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Steffensen's method Generalization to Banach space Steffensen's_method > Generalization to Banach space Note that for arguments x {\displaystyle ~x~} close to some fixed point x ⋆ {\displaystyle ~x_{\star }~} , fixed point functions F {\displaystyle ~F~} and their linear operators L {\displaystyle ~L~} meeting the marked (𝄋) condition, F ′ ( x ) ≈ L ( F ( x ) , x ) ≈ I {\displaystyle ~F'(x)\approx L{\bigl (}\,F\left(x\right),\,x\,{\bigr )}\approx I~} where I {\displaystyle ~I~} is the identity operator. In the case that division is possible in the Banach space, the generalized iteration formula is given by x n + 1 = x n + − 1 , {\displaystyle x_{n+1}=x_{n}+{\Bigl }^{-1}{\Bigl }~,} for n = 1 , 2 , 3 , .
Base motive Definition Base_motive > Definition This flexibility involves goal-directed behavior that changes as the animal learns through new experiences. Rats, for example, can learn to traverse through complicated mazes to satisfy their hunger. The feeding behavior of flies, on the other hand, is not flexible in this sense.
Büchi automaton Closure properties Büchi_automaton > Closure properties (q,a,f)\in \Delta _{C}\}} if I C ∩ F C is empty then I ′ = I C otherwise I ′ = I C ∪ I A {\displaystyle \scriptstyle {\text{ if }}I_{C}\cap F_{C}{\text{ is empty then }}I'=I_{C}{\text{ otherwise }}I'=I_{C}\cup I_{A}} ω-closure: If L ( C ) {\displaystyle \scriptstyle L(C)} does not contain the empty word then there is a Büchi automaton that recognizes the language L ( C ) ω . {\displaystyle \scriptstyle L(C)^{\omega }.} Proof: The Büchi automaton that recognizes L ( C ) ω {\displaystyle \scriptstyle L(C)^{\omega }} is constructed in two stages.
Radiant energy Open systems Radiant_energy > Analysis > Open systems Radiant energy is one of the mechanisms by which energy can enter or leave an open system. Such a system can be man-made, such as a solar energy collector, or natural, such as the Earth's atmosphere. In geophysics, most atmospheric gases, including the greenhouse gases, allow the Sun's short-wavelength radiant energy to pass through to the Earth's surface, heating the ground and oceans. The absorbed solar energy is partly re-emitted as longer wavelength radiation (chiefly infrared radiation), some of which is absorbed by the atmospheric greenhouse gases. Radiant energy is produced in the sun as a result of nuclear fusion.
Gesture control Summary Gesture_recognition Focuses in the field include emotion recognition from face and hand gesture recognition since they are all expressions. Users can make simple gestures to control or interact with devices without physically touching them. Many approaches have been made using cameras and computer vision algorithms to interpret sign language, however, the identification and recognition of posture, gait, proxemics, and human behaviors is also the subject of gesture recognition techniques. Gesture recognition can be seen as a way for computers to begin to understand human body language, thus building a better bridge between machines and humans than older text user interfaces or even GUIs (graphical user interfaces), which still limit the majority of input to keyboard and mouse and interact naturally without any mechanical devices.
Causality (physics) As a physical concept Causality_(physics) > As a physical concept However, the principle of locality is disputed: whether it strictly holds depends on the interpretation of quantum mechanics chosen, especially for experiments involving quantum entanglement that satisfy Bell's Theorem. Despite these subtleties, causality remains an important and valid concept in physical theories. For example, the notion that events can be ordered into causes and effects is necessary to prevent (or at least outline) causality paradoxes such as the grandfather paradox, which asks what happens if a time-traveler kills his own grandfather before he ever meets the time-traveler's grandmother. See also Chronology protection conjecture.
Relative cost of electricity generated by different sources Turkey Relative_cost_of_electricity_generated_by_different_sources > Regional studies > Turkey As of March 2021 for projects starting generating electricity in Turkey from renewable energy in Turkey in July feed-in-tariffs in lira per kWh are: wind and solar 0.32, hydro 0.4, geothermal 0.54, and various rates for different types of biomass: for all these there is also a bonus of 0.08 per kWh if local components are used. Tariffs will apply for 10 years and the local bonus for 5 years. Rates are determined by the presidency, and the scheme replaces the previous USD-denominated feed-in-tariffs for renewable energy.
Statistical inference Bayesian inference, subjectivity and decision theory Sampling_statistics > Paradigms for inference > Bayesian inference > Bayesian inference, subjectivity and decision theory Given assumptions, data and utility, Bayesian inference can be made for essentially any problem, although not every statistical inference need have a Bayesian interpretation. Analyses which are not formally Bayesian can be (logically) incoherent; a feature of Bayesian procedures which use proper priors (i.e. those integrable to one) is that they are guaranteed to be coherent. Some advocates of Bayesian inference assert that inference must take place in this decision-theoretic framework, and that Bayesian inference should not conclude with the evaluation and summarization of posterior beliefs.
Copenhagen interpretation of quantum mechanics Origin and use of the term Copenhagen_interpretation_of_quantum_mechanics > Origin and use of the term Lectures with the titles 'The Copenhagen Interpretation of Quantum Theory' and 'Criticisms and Counterproposals to the Copenhagen Interpretation', that Heisenberg delivered in 1955, are reprinted in the collection Physics and Philosophy. Before the book was released for sale, Heisenberg privately expressed regret for having used the term, due to its suggestion of the existence of other interpretations, that he considered to be "nonsense". In a 1960 review of Heisenberg's book, Bohr's close collaborator Léon Rosenfeld called the term an "ambiguous expression" and suggested it be discarded. However, this did not come to pass, and the term entered widespread use.
Linear time-invariant system Overview Linear_time-invariant_system > Overview Most LTI systems are considered "easy" to analyze, at least compared to the time-varying and/or nonlinear case. Any system that can be modeled as a linear differential equation with constant coefficients is an LTI system. Examples of such systems are electrical circuits made up of resistors, inductors, and capacitors (RLC circuits).
