data. A scalar approach would be something like: This could be vectorized to look something like: Here, c represents the four array elements from c to c and the vector processor can perform four operations for a single vector instruction. Since the four vector operations complete in roughly the same time as one scalar instruction, the vector approach can run up to four times faster than the original code. There are two distinct compiler approaches: one based on the conventional vectorization technique and the other based on loop unrolling.
Thermionic emission Photon-enhanced thermionic emission Richardson–Dushman_effect > Photon-enhanced thermionic emission Photon-enhanced thermionic emission (PETE) is a process developed by scientists at Stanford University that harnesses both the light and heat of the sun to generate electricity and increases the efficiency of solar power production by more than twice the current levels. The device developed for the process reaches peak efficiency above 200 °C, while most silicon solar cells become inert after reaching 100 °C. Such devices work best in parabolic dish collectors, which reach temperatures up to 800 °C. Although the team used a gallium nitride semiconductor in its proof-of-concept device, it claims that the use of gallium arsenide can increase the device's efficiency to 55–60 percent, nearly triple that of existing systems, and 12–17 percent more than existing 43 percent multi-junction solar cells.
Transactional memory Summary Transactional_memory In computer science and engineering, transactional memory attempts to simplify concurrent programming by allowing a group of load and store instructions to execute in an atomic way. It is a concurrency control mechanism analogous to database transactions for controlling access to shared memory in concurrent computing. Transactional memory systems provide high-level abstraction as an alternative to low-level thread synchronization. This abstraction allows for coordination between concurrent reads and writes of shared data in parallel systems.
Newton's laws of motion Prerequisites Newton's_laws_of_motion > Prerequisites Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. : 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions.
Smooth surface Riemannian connection and parallel transport Differential_geometry_of_surfaces > Riemannian connection and parallel transport The classical approach of Gauss to the differential geometry of surfaces was the standard elementary approach which predated the emergence of the concepts of Riemannian manifold initiated by Bernhard Riemann in the mid-nineteenth century and of connection developed by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early twentieth century. The notion of connection, covariant derivative and parallel transport gave a more conceptual and uniform way of understanding curvature, which not only allowed generalisations to higher dimensional manifolds but also provided an important tool for defining new geometric invariants, called characteristic classes. The approach using covariant derivatives and connections is nowadays the one adopted in more advanced textbooks.
Branch-and-bound algorithm Overview Branch-and-bound_algorithm > Overview However, an optimal solution among SI must be contained in at least one of the subsets.) bound(I) computes a lower bound on the value of any candidate solution in the space represented by I, that is, bound(I) ≤ f(x) for all x in SI. solution(I) determines whether I represents a single candidate solution.
Medical simulation Environment Medical_simulation > Debriefing & Education in Medical Simulation > Environment The debriefing environment consists of two main features: the physical setting, as well as the psychological environment.
Clastic rocks Shallow burial (eogenesis) Clastic_rock > Sedimentary clastic rocks > Diagenesis of siliciclastic sedimentary rocks > Shallow burial (eogenesis) Due to the shallow depths, sediments undergo only minor compaction and grain rearrangement during this stage. Organisms rework sediment near the depositional interface by burrowing, crawling, and in some cases sediment ingestion.
Quantum carpet Quantum revivals Quantum_carpet > Quantum carpets that demonstrate theoretical principles > Quantum revivals This continues to occur with periodic regularity. Quantum revivals, the periodic expansion and contraction of wave packets, are responsible for the restoration of the pattern. Although quantum revivals are mathematically complex, they are simple and easy to visualize on quantum carpets, as patterns expanding and reforming. Thus, quantum carpets provide clear visual evidence of quantum revivals.
Homological algebra Abelian categories Homological_algebra > Standard tools > Abelian categories The class of Abelian categories is closed under several categorical constructions, for example, the category of chain complexes of an Abelian category, or the category of functors from a small category to an Abelian category are Abelian as well. These stability properties make them inevitable in homological algebra and beyond; the theory has major applications in algebraic geometry, cohomology and pure category theory.
Comparative Advantage Empirical approach to comparative advantage Comparative_Advantage > Empirical approach to comparative advantage For example, the Ricardian model predicts that technological differences in countries result in differences in labor productivity. The differences in labor productivity in turn determine the comparative advantages across different countries. Testing the Ricardian model for instance involves looking at the relationship between relative labor productivity and international trade patterns. A country that is relatively efficient in producing shoes tends to export shoes.
Poly(methyl acrylate) Uses Poly(methyl_acrylate) > Uses Also used in leather finishing and textiles.Derivatives of this polymer are commonly used in orally administerd pharmaceutical formulations to target specific regions of the gastrointestinal tract. == References ==
Psychiatry Subspecialties Psychiatry > Theory and focus > Subspecialties The field of psychiatry has many subspecialties that require additional training and certification by the American Board of Psychiatry and Neurology (ABPN). Such subspecialties include: Addiction psychiatry, addiction medicine Brain injury medicine Child and adolescent psychiatry Clinical neurophysiology Consultation-liaison psychiatry Forensic psychiatry Geriatric psychiatry Hospice and palliative medicine Sleep medicine Additional psychiatry subspecialties, for which the ABPN does not provide formal certification, include: Biological psychiatry Cognitive diseases, as in various forms of dementia Community psychiatry Cross-cultural psychiatry Emergency psychiatry Evolutionary psychiatry Global mental health Learning disabilities Military psychiatry Neurodevelopmental disorders Neuropsychiatry Social psychiatryAddiction psychiatry focuses on evaluation and treatment of individuals with alcohol, drug, or other substance-related disorders, and of individuals with dual diagnosis of substance-related and other psychiatric disorders. Biological psychiatry is an approach to psychiatry that aims to understand mental disorders in terms of the biological function of the nervous system. Child and adolescent psychiatry is the branch of psychiatry that specializes in work with children, teenagers, and their families.
