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Computable analysis Computable functions Computable_analysis > Basic constructions > Computable functions Computable functions are represented as programs on a Type 2 Turing machine. A program is considered total (in the sense of a total function as opposed to partial function) if it takes finite time to write any number of symbols on the output tape regardless of the input. A total programs run forever, generating increasingly more digits of the output. |
Computability theory (computation) Inductive inference Computability_theory_(computation) > Areas of research > Inductive inference This is the computability-theoretic branch of learning theory. It is based on E. Mark Gold's model of learning in the limit from 1967 and has developed since then more and more models of learning. The general scenario is the following: Given a class S of computable functions, is there a learner (that is, computable functional) which outputs for any input of the form (f(0), f(1), ..., f(n)) a hypothesis. A learner M learns a function f if almost all hypotheses are the same index e of f with respect to a previously agreed on acceptable numbering of all computable functions; M learns S if M learns every f in S. Basic results are that all computably enumerable classes of functions are learnable while the class REC of all computable functions is not learnable. Many related models have been considered and also the learning of classes of computably enumerable sets from positive data is a topic studied from Gold's pioneering paper in 1967 onwards. |
Primary adrenal insufficiency Summary Autoimmune_adrenalitis If symptoms worsen, an injection of corticosteroid is recommended (people need to carry a dose with them). Often, large amounts of intravenous fluids with the sugar dextrose are also required. With appropriate treatment, long-term outcomes are typically favorable, and most people are able to lead a reasonably normal life. |
Thompson's construction algorithm Small Example Thompson's_construction_algorithm > Example > Small Example The picture below shows the result of Thompson's construction on (ε|a*b). The purple oval corresponds to a, the teal oval corresponds to a*, the green oval corresponds to b, the orange oval corresponds to a*b, and the blue oval corresponds to ε. |
Contact mechanics History Frictionless_contact_mechanics > History The Derjaguin model came to be known as the DMT (after Derjaguin, Muller and Toporov) model, and the Johnson et al. model came to be known as the JKR (after Johnson, Kendall and Roberts) model for adhesive elastic contact. This rejection proved to be instrumental in the development of the Tabor and later Maugis parameters that quantify which contact model (of the JKR and DMT models) represent adhesive contact better for specific materials. Further advancement in the field of contact mechanics in the mid-twentieth century may be attributed to names such as Bowden and Tabor. |
Nutrient budgeting Assumptions Nutrient_budgeting > Assumptions A nutrient budget isn't as exact as a financial statement. An assortment of variables affects each tract of land. For example, some areas may have had too much manure applied over time or it may have been unevenly distributed, and previous flooding could affect results. Limits and assumptions should be incorporated when compiling a budget including the average nutrient removal coefficient values if they are not specific to a certain field. |
Renewable sources of energy Photovoltaic development Cleaner_energy > Mainstream technologies > Solar energy > Photovoltaic development Photovoltaics (PV) is rapidly-growing with global capacity increasing from 230 GW at the end of 2015 to 890 GW in 2021.PV uses solar cells assembled into solar panels to convert sunlight into electricity. PV systems range from small, residential and commercial rooftop or building integrated installations, to large utility-scale photovoltaic power station. The predominant PV technology is crystalline silicon, while thin-film solar cell technology accounts for about 10 percent of global photovoltaic deployment. In recent years, PV technology has improved its electricity generating efficiency, reduced the installation cost per watt as well as its energy payback time, and reached grid parity.Building-integrated photovoltaics or "onsite" PV systems use existing land and structures and generate power close to where it is consumed.Photovoltaics grew fastest in China between 2016 and 2021 adding 560 GW, more than all advanced economies combined. |
Security printing Polymer Security_printing > Features detectable by humans > Substrate > Polymer Some countries, including Canada, Nigeria, Romania, Mexico, Hong Kong, New Zealand, Israel, Singapore, Malaysia, United Kingdom and Australia, produce polymer (plastic) banknotes, to improve longevity and to make counterfeiting more difficult. Polymer can include transparent windows, diffraction grating and raised printing. Transparent Windows |
Lie superalgebra Historical Lie_superbracket > References > Historical Frölicher, A.; Nijenhuis, A. (1956). "Theory of vector valued differential forms. Part I". |
Memistor Essence Memistor > Essence In one of the technical reports the memistor was described as follows: Like the transistor, the memistor is a 3-terminal element. The conductance between two of the terminals is controlled by the time integral of the current in the third, rather than its instantaneous value as in the transistor. Reproducible elements have been made which are continuously variable (thousands of possible analog storage levels), and which typically vary in resistance from 100 ohms to 1 ohm, and cover this range in about 10 seconds with several milliamperes of plating current. Adaptation is accomplished by direct current while sensing the neuron logical structure is accomplished nondestructively by passing alternating currents through the arrays of memistor cells. |
Mechanical drawing Schematic drawing Mechanical_systems_drawing > Sets of drawings > United Kingdom > Schematic drawing The schematic is a line diagram, not necessarily to scale, that describes interconnection of components in a system. The main features of a schematic drawing show: A two dimensional layout with divisions that show distribution of the system between building levels, or an isometric-style layout that shows distribution of systems across individual floor levels All functional components that make up the system, i.e., plant items, pumps, fans, valves, strainers, terminals, electrical switchgear, distribution and components Symbols and line conventions, in accordance with industry standard guidance Labels for pipe, duct, and cable sizes where not shown elsewhere Components that have a sensing and control function, and links between them—building management systems, fire alarms and HV controls Major components, so their whereabouts in specifications and other drawings can be easily determined |
Glycogen synthase Regulation Glycogen_synthase > Regulation The reaction is highly regulated by allosteric effectors such as glucose 6-phosphate (activator) and by phosphorylation reactions (deactivating). Glucose-6-phosphate allosteric activating action allows glycogen synthase to operate as a glucose-6-phosphate sensor. The inactivating phosphorylation is triggered by the hormone glucagon, which is secreted by the pancreas in response to decreased blood glucose levels. |