Distributional derivative Summary Distributional_derivative This leads to the space of (all) distributions on U {\displaystyle U} , usually denoted by D ′ ( U ) {\displaystyle {\mathcal {D}}'(U)} (note the prime), which by definition is the space of all distributions on U {\displaystyle U} (that is, it is the continuous dual space of C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)} ); it is these distributions that are the main focus of this article. Definitions of the appropriate topologies on spaces of test functions and distributions are given in the article on spaces of test functions and distributions. This article is primarily concerned with the definition of distributions, together with their properties and some important examples.
Electronic Numbering System details Electronic_Numbering > System details This is sent to ENUM servers on the Internet, which send back the NAPTR records associated with the name. The access information and any priority indicated for them are stored in these. The user gets the requested address back on his PC or terminal. ENUM therefore in fact functions as a mechanism for translating a telephone number into a domain name with the requested address or number associated with it, but without the user viewing how this is done, just as he is currently unaware that he is using the DNS when he makes a connection with the Internet or what is going on at the telephone switch when he makes a call.
Strain theory (sociology) Studies Strain_theory_(sociology) > Studies He analyzes a large body of data on delinquency collected in Western Contra Costa County, California that contrast with strain theory.In addition to the study done by Hirschi, strain theory was explored in a 2001 study conducted by Jason D. Boardman (and others). The study explored how societal strain and stress can lead to drug use by individuals, in particular how one's neighborhood environment can affect their susceptibility to drug abuse.
Multi-binomial theorem Combinatorial interpretation Negative_binomial_theorem > Binomial coefficients > Combinatorial interpretation The binomial coefficient ( n k ) {\displaystyle {\tbinom {n}{k}}} can be interpreted as the number of ways to choose k elements from an n-element set. This is related to binomials for the following reason: if we write (x + y)n as a product then, according to the distributive law, there will be one term in the expansion for each choice of either x or y from each of the binomials of the product. For example, there will only be one term xn, corresponding to choosing x from each binomial. However, there will be several terms of the form xn−2y2, one for each way of choosing exactly two binomials to contribute a y. Therefore, after combining like terms, the coefficient of xn−2y2 will be equal to the number of ways to choose exactly 2 elements from an n-element set.
Infinite loop Multi-party loops Infinite_recursion > Multi-party loops An example of an email loop is if someone receives mail from a no reply inbox, but their auto-response is on. They will reply to the no reply inbox, triggering the "this is a no reply inbox" response. This will be sent to the user, who then sends an auto reply to the no-reply inbox, and so on and so forth.
Gas volume Heat and work Gas_volume > Heat and work Mechanical work performed on a working fluid causes a change in the mechanical constraints of the system; in other words, for work to occur, the volume must be altered. Hence, volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved. Volume is one of a pair of conjugate variables, the other being pressure. As with all conjugate pairs, the product is a form of energy.
Eyes-on-the-Road-Benefit Exogenous saccadic gaze Automotive_head-up_display > Eyes-on-the-Road-Benefit > Aetiology > Exogenous saccadic gaze Exogenous cues can also be irrelevant, and often dangerous, leading to distraction from goal behaviours, such as the flashing of a cellphone taking one's eyes off the road. By superimposing vital driving information onto the horizon in a driver's direct line of sight, HUDS allow important exogenous cues, like the movements of other vehicles to draw the gaze of a driver whilst they monitor vital vehicle feedback such as speed or revolution count. It is theorized that this can facilitate faster reaction times to hazards and improve situational awareness. A collaborative project between Faurecia Groupe and Indian Institute of Science developed an eye gaze and finger controlled head up display for cars that can also automatically estimate drivers’ cognitive load and distraction.
Circuit theory Summary Non-linear_circuits In electrical engineering and electronics, a network is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values; however, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to linear network analysis.
Ferrite (magnet) Summary Ferrite_(magnet) A ferrite is a ceramic material made by mixing and firing iron(III) oxide (Fe2O3, rust) with one or more additional metallic elements, such as strontium, barium, manganese, nickel, and zinc. They are ferrimagnetic, meaning they are attracted by magnetic fields and can be magnetized to become permanent magnets. Unlike other ferromagnetic materials, most ferrites are not electrically conductive, making them useful in applications like magnetic cores for transformers to suppress eddy currents. Ferrites can be divided into two families based on their resistance to being demagnetized (magnetic coercivity).
Transcriptome Relation to other ome fields Transcriptome > Relation to other ome fields The term meiome is used in functional genomics to describe the meiotic transcriptome or the set of RNA transcripts produced during the process of meiosis. Meiosis is a key feature of sexually reproducing eukaryotes, and involves the pairing of homologous chromosome, synapse and recombination. Since meiosis in most organisms occurs in a short time period, meiotic transcript profiling is difficult due to the challenge of isolation (or enrichment) of meiotic cells (meiocytes).
Tamper evidence Summary Tamper_resistance Tamperproofing, conceptually, is a methodology used to hinder, deter or detect unauthorised access to a device or circumvention of a security system. Since any device or system can be foiled by a person with sufficient knowledge, equipment, and time, the term "tamperproof" is a misnomer unless some limitations on the tampering party's resources is explicit or assumed. Tamper resistance is resistance to tampering (intentional malfunction or sabotage) by either the normal users of a product, package, or system or others with physical access to it.
Mast aft rig Advantages Mast_aft_rig > Advantages The cutter, with its use of multiple foresails, achieves the same goal of placing a higher percentage of the sail area in staysails.By moving the mast toward the back of the sailboat, designers can increase the size and driving power of the more efficient foresails. The mainsail is reduced in size or eliminated altogether. An advantage of using foresails, also called staysails, is that they may be rigged for roller furling.
Theory of elasticity Response models Solid_Mechanics > Response models Thermoelasticity - There is coupling of mechanical with thermal responses. In general, thermoelasticity is concerned with elastic solids under conditions that are neither isothermal nor adiabatic. The simplest theory involves the Fourier's law of heat conduction, as opposed to advanced theories with physically more realistic models.