Random error Drift Observational_error > Sources > Sources of systematic error > Drift If the zero reading is consistently above or below zero, a systematic error is present. If this cannot be eliminated, potentially by resetting the instrument immediately before the experiment then it needs to be allowed by subtracting its (possibly time-varying) value from the readings, and by taking it into account while assessing the accuracy of the measurement. If no pattern in a series of repeated measurements is evident, the presence of fixed systematic errors can only be found if the measurements are checked, either by measuring a known quantity or by comparing the readings with readings made using a different apparatus, known to be more accurate.
Observational study Motivation Observational_study > Motivation Membership in this "treated" group is not controlled by the investigator: the group is formed after the "treatment" has been assigned. The investigator may simply lack the requisite influence. Suppose a scientist wants to study the public health effects of a community-wide ban on smoking in public indoor areas.
Technologies in Minority Report Autonomous cars Technologies_in_Minority_Report > Technologies in development > Autonomous cars As Artificial Intelligence and ground-sensing technologies like LIDAR began to improve in the 2000s, major automotive manufacturers such as Ford, Nissan and General Motors began developing self-driving prototypes. Google began developing a self-driving vehicle prototype, named Waymo in 2009 while Tesla Motors rolled out the autopilot feature on their Model S vehicle in 2015. In 2011, the State of Nevada became the first jurisdiction in the world to formally legalise autonomous vehicles on public roads. Countries such as the United Kingdom (2013) France (2014), Switzerland (2015) and Singapore (2016) passed laws which allowed the testing of autonomous vehicles on public roads, with a view to further changes in legislation as the technologies improves.
Continuous passive motion Summary Continuous_passive_motion Continuous passive motion (CPM) devices are used during the first phase of rehabilitation following a soft tissue surgical procedure or trauma. The goals of phase 1 rehabilitation are: control post-operative pain, reduce inflammation, provide passive motion in a specific plane of movement, and protect the healing repair or tissue. CPM is carried out by a CPM device, which constantly moves the joint through a controlled range of motion; the exact range is dependent upon the joint, but in most cases the range of motion is increased over time. CPM is used following various types of reconstructive joint surgery such as knee replacement and ACL reconstruction.
Nonlinear dimensionality reduction Applications of NLDR Manifold_learning > Applications of NLDR The intrinsic dimensionality is two, because two variables (rotation and scale) were varied in order to produce the data. Information about the shape or look of a letter 'A' is not part of the intrinsic variables because it is the same in every instance. Nonlinear dimensionality reduction will discard the correlated information (the letter 'A') and recover only the varying information (rotation and scale).
Aleph nought Fixed points of omega Aleph_nought > Fixed points of omega The first such is the limit of the sequence ω , ω ω , ω ω ω , … . {\displaystyle \omega ,\,\omega _{\omega },\,\omega _{\omega _{\omega }},\,\ldots ~.}
Economic models Comparison with models in other sciences Economic_models > Tests of macroeconomic predictions > Comparison with models in other sciences Complex systems specialist and mathematician David Orrell wrote on this issue in his book Apollo's Arrow and explained that the weather, human health and economics use similar methods of prediction (mathematical models). Their systems—the atmosphere, the human body and the economy—also have similar levels of complexity. He found that forecasts fail because the models suffer from two problems: (i) they cannot capture the full detail of the underlying system, so rely on approximate equations; (ii) they are sensitive to small changes in the exact form of these equations.
Static forces and virtual-particle exchange The interaction energy Static_forces_and_virtual-particle_exchange > Selected examples > Magnetostatics > Magnetic interaction between current loops in a simple plasma or electron gas > The interaction energy : 110–112 This wave generates Hall currents that interact and modify the electromagnetic field. The dispersion relation for extraordinary waves is: 112 which gives for the propagator where in analogy with the Darwin propagator. Here, the upper hybrid frequency is given by the cyclotron frequency is given by (Gaussian units) and the plasma frequency (Gaussian units) Here n is the electron density, e is the magnitude of the electron charge, and m is the electron mass. The interaction energy becomes, for like currents,
Gravity anomalies Definition Gravity_anomalies > Definition Correcting for these effects removed most of this anomaly.To understand the nature of the gravity anomaly due to the subsurface, a number of corrections must be made to the measured gravity value. Different theoretical models will include different corrections to the value of gravity, and so a gravity anomaly is always specified with reference to a particular model. The Bouguer, free-air, and isostatic gravity anomalies are each based on different theoretical corrections to the value of gravity.
Yang-Mills field Quantization Yang–Mills_field > Quantization Most of the difficulties that research meets is just managing the theory at low energies. That is the interesting case, being inherent to the description of hadronic matter and, more generally, to all the observed bound states of gluons and quarks and their confinement (see hadrons). The most used method to study the theory in this limit is to try to solve it on computers (see lattice gauge theory).
Matrix scheme Operation Matrix_scheme > Operation When a pre-defined number of people have purchased the token product, the person currently at the top of the list receives their reward item, and the next person in the list moves to the top. The rewards for those at the top of the matrix list are usually high-demand consumer electronics, such as portable digital audio players, high-definition television sets, laptops, and cellphones. Reaching the point on the list where one receives the expensive goods is termed "cycling".
Membrane curvature Summary Membrane_curvature The lipids will then "aggregate" and form various phases and structures. According to the conditions (concentration, temperature, ionic strength of solution, etc.) and the chemical structures of the lipid, different phases will be observed. For instance, the lipid POPC (palmitoyl oleyl phosphatidyl choline) tends to form lamellar vesicles in solution, whereas smaller lipids (lipids with shorter acyl chains, up to 8 carbons in length), such as detergents, will form micelles if the CMC (critical micelle concentration) was reached. There are five commonly proposed mechanisms by which membrane curvature is created, maintained, or controlled: lipid composition, shaped transmembrane proteins, protein motif insertion/BAR domains, protein scaffolding, and cytoskeleton scaffolding.