Hereditary CNS demyelinating disease Summary Hereditary_CNS_demyelinating_disease A hereditary CNS demyelinating disease is a demyelinating central nervous system disease that is primarily due to an inherited genetic condition. (This is in contrast to autoimmune demyelinating conditions, such as multiple sclerosis, or conditions such as central pontine myelinolysis that are associated with acute acquired insult. )Examples include: Alexander disease Canavan disease Krabbe disease leukoencephalopathy with vanishing white matter megalencephalic leukoencephalopathy with subcortical cysts metachromatic leukodystrophy X-linked adrenoleukodystrophy |
Adenosine Triphosphate Summary Adenosine_Triphosphate Adenosine triphosphate (ATP) is an organic compound that provides energy to drive and support many processes in living cells, such as muscle contraction, nerve impulse propagation, condensate dissolution, and chemical synthesis. Found in all known forms of life, ATP is often referred to as the "molecular unit of currency" of intracellular energy transfer. When consumed in metabolic processes, it converts either to adenosine diphosphate (ADP) or to adenosine monophosphate (AMP). |
Irreducibly complex Intelligent design Irreducible_complexity > History > Intelligent design (The judge ruled that "intelligent design is not science and is essentially religious in nature". )According to the theory of evolution, genetic variations occur without specific design or intent. The environment "selects" the variants that have the highest fitness, which are then passed on to the next generation of organisms. |
Buffer overflow Barriers to exploitation DLL_trampolining > Exploitation > Barriers to exploitation Manipulation of the buffer, which occurs before it is read or executed, may lead to the failure of an exploitation attempt. These manipulations can mitigate the threat of exploitation, but may not make it impossible. Manipulations could include conversion to upper or lower case, removal of metacharacters and filtering out of non-alphanumeric strings. |
Machine torque Proof Force_moment > Relationship between torque, power, and energy > Proof In the case of torque, the unit is assigned to a vector, whereas for energy, it is assigned to a scalar. This means that the dimensional equivalence of the newton-metre and the joule may be applied in the former, but not in the latter case. This problem is addressed in orientational analysis, which treats the radian as a base unit rather than as a dimensionless unit. |
Photoemission electron microscopy Energy filter Photoemission_electron_microscopy > Photoemission electron microscope > Energy filter An energy filter can be added to the instrument in order to select the electrons that will contribute to the image. This option is particularly used for analytical applications of the PEEM. By using an energy filter, a PEEM microscope can be seen as imaging Ultra-violet photoelectron spectroscopy (UPS) or X-ray photoelectron spectroscopy (XPS). By using this method, spatially resolved photoemission spectra can be acquired with spatial resolutions on the 100 nm scale and with sub-eV resolution. Using such instrument, one can acquire elemental images with chemical state sensibility or work function maps. Also, since the photoelectron are emitted only at the very surface of the material, surface termination maps can be acquired. |
Membrane models Henderson and Unwin's membrane theory Membrane_models > Henderson and Unwin's membrane theory The dimensions of the channel within the membrane were narrower but could not be resolved (Unwin and Zampighi, 1980). A small radical movement of the sub-units at the cytoplasmic ends could reduce the sub-unit inclination tangential to six-fold axis and close the channel.Further details of the molecular organization should emerge as more methods of preparation become available, so that high-resolution 3-dimensional images comparable to the purple membranes are obtained. By using ingenious procedures for the analysis of periodic arrays of biological macromolecules, in which data from low-dose electron images and diffraction patterns were combined, Henderson and Unwin (1975) reconstructed a three-dimensional image of purple membranes at 0.7 nm resolution. |
Tree height measurement Clinometer and tape method Tree_height_measurement > Approximate tree heights > Clinometer and tape method The top of the tree therefore has a different baseline length than the bottom of the tree resulting in height errors: (top to bottom offset distance x tan Θ) = height error The error almost always incorrectly adds to the height of the tree. For example, if measuring a tree at an angle of 64 degrees, given an average offset of 8.3 feet (2.5 m) in the direction of the measurer, the height of the tree would be overestimated by 17 feet (5.2 m). This type of error will be present in all of the readings using the tangent method, except in the cases where the highest point of the tree actually is located directly above the base of the tree, and except in this unusual case, the result is not repeatable as a different height reading would be obtained depending on the direction and position from which the measurement was taken. |
Polysulfone Structure-property relationship Polysulfone > Properties > Structure-property relationship Therefore, flexible elements must be incorporated into the chains, this is done in the form of ether groups. Ether groups allow a free rotation of the polymer chains. This leads to a significantly reduced melting point and also improves the mechanical properties by an increased impact strength. |
False proof Analysis False_proof > Analysis Mathematical analysis as the mathematical study of change and limits can lead to mathematical fallacies — if the properties of integrals and differentials are ignored. For instance, a naive use of integration by parts can be used to give a false proof that 0 = 1. Letting u = 1/log x and dv = dx/x, we may write: ∫ 1 x log x d x = 1 + ∫ 1 x log x d x {\displaystyle \int {\frac {1}{x\,\log x}}\,dx=1+\int {\frac {1}{x\,\log x}}\,dx} after which the antiderivatives may be cancelled yielding 0 = 1. The problem is that antiderivatives are only defined up to a constant and shifting them by 1 or indeed any number is allowed. The error really comes to light when we introduce arbitrary integration limits a and b. ∫ a b 1 x log x d x = 1 | a b + ∫ a b 1 x log x d x = 0 + ∫ a b 1 x log x d x = ∫ a b 1 x log x d x {\displaystyle \int _{a}^{b}{\frac {1}{x\,\log x}}\,dx=1|_{a}^{b}+\int _{a}^{b}{\frac {1}{x\,\log x}}\,dx=0+\int _{a}^{b}{\frac {1}{x\log x}}\,dx=\int _{a}^{b}{\frac {1}{x\log x}}\,dx} Since the difference between two values of a constant function vanishes, the same definite integral appears on both sides of the equation. |
Glossary of chemistry terms C Glossary_of_chemistry_terms > C counterion The ion that is the counterpart to an oppositely charged ion in a dissociated ionic species; the cation that pairs with a given anion, or vice versa. For example, Na+ is the counterion to Cl−, and vice versa, in solutions of sodium chloride (NaCl). covalent bond Also molecular bond. |
Base dissociation constant Micro-constants Acid–base_equilibrium > Experimental determination > Micro-constants For example, monoprotonation can occur at a terminal −NH2 group or at internal −NH− groups. The Kb values for dissociation of spermine protonated at one or other of the sites are examples of micro-constants. They cannot be determined directly by means of pH, absorbance, fluorescence or NMR measurements; a measured Kb value is the sum of the K values for the micro-reactions. |
Freeman Dyson Quantum physics and prime numbers Freeman_Dyson > Concepts > Quantum physics and prime numbers Mathematicians define a quasicrystal as a set of discrete points whose Fourier transform is also a set of discrete points. Odlyzko has done extensive computations of the Fourier transform of the nontrivial zeros of the zeta function, and they seem to form a one-dimensional quasicrystal. This would in fact follow from the Riemann hypothesis. |