Timeline of biotechnology 2020 Timeline_of_biotechnology > 21st century > 2020 16 March – Scientists present new multiplexed CRISPR technology, called CHyMErA (Cas Hybrid for Multiplexed Editing and Screening Applications), that can be used to analyse which or how genes act together by simultaneously removing multiple genes or gene-fragments using both Cas9 and Cas12a. 10 April – Scientists report to have achieved wireless control of adrenal hormone secretion in genetically unmodified rats through the use of injectable, magnetic nanoparticles (MNPs) and remotely applied alternating magnetic fields heats them up.
2-Norbornyl cation Formation 2-Norbornyl_cation > Formation The 2-norbornyl cation can be made by a multitude of synthetic routes. These routes can be grouped into three different classes: σ Formation, π Formation, and Formation by Rearrangement. Each of these is discussed separately below.
Process duct work Resources Process_duct_work > Resources Finite element design of process duct work is possible, but a requirement of design theory and allowable stresses is required to properly interpret the finite element model. ASCE - Structural Design of Air & Gas Ducts for Power Stations and Industrial Boiler Applications Roark & Young. Formulas for stress & Strain, various editions US Steel Plate, Plate Structures, Volume I & II US Steel Plate, Steels for Elevated Service Temperatures 1974 AISC, On Line steel temperature versus Yield, and steel temperature versus Young's modulus charts.
Renewable heat Summary Renewable_heat Renewable heat is an application of renewable energy referring to the generation of heat from renewable sources; for example, feeding radiators with water warmed by focused solar radiation rather than by a fossil fuel boiler. Renewable heat technologies include renewable biofuels, solar heating, geothermal heating, heat pumps and heat exchangers. Insulation is almost always an important factor in how renewable heating is implemented.
Boundary problem (in spatial analysis) Summary Boundary_problem A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with areal data, statistics should be interpreted based upon the boundary.
Linear probing Operations Linear_probing > Operations Linear probing is a component of open addressing schemes for using a hash table to solve the dictionary problem. In the dictionary problem, a data structure should maintain a collection of key–value pairs subject to operations that insert or delete pairs from the collection or that search for the value associated with a given key. In open addressing solutions to this problem, the data structure is an array T (the hash table) whose cells T (when nonempty) each store a single key–value pair.
Euler approximations Global truncation error Eulerian_method > Global truncation error The precise form of this bound is of little practical importance, as in most cases the bound vastly overestimates the actual error committed by the Euler method. What is important is that it shows that the global truncation error is (approximately) proportional to h {\displaystyle h} . For this reason, the Euler method is said to be first order.
Ohms Law Circuit analysis Ohm’s_law > Circuit analysis In circuit analysis, three equivalent expressions of Ohm's law are used interchangeably: Each equation is quoted by some sources as the defining relationship of Ohm's law, or all three are quoted, or derived from a proportional form, or even just the two that do not correspond to Ohm's original statement may sometimes be given.The interchangeability of the equation may be represented by a triangle, where V (voltage) is placed on the top section, the I (current) is placed to the left section, and the R (resistance) is placed to the right. The divider between the top and bottom sections indicates division (hence the division bar).
Harvest mite Nymph Harvest_mite > Life cycle > Nymph Once the larva has engorged itself on skin and has fallen off its host, it develops to its nymph stage. The nymph is sexually immature, but more closely resembles the adult. This stage consists of three phases, the protonymph, deutonymph, and tritonymph. The protonymph and tritonymph morphologies are unusual in species of Trombiculidae.
Space complexity Summary Space_complexity The space complexity of an algorithm or a computer program is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. This includes the memory space used by its inputs, called input space, and any other (auxiliary) memory it uses during execution, which is called auxiliary space. Similar to time complexity, space complexity is often expressed asymptotically in big O notation, such as O ( n ) , {\displaystyle O(n),} O ( n log ⁡ n ) , {\displaystyle O(n\log n),} O ( n α ) , {\displaystyle O(n^{\alpha }),} O ( 2 n ) , {\displaystyle O(2^{n}),} etc., where n is a characteristic of the input influencing space complexity.
Internet Layer IETF standards Internet_Layer > IETF standards doi:10.17487/RFC0791. STD 5. RFC 791.
Ion gradient Overview Electrochemical_gradients > Overview Electrochemical energy is one of the many interchangeable forms of potential energy through which energy may be conserved. It appears in electroanalytical chemistry and has industrial applications such as batteries and fuel cells. In biology, electrochemical gradients allow cells to control the direction ions move across membranes. In mitochondria and chloroplasts, proton gradients generate a chemiosmotic potential used to synthesize ATP, and the sodium-potassium gradient helps neural synapses quickly transmit information.
Everything Engine Hard links Everything_Engine > Links > Hard links Hard links in E2 are simply words or phrases surrounded by . Any words inside square brackets in a writeup will become a link to the E2 node of that title. If a node with that title does not yet exist, following the link will bring up the option to create it. For the longest part of its existence, E2 did not permit links to third-party web sites in submitted content.
Laboratory informatics system Electronic data exchange Laboratory_information_system > Technology > Operations > Electronic data exchange The exponentially growing volume of data created in laboratories, coupled with increased business demands and focus on profitability, have pushed LIMS vendors to increase attention to how their LIMS handles electronic data exchanges. Attention must be paid to how an instrument's input and output data is managed, how remote sample collection data is imported and exported, and how mobile technology integrates with the LIMS. The successful transfer of data files in spreadsheets and other formats is a pivotal aspect of the modern LIMS. In fact, the transition "from proprietary databases to standardized database management systems such as MySQL" has arguably had one of the biggest impacts on how data is managed and exchanged in laboratories. In addition to mobile and database electronic data exchange, many LIMS support real-time data exchange with Electronic Health Records used in core hospital or clinic operations.