Lorentz interval Gravitation Spacetime_geometry > Spacetime in special relativity > Gravitation In general relativity, spacetime is no longer a static background, but actively interacts with the physical systems that it contains. Spacetime curves in the presence of matter, can propagate waves, bends light, and exhibits a host of other phenomena. : 221 A few of these phenomena are described in the later sections of this article.
Posner cueing task Method Posner_cueing_task > Method To measure reaction time (RT), a response mechanism is placed in front of the observer, usually a computer keyboard which is pressed upon detection of a target. Following a set inter-trial interval, usually between 2500 and 5000 ms, the entire paradigm is repeated for a set number of trials predetermined by the experimenter. The paradigm appears to be very effective in recasting attentional allocation.
Moyamoya disease Summary Moyamoya_disease Moyamoya disease is a disease in which certain arteries in the brain are constricted. Blood flow is blocked by constriction and blood clots (thrombosis). A collateral circulation develops around the blocked vessels to compensate for the blockage, but the collateral vessels are small, weak, and prone to bleeding, aneurysm and thrombosis. On conventional angiography, these collateral vessels have the appearance of a "puff of smoke" (described as "もやもや (moyamoya)" in Japanese).When moyamoya is diagnosed by itself, with no underlying correlational conditions, it is diagnosed as moyamoya disease.
Forbidden input Examples Forbidden_input > Examples Examples of don't-care terms are the binary values 1010 through 1111 (10 through 15 in decimal) for a function that takes a binary-coded decimal (BCD) value, because a BCD value never takes on such values (so called pseudo-tetrades); in the pictures, the circuit computing the lower left bar of a 7-segment display can be minimized to a b + a c by an appropriate choice of circuit outputs for dcba = 1010…1111. Write-only registers, as frequently found in older hardware, are often a consequence of don't-care optimizations in the trade-off between functionality and the number of necessary logic gates.Don't-care states can also occur in encoding schemes and communication protocols.
Wrought Iron Bridge Company Products Wrought_Iron_Bridge_Company > Products The Wrought Iron Bridge Company specialized in relatively short-span iron truss bridges. Most were built for highway use, as the railroads were all privately owned at the time and employed their own engineers. The company supplied a catalog of bridge designs and mass-produced the parts to build these designs. Once a bridge was ordered, the pieces were shipped by train to the nearest station. Thus, local contractors were able to assemble a bridge very quickly, much like a model.
Shock (circulatory) Epidemiology Circulatory_shock > Epidemiology Septic shock (a form of distributive shock), is the most common form of shock. Shock from blood loss occurs in about 1–2% of trauma cases. Overall, up to one-third of people admitted to the intensive care unit (ICU) are in circulatory shock. Of these, cardiogenic shock accounts for approximately 20%, hypovolemic about 20%, and septic shock about 60% of cases.
Photo-electric effect Summary Photo-electric_effect The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, solid state, and quantum chemistry to draw inferences about the properties of atoms, molecules and solids. The effect has found use in electronic devices specialized for light detection and precisely timed electron emission.
Exchange forces Exchange of force carriers in particle physics Exchange_force > Exchange of force carriers in particle physics These particles can be thought of somewhat analogously to basketballs tossed between matter particles (which are like the basketball players). What we normally think of as "forces" are actually the effects of force carrier particles on matter particles. The basketball animation is, of course, a very crude analogy since it can only explain repulsive forces and gives no hint of how exchanging particles can result in attractive forces.
Lebesgue constant Definition Lebesgue_constant > Definition , x n {\displaystyle x_{0},...,x_{n}} and an interval {\displaystyle } containing all the interpolation nodes. The process of interpolation maps the function f {\displaystyle f} to a polynomial p {\displaystyle p} . This defines a mapping X {\displaystyle X} from the space C() of all continuous functions on to itself.
Signaling cascade Neurons Signalling_cascade > Cell-specific biochemical cascades > Neurons The LKB1/NUAK1 signalling pathway regulates terminal axon branching at cortical neurons, via local immobilized mitochondria capture. Besides NUAK1, LKB1 kinase acts under other effectors enzymes as SAD-A/B and MARK, therefore regulating neuronal polarization and axonal growth, respectively. These kinase cascades implicates also Tau and others MAP. An extended knowledge of these and others neuronal pathways could provide new potential therapeutic targets for several neurodegenerative chronic diseases as Alzheimer's, Parkinson's and Huntington's disease, and also amyotrophic lateral sclerosis.
Quantum measurement Quantum systems as measuring devices Measurement_in_quantum_theory > History of the measurement concept > Quantum systems as measuring devices : 24 But the devices used to build the experimental apparatus are themselves physical systems, and so quantum mechanics should be applicable to them as well. Beginning in the 1950s, Rosenfeld, von Weizsäcker and others tried to develop consistency conditions that expressed when a quantum-mechanical system could be treated as a measuring apparatus. One proposal for a criterion regarding when a system used as part of a measuring device can be modeled semiclassically relies on the Wigner function, a quasiprobability distribution that can be treated as a probability distribution on phase space in those cases where it is everywhere non-negative. : 375
Paul Flory Research Paul_Flory > Research Some work completed by Paul Flory during his time includes the development in the quantitative correlations between the chain molecules and chemical structure of properties. This has to do with the way polymers are composed and what are composed of polymers. One piece of material formed through polymers is plastic.