Tactile signing Kinds Tactile_signing > Kinds The sign language used in hand-over-hand signing is often a slightly modified version of the local sign language; this is especially the case when used by people who have learned to read sign visually before losing their vision as with Usher syndrome. The sign language used may also be a manually coded version of the local oral language (such as Signed English), or a mid-way point between the two known as contact signing. Tracking: The listener lightly places their hand(s) on the wrists or forearms of the signer to help them track the signs visually (as the listener knows the location of their own hands and is thus able to focus on the signer's hand(s) as they move in space. |
Observational bias Paradoxes Observational_bias > Paradoxes In isolation, quantum objects are represented by a wave function which often exists in a superposition or mixture of different states. However, when an observation is made to determine the actual location or state of the object, it always finds the object in a single state, not a "mixture". The interaction of the observation process appears to "collapse" the wave function into a single state. So any interaction between an isolated wave function and the external world that results in this wave function collapse is called an observation or measurement, whether or not it is part of a deliberate observation process. |
Envelope proteins Summary Envelope_proteins Therefore, optimal budding and release may be dependent on a coordinated "push-and-pull" action between core and spike, where oligomerization of both components is essential.They may help viruses avoid the host immune system. TAM receptor tyrosine kinases increase phagocytic clearance of apoptotic cells and inhibit immunological responses brought on by Toll-like receptors and type I interferons (IFNs) when they are activated by the ligands Gas6 and Protein S. The phospholipid phosphatidylserine may be seen on the membranes of several enveloped viruses, which they employ to bind Gas6 and Protein S to activate TAM receptors. Ligand-coated viruses stimulate type I IFN signaling, activate TAM receptors on dendritic cells (DCs), and suppress type II interferon signaling to circumvent host defenses and advance infection.TAM-deficient DCs exhibit type I IFN responses that are more pronounced than those of wild-type cells in response to viral exposure. |
Organic electronics Features Organic_electronics > Features Conductive polymers are lighter, more flexible, and less expensive than inorganic conductors. This makes them a desirable alternative in many applications. It also creates the possibility of new applications that would be impossible using copper or silicon. Organic electronics not only includes organic semiconductors, but also organic dielectrics, conductors and light emitters. New applications include smart windows and electronic paper. Conductive polymers are expected to play an important role in the emerging science of molecular computers. |
Electric plane Batteries Solar_powered_aircraft > Power storage > Batteries Batteries are the most common onboard energy storage component of electric aircraft, due to their relatively high storage capacity. Batteries first powered airships in the nineteenth century but the lead-acid batteries were very heavy and it was not until the arrival of other chemistries, such as nickel-cadmium (NiCd) later in the twentieth century, that batteries became practical for heavier-than-air aircraft. Modern batteries are mostly rechargeable types based on lithium technologies. Lithium polymer (LiPo), a type of lithium-ion batteries (LIB), have long been applied in unmanned flight for their light weight and rechargeability. |
Ribosomal pause Rescue mechanisms Ribosomal_pause > Resolution and effects on gene expression > Rescue mechanisms It recruits RF2. Alternative ribosome-rescue factor B (ArfB) is another alternative from E. coli. It works like a GGQ-release factor itself, releasing the peptide from tRNA. At the same time, it fits into the mRNA tunnel to remove the mRNA.In eukaryotes, the main mechanism involves PELO:HBS1L. |
Specified complexity Summary Specified_complexity A study by Wesley Elsberry and Jeffrey Shallit states: "Dembski's work is riddled with inconsistencies, equivocation, flawed use of mathematics, poor scholarship, and misrepresentation of others' results." Another objection concerns Dembski's calculation of probabilities. According to Martin Nowak, a Harvard professor of mathematics and evolutionary biology, "We cannot calculate the probability that an eye came about. We don't have the information to make the calculation." |
Infinite element method Summary Infinite_element_method The infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The method divides the domain concerned into sections of infinite length. In contrast with a finite element which is approximated by polynomial expressions on a finite support, the unbounded length of the infinite element is fitted with functions allowing the evaluation of the field at the asymptote. |
Lemierre's syndrome Summary Lemierre's_syndrome The inflammation surrounding the vein and compression of the vein may lead to blood clot formation. Pieces of the potentially infected clot can break off and travel through the right heart into the lungs as emboli, blocking branches of the pulmonary artery that carry blood with little oxygen from the right side of the heart to the lungs.Sepsis following a throat infection was first described by Hugo Schottmüller in 1918. In 1936, André Lemierre published a series of 20 cases where throat infections were followed by identified anaerobic sepsis, of whom 18 died. |
Friction drilling Principle Friction_drilling > Principle Lubricants help prevent work-material from adhering to the bit. Unlike drilling, material that is flowed is not lost but it forms a sleeve around the hole. The length of that sleeve is up to 3 times the original thickness of the material. |
Renal function Glomerular filtration rate Estimated_GFR > Blood tests > Glomerular filtration rate Staging of chronic kidney disease is based on categories of GFR as well as albuminuria and cause of kidney disease.Central to the physiologic maintenance of GFR is the differential basal tone of the afferent and efferent arterioles (see diagram). In other words, the filtration rate is dependent on the difference between the higher blood pressure created by vasoconstriction of the input or afferent arteriole versus the lower blood pressure created by lesser vasoconstriction of the output or efferent arteriole. GFR is equal to the renal clearance ratio when any solute is freely filtered and is neither reabsorbed nor secreted by the kidneys. |
Open standardization Quotes Open_Standards > Quotes EU Commissioner Erkki Liikanen: "Open standards are important to help create interoperable and affordable solutions for everybody. They also promote competition by setting up a technical playing field that is level to all market players. This means lower costs for enterprises and, ultimately, the consumer." |
Anionic addition polymerization Summary Anionic_addition_polymerization In polymer chemistry, anionic addition polymerization is a form of chain-growth polymerization or addition polymerization that involves the polymerization of monomers initiated with anions. The type of reaction has many manifestations, but traditionally vinyl monomers are used. Often anionic polymerization involves living polymerizations, which allows control of structure and composition. |