History of the periodic table Comprehensive formalizations History_of_the_periodic_table > Comprehensive formalizations Properties of the elements, and thus properties of light and heavy bodies formed by them, are in a periodic dependence on their atomic weight. French geologist Alexandre-Émile Béguyer de Chancourtois noticed that the elements, when ordered by their atomic weights, displayed similar properties at regular intervals. In 1862, he devised a three-dimensional chart, named the "telluric helix", after the element tellurium, which fell near the center of his diagram. With the elements arranged in a spiral on a cylinder by order of increasing atomic weight, de Chancourtois saw that elements with similar properties lined up vertically.
Expressive aphasia Less common Expressive_aphasia > Causes > Less common Autoimmune disease Paraneoplastic syndrome Micrometastasis neurodegenerative disorders Certain infections (e.g., Bartonella henselae) Metabolic disease (e.g., hyperosmolar hyperglycemic state)
Decibel Perception 20_log_rule > Uses > Perception The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see Weber–Fechner law), making the dB scale a useful measure.
Audio system measurements Digital Audio_quality_measurement > Measurable performance > Digital Such an algorithm compares the relative rates of two or more devices and drops or adds samples from the streams of any devices that drift too far from the master device. Sample rate will also vary slightly over time, as crystals change in temperature, etc. See also clock recoveryLinearity Differential non-linearity and integral non-linearity are two measurements of the accuracy of an analog-to-digital converter. Basically, they measure how close the threshold levels for each bit are to the theoretical equally-spaced levels.
Horse tack Halters Horse_tack > Headgear > Halters Halters have no bit.In Australian and British English, a halter is a rope with a spliced running loop around the nose and another over the poll, used mainly for unbroken horses or for cattle. The lead rope cannot be removed from the halter.
Resistors in parallel Nonideal properties Resistors_in_series > Nonideal properties Practical resistors are also specified as having a maximum power rating which must exceed the anticipated power dissipation of that resistor in a particular circuit: this is mainly of concern in power electronics applications. Resistors with higher power ratings are physically larger and may require heat sinks. In a high-voltage circuit, attention must sometimes be paid to the rated maximum working voltage of the resistor. While there is no minimum working voltage for a given resistor, failure to account for a resistor's maximum rating may cause the resistor to incinerate when current is run through it.
Signal transducer Second messengers Signal_transduction > Second messengers First messengers are the signaling molecules (hormones, neurotransmitters, and paracrine/autocrine agents) that reach the cell from the extracellular fluid and bind to their specific receptors. Second messengers are the substances that enter the cytoplasm and act within the cell to trigger a response. In essence, second messengers serve as chemical relays from the plasma membrane to the cytoplasm, thus carrying out intracellular signal transduction.
Joint attention Intention Joint_attention > Humans > Intention Individuals locate objects with their eyes, move towards the object, and then use hands to make contact with and manipulate the object. Change in gaze direction is one of several behavioral cues that individuals use in combination with changes in facial and vocal displays and body posture to mark the intention to act on an object. Individuals who seek or follow a joint focus of attention display knowledge that what is in their awareness is also in another's awareness.
Marine forensics Currents Marine_forensics > Environmental Factors > Currents Currents in water are a crucial factor to consider during marine investigations as they can answer many questions. If currents are involved in the body of water, it can drag/drift the evidence in question for a large distance to a location that does not match the wounds on the body adding confusion to the investigation. From drifting for a long distance, the remains/evidence can bump into artifacts like rocks or trees causing post-mortem injuries and abrasions which can confuse investigators understanding the true cause of death. Due to the buoyancy in saltwater like oceans, most remains float and will catch a tidal current causing it to drift for hundreds of kilometers, making it near impossible to find the remains, showing why marine investigators need to work as fast as possible at recovering evidence. In freshwater, currents won't move the evidence too far from where it first was, but they risk getting post-mortem injuries from waterfalls, rapids, and narrow banks (geography). Furthermore, when pollution from industrialization contaminates the water, tidal currents and river currents are able to spread it quite quickly with speeds from 5–100 miles per day, proving again why investigators need to be vigilant and work quickly at recovering evidence.
Free energy (thermodynamics) History Free_energy_(thermodynamics) > History In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of thermochemistry by showing that the heat given out in a reaction is equal to the heat absorbed in the reverse reaction. They also investigated the specific heat and latent heat of a number of substances, and amounts of heat given out in combustion. In a similar manner, in 1840 Swiss chemist Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step process or in a number of stages.
Parsing algorithm Overview of process Syntactic_analysis > Computer languages > Overview of process These rules can be formally expressed with attribute grammars. The final phase is semantic parsing or analysis, which is working out the implications of the expression just validated and taking the appropriate action. In the case of a calculator or interpreter, the action is to evaluate the expression or program; a compiler, on the other hand, would generate some kind of code. Attribute grammars can also be used to define these actions.
Class analysis Class size Class_analysis > Class size Sociologist Erik Olin Wright splits class analysis into macro and micro levels. The foundation of class analysis on a macro level can be identified with class structure. Examples of such class structure in a macro level can be analyzed within a firm, city, country, or the entire world. On a micro level, class analysis focuses on the effects that the class may have on an individual.
Shock resistance Toughness and strength Impact_strength > Toughness and strength Toughness is related to the area under the stress–strain curve. In order to be tough, a material must be both strong and ductile. For example, brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough. To be tough, a material should withstand both high stresses and high strains. Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.
Mutual exclusion Hardware solutions Mutual_exclusion > Enforcing mutual exclusion > Hardware solutions If a critical section is long, then the system clock will drift every time a critical section is executed because the timer interrupt is no longer serviced, so tracking time is impossible during the critical section. Also, if a process halts during its critical section, control will never be returned to another process, effectively halting the entire system. A more elegant method for achieving mutual exclusion is the busy-wait.
Prediction of crystal properties by numerical simulation Basic theory Prediction_of_crystal_properties_by_numerical_simulation > Ab Initio Calculations > Basic theory Density functional theory seeks to solve for an approximate form of the electronic density of a system. In general, atoms are split into ionic cores and valence electrons. The ionic cores (nuclei plus non-bonding electrons) are assumed to be stable and are treated as a single object. Each valence electron is treated separately.
