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In non-finite clauses (clauses in which the verb is left unconjugated), the relativizer appears as an object of preposition, or in other words, directly after a preposition in the sentence. These relative clauses appear to be introduced by the preposition itself, but they are actually introduced by both the preposition and the relativizer, since these two grammatical particles form a "prepositional phrase"; and it is this phrase that introduces the clause. For example: 35) A yard in which to have a party 36) The baker in whom to place your trust 37) A student *who to talk to us just walked in Note that (37) is ungrammatical because the relativizer introduces a non-finite relative clause, but it is not contained within a propositional phrase. | https://en.wikipedia.org/wiki/Relativizer |
In non-fuzzy clustering (also known as hard clustering), data are divided into distinct clusters, where each data point can only belong to exactly one cluster. In fuzzy clustering, data points can potentially belong to multiple clusters. For example, an apple can be red or green (hard clustering), but an apple can also be red AND green (fuzzy clustering). | https://en.wikipedia.org/wiki/Fuzzy_clustering |
Here, the apple can be red to a certain degree as well as green to a certain degree. Instead of the apple belonging to green and not red , the apple can belong to green and red . These value are normalized between 0 and 1; however, they do not represent probabilities, so the two values do not need to add up to 1. | https://en.wikipedia.org/wiki/Fuzzy_clustering |
In non-grey, non-white horses, the genes extension (MC1R) and agouti (ASIP) together determine whether a horse will be chestnut, bay or black.The agouti gene codes for a molecule called the agouti-signaling protein, or ASIP. The ASIP protein blocks the signal for black pigment production, causing the elimination of black eumelanin in hair, resulting in lighter colors. The dominant allele of ASIP (A) results in a horse with a red colored coat (bay), while the recessive allele (ee) results in a completely black horse.ASIP is not present everywhere, which allows some areas to be black while others are red. ASIP can also be limited by the phase of hair growth, allowing the tips of the hairs to be black while the base is red. | https://en.wikipedia.org/wiki/Equine_coat_color_genetics |
This can be observed in horses which have their winter coats clipped. When shaved close, the black tip is shorn off leaving the phaeomelanic bottom of the shaft. This produces a dull, orange-gold appearance on the body coat which is lost with the spring shed. | https://en.wikipedia.org/wiki/Equine_coat_color_genetics |
This is not usually seen in dark bays, which have little red in the hair shaft. A mutation to agouti removes the ability to block the black signal, resulting in a fully black horse. | https://en.wikipedia.org/wiki/Equine_coat_color_genetics |
The dominant, wildtype, allele of agouti is called A, and the non-agouti mutation is called a.The extension gene codes for a molecule called the Melanocortin 1 receptor, or MC1R. This receptor straddles the membrane of pigment cells, and when activated it signals the cell to produce black pigment instead of red. Extension does not affect skin color. The dominant, wildtype, allele of extension is called E, and the non-extension mutation is called e. Extension is epistatic to agouti, meaning that if a horse has two e alleles, it will be chestnut no matter what genotype it has at agouti. | https://en.wikipedia.org/wiki/Equine_coat_color_genetics |
In non-homogeneous media, the diffusion coefficient varies in space, D = D(x). This dependence does not affect Fick's first law but the second law changes: In anisotropic media, the diffusion coefficient depends on the direction. It is a symmetric tensor Dji = Dij. Fick's first law changes to it is the product of a tensor and a vector: For the diffusion equation this formula gives The symmetric matrix of diffusion coefficients Dij should be positive definite. | https://en.wikipedia.org/wiki/Diffusion_constant |
It is needed to make the right hand side operator elliptic. For inhomogeneous anisotropic media these two forms of the diffusion equation should be combined in The approach based on Einstein's mobility and Teorell formula gives the following generalization of Fick's equation for the multicomponent diffusion of the perfect components: where φi are concentrations of the components and Dij is the matrix of coefficients. | https://en.wikipedia.org/wiki/Diffusion_constant |
Here, indices i and j are related to the various components and not to the space coordinates.The Chapman–Enskog formulae for diffusion in gases include exactly the same terms. These physical models of diffusion are different from the test models ∂tφi = Σj Dij Δφj which are valid for very small deviations from the uniform equilibrium. Earlier, such terms were introduced in the Maxwell–Stefan diffusion equation. For anisotropic multicomponent diffusion coefficients one needs a rank-four tensor, for example Dij,αβ, where i, j refer to the components and α, β = 1, 2, 3 correspond to the space coordinates. | https://en.wikipedia.org/wiki/Diffusion_constant |