Wireless security End-to-end encryption Wireless_LAN_Security > Security measures > End-to-end encryption With encryption on the router level or VPN, a single switch encrypts all traffic, even UDP and DNS lookups. With end-to-end encryption on the other hand, each service to be secured must have its encryption "turned on", and often every connection must also be "turned on" separately. For sending emails, every recipient must support the encryption method, and must exchange keys correctly. |
Jane S. Richardson Scientific work and contributions Jane_S._Richardson > Scientific work and contributions By 1977 she published her findings on protein relatedness in Nature, with a paper entitled "β-sheet topology and the relatedness of proteins".As Richardson developed the ribbon diagram to illustrate her findings over the course of her taxonomic research, her iconic images first appeared in the review journal Advances in Protein Chemistry in an article titled "The anatomy and taxonomy of protein structure" 1981, an early hallmark publication in structural bioinformatics. The diagrams have since become a standard way of visualizing protein structure, specifically depicting beta-sheet topology and connections between amino acid sequences, or peptides, that make up proteins. The protein folding process involves four levels: primary structures, secondary structures, tertiary structures, and quaternary structures. |
Byte order Files and filesystems Endianness > Files and filesystems Intel CPUs are little-endian, while Motorola 680x0 CPUs are big-endian. This explicit signature allows a TIFF reader program to swap bytes if necessary when a given file was generated by a TIFF writer program running on a computer with a different endianness. As a consequence of its original implementation on the Intel 8080 platform, the operating system-independent File Allocation Table (FAT) file system is defined with little-endian byte ordering, even on platforms using another endianness natively, necessitating byte-swap operations for maintaining the FAT on these platforms. ZFS, which combines a filesystem and a logical volume manager, is known to provide adaptive endianness and to work with both big-endian and little-endian systems. |
PROPT Summary PROPT The PROPT MATLAB Optimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters estimation problems. The platform was developed by MATLAB Programming Contest Winner, Per Rutquist in 2008. The most recent version has support for binary and integer variables as well as an automated scaling module. |
DNA strand ssDNA vs. dsDNA Deoxyribonucleic_Acid > Properties > Base pairing > ssDNA vs. dsDNA In biology, parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters, tend to have a high AT content, making the strands easier to pull apart.In the laboratory, the strength of this interaction can be measured by finding the melting temperature Tm necessary to break half of the hydrogen bonds. When all the base pairs in a DNA double helix melt, the strands separate and exist in solution as two entirely independent molecules. These single-stranded DNA molecules have no single common shape, but some conformations are more stable than others. |
Quantum point contact Applications Quantum_point_contact > Applications In device physics, the configuration of QPCs is used for demonstrating a fully ballistic field-effect transistor. Another application of the device is its use as a switch. A nickel wire is brought close enough to a gold surface and then, by the use of a piezoelectric actuator, the distance between the wire and the surface can be changed and thus, the transport characteristics of the device change between electron tunneling and ballistic. |
Heinz Falk Scientific articles Heinz_Falk > Published works > Scientific articles Mh. Chem., 136, 1221-1231 (2005) David Geißlmeir, Walther G. Jary and Heinz Falk, The TEMPO/Copper Catalyzed Oxidation of Primary Alcohols to Aldehydes Using Oxygen as Stoichiometric Oxidant. Mh. |
Inverse search Summary Inverse_search Inverse search (also called "reverse search") is a feature of some non-interactive typesetting programs, such as LaTeX and GNU LilyPond. These programs read an abstract, textual, definition of a document as input, and convert this into a graphical format such as DVI or PDF. In a windowing system, this typically means that the source code is entered in one editor window, and the resulting output is viewed in a different output window. Inverse search means that a graphical object in the output window works as a hyperlink, which brings you back to the line and column in the editor, where the clicked object was defined. The inverse search feature is particularly useful during proofreading. |
Trace metal stable isotope biogeochemistry Fractionation as a result of diffusion Trace_metal_stable_isotope_biogeochemistry > Iron > Equilibrium Isotope Fractionation > Fractionation as a result of diffusion Kinetic fractionation of dissolved iron occurs as a result of diffusion. When isotopes diffuse, the lower mass isotopes diffuse more quickly than the heavier isotopes, resulting in fractionation. This difference in diffusion rates has been approximated as: D 1 D 2 = ( m 1 m 2 ) β {\displaystyle {\frac {D_{1}}{D_{2}}}=\left({\frac {m_{1}}{m_{2}}}\right)^{\beta }} In this equation, D1 and D2 are the diffusivities of the isotopes, m1 and m2 are the masses of the isotopes, and β, which can vary between 0 and 0.5, depending on the system. |
Cross-validation (statistics) Leave-one-out cross-validation Cross-validation_(statistics) > Types > Exhaustive cross-validation > Leave-one-out cross-validation Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1. The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C p n {\displaystyle C_{p}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate.Pseudo-code algorithm: Input: x, {vector of length N with x-values of incoming points} y, {vector of length N with y-values of the expected result} interpolate( x_in, y_in, x_out ), { returns the estimation for point x_out after the model is trained with x_in-y_in pairs} Output: err, {estimate for the prediction error} Steps: err ← 0 for i ← 1, ..., N do // define the cross-validation subsets x_in ← (x, ..., x, x, ..., x) y_in ← (y, ..., y, y, ..., y) x_out ← x y_out ← interpolate(x_in, y_in, x_out) err ← err + (y − y_out)^2 end for err ← err/N |
Rule of product Summary Rule_of_product In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions. |
Reverse Fatou lemma Proof Reverse_Fatou_lemma > Standard statement > Proof Fatou's lemma does not require the monotone convergence theorem, but the latter can be used to provide a quick proof. A proof directly from the definitions of integrals is given further below. In each case, the proof begins by analyzing the properties of g n ( x ) = inf k ≥ n f k ( x ) {\displaystyle \textstyle g_{n}(x)=\inf _{k\geq n}f_{k}(x)} . These satisfy: the sequence { g n ( x ) } n {\displaystyle \{g_{n}(x)\}_{n}} is pointwise non-decreasing at any x and g n ≤ f n {\displaystyle g_{n}\leq f_{n}} , ∀ n ∈ N {\displaystyle \forall n\in \mathbb {N} } .Since f ( x ) = lim inf n → ∞ f n ( x ) = lim n → ∞ inf k ≥ n f k ( x ) = lim n → ∞ g n ( x ) {\displaystyle f(x)=\liminf _{n\to \infty }f_{n}(x)=\lim _{n\to \infty }\inf _{k\geq n}f_{k}(x)=\lim _{n\to \infty }{g_{n}(x)}} , we immediately see that f is measurable. |