Approximations of π Polygon approximation to a circle Software_for_calculating_π > Development of efficient formulae > Polygon approximation to a circle Then, P 2 n = 2 p n P n p n + P n , p 2 n = p n P 2 n . {\displaystyle P_{2n}={\frac {2p_{n}P_{n}}{p_{n}+P_{n}}},\quad \quad p_{2n}={\sqrt {p_{n}P_{2n}}}.} Archimedes uses this to successively compute P12, p12, P24, p24, P48, p48, P96 and p96.
RNA Interference Variation among organisms RNA_Interference > Cellular mechanism > Variation among organisms Organisms vary in their ability to take up foreign dsRNA and use it in the RNAi pathway. The effects of RNAi can be both systemic and heritable in plants and C. elegans, although not in Drosophila or mammals. In plants, RNAi is thought to propagate by the transfer of siRNAs between cells through plasmodesmata (channels in the cell walls that enable communication and transport). Heritability comes from methylation of promoters targeted by RNAi; the new methylation pattern is copied in each new generation of the cell.
Submarine Sensors Diesel-electric_submarine > Technology > Sensors A submarine can have a variety of sensors, depending on its missions. Modern military submarines rely almost entirely on a suite of passive and active sonars to locate targets. Active sonar relies on an audible "ping" to generate echoes to reveal objects around the submarine. Active systems are rarely used, as doing so reveals the sub's presence.
Life history theory r/K selection theory Life_history_theory > Characteristics > r/K selection theory K-selected organisms subsist near the carrying capacity of their environment (K), produce a relatively low number of offspring over a longer span of time, and have high parental investment. They are more suited to life in a stable environment in which they can rely on a long lifespan and a low mortality rate that will allow them to reproduce multiple times with a high offspring survival rate.Some organisms that are very r-selected are semelparous, only reproducing once before they die.
Candida albicans CRISPR/Cas9 Candida_albicans > Genetic and genomic tools > CRISPR/Cas9 CRISPR/Cas9 has been adapted to be used in C. albicans. Several studies have been performed using this system.
Carrier mobility Variable Range Hopping Field-effect_mobility > Disordered Semiconductors > Variable Range Hopping At low temperature, or in system with a large degree of structural disorder (such as fully amorphous systems), electrons cannot access delocalized states. In such a system, electrons can only travel by tunnelling for one site to another, in a process called variable range hopping. In the original theory of variable range hopping, as developed by Mott and Davis, the probability P i j {\displaystyle P_{ij}} , of an electron hopping from one site i {\displaystyle i} , to another site j {\displaystyle j} , depends on their separation in space r i j {\displaystyle r_{ij}} , and their separation in energy Δ E i j {\displaystyle \Delta E_{ij}} . Here P 0 {\displaystyle P_{0}} is a prefactor associated with the phonon frequency in the material, and α {\displaystyle \alpha } is the wavefunction overlap parameter. The mobility in a system governed by variable range hopping can be shown to be: where μ 0 {\displaystyle \mu _{0}} is a mobility prefactor, T 0 {\displaystyle T_{0}} is a parameter (with dimensions of temperature) that quantifies the width of localized states, and d {\displaystyle d} is the dimensionality of the system.
Fission-fusion hybrid Fuel cycle Nuclear_fusion–fission_hybrid > Fuel cycle Small amounts of tritium are also produced by neutron activation in nuclear fission reactors, particularly when heavy water is used as a neutron moderator or coolant. The third component is externally derived fissionable materials from demilitarized supplies of fissionables, or commercial nuclear fuel and waste streams. Fusion driven fission also offers the possibility of using thorium as a fuel, which would greatly increase the potential amount of fissionables available. The extremely energetic nature of the fast neutrons emitted during the fusion events (up to 0.17 the speed of light) can allow normally non-fissioning 238U to undergo fission directly (without conversion first to 239Pu), enabling refined natural Uranium to be used with very low enrichment, while still maintaining a deeply subcritical regime.
Hidden dependency Design maneuvers Cognitive_dimensions_of_notations > Design maneuvers A design maneuver is a change made by the designer in the notation design, to alter its position within a particular dimension. Dimensions are created to be pairwise independent, so that the design can be altered in one dimension while keeping a second one constant.But this usually results in a trade-off between dimensions. A modification increasing the usability of the notation in one dimension (while keeping a second one constant) will typically reduce its usability in a third dimension.
Model of hierarchical complexity Overview Model_of_hierarchical_complexity > Overview It is different from previous proposals about developmental stage applied to humans; instead of attributing behavioral changes across a person's age to the development of mental structures or schema, this model posits that task sequences of task behaviors form hierarchies that become increasingly complex. Because less complex tasks must be completed and practiced before more complex tasks can be acquired, this accounts for the developmental changes seen, for example, in individual persons' performance of complex tasks. (For example, a person cannot perform arithmetic until the numeral representations of numbers are learned.
Completeness (logic) Refutation completeness Completeness_(logic) > Forms of completeness > Refutation completeness A formal system S is refutation-complete if it is able to derive false from every unsatisfiable set of formulas. That is, Γ ⊨ S ⊥ → Γ ⊢ S ⊥ . {\displaystyle \Gamma \models _{\mathcal {S}}\bot \to \ \Gamma \vdash _{\mathcal {S}}\bot .}
Interpretations of quantum mechanics Comparisons Quantum_ontology > Comparisons Nevertheless, designing experiments which would test the various interpretations is the subject of active research. Most of these interpretations have variants. For example, it is difficult to get a precise definition of the Copenhagen interpretation as it was developed and argued by many people.
Tug of war (astronomy) Summary Tug_of_war_(astronomy) The tug of war in astronomy is the ratio of planetary and solar attractions on a natural satellite. The term was coined by Isaac Asimov in The Magazine of Fantasy and Science Fiction in 1963.
Byte code Execution Byte_code > Execution The implementation of Perl and Ruby 1.8 instead work by walking an abstract syntax tree representation derived from the source code. More recently, the authors of V8 and Dart have challenged the notion that intermediate bytecode is needed for fast and efficient VM implementation. Both of these language implementations currently do direct JIT compiling from source code to machine code with no bytecode intermediary.