Discrete-time Fourier transform Definition Discrete-time_Fourier_transform > Definition The discrete-time Fourier transform of a discrete sequence of real or complex numbers x, for all integers n, is a Trigonometric series, which produces a periodic function of a frequency variable. When the frequency variable, ω, has normalized units of radians/sample, the periodicity is 2π, and the DTFT series is:: p.147 The discrete-time Fourier transform is analogous to a Fourier series, except instead of starting with a periodic function of time and producing discrete sequence over frequency, it starts with a discrete sequence in time and produces a periodic function in frequency. The utility of this frequency domain function is rooted in the Poisson summation formula. Let X(f) be the Fourier transform of any function, x(t), whose samples at some interval T (seconds) are equal (or proportional) to the x sequence, i.e. T⋅x(nT) = x. Then the periodic function represented by the Fourier series is a periodic summation of X(f) in terms of frequency f in hertz (cycles/sec): The integer k has units of cycles/sample, and 1/T is the sample-rate, fs (samples/sec).
Skin effect Mitigation Skin_effect > Mitigation This results in superior performance (i.e. higher current with lower temperature rise) from wide thin conductors (for example, "ribbon" conductors) in which the effects from corners are effectively eliminated. It follows that a transformer with a round core will be more efficient than an equivalent-rated transformer having a square or rectangular core of the same material. Solid or tubular conductors may be silver-plated to take advantage of silver's higher conductivity.
Virtual team Technology Agility Virtual_team > Management > Technology Agility Therefore, team members must choose technology carefully, in order to offer the affordances needed at a given point in time, as each technology brings with it a number of affordances as well as constraints for interaction. An affordance is a purpose for use, and technology affordances refer to the mutually supportive relationship between human-endowed purposes to an activity and the technology use. Importantly, the need for certain affordances change over time as teams’ tasks evolve.
General adversarial network Fast gradient sign method General_adversarial_network > Specific attack types > Adversarial examples > White box attacks > Fast gradient sign method One of the very first proposed attacks for generating adversarial examples was proposed by Google researchers Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy. The attack was called fast gradient sign method (FGSM), and it consists of adding a linear amount of in-perceivable noise to the image and causing a model to incorrectly classify it. This noise is calculated by multiplying the sign of the gradient with respect to the image we want to perturb by a small constant epsilon. As epsilon increases, the model is more likely to be fooled, but the perturbations become easier to identify as well.
Differential calculus Taylor polynomials and Taylor series Differential_calculus > Applications of derivatives > Taylor polynomials and Taylor series The Taylor series is frequently a very good approximation to the original function. Functions which are equal to their Taylor series are called analytic functions. It is impossible for functions with discontinuities or sharp corners to be analytic; moreover, there exist smooth functions which are also not analytic.
Abel map Construction of the map Abel_map > Construction of the map In complex algebraic geometry, the Jacobian of a curve C is constructed using path integration. Namely, suppose C has genus g, which means topologically that H 1 ( C , Z ) ≅ Z 2 g . {\displaystyle H_{1}(C,\mathbb {Z} )\cong \mathbb {Z} ^{2g}.} Geometrically, this homology group consists of (homology classes of) cycles in C, or in other words, closed loops.
Peer-to-peer network Intellectual property law and illegal sharing Peer-to-peer_networking > Political implications > Intellectual property law and illegal sharing Fair use exceptions allow limited use of copyrighted material to be downloaded without acquiring permission from the rights holders. These documents are usually news reporting or under the lines of research and scholarly work. Controversies have developed over the concern of illegitimate use of peer-to-peer networks regarding public safety and national security.
Animal disease model Disease models Animal_disease_model > Disease models Animal models serving in research may have an existing, inbred or induced disease or injury that is similar to a human condition. These test conditions are often termed as animal models of disease. The use of animal models allows researchers to investigate disease states in ways which would be inaccessible in a human patient, performing procedures on the non-human animal that imply a level of harm that would not be considered ethical to inflict on a human. As in noted the introduction, animal models can be classified as homologous, isomorphic or predictive.
Sympto-thermal method Development of calendar-based methods Fertility_awareness > History > Development of calendar-based methods One book states that periodic abstinence was recommended "by a few secular thinkers since the mid-nineteenth century," but the dominant force in the twentieth century popularization of fertility awareness-based methods was the Roman Catholic Church. In 1905 Theodoor Hendrik van de Velde, a Dutch gynecologist showed that women only ovulate once per menstrual cycle. In the 1920s, Kyusaku Ogino, a Japanese gynecologist, and Hermann Knaus, from Austria, independently discovered that ovulation occurs about fourteen days before the next menstrual period.
Scale (music) Pitch Scale_(music) > Background > Pitch A single scale can be manifested at many different pitch levels. For example, a C major scale can be started at C4 (middle C; see scientific pitch notation) and ascending an octave to C5; or it could be started at C6, ascending an octave to C7.
Phenol coefficient Summary Phenol_coefficient The Phenol coefficient, is now largely of historical interest, although the principles upon which it is based are still used. It is a measure of the bactericidal activity of a chemical compound in relation to phenol. When listed numerically, the figure expressing the disinfecting power of a substance by relating it to the disinfecting power of phenol may be a function of the standardized test performed. For example, the Rideal–Walker method, introduced in 1903 gives a Rideal–Walker coefficient and the U.S.
Theories of everything Summary Theory_of_Everything Since the usual domains of applicability of general relativity and quantum mechanics are so different, most situations require that only one of the two theories be used. : 842–844 The two theories are considered incompatible in regions of extremely small scale – the Planck scale – such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the Big Bang). To resolve the incompatibility, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three interactions, must be discovered to harmoniously integrate the realms of general relativity and quantum mechanics into a seamless whole: a theory of everything may be defined as a comprehensive theory that, in principle, would be capable of describing all physical phenomena in this universe.
Glossary of set theory C Glossary_of_set_theory > C The cofinality cof(I) of an ideal I of subsets of a set X is the smallest cardinality of a subset B of I such that every element of I is a subset of something in B. Cohen 1. Paul Cohen 2. Cohen forcing is a method for constructing models of ZFC 3.
Chen's theorem Summary Chen's_theorem In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). It is a weakened form of Goldbach's conjecture, which states that every even number is the sum of two primes.