Adjustable-speed drive Eddy current drives Variable_speed_drive > Types of drives > Electric adjustable speed drives > Eddy current drives An eddy current drive (sometimes called a Dynamatic drive, after one of the most common brand names) consists of a fixed speed motor (generally an induction motor) and an eddy current clutch. The clutch contains a fixed speed rotor and an adjustable speed rotor separated by a small air gap. A direct current in a field coil produces a magnetic field that determines the torque transmitted from the input rotor to the output rotor. The controller provides closed loop speed regulation by varying clutch current, only allowing the clutch to transmit enough torque to operate at the desired speed. |
Sentence processing Modular vs. interactive Language_comprehension > Theories > Architectural issues > Modular vs. interactive Several syntactic hypotheses can be considered at a time. The interactive model demonstrates an on-line interaction between the structural and lexical and phonetic levels of sentence processing. Each word, as it is heard in the context of normal discourse, is immediately entered into the processing system at all levels of description, and is simultaneously analyzed at all these levels in the light of whatever information is available at each level at that point in the processing of the sentence. |
Kepler-90g Summary Kepler-90g Kepler-90g (also known by its Kepler Object of Interest designation KOI-351.02) is a super-puff exoplanet orbiting the early G-type main sequence star Kepler-90, one of eight planets around this star discovered using NASA's Kepler space telescope. It is located about 2,840 light-years (870 pc) from Earth, in the constellation Draco. The exoplanet was found by using the transit method, in which the dimming effect that a planet causes as it crosses in front of its star is measured. It orbits its parent star about every 210.5 days at a distance of 0.71 astronomical units.Kepler-90g's orbital period changes by 25.7 hours between two consecutive transits, caused by gravitational perturbations from other planets in the system. |
Switching regulator Electromechanical regulators Voltage_stabiliser > Electromechanical regulators The large inductance of the field coil stores the energy delivered to the magnetic field in an iron core so the pulsed field current does not result in as strongly pulsed a field. Both types of rotating machine produce a rotating magnetic field that induces an alternating current in the coils in the stator. |
Meaningful learning Nature of meaningful learning Meaningful_learning > Nature of meaningful learning There are many ways to understand and define meaningful learning; it incorporates many facets of cognition. Similar types of learning include active learning, deeper learning, and integrative learning. Ausubel (1967:10) focused on meaningful learning as "a clearly articulated and precisely differentiated conscious experience that emerges when potentially meaningful signs, symbols, concepts, or propositions are related to and incorporated within a given individual's cognitive structure" (Takač 2008, p. 26). |
Process scheduler Long-term scheduling Dispatch_latency > Types of operating system schedulers > Process scheduler > Long-term scheduling The long-term scheduler, or admission scheduler, decides which jobs or processes are to be admitted to the ready queue (in main memory); that is, when an attempt is made to execute a program, its admission to the set of currently executing processes is either authorized or delayed by the long-term scheduler. Thus, this scheduler dictates what processes are to run on a system, the degree of concurrency to be supported at any one time – whether many or few processes are to be executed concurrently, and how the split between I/O-intensive and CPU-intensive processes is to be handled. The long-term scheduler is responsible for controlling the degree of multiprogramming. In general, most processes can be described as either I/O-bound or CPU-bound. |
Acid-base chemistry Brønsted–Lowry definition Acid-base_chemistry > Acid–base definitions > Brønsted–Lowry definition The Brønsted–Lowry model expanded what could be pH tested using insoluble and soluble solutions (gas, liquid, solid). The general formula for acid–base reactions according to the Brønsted–Lowry definition is: HA + B → BH+ + A−where HA represents the acid, B represents the base, BH+ represents the conjugate acid of B, and A− represents the conjugate base of HA. For example, a Brønsted–Lowry model for the dissociation of hydrochloric acid (HCl) in aqueous solution would be the following: HCl + H2O ⇌ H3O+ + Cl−The removal of H+ from the HCl produces the chloride ion, Cl−, the conjugate base of the acid. |
War cycles The Foundation for the Study of Cycles War_cycles > The Foundation for the Study of Cycles New York: H. Holt and Company. LCCN 47001975. Dewey, Edward R. |
Direct Current High-voltage power transmission DC_voltage > Applications > High-voltage power transmission High-voltage direct current (HVDC) electric power transmission systems use DC for the bulk transmission of electrical power, in contrast with the more common alternating current systems. For long-distance transmission, HVDC systems may be less expensive and suffer lower electrical losses. |
Adrenal gland Zona glomerulosa Adrenal_glands > Structure > Adrenal cortex > Zona glomerulosa The outermost zone of the adrenal cortex is the zona glomerulosa. It lies immediately under the fibrous capsule of the gland. Cells in this layer form oval groups, separated by thin strands of connective tissue from the fibrous capsule of the gland and carry wide capillaries.This layer is the main site for production of aldosterone, a mineralocorticoid, by the action of the enzyme aldosterone synthase. Aldosterone plays an important role in the long-term regulation of blood pressure. |
Vertex (graph) Types of vertices Vertex_(graph) > Types of vertices The vertex space of a graph is a vector space having a set of basis vectors corresponding with the graph's vertices. A graph is vertex-transitive if it has symmetries that map any vertex to any other vertex. In the context of graph enumeration and graph isomorphism it is important to distinguish between labeled vertices and unlabeled vertices. |
Insulin signal transduction pathway Positive Insulin_signal_transduction_pathway_and_regulation_of_blood_glucose > Feedback mechanisms > Positive An example of positive feedback mechanism in the insulin transduction pathway is the activation of some enzymes that inhibit other enzymes from slowing or stopping the insulin transduction pathway which results in improved intake of the glucose. One of these pathways, involves the PI(3)K enzyme (Phosphoinositide 3-kinase). This pathway is responsible for activating glycogen, lipid-protein synthesis, and specific gene expression of some proteins which will help in the intake of glucose. |
Lateral ventricles Summary Lateral_ventricles The lateral ventricles are the two largest ventricles of the brain and contain cerebrospinal fluid (CSF). Each cerebral hemisphere contains a lateral ventricle, known as the left or right lateral ventricle, respectively. Each lateral ventricle resembles a C-shaped cavity that begins at an inferior horn in the temporal lobe, travels through a body in the parietal lobe and frontal lobe, and ultimately terminates at the interventricular foramina where each lateral ventricle connects to the single, central third ventricle. Along the path, a posterior horn extends backward into the occipital lobe, and an anterior horn extends farther into the frontal lobe. |