Glossary of areas of mathematics C Glossary_of_areas_of_mathematics > C Complex analytic geometry the application of complex numbers to plane geometry. Complex differential geometry a branch of differential geometry that studies complex manifolds. Complex dynamics the study of dynamical systems defined by iterated functions on complex number spaces.
Sodar Doppler sodar Sodar > Doppler sodar Operating frequencies range from less than 1000 Hz to over 4000 Hz, with power levels up to several hundred watts. Due to the attenuation characteristics of the atmosphere, high power, lower frequency sodars will generally produce greater height coverage. Some sodars can be operated in different modes to better match vertical resolution and range to the application. This is accomplished through a relaxation between pulse length and maximum altitude.
Area of a triangle Using line integrals Area_of_a_triangle > Using line integrals Furthermore, the choice of coordinate system defined by L commits to only two degrees of freedom rather than the usual three, since the weight is a local distance (e.g. xi+1 − xi in the above) whence the method does not require choosing an axis normal to L. When working in polar coordinates it is not necessary to convert to Cartesian coordinates to use line integration, since the line integral between consecutive vertices (ri,θi) and (ri+1,θi+1) of a polygon is given directly by riri+1sin(θi+1 − θi)/2. This is valid for all values of θ, with some decrease in numerical accuracy when \|θ\| is many orders of magnitude greater than π. With this formulation negative area indicates clockwise traversal, which should be kept in mind when mixing polar and cartesian coordinates. Just as the choice of y-axis (x = 0) is immaterial for line integration in cartesian coordinates, so is the choice of zero heading (θ = 0) immaterial here.
Hippo signaling pathway In cancer Hippo_signaling_pathway > In cancer In fruitfly, the Hippo signaling pathway involves a kinase cascade involving the Salvador (Sav), Warts (Wts) and Hippo (Hpo) protein kinases. Many of the genes involved in the Hippo signaling pathway are recognized as tumor suppressors, while Yki/YAP/TAZ is identified as an oncogene. YAP/TAZ can reprogram cancer cells into cancer stem cells. YAP has been found to be elevated in some human cancers, including breast cancer, colorectal cancer, and liver cancer.
Parameter Mathematical functions Parameter > Mathematical functions Mathematical functions have one or more arguments that are designated in the definition by variables. A function definition can also contain parameters, but unlike variables, parameters are not listed among the arguments that the function takes. When parameters are present, the definition actually defines a whole family of functions, one for every valid set of values of the parameters. For instance, one could define a general quadratic function by declaring f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} ;Here, the variable x designates the function's argument, but a, b, and c are parameters that determine which particular quadratic function is being considered.
Optimizing compiler Factors affecting optimization Compiler_analysis > Factors affecting optimization Temporary/intermediate results can be left in registers without writing to and reading back from memory.RISC vs CISC: CISC instruction sets often have variable instruction lengths, often have a larger number of possible instructions that can be used, and each instruction could take differing amounts of time. RISC instruction sets attempt to limit the variability in each of these: instruction sets are usually constant length, with few exceptions, there are usually fewer combinations of registers and memory operations, and the instruction issue rate (the number of instructions completed per time period, usually an integer multiple of the clock cycle) is usually constant in cases where memory latency is not a factor. There may be several ways of carrying out a certain task, with CISC usually offering more alternatives than RISC.
Adiabatic engine Summary Carnot_heat_engine The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator or heat pump rather than a heat engine. Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state.
Testosterone and the cardiovascular system Summary Testosterone_and_the_cardiovascular_system Testosterone and the cardiovascular system are the effects that the male hormone testosterone has on the cardiovascular system. The predominant androgen in men, testosterone, has shown to substantially decline throughout the aging process. The decline in both serum and total testosterone with age have been linked to several disease states in men. In particular, cardiac failure and ischemic heart disease have been linked to this natural biochemical decline in testosterone. Previously, the higher cardiovascular risk in men has been attributed in part to the negative effects of systemic testosterone, however, more recent research has highlighted the protective nature of testosterone against cardiovascular disease. The magnitude and mechanism of action by which low testosterone in men is influential in the pathogenesis of cardiovascular risk and the potential benefits of testosterone therapy has yet to be fully determined.
Graviscalar Summary Graviscalar In theoretical physics, the hypothetical particle called the graviscalar or radion emerges as an excitation of general relativity's metric tensor, i.e. gravitational field, but is indistinguishable from a scalar in four dimensions, as shown in Kaluza–Klein theory. The scalar field ϕ {\displaystyle \phi } comes from a component of the metric tensor g 55 {\displaystyle g_{55}} where the figure 5 labels an additional fifth dimension. The only variations in the scalar field represent variations in the size of the extra dimension.
Kinetic Isotope Effects of RuBisCO Rate of carboxylation (VC) and Michaelis-Menten constant (KC) Intrinsic_KIE_of_RuBisCO > Ecological trade-offs influence isotope effects > Rate of carboxylation (VC) and Michaelis-Menten constant (KC) The rate of carboxylation (VC) is the rate that RuBisCO fixes CO2 to RuBP under substrate saturated conditions. A higher value of VC corresponds to a higher rate of carboxylation. This rate of carboxylation can also be represented through its Michaelis-Menten constant KC, with a higher value of KC corresponding to a higher rate of carboxylation.
Alpha emission Toxicity Alpha_decay > Toxicity Highly charged and heavy, alpha particles lose their several MeV of energy within a small volume of material, along with a very short mean free path. This increases the chance of double-strand breaks to the DNA in cases of internal contamination, when ingested, inhaled, injected or introduced through the skin. Otherwise, touching an alpha source is typically not harmful, as alpha particles are effectively shielded by a few centimeters of air, a piece of paper, or the thin layer of dead skin cells that make up the epidermis; however, many alpha sources are also accompanied by beta-emitting radio daughters, and both are often accompanied by gamma photon emission. Relative biological effectiveness (RBE) quantifies the ability of radiation to cause certain biological effects, notably either cancer or cell-death, for equivalent radiation exposure.