In non-human animal research, gender is commonly used to refer to the biological sex of the animals. According to biologist Michael J. Ryan, gender identity is a concept exclusively applied to humans. Also, in a letter Ellen Ketterson writes, "hen asked, my colleagues in the Department of Gender Studies agreed that the term gender could be properly applied only to humans, because it involves one's self-concept as man or woman. Sex is a biological concept; gender is a human social and cultural concept." | https://en.wikipedia.org/wiki/Gender |
However, Poiani (2010) notes that the question of whether behavioural similarities across species can be associated with gender identity or not is "an issue of no easy resolution", and suggests that mental states, such as gender identity, are more accessible in humans than other species due to their capacity for language. Polani suggests that the potential number of species with members possessing a gender identity must be limited due to the requirement for self-consciousness.Jacques Balthazart suggests that "there is no animal model for studying sexual identity. It is impossible to ask an animal, whatever its species, to what sex it belongs." | https://en.wikipedia.org/wiki/Gender |
He notes that "this would imply that the animal is aware of its own body and sex, which is far from proved", despite recent research demonstrating sophisticated cognitive skills among non-human primates and other species. Hird (2006) has also stated that whether or not non-human animals consider themselves to be feminine or masculine is a "difficult, if not impossible, question to answer", as this would require "judgements about what constitutes femininity or masculinity in any given species". Nonetheless, she asserts that "non-human animals do experience femininity and masculinity to the extent that any given species' behaviour is gender segregated. "Despite this, Poiani and Dixson emphasise the applicability of the concept of gender role to non-human animals such as rodents throughout their book. The concept of gender role has also been applied to non-human primates such as rhesus monkeys. | https://en.wikipedia.org/wiki/Gender |
In non-human animals, EEG signals are usually recorded using electrodes implanted in the brain; the majority of theta studies have involved electrodes implanted in the hippocampus. In humans, because invasive studies are not ethically permissible except in some neurological patients, the largest number of EEG studies have been conducted using electrodes glued to the scalp. The signals picked up by scalp electrodes are comparatively small and diffuse and arise almost entirely from the cerebral cortex for the hippocampus is too small and too deeply buried to generate recognizable scalp EEG signals. Human EEG recordings show clear theta rhythmicity in some situations, but because of the technical difficulties, it has been difficult to tell whether these signals have any relationship with the hippocampal theta signals recorded from other species. | https://en.wikipedia.org/wiki/Theta_rhythm |
In contrast to the situation in rats, where long periods of theta oscillations are easily observed using electrodes implanted at many sites, theta has been difficult to pin down in primates, even when intracortical electrodes have been available. Green and Arduini (1954), in their pioneering study of theta rhythms, reported only brief bursts of irregular theta in monkeys. Other investigators have reported similar results, although Stewart and Fox (1991) described a clear 7–9 Hz theta rhythm in the hippocampus of urethane-anesthetized macaques and squirrel monkeys, resembling the type 2 theta observed in urethane-anesthetized rats. | https://en.wikipedia.org/wiki/Theta_rhythm |
Most of the available information on human hippocampal theta comes from a few small studies of epileptic patients with intracranially implanted electrodes used as part of a treatment plan. In the largest and most systematic of these studies, Cantero et al. (2003) found that oscillations in the 4–7 Hz frequency range could be recorded from both the hippocampus and neocortex. The hippocampal oscillations were associated with REM sleep and the transition from sleep to waking, and came in brief bursts, usually less than a second long. | https://en.wikipedia.org/wiki/Theta_rhythm |
Cortical theta oscillations were observed during the transition from sleep and during quiet wakefulness; however, the authors were unable to find any correlation between hippocampal and cortical theta waves, and concluded that the two processes are probably controlled by independent mechanisms. Studies have shown an association of hypnosis with stronger theta-frequency activity as well as with changes to the gamma-frequency activity (Jensen et al., 2015). Also, increased theta waves have been seen in humans in 'no thought' meditation. | https://en.wikipedia.org/wiki/Theta_rhythm |