Pars nervosa Summary Posterior_pituitary The posterior pituitary (or neurohypophysis) is the posterior lobe of the pituitary gland which is part of the endocrine system. The posterior pituitary is not glandular as is the anterior pituitary. Instead, it is largely a collection of axonal projections from the hypothalamus that terminate behind the anterior pituitary, and serve as a site for the secretion of neurohypophysial hormones (oxytocin and vasopressin) directly into the blood. The hypothalamic–neurohypophyseal system is composed of the hypothalamus (the paraventricular nucleus and supraoptic nucleus), posterior pituitary, and these axonal projections. |
Geodynamics Elastic Geodynamics > Deformation of rocks > Elastic Elastic deformation is always reversible, which means that if the stress field associated with elastic deformation is removed, the material will return to its previous state. Materials only behave elastically when the relative arrangement along the axis being considered of material components (e.g. atoms or crystals) remains unchanged. This means that the magnitude of the stress cannot exceed the yield strength of a material, and the time scale of the stress cannot approach the relaxation time of the material. If stress exceeds the yield strength of a material, bonds begin to break (and reform), which can lead to ductile or brittle deformation. |
Group (mathematics) Examples and applications Group_(mathematics) > Examples and applications By means of this connection, topological properties such as proximity and continuity translate into properties of groups. For example, elements of the fundamental group are represented by loops. The second image shows some loops in a plane minus a point. |
Verification and validation of computer simulation models Validation Verification_and_validation_of_computer_simulation_models > Validation Validate model assumptions. Step 3. Compare the model input-output transformations to corresponding input-output transformations for the real system. |
Data Intensive Computing Characteristics Data-intensive_computing > Characteristics Several common characteristics of data-intensive computing systems distinguish them from other forms of computing: The principle of collection of the data and programs or algorithms is used to perform the computation. To achieve high performance in data-intensive computing, it is important to minimize the movement of data. This characteristic allows processing algorithms to execute on the nodes where the data resides reducing system overhead and increasing performance. Newer technologies such as InfiniBand allow data to be stored in a separate repository and provide performance comparable to collocated data. |
Selective serotonin reuptake inhibitor Antidepressants Selective_serotonin_reuptake_inhibitor > List of SSRIs > Never marketed > Antidepressants Alaproclate (GEA-654) Centpropazine Cericlamine (JO-1017) Femoxetine (Malexil; FG-4963) Ifoxetine (CGP-15210) Omiloxetine Panuramine (WY-26002) Pirandamine (AY-23713) Seproxetine ((S)-norfluoxetine) |
TI-89 Programming TI-89_Titanium > TI-89 > Programming The TI-89 is directly programmable in a language called TI-BASIC 89, TI's derivative of BASIC for calculators. With the use of a PC, it is also possible to develop more complex programs in Motorola 68000 assembly language or C, translate them to machine language, and copy them to the calculator. Two software development kits for C programming are available; one is TI Flash Studio, the official TI SDK, and the other is TIGCC, a third-party SDK based on GCC. In addition, there is a third party flash application called GTC that allows the writing and compilation of c programs directly on the calculator. |
Wave characteristic method Advantages Wave_characteristic_method > Advantages The WM has the very significant advantage that computations need be made only at nodes in the piping system. Other techniques such as the method of characteristics (MOC) require calculations at equally spaced interior points in a pipeline. This requirement can easily increase the number of calculations by a factor of 10 or more. However, virtually identical solutions are obtained by the WM and the MOC. |
Search engine optimization Preventing crawling Search_engine_optimisation > Methods > Preventing crawling To avoid undesirable content in the search indexes, webmasters can instruct spiders not to crawl certain files or directories through the standard robots.txt file in the root directory of the domain. Additionally, a page can be explicitly excluded from a search engine's database by using a meta tag specific to robots (usually ). When a search engine visits a site, the robots.txt located in the root directory is the first file crawled. The robots.txt file is then parsed and will instruct the robot as to which pages are not to be crawled. |
Quantum noise Classical to quantum noise Quantum_noise > Basics of noise theory > Classical to quantum noise To study quantum noise, one replaces the corresponding classical measurements with quantum operators, e.g., where ⟨ ⋅ ⟩ {\displaystyle \langle \cdot \rangle } are the quantum statistical average using the density matrix in the Heisenberg picture. |
CircuiTikZ Summary CircuiTikZ CircuiTikZ is a TikZ add-on for typesetting circuit diagrams in a TeX environment such as LaTeX. It was started by Massimo Redaelli in 2007 when he had to create exams at the Polytechnic University of Milan as a research assistant. After he left University in 2010 the project began to stumble. From 2015 on the further development mainly takes place at the Institute for Electronics Engineering of the Friedrich-Alexander-Universität Erlangen-Nürnberg. CircuiTikZ is widely used for publications and books in the academic environment of electronics.CircuiTikZ is released under the LaTeX Project Public License and/or the GNU General Public License. |
Dirac comb Summary Dirac_comb This implies Because the Dirac comb function is periodic, it can be represented as a Fourier series based on the Dirichlet kernel: The Dirac comb function allows one to represent both continuous and discrete phenomena, such as sampling and aliasing, in a single framework of continuous Fourier analysis on tempered distributions, without any reference to Fourier series. The Fourier transform of a Dirac comb is another Dirac comb. Owing to the Convolution Theorem on tempered distributions which turns out to be the Poisson summation formula, in signal processing, the Dirac comb allows modelling sampling by multiplication with it, but it also allows modelling periodization by convolution with it. |
Gene expression programming Replication and selection Gene_expression_programming > The basic gene expression algorithm > Reproduction with modification > Replication and selection But the replication of strings is trivial in artificial evolutionary systems, where only an instruction to copy strings is required to pass all the information in the genome from generation to generation. The replication of the selected programs is a fundamental piece of all artificial evolutionary systems, but for evolution to occur it needs to be implemented not with the usual precision of a copy instruction, but rather with a few errors thrown in. Indeed, genetic diversity is created with genetic operators such as mutation, recombination, transposition, inversion, and many others. |
Acidity function Summary Acidity_function An acidity function is a measure of the acidity of a medium or solvent system, usually expressed in terms of its ability to donate protons to (or accept protons from) a solute (Brønsted acidity). The pH scale is by far the most commonly used acidity function, and is ideal for dilute aqueous solutions. Other acidity functions have been proposed for different environments, most notably the Hammett acidity function, H0, for superacid media and its modified version H− for superbasic media. The term acidity function is also used for measurements made on basic systems, and the term basicity function is uncommon. |