Orthoptic (geometry) Orthoptic of a parabola Orthoptic_(geometry) > Orthoptic of a parabola The tangent has the equation y = m x + n {\displaystyle y=mx+n} with the still unknown n, which can be determined by inserting the coordinates of the parabola point. One gets y = m x − m 2 4 a . {\displaystyle y=mx-{\tfrac {m^{2}}{4a}}\;.}
Bacterial cell structure Intracellular membranes Bacterial_cell_structure > Intracellular (internal) structures > Intracellular membranes Intracellular membranes are also found in bacteria belonging to the poorly studied Planctomycetota group, although these membranes more closely resemble organellar membranes in eukaryotes and are currently of unknown function. Chromatophores are intracellular membranes found in phototrophic bacteria. Used primarily for photosynthesis, they contain bacteriochlorophyll pigments and carotenoids.
Information value theory Simple Information_value_theory > Definitions > Simple A simple example best illustrates the concept: Consider the decision situation with one decision, for example deciding on a 'Vacation Activity'; and one uncertainty, for example what will the 'Weather Condition' be? But we will only know the 'Weather Condition' after we have decided and begun the 'Vacation Activity'. The Value of perfect information on Weather Condition captures the value of being able to know Weather Condition even before making the Vacation Activity decision. It is quantified as the highest price the decision-maker is willing to pay for being able to know Weather Condition before making the Vacation Activity decision.
Airspeed Summary Air_speed The measurement and indication of airspeed is ordinarily accomplished on board an aircraft by an airspeed indicator ("ASI") connected to a pitot-static system. The pitot-static system comprises one or more pitot probes (or tubes) facing the on-coming air flow to measure pitot pressure (also called stagnation, total or ram pressure) and one or more static ports to measure the static pressure in the air flow. These two pressures are compared by the ASI to give an IAS reading.
Current reversal Current–voltage relation Parallel-plate_capacitor > Theory of operation > Current–voltage relation Thus the charge on the electrodes is equal to the integral of the current as well as proportional to the voltage, as discussed above. As with any antiderivative, a constant of integration is added to represent the initial voltage V(t0). This is the integral form of the capacitor equation: Taking the derivative of this and multiplying by C yields the derivative form: for C independent of time, voltage and electric charge. The dual of the capacitor is the inductor, which stores energy in a magnetic field rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance L.
Neuroscience of rhythm Circadian rhythms Neuroscience_of_rhythm > Autonomic rhythms > Circadian rhythms The SCN is then able to influence the sleep wake cycle, acting as the "apex of a hierarchy" that governs physiological timing functions. "Rest and sleep are the best example of self-organized operations within neuronal circuits".
Proton-pump inhibitors Summary Proton-pump_inhibitor Proton-pump inhibitors (PPIs) are a class of medications that cause a profound and prolonged reduction of stomach acid production. They do so by irreversibly inhibiting the stomach's H+/K+ ATPase proton pump.They are the most potent inhibitors of acid secretion available. Proton-pump inhibitors have largely superseded the H2-receptor antagonists, a group of medications with similar effects but a different mode of action, and antacids.PPIs are among the most widely sold medications in the world. The class of proton-pump inhibitor medications is on the World Health Organization's List of Essential Medicines. Omeprazole is the specific listed example.
Fine Guidance Sensor and Near Infrared Imager and Slitless Spectrograph Summary Fine_Guidance_Sensor_and_Near_Infrared_Imager_and_Slitless_Spectrograph The instrument has four different observing modes.Physically the FGS and NIRISS are combined, but optically they are separate with the FGS being used by the telescope to point it, whereas NIRISS is an independent science instrument. The spectroscopic mode is capable of doing exoplanet spectroscopy. The detector for NIRISS is a 2048 × 2048 pixel mercury cadmium telluride (HgCdTe) array, where each pixel is 18 microns on a side according to the STSCi.
Solver Solver types Solver > Solver types This induces an exponential computational time that dramatically limits their usability. Modern solvers use a more specialized approach that takes advantage of the structure of the problems so that the solver spends as little time as possible backtracking. For problems of a particular class (e.g., systems of non-linear equations) multiple algorithms are usually available. Some solvers implement multiple algorithms.
Henderson–Hasselbalch equation Derivation, assumptions and limitations Henderson–Hasselbalch_equation > Derivation, assumptions and limitations Phosphoric acid is such an acid. Assumption 2. The self-ionization of water can be ignored.
The Turing Test (video game) Plot The_Turing_Test_(video_game) > Plot As the tests get harder, T.O.M. realizes that these are designed to be solved by a combination of human and artificial intelligence, a manner similar to that of the actual Turing test. They enter an area where one of the remaining crew-members, Sarah, warns Ava over the communication systems that she is actually being controlled by T.O.M.
Class-A amplifier Summary Class-A_amplifier In electronics, power amplifier classes are letter symbols applied to different power amplifier types. The class gives a broad indication of an amplifier's characteristics and performance. The classes are related to the time period that the active amplifier device is passing current, expressed as a fraction of the period of a signal waveform applied to the input.
Doppler echocardiography Phase based method Doppler_echocardiography > 2D Doppler imaging > Speckle tracking > Sub pixel accuracy > Phase based method The main idea of this method is to generate synthetic lateral phase and use it to find the phase that crosses zero at the peak lag. The right figure illustrates the procedure of creating the synthetic lateral phase, as a first step. Basically, the lateral spectrum is split in two to generate two spectra with nonzero center frequencies. The cross correlation is done for both the up signal and down signal, creating R u p {\displaystyle R_{up}} and R d o w n {\displaystyle R_{down}} respectively.
Protocell Energy gradient Protocell > Selectivity for compartmentalization > Energy gradient A March 2014 study by NASA's Jet Propulsion Laboratory demonstrated a unique way to study the origins of life: fuel cells. Fuel cells are similar to biological cells in that electrons are also transferred to and from molecules. In both cases, this results in electricity and power. The study states that one important factor was that the Earth provides electrical energy at the seafloor. "This energy could have kick-started life and could have sustained life after it arose. Now, we have a way of testing different materials and environments that could have helped life arise not just on Earth, but possibly on Mars, Europa and other places in the Solar System."