Common integrals in quantum field theory Integration over a magnetic wave function Common_integrals_in_quantum_field_theory > Bessel functions > Integration over a magnetic wave function The two-dimensional integral over a magnetic wave function is Here, M is a confluent hypergeometric function. For an application of this integral see Charge density spread over a wave function.
Copernican Revolution Johannes Kepler Copernican_Revolution > Reception > Johannes Kepler Kepler found employment as an assistant to Tycho Brahe and, upon Brahe's unexpected death, replaced him as imperial mathematician of Emperor Rudolph II. He was then able to use Brahe's extensive observations to make remarkable breakthroughs in astronomy, such as the three laws of planetary motion. Kepler would not have been able to produce his laws without the observations of Tycho, because they allowed Kepler to prove that planets traveled in ellipses, and that the Sun does not sit directly in the center of an orbit but at a focus. Galileo Galilei came after Kepler and developed his own telescope with enough magnification to allow him to study Venus and discover that it has phases like a moon.
Logistic map Summary Feigenbaum_fractal The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where xn is a number between zero and one, which represents the ratio of existing population to the maximum possible population. This nonlinear difference equation is intended to capture two effects: reproduction, where the population will increase at a rate proportional to the current population when the population size is small, starvation (density-dependent mortality), where the growth rate will decrease at a rate proportional to the value obtained by taking the theoretical "carrying capacity" of the environment less the current population.The usual values of interest for the parameter r are those in the interval , so that xn remains bounded on .
List of prime numbers Proth primes List_of_prime_numbers > Lists of primes by type > Proth primes Of the form k×2n + 1, with odd k and k < 2n. 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS: A080076)
System programming language Summary System_programming_language Some languages straddle the system and application domains, bridging the gap between these uses. The canonical example is C, which is used widely for both system and application programming. Some modern languages also do this such as Rust and Swift.
Chemotherapy drug Infertility Antineoplastic_agents > Adverse effects > Infertility This loss is not necessarily a direct effect of the chemotherapeutic agents, but could be due to an increased rate of growth initiation to replace damaged developing follicles.People may choose between several methods of fertility preservation prior to chemotherapy, including cryopreservation of semen, ovarian tissue, oocytes, or embryos. As more than half of cancer patients are elderly, this adverse effect is only relevant for a minority of patients. A study in France between 1999 and 2011 came to the result that embryo freezing before administration of gonadotoxic agents to females caused a delay of treatment in 34% of cases, and a live birth in 27% of surviving cases who wanted to become pregnant, with the follow-up time varying between 1 and 13 years.Potential protective or attenuating agents include GnRH analogs, where several studies have shown a protective effect in vivo in humans, but some studies show no such effect. Sphingosine-1-phosphate (S1P) has shown similar effect, but its mechanism of inhibiting the sphingomyelin apoptotic pathway may also interfere with the apoptosis action of chemotherapy drugs.In chemotherapy as a conditioning regimen in hematopoietic stem cell transplantation, a study of people conditioned with cyclophosphamide alone for severe aplastic anemia came to the result that ovarian recovery occurred in all women younger than 26 years at time of transplantation, but only in five of 16 women older than 26 years.
Phenol Acidity C6H5OH > Properties > Acidity Phenol is a weak acid. (pH 6.6). In aqueous solution in the pH range ca. 8 - 12 it is in equilibrium with the phenolate anion C6H5O− (also called phenoxide or carbolate): C 6 H 5 OH ↽ − − ⇀ C 6 H 5 O − + H + {\displaystyle {\ce {C6H5OH <=> C6H5O- + H+}}} Phenol is more acidic than aliphatic alcohols.
Photographic lens design Aperture control Photographic_lens_design > Design > Aperture control Either a manual ring, or an electronic motor controls the angle of the diaphragm leaves and thus the size of the opening. The placement of the diaphragm within the lens structure is constrained by the need to achieve even illumination over the whole film plane at all apertures and the requirement to not interfere with the movement of any movable lens element. Typically the diaphragm is situated at about the level of the optical centre of the lens.
Seiberg–Witten gauge theory Summary Seiberg–Witten_gauge_theory In theoretical physics, Seiberg–Witten theory is an N = 2 {\displaystyle {\mathcal {N}}=2} supersymmetric gauge theory with an exact low-energy effective action (for massless degrees of freedom), of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory is known as N = 2 {\displaystyle {\mathcal {N}}=2} supersymmetric Yang–Mills theory, as the field content is a single N = 2 {\displaystyle {\mathcal {N}}=2} vector supermultiplet, analogous to the field content of Yang–Mills theory being a single vector gauge field (in particle theory language) or connection (in geometric language). The theory was studied in detail by Nathan Seiberg and Edward Witten (Seiberg & Witten 1994).
Germ line Epigenetic alterations Germline > Epigenetic alterations Epigenetic alterations of DNA include modifications that affect gene expression, but are not caused by changes in the sequence of bases in DNA. A well-studied example of such an alteration is the methylation of DNA cytosine to form 5-methylcytosine. This usually occurs in the DNA sequence CpG, changing the DNA at the CpG site from CpG to 5-mCpG. Methylation of cytosines in CpG sites in promoter regions of genes can reduce or silence gene expression.
Seismometer Teleseismometers Seismic_station > Modern instruments > Teleseismometers The modern broadband seismograph can record a very broad range of frequencies. It consists of a small "proof mass", confined by electrical forces, driven by sophisticated electronics. As the earth moves, the electronics attempt to hold the mass steady through a feedback circuit. The amount of force necessary to achieve this is then recorded.