In non-human primates the following structural connections of the posterior cingulate cortex are well documented: Reciprocal connection with other regions of the posteromedial cortex. High connectivity to other paralimbic and limbic structures. Reciprocal connections to the medial temporal lobe. | https://en.wikipedia.org/wiki/Posterior_cingulate |
Dense connections to the hippocampal formation, the parahippocampal cortex, the ventromedial prefrontal cortex, and subgenual parts of the anterior cingulate cortex. Prominent connections to the areas of heteromodal association in the front, temporal and parietal lobes. Strong reciprocal connections to the dorsolateral prefrontal cortex (roughly Brodmann area 46) and the frontal poles (Brodmann areas 10 and 11). | https://en.wikipedia.org/wiki/Posterior_cingulate |
Less prominent connections to Brodmann areas 9/46, 8 and 9. Connections to the dorsal parts of the anterior cingulate cortex. Dense connections to the thalamus in the form of a continuous strip that crosses numerous pulvinar nuclei and the striatum.As is true in other areas of the posteromedial cortex, the posterior cingulate cortex has no apparent connections to primary sensory or motor areas. Thus, it is unlikely to be involved in low-level sensory or motor processing. | https://en.wikipedia.org/wiki/Posterior_cingulate |
In non-human primates, paternal investment is often dependent on the type of mating system exhibited by each species. Mating systems influence paternity certainty and the likelihood that a male is providing care towards his own biological offspring. Paternal certainty is high in monogamous pair-bonded species and males are less likely to be at risk for caring for unrelated offspring and not contributing to their own fitness. In contrast, polygamous primate societies create paternity uncertainty and males are more at risk of providing care for unrelated offspring and compromising their own fitness. | https://en.wikipedia.org/wiki/Paternal_care |
Paternal care by male non-human primates motivated by biological paternity utilize past mating history and phenotypic matching in order to recognize their own offspring. Comparing male care efforts exhibited by the same species can provide insight on the significant relationship between paternity certainty and the amount of paternal care exhibited by a male. For example, Siamangs (Symphalangus syndactylus) utilize both polyandrous and monogamous mating systems but, it was found that monogamous males are more likely to carry infants and contribute to parental duties compared to those in promiscuous mating systems. Studies in Primatology have used primate mating systems and social organization to help theorize the evolutionary significance of paternal care in Primates. | https://en.wikipedia.org/wiki/Paternal_care |
In non-human primates, the plasma half-life of the prodrug is 20 minutes, with the main metabolite being the nucleoside, GS-441524. Two hours post injection, the main metabolite GS-441524 is present at micromolar concentrations, whilst intact Remdesivir is no longer detectable. Because of this rapid extracellular conversion to the nucleoside GS-441524, some researchers have questioned whether the active nucleotide triphosphate is truly derived from Remdesivir pro-drug removal or whether it occurs by GS-441524 phosphorylation, and whether direct administration of GS-441524 would constitute a cheaper and easier to administer COVID‑19 drug compared to Remdesivir. The activated nucleotide triphosphate form has sustained intracellular levels in PBMC and presumably in other cells as well. | https://en.wikipedia.org/wiki/Remdesivir |
In non-human vertebrates, the parietal bones typically form the rear or central part of the skull roof, lying behind the frontal bones. In many non-mammalian tetrapods, they are bordered to the rear by a pair of postparietal bones that may be solely in the roof of the skull, or slope downwards to contribute to the back of the skull, depending on the species. In the living tuatara, and many fossil species, a small opening, the parietal foramen, lies between the two parietal bones. This opening is the location of a third eye in the midline of the skull, which is much smaller than the two main eyes. | https://en.wikipedia.org/wiki/Parietal_bone |
In non-indigenous use, the frog secretion is described and marketed as a "detox" treatment, cleanse, purge, and as a "vaccine", which is "good for everything". Kambo has been marketed both as a "scientific" remedy, emphasizing the biochemistry, and as a "spiritual" remedy, emphasizing its indigenous origins. Purging (deliberate vomiting) has been a popular treatment since the 1800s. "Detox" has been described by Edzard Ernst, emeritus professor of complementary medicine, as a term for conventional medical treatments for addiction, which has been "hijacked by entrepreneurs, quacks, and charlatans to sell a bogus treatment. "In Brazil, given the growth in the consumption of kambo in urban centers, there has been criticism by indigenous people, academics and communicators regarding the cultural appropriation of indigenous knowledge, the process of extracting the secretion of the Phyllomedusa bicolor frog, the form of transmission of wisdom, and the price charged by the ritual and the mystification of the origin of the frog.There is also concern about pharmacological patents on the peptides identified in kambo (see biopiracy), the commercialization of the kambo outside its place of origin, and the unknown impact on frog populations, since many more are now removed from their natural habitats.In light of the chemical complexity of the frog toxins, and their complex and potentially fatal effects, the authors of a 2022 review on the diagnosis and treatment of kambo cases said they urged "strict surveillance of the websites that encourage the use of this substance and urge greater control of e-commerce or illicit trafficking of animals and secretions, including through the dark web". | https://en.wikipedia.org/wiki/Kambo_cleanse |