Periodic table (crystal structure) Body centred cubic Double_hexagonal_close_packed > Usual crystal structures > Body centred cubic This is not a close packed structure. In this each metal atom is at the centre of a cube with 8 nearest neighbors, however the 6 atoms at the centres of the adjacent cubes are only approximately 15% further away so the coordination number can therefore be considered to be 14 when these are ong one 4 fold axe structure becomes face-centred cubic (cubic close packed).
Three-hand effect Summary Three-hand_effect The three-hand effect (or three-hand technique) is a means of playing on the piano with only two hands, but producing the impression that one is using three hands. Typically this effect is produced by keeping the melody in the middle register, with accompanying arpeggios in the treble and bass registers.
Duplicating machines How digital duplicators work Duplicating_machines > Digital duplicators > How digital duplicators work The new master is fed into the clamp which closes, then the drum is turned, pulling the master onto the drum. The outside of the drum is covered in screens and the inside is coated in ink. The screens make sure the ink flow is regulated.
Lie groupoid Trivial and extreme cases Lie_groupoid > Examples > Trivial and extreme cases Lie groupoids G ⇉ ∗ {\displaystyle G\rightrightarrows {*}} with one object are the same thing as Lie groups. Given any manifold M {\displaystyle M} , there is a Lie groupoid M × M ⇉ M {\displaystyle M\times M\rightrightarrows M} called the pair groupoid, with precisely one morphism from any object to any other. The two previous examples are particular cases of the trivial groupoid M × G × M ⇉ M {\displaystyle M\times G\times M\rightrightarrows M} , with structure maps s ( x , g , y ) = y {\displaystyle s(x,g,y)=y} , t ( x , g , y ) = x {\displaystyle t(x,g,y)=x} , m ( ( x , g , y ) , ( y , h , z ) ) = ( x , g h , z ) {\displaystyle m((x,g,y),(y,h,z))=(x,gh,z)} , u ( x ) = ( x , 1 , x ) {\displaystyle u(x)=(x,1,x)} and i ( x , g , y ) = ( y , g − 1 , x ) {\displaystyle i(x,g,y)=(y,g^{-1},x)} .
Bayesian model reduction Neuroimaging Bayesian_model_reduction > Applications > Neuroimaging Bayesian model reduction was initially developed for use in neuroimaging analysis, in the context of modelling brain connectivity, as part of the dynamic causal modelling framework (where it was originally referred to as post-hoc Bayesian model selection). Dynamic causal models (DCMs) are differential equation models of brain dynamics. The experimenter specifies multiple competing models which differ in their priors – e.g. in the choice of parameters which are fixed at their prior expectation of zero.
Codec listening test ABX test Codec_listening_test > Testing methods > ABX test In an ABX test, the listener has to identify an unknown sample X as being A or B, with A (usually the original) and B (usually the encoded version) available for reference. The outcome of a test must be statistically significant. This setup ensures that the listener is not biased by their expectations, and that the outcome is not likely to be the result of chance. If sample X cannot be determined reliably with a low p-value in a predetermined number of trials, then the null hypothesis cannot be rejected and it cannot be proved that there is a perceptible difference between samples A and B. This usually indicates that the encoded version will actually be transparent to the listener.
Geometric continuity Smooth partitions of unity Smooth_mapping > Other concepts > Smooth partitions of unity Smooth functions with given closed support are used in the construction of smooth partitions of unity (see partition of unity and topology glossary); these are essential in the study of smooth manifolds, for example to show that Riemannian metrics can be defined globally starting from their local existence. A simple case is that of a bump function on the real line, that is, a smooth function f that takes the value 0 outside an interval and such that Given a number of overlapping intervals on the line, bump functions can be constructed on each of them, and on semi-infinite intervals ( − ∞ , c ] {\displaystyle (-\infty ,c]} and [ d , + ∞ ) {\displaystyle [d,+\infty )} to cover the whole line, such that the sum of the functions is always 1. From what has just been said, partitions of unity don't apply to holomorphic functions; their different behavior relative to existence and analytic continuation is one of the roots of sheaf theory. In contrast, sheaves of smooth functions tend not to carry much topological information.
Hemicontinuity Summary Upper_hemicontinuous In mathematics, the notion of the continuity of functions is not immediately extensible to set-valued functions between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension. A set-valued function that has both properties is said to be continuous in an analogy to the property of the same name for single-valued functions. Roughly speaking, a function is upper hemicontinuous if when (1) a convergent sequence of points in the domain maps to a sequence of sets in the range which (2) contain another convergent sequence, then the image of the limiting point in the domain must contain the limit of the sequence in the range. Lower hemicontinuity essentially reverses this, saying if a sequence in the domain converges, given a point in the range of the limit, then you can find a sub-sequence whose image contains a convergent sequence to the given point.
Powered speaker Differences Amplified_loudspeaker > Differences The terms "powered" and "active" have been used interchangeably in loudspeaker designs, however, a differentiation may be made between the terms: In a passive loudspeaker system the low-level audio signal is first amplified by an external power amplifier before being sent to the loudspeaker where the signal is split by a passive crossover into the appropriate frequency ranges before being sent to the individual drivers. This design is common in home audio as well as professional concert audio. A powered loudspeaker works the same way as a passive speaker, but the power amplifier is built into the loudspeaker enclosure. This design is common in compact personal speakers such as those used to amplify portable digital music devices.
Trilinear coordinates Circumconics Trilinear_coordinates > Formulas > Quadratic curves > Circumconics The equation in trilinear coordinates of the circumconic with center x': y': z' is: p. 203 y z ( x ′ − y ′ − z ′ ) + z x ( y ′ − z ′ − x ′ ) + x y ( z ′ − x ′ − y ′ ) = 0. {\displaystyle yz(x'-y'-z')+zx(y'-z'-x')+xy(z'-x'-y')=0.}

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