Materials Technology Composites Material_Sciences > Industry > Composites Another application of materials science in industry is making composite materials. These are structured materials composed of two or more macroscopic phases. Applications range from structural elements such as steel-reinforced concrete, to the thermal insulating tiles, which play a key and integral role in NASA's Space Shuttle thermal protection system, which is used to protect the surface of the shuttle from the heat of re-entry into the Earth's atmosphere. One example is reinforced Carbon-Carbon (RCC), the light gray material, which withstands re-entry temperatures up to 1,510 °C (2,750 °F) and protects the Space Shuttle's wing leading edges and nose cap.
Outliers ratio Summary Outliers_ratio In objective video quality assessment, the outliers ratio (OR) is a measure of the performance of an objective video quality metric. It is the ratio of "false" scores given by the objective metric to the total number of scores. The "false" scores are the scores that lie outside the interval {\displaystyle } where MOS is the mean opinion score and σ is the standard deviation of the MOS. == References ==
Area formula Non-metric units Area > Units > Conversions > Non-metric units In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units. 1 foot = 12 inches,the relationship between square feet and square inches is 1 square foot = 144 square inches,where 144 = 122 = 12 × 12. Similarly: 1 square yard = 9 square feet 1 square mile = 3,097,600 square yards = 27,878,400 square feetIn addition, conversion factors include: 1 square inch = 6.4516 square centimetres 1 square foot = 0.09290304 square metres 1 square yard = 0.83612736 square metres 1 square mile = 2.589988110336 square kilometres
Electrostatic induction Charging an object by induction Electrostatic_induction > Charging an object by induction But when the inducing charge is moved away, the charge is released and spreads throughout the electroscope terminal to the leaves, so the gold leaves move apart again. The sign of the charge left on the electroscope after grounding is always opposite in sign to the external inducing charge. The two rules of induction are: If the object is not grounded, the nearby charge will induce equal and opposite charges in the object. If any part of the object is momentarily grounded while the inducing charge is near, a charge opposite in polarity to the inducing charge will be attracted from ground into the object, and it will be left with a charge opposite to the inducing charge.
Mathematical equations Summary Mathematical_equations In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation.Solving an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation.
Mixed state (physics) Schrödinger picture vs. Heisenberg picture Mixed_state_(physics) > Wave function representations > Schrödinger picture vs. Heisenberg picture (This approach was taken in the earlier part of the discussion above, with a time-varying state \| Ψ ( t ) ⟩ = ∑ n C n ( t ) \| Φ n ⟩ {\textstyle \|\Psi (t)\rangle =\sum _{n}C_{n}(t)\|\Phi _{n}\rangle } .) Conceptually (and mathematically), the two approaches are equivalent; choosing one of them is a matter of convention. Both viewpoints are used in quantum theory.
Epidemiology of schizophrenia Summary Epidemiology_of_schizophrenia Schizophrenia affects around 0.3–0.7% of people at some point in their life, or 21 million people worldwide as of 2020 (about one of every 285). By using precise methods in its diagnosis and a large, representative population, schizophrenia seems to occur with relative consistency over time during the last half-century.While it is claimed that schizophrenia occurs at similar rates worldwide, its prevalence and incidence varies across the world, within countries, and at the local and neighborhood level. It causes approximately 1% of worldwide disability-adjusted life years (DALYs). The rate of schizophrenia varies up to threefold depending on how it is defined.
Plain language Accessibility Plain_language > Purposes > Accessibility Some scholars promote plain language use as a means of making documents accessible, especially for disabled readers or those who lack the expertise and education to understand overly technical documents. Simpler language can decrease a reader's cognitive load, and improve information retention in readers who normally struggle to read complex documents. Changes in font, text size, and colour can make texts more readable for individuals with impaired vision. Some scholars view plain language from a social justice perspective as a means of increasing equal access to information, especially for marginalized populations that might have decreased access to education.
Kinetic diagram What is included Free-body_diagram > Features > What is included The external forces: These are indicated by labelled arrows. In a fully solved problem, a force arrow is capable of indicating the direction and the line of action the magnitude the point of application a reaction, as opposed to an applied force, if a hash is present through the stem of the arrowOften a provisional free body is drawn before everything is known. The purpose of the diagram is to help to determine magnitude, direction, and point of application of external loads.
Dulong–Petit law History Dulong–Petit_law > History The value of 3R is about 25 joules per kelvin, and Dulong and Petit essentially found that this was the heat capacity of certain solid elements per mole of atoms they contained. The Kopp's law developed in 1865 by Hermann Franz Moritz Kopp extended the Dulong–Petit law to chemical compounds from further experimental data. Amedeo Avogadro remarked in 1833 that the law did not fit the experimental data of carbon samples.
Angular acceleration Particle in two dimensions Angular_acceleration > Orbital angular acceleration of a point particle > Particle in two dimensions {\displaystyle \alpha ={\frac {a_{\perp }}{r}}.} In two dimensions, angular acceleration is a number with plus or minus sign indicating orientation, but not pointing in a direction. The sign is conventionally taken to be positive if the angular speed increases in the counter-clockwise direction or decreases in the clockwise direction, and the sign is taken negative if the angular speed increases in the clockwise direction or decreases in the counter-clockwise direction. Angular acceleration then may be termed a pseudoscalar, a numerical quantity which changes sign under a parity inversion, such as inverting one axis or switching the two axes.
Axiom of Choice Statements consistent with the negation of AC Axiom_of_Choice > Statements consistent with the negation of AC There exists a model of ZF¬C in which every set in Rn is measurable. Thus it is possible to exclude counterintuitive results like the Banach–Tarski paradox which are provable in ZFC. Furthermore, this is possible whilst assuming the Axiom of dependent choice, which is weaker than AC but sufficient to develop most of real analysis.
Eads Bridge History Eads_Bridge > History It was determined that Eads' original estimation of an allowable load of 3,000 pounds per foot (4,500 kg/m) could be raised to 5,000 pounds per foot (7,400 kg/m). The Eads Bridge is still considered one of the greatest bridges ever built.The Eads Bridge had long hosted only passenger trains on its rail deck. In the late 20th century, however, passenger traffic had declined because of individual automobile use, and the railroad industry was restructuring.