Symmetric fair cake-cutting Procedures Symmetric_fair_cake-cutting > Procedures Every procedure can be made "symmetric ex-ante" by randomization. For example, in the asymmetric divide-and-choose, the divider can be selected by tossing a coin. However, such a procedure is not symmetric ex-post. Therefore, the research regarding symmetric fair cake-cutting focuses on deterministic algorithms. |
Watt-hour meter Direct current Energy_meter > History > Direct current Thomas Edison at first worked on a direct current (DC) electromechanical meter with a direct reading register, but instead developed an electrochemical metering system, which used an electrolytic cell to totalise current consumption. At periodic intervals the plates were removed and weighed, and the customer billed. The electrochemical meter was labor-intensive to read and not well received by customers. |
Panopticon Software Technology overview Panopticon_Software > Technology overview Panopticon's technology relies on in-memory OLAP cubes, which are displayed through a series of visualizations including treemapping. This allows the user to load data, select variables and hierarchical structures, and navigate through the resultant visualization, filtering, zooming and drilling (sometimes called slicing and dicing), to identify outliers, correlations and trends. Its streaming OLAP implementation takes an in-memory OLAP cube and allows data to be streamed through it. This combination makes the company's products attractive to industry verticals that require live streaming data, such as financial market data, utility grid monitoring and telecommunications network traffic analysis. |
Amino acid residues Protein structure databases Protein_conformation > Protein structure databases A protein structure database is a database that is modeled around the various experimentally determined protein structures. The aim of most protein structure databases is to organize and annotate the protein structures, providing the biological community access to the experimental data in a useful way. Data included in protein structure databases often includes 3D coordinates as well as experimental information, such as unit cell dimensions and angles for x-ray crystallography determined structures. Though most instances, in this case either proteins or a specific structure determinations of a protein, also contain sequence information and some databases even provide means for performing sequence based queries, the primary attribute of a structure database is structural information, whereas sequence databases focus on sequence information, and contain no structural information for the majority of entries. Protein structure databases are critical for many efforts in computational biology such as structure based drug design, both in developing the computational methods used and in providing a large experimental dataset used by some methods to provide insights about the function of a protein. |
GAMESS (US) Abilities GAMESS_(US) > Abilities GAMESS (US) can perform several general computational chemistry calculations, including Hartree–Fock method, density functional theory (DFT), generalized valence bond (GVB), and multi-configurational self-consistent field (MCSCF). Correlation corrections after these SCF calculations can be estimated by configuration interaction (CI), second order Møller–Plesset perturbation theory (MP2), and coupled cluster (CC) theory. Solvent effect can be considered using quantum mechanics and molecular mechanics through discrete effective fragment potentials or continuum models (such as PCM). |
HTTP protocol HTTP data exchange HTTP_requests > HTTP data exchange HTTP is a stateless application-level protocol and it requires a reliable network transport connection to exchange data between client and server. In HTTP implementations, TCP/IP connections are used using well known ports (typically port 80 if the connection is unencrypted or port 443 if the connection is encrypted, see also List of TCP and UDP port numbers). In HTTP/2, a TCP/IP connection plus multiple protocol channels are used. In HTTP/3, the application transport protocol QUIC over UDP is used. |
C20H30BrNO3 Side effects C20H30BrNO3 > Side effects If ipratropium is inhaled, side effects resembling those of other anticholinergics are minimal. However, dry mouth and sedation have been reported. Also, effects such as skin flushing, tachycardia, acute angle-closure glaucoma, nausea, palpitations and headache have been observed. |
Laplace domain History Laplace_transforms > History From 1744, Leonhard Euler investigated integrals of the form as solutions of differential equations, but did not pursue the matter very far. Joseph-Louis Lagrange was an admirer of Euler and, in his work on integrating probability density functions, investigated expressions of the form which some modern historians have interpreted within modern Laplace transform theory.These types of integrals seem first to have attracted Laplace's attention in 1782, where he was following in the spirit of Euler in using the integrals themselves as solutions of equations. However, in 1785, Laplace took the critical step forward when, rather than simply looking for a solution in the form of an integral, he started to apply the transforms in the sense that was later to become popular. |
Electromagnetic wave equation Multipole expansion Electromagnetic_wave_equation > Solutions to the homogeneous electromagnetic wave equation > Multipole expansion Assuming monochromatic fields varying in time as e − i ω t {\displaystyle e^{-i\omega t}} , if one uses Maxwell's Equations to eliminate B, the electromagnetic wave equation reduces to the Helmholtz equation for E: with k = ω/c as given above. Alternatively, one can eliminate E in favor of B to obtain: A generic electromagnetic field with frequency ω can be written as a sum of solutions to these two equations. The three-dimensional solutions of the Helmholtz Equation can be expressed as expansions in spherical harmonics with coefficients proportional to the spherical Bessel functions. However, applying this expansion to each vector component of E or B will give solutions that are not generically divergence-free (∇ ⋅ E = ∇ ⋅ B = 0), and therefore require additional restrictions on the coefficients. |
BKT transition Disordered phases with different correlations Kosterlitz-Thouless_transition > XY model > Disordered phases with different correlations In the XY model in two dimensions, a second-order phase transition is not seen. However, one finds a low-temperature quasi-ordered phase with a correlation function (see statistical mechanics) that decreases with the distance like a power, which depends on the temperature. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a Kosterlitz–Thouless transition. It is a phase transition of infinite order. |
Capacitor AC circuits Parallel_plate_capacitor > Theory of operation > AC circuits The ratio of peak voltage to peak current is due to capacitive reactance (denoted XC). XC approaches zero as ω approaches infinity. If XC approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies. |
Linear variable differential transformer Operation Linear_variable_differential_transformer > Operation This voltage is in phase with the primary voltage. When the core moves in the other direction, the output voltage also increases from zero, but its phase is opposite to that of the primary. The phase of the output voltage determines the direction of the displacement (up or down) and amplitude indicates the amount of displacement. |