Campylobacter pylori Adaptation to the stomach Campylobacter_pylori > Pathophysiology > Adaptation to the stomach It has been proposed that BabA's acid responsiveness enables adherence while also allowing an effective escape from unfavorable environment at pH that is harmful to the organism. Another such adhesin, SabA, binds to increased levels of sialyl-Lewis X (sLeX) antigen expressed on gastric mucosa.In addition to using chemotaxis to avoid areas of low pH, H. pylori also neutralizes the acid in its environment by producing large amounts of urease, which breaks down the urea present in the stomach to carbon dioxide and ammonia.
Hierarchy Nomenclature Hierarchy > Nomenclature The root of an inverted-tree structure Member, a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached Orphan, a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level Leaf, a member in any level of a dimension without subordinates in the hierarchy Neighbour: a member adjacent to another member in the same (level or rank).
Cohesive end Single-stranded DNA molecules Sticky_and_blunt_ends > Single-stranded DNA molecules A single-stranded non-circular DNA molecule has two non-identical ends, the 3' end and the 5' end (usually pronounced "three prime end" and "five prime end"). The numbers refer to the numbering of carbon atoms in the deoxyribose, which is a sugar forming an important part of the backbone of the DNA molecule. In the backbone of DNA the 5' carbon of one deoxyribose is linked to the 3' carbon of another by a phosphodiester bond linkage. The 5' carbon of this deoxyribose is again linked to the 3' carbon of the next, and so forth.
Differential and integral calculus Modern Differential_and_integral_calculus > History > Modern Newton called his calculus "the science of fluxions", a term that endured in English schools into the 19th century. : 100 The first complete treatise on calculus to be written in English and use the Leibniz notation was not published until 1815. Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. One of the first and most complete works on both infinitesimal and integral calculus was written in 1748 by Maria Gaetana Agnesi.
Mainstreaming (education) Summary Mainstreaming_(education) In comparison, inclusion students are regular education classroom students who receive special education services. Usually whether is not a student's education is mainstreamed or inclusion is based on which is the least restrictive environment, which can be determined in the student's IEP. Dr. Kenneth Shore comments on the least restrictive environment by claiming, "Determining what is the least restrictive environment for a particular student requires balancing the need for the child to learn to integrate socially with his non-disabled peers with the need for the child to receive instruction appropriate to his abilities."
Genomic control Summary Genomic_control Devlin and Roeder (1999) mostly considered the situation where α = 0.05 {\displaystyle \alpha =0.05} gives a 95% confidence level and not smaller p-values. Marchini et al. (2004) demonstrates by simulation that genomic control can lead to an anti-conservative p-value if this value is very small and the two populations (case and control) are extremely distinct.
Eisenstein criterion Indirect (after transformation) Eisenstein_criterion > Examples > Indirect (after transformation) Since the substitution is an automorphism of the ring Q, the fact that we obtain an irreducible polynomial after substitution implies that we had an irreducible polynomial originally. In this particular example it would have been simpler to argue that H (being monic of degree 2) could only be reducible if it had an integer root, which it obviously does not; however the general principle of trying substitutions in order to make Eisenstein's criterion apply is a useful way to broaden its scope. Another possibility to transform a polynomial so as to satisfy the criterion, which may be combined with applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero (without which it would be divisible by x anyway). This is so because such polynomials are reducible in R if and only if they are reducible in R (for any integral domain R), and in that ring the substitution of x−1 for x reverses the order of the coefficients (in a manner symmetric about the constant coefficient, but a following shift in the exponent amounts to multiplication by a unit). As an example 2x5 − 4x2 − 3 satisfies the criterion for p = 2 after reversing its coefficients, and (being primitive) is therefore irreducible in Z.
Evolutionary approaches to schizophrenia Sexual selection and sex differences in schizophrenia Evolutionary_approaches_to_schizophrenia > Sexual selection and sex differences in schizophrenia This theory hypothesizes that there is a difference in the onset of psychosis between the male and female genders, and this onset difference causes relation in a man to sexual dimorphism in the cerebral cortex. More specifically, this theory hypothesizes that the onset of psychosis in the male brain leads to the cortex developing more laterally, or asymmetrically, then a female with the same psychosis. This is important in that, since schizophrenia is often correlated with a basal level of intelligence within individuals, it becomes increasingly vital to examine the morphology of schizophrenic brains, as compared to brains without psychosis, to examine if there are physical changes underlying this lapse in intelligence.
Duality (mathematics) Summary Duality_(mathematics) It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics".Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold.From a category theory viewpoint, duality can also be seen as a functor, at least in the realm of vector spaces. This functor assigns to each space its dual space, and the pullback construction assigns to each arrow f: V → W its dual f∗: W∗ → V∗.
Lin–Kernighan heuristic Limitations Lin–Kernighan_heuristic > Derivation > Limitations The closed alternating trails found by the above method are all connected, but the symmetric difference T △ T ′ {\displaystyle T\mathbin {\triangle } T'} of two tours need not be, so in general this method of alternating trails cannot explore the full neighbourhood of a trail T {\displaystyle T} . The literature on the Lin–Kernighan heuristic uses the term sequential exchanges for those that are described by a single alternating trail. The smallest non-sequential exchange would however replace 4 edges and consist of two cycles of 4 edges each (2 edges added, 2 removed), so it is long compared to the typical Lin–Kernighan exchange, and there are few of these compared to the full set of 4-edge exchanges. In at least one implementation by Lin & Kernighan there was an extra final step considering such non-sequential exchanges of 4 edges before declaring a tour locally optimal, which would mean the tours produced are 4-opt unless one introduces further constraints on the search (which Lin and Kernighan in fact did).
Three-way handshake Summary TCP_port Applications that do not require reliable data stream service may use the User Datagram Protocol (UDP) instead, which provides a connectionless datagram service that prioritizes time over reliability. TCP employs network congestion avoidance. However, there are vulnerabilities in TCP, including denial of service, connection hijacking, TCP veto, and reset attack.
Primary progressive multiple sclerosis Prognosis Multiple_Sclerosis > Prognosis The availability of treatments that modify the course of multiple sclerosis beginning in the 1990s, known as disease-modifying therapies (DMTs), has improved prognosis. These treatments can reduce relapses and slow progression, but as of 2022 there is no cure.The prognosis of MS depends on the subtype of the disease, and there is considerable individual variation in the progression of the disease. In relapsing MS, the most common subtype, a 2016 cohort study found that after a median of 16.8 years from onset, one in ten needed a walking aid, and almost two in ten transitioned to secondary progressive MS, a form characterized by more progressive decline. With treatments available in the 2020s, relapses can be eliminated or substantially reduced.
Magnetic Anomaly Ground-based Magnetic_anomalies > Data acquisition > Ground-based In ground-based surveys, measurements are made at a series of stations, typically 15 to 60 m apart. Usually a proton precession magnetometer is used and it is often mounted on a pole. Raising the magnetometer reduces the influence of small ferrous objects that were discarded by humans. To further reduce unwanted signals, the surveyors do not carry metallic objects such as keys, knives or compasses, and objects such as motor vehicles, railway lines, and barbed wire fences are avoided.
Blood poisoning Epidemiology Blood_poisoning > Epidemiology Sepsis causes millions of deaths globally each year and is the most common cause of death in people who have been hospitalized. The number of new cases worldwide of sepsis is estimated to be 18 million cases per year. In the United States sepsis affects approximately 3 in 1,000 people, and severe sepsis contributes to more than 200,000 deaths per year.Sepsis occurs in 1–2% of all hospitalizations and accounts for as much as 25% of ICU bed utilization. Due to it rarely being reported as a primary diagnosis (often being a complication of cancer or other illness), the incidence, mortality, and morbidity rates of sepsis are likely underestimated.
Nephritic syndrome Laboratory testing Nephritic_syndrome > Diagnosis > Laboratory testing Some findings on urinalysis that are consistent with nephritic syndrome include red blood cells (hematuria), red blood cell casts, proteinuria, and possibly white blood cells (pyuria).If nephritic syndrome is identified and diagnosed, then it is important for the physician to determine the underlying cause. To do this, he/she may order any of a large variety of relevant lab tests, some of which are included here: Blood culture - This is the process where a sample of the patient's blood is sent to the microbiology lab to attempt to isolate and grow any bacteria that may be circulating in the blood, in order to identify the pathogen. This is helpful if the physician suspects infection as the underlying cause of the nephritic syndrome.
Island biogeography Species-area relationships Island_biogeography > Species-area relationships In this equation, S {\displaystyle S} represents the measure of diversity of a species (for example, the number of species) and c {\displaystyle c} is a constant representing the y-intercept. A {\displaystyle A} represents the area of the island or space that is being examined and z {\displaystyle z} represents the slope of the area curve.This function can also be expressed as a logarithmic function: l o g ( S ) = l o g ( c ) + z l o g ( A ) {\displaystyle log(S)=log(c)+zlog(A)} This expression of the function allows for the function to be drawn as a linear function. However, the core meaning of the function is the same: the area of the island dictates the species area relationship.
Glossary of artificial intelligence F Glossary_of_artificial_intelligence > F frame problem The problem of finding adequate collections of axioms for a viable description of a robot environment. friendly artificial intelligence Also friendly AI or FAI. A hypothetical artificial general intelligence (AGI) that would have a positive effect on humanity.
Static equilibrium Stability Mechanical_equilibrium > Stability An important property of systems at mechanical equilibrium is their stability.
Strain crystallization Summary Strain_crystallization Strain crystallization is a phenomenon in which an initially amorphous solid material undergoes a phase transformation due to the application of strain. Strain crystallization occurs in natural rubber, as well as other elastomers and polymers. The phenomenon has important effects on strength and fatigue properties.
Baker's map Summary Baker's_map In physics, a chain of coupled baker's maps can be used to model deterministic diffusion. As with many deterministic dynamical systems, the baker's map is studied by its action on the space of functions defined on the unit square. The baker's map defines an operator on the space of functions, known as the transfer operator of the map. The baker's map is an exactly solvable model of deterministic chaos, in that the eigenfunctions and eigenvalues of the transfer operator can be explicitly determined.
Artificial induction of immunity Adjuvants Artificial_induction_of_immunity > Adjuvants Adjuvants are also used in other ways in researching the immune system.A more contemporary approach for "boosting" the immune response to simpler immunogenic molecules (known as antigens) is to conjugate the antigens. Conjugation is the attachment to the antigen of another substance which also generates an immune response, thus amplifying the overall response and causing a more robust immune memory to the antigen. For example, a toxoid might be attached to a polysaccharide from the capsule of the bacteria responsible for most lobar pneumonia.
Characteristic number (physics) Other quantities produced by nondimensionalization Dimensionless_quantities > Other quantities produced by nondimensionalization Physics often uses dimensionless quantities to simplify the characterization of systems with multiple interacting physical phenomena. These may be found by applying the Buckingham π theorem or otherwise may emerge from making partial differential equations unitless by the process of nondimensionalization. Engineering, economics, and other fields often extend these ideas in design and analysis of the relevant systems.
Absorption maximum Summary Absorption_curve Absorption spectroscopy is employed as an analytical chemistry tool to determine the presence of a particular substance in a sample and, in many cases, to quantify the amount of the substance present. Infrared and ultraviolet–visible spectroscopy are particularly common in analytical applications. Absorption spectroscopy is also employed in studies of molecular and atomic physics, astronomical spectroscopy and remote sensing.

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