Hypergraph removal lemma Proof idea of the hypergraph removal lemma Hypergraph_removal_lemma > Proof idea of the hypergraph removal lemma The high level idea of the proof is similar to that of graph removal lemma. We prove a hypergraph version of Szemerédi's regularity lemma (partition hypergraphs into pseudorandom blocks) and a counting lemma (estimate the number of hypergraphs in an appropriate pseudorandom block). The key difficulty in the proof is to define the correct notion of hypergraph regularity. |
Elastic collision One-dimensional Newtonian Elastic_interaction > Equations > One-dimensional Newtonian In any collision, momentum is conserved; but in an elastic collision, kinetic energy is also conserved. Consider particles 1 and 2 with masses m1, m2, and velocities u1, u2 before collision, v1, v2 after collision. The conservation of momentum before and after the collision is expressed by: Likewise, the conservation of the total kinetic energy is expressed by: These equations may be solved directly to find v 1 , v 2 {\displaystyle v_{1},v_{2}} when u 1 , u 2 {\displaystyle u_{1},u_{2}} are known: If both masses are the same, we have a trivial solution: This simply corresponds to the bodies exchanging their initial velocities with each other.As can be expected, the solution is invariant under adding a constant to all velocities (Galilean relativity), which is like using a frame of reference with constant translational velocity. Indeed, to derive the equations, one may first change the frame of reference so that one of the known velocities is zero, determine the unknown velocities in the new frame of reference, and convert back to the original frame of reference. |
Henstock integral General Henstock_integral > References > General ISBN 978-0-8218-0845-0. A Modern Integration Theory in 21st Century Bartle, Robert G.; Sherbert, Donald R. (1999). |
Insulin therapy Dosage units Insulin_therapy > Dosage and timing > Dosage units The unit of insulin was set by the insulin committee at the University of Toronto. The unit evolved eventually to the old USP insulin unit, where one unit (U) of insulin was set equal to the amount of insulin required to reduce the concentration of blood glucose in a fasting rabbit to 45 m g/d L (2.5 m mol/L). Once the chemical structure and mass of insulin was known, the unit of insulin was defined by the mass of pure crystalline insulin required to obtain the USP unit. The unit of measurement used in insulin therapy is not part of the International System of Units (abbreviated SI) which is the modern form of the metric system. Instead the pharmacological international unit (IU) is defined by the WHO Expert Committee on Biological Standardization. |
Augustin-Jean Fresnel First attempt (1815) Augustin-Jean_Fresnel > Contributions to physical optics > Diffraction > First attempt (1815) On 12 July 1815, as Fresnel was about to leave Paris, Arago left him a note on a new topic: I do not know of any book that contains all the experiments that physicists are doing on the diffraction of light. M'sieur Fresnel will only be able to get to know this part of the optics by reading the work by Grimaldi, the one by Newton, the English treatise by Jordan, and the memoirs of Brougham and Young, which are part of the collection of the Philosophical Transactions. Fresnel would not have ready access to these works outside Paris, and could not read English. But, in Mathieu—with a point-source of light made by focusing sunlight with a drop of honey, a crude micrometer of his own construction, and supporting apparatus made by a local locksmith—he began his own experiments. |
24 (number) In number theory and algebra 24_(number) > In mathematics > In number theory and algebra 24 = 4!, the factorial of 4. It is the largest factorial that does not contain a trailing zero at the end of its digits (since factorial of any integer greater than 4 is divisible by both 2 and 5), and represents the number of ways to order 4 distinct items: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,3,4,2), (1,4,2,3), (1,4,3,2), (2,1,3,4), (2,1,4,3), (2,3,1,4), (2,3,4,1), (2,4,1,3), (2,4,3,1), (3,1,2,4), (3,1,4,2), (3,2,1,4), (3,2,4,1), (3,4,1,2), (3,4,2,1), (4,1,2,3), (4,1,3,2), (4,2,1,3), (4,2,3,1), (4,3,1,2), (4,3,2,1). 24 is the only nontrivial solution to the cannonball problem; that is, 12 + 22 + 32 + … + 242 is a perfect square (702). |
Entropy and life Objections Entropy_and_life > Objections Even in those physical systems where equilibrium could be relevant, (1) living systems cannot persist in isolation, and (2) the second principle of thermodynamics does not require that free energy be transformed into entropy along the shortest path: living organisms absorb energy from sunlight or from energy-rich chemical compounds and finally return part of such energy to the environment as entropy (generally in the form of heat and low free-energy compounds such as water and carbon dioxide). A contribution to this line of study, and an attempt to solve those conceptual limits, has been given by the Belgian scientist Ilya Prigogine throughout all his research, that lead him also to win the Nobel prize in 1977. One of his major contributions was the concept of dissipative system, which describes the thermodynamics of open systems in non-equilibrium states. |
Nullary operation Varying arity Nullary_operation > Examples > Varying arity In computer science, a function that accepts a variable number of arguments is called variadic. In logic and philosophy, predicates or relations accepting a variable number of arguments are called multigrade, anadic, or variably polyadic. |
History of scientific method Aristotle History_of_scientific_method > Early methodology > Aristotle This leads to the question of how the primary premises are found or developed, and as mentioned above, Aristotle allowed that induction would be required for this task. Towards the end of the Posterior Analytics, Aristotle discusses knowledge imparted by induction. Thus it is clear that we must get to know the primary premises by induction; for the method by which even sense-perception implants the universal is inductive. |
Flexibility method Advantages and disadvantages Flexibility_method > Advantages and disadvantages While the choice of redundant forces in (4) appears to be arbitrary and troublesome for automatic computation, this objection can be overcome by proceeding from (3) directly to (5) using a modified Gauss–Jordan elimination process. This is a robust procedure that automatically selects a good set of redundant forces to ensure numerical stability. It is apparent from the above process that the matrix stiffness method is easier to comprehend and to implement for automatic computation. It is also easier to extend for advanced applications such as non-linear analysis, stability, vibrations, etc. For these reasons, the matrix stiffness method is the method of choice for use in general purpose structural analysis software packages. |
Database index Column order Clustered_index > Column order Some databases can do this, others just won't use the index. In the phone book example with a composite index created on the columns (city, last_name, first_name), if we search by giving exact values for all the three fields, search time is minimal—but if we provide the values for city and first_name only, the search uses only the city field to retrieve all matched records. Then a sequential lookup checks the matching with first_name. So, to improve the performance, one must ensure that the index is created on the order of search columns. |
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