In non-inertial coordinates, which include accelerated coordinates in special relativity and all coordinates in general relativity, the acceleration four-vector is related to the four-velocity through an absolute derivative with respect to proper time. In inertial coordinates the Christoffel symbols Γ λ μ ν {\displaystyle \Gamma ^{\lambda }{}_{\mu \nu }} are all zero, so this formula is compatible with the formula given earlier. In special relativity the coordinates are those of a rectilinear inertial frame, so the Christoffel symbols term vanishes, but sometimes when authors use curved coordinates in order to describe an accelerated frame, the frame of reference isn't inertial, they will still describe the physics as special relativistic because the metric is just a frame transformation of the Minkowski space metric. In that case this is the expression that must be used because the Christoffel symbols are no longer all zero. | https://en.wikipedia.org/wiki/Four-acceleration |
In non-inflammatory conditions, plasma albumin concentration, size, shape, and number of red blood cells, and the concentration of immunoglobulin can affect the ESR. Non-inflammatory conditions that can cause raised ESR include anemia, kidney failure, obesity, ageing, and female sex. ESR is also higher in women during menstruation and pregnancy. The value of ESR does not change whether dialysis is performed or not. Therefore, ESR is not a reliable measure of inflammation in those with kidney injuries as the ESR value is already elevated. | https://en.wikipedia.org/wiki/Erythrocyte_sedimentation_rate |
In non-linear digital video editing, as well as in video compositing software, a key frame is a frame used to indicate the beginning or end of a change made to a parameter. For example, a key frame could be set to indicate the point at which audio will have faded up or down to a certain level. | https://en.wikipedia.org/wiki/Key_frame |
In non-linear preferential attachment (NLPA), existing nodes in the network gain new edges proportionally to the node degree raised to a constant positive power, α {\displaystyle \alpha } . Formally, this means that the probability that node i {\displaystyle i} gains a new edge is given by p i = k i α ∑ j k j α . {\displaystyle p_{i}={\frac {k_{i}^{\alpha }}{\sum _{j}k_{j}^{\alpha }}}.} If α = 1 {\displaystyle \alpha =1} , NLPA reduces to the BA model and is referred to as "linear". | https://en.wikipedia.org/wiki/Terrorist_network_analysis |
If 0 < α < 1 {\displaystyle 0<\alpha <1} , NLPA is referred to as "sub-linear" and the degree distribution of the network tends to a stretched exponential distribution. If α > 1 {\displaystyle \alpha >1} , NLPA is referred to as "super-linear" and a small number of nodes connect to almost all other nodes in the network. For both α < 1 {\displaystyle \alpha <1} and α > 1 {\displaystyle \alpha >1} , the scale-free property of the network is broken in the limit of infinite system size. However, if α {\displaystyle \alpha } is only slightly larger than 1 {\displaystyle 1} , NLPA may result in degree distributions which appear to be transiently scale free. | https://en.wikipedia.org/wiki/Terrorist_network_analysis |
In non-magnetic electrical conductors like aluminum, nickel, or copper, an alternating electromagnetic field will induce Eddy currents in the material. These currents generate thermal energy through Joule heating. Ferromagnetic materials like iron and carbon steels will see heating from both Eddy current formation and Hysteresis losses. | https://en.wikipedia.org/wiki/Implant_induction_welding_of_thermoplastics |
In non-mammalian synapsids, the jaw is composed of four bony elements and referred to as a quadro-articular jaw because the joint is between the articular and quadrate bones. In therapsids (advanced synapsids including mammal), the jaw is simplified into an articulation between the dentary and the squamous part of the temporal bone, and hence referred to as a dentary-squamosal jaw. | https://en.wikipedia.org/wiki/Squamosal_bone |
In non-mammalian vertebrates, the zygomatic bone is referred to as the jugal bone, since these animals have no zygomatic arch. It is found in most reptiles, amphibians, and birds. It is connected to the quadratojugal and maxilla, as well as other bones, which may vary by species. This bone is considered key in the determination of general traits of the skull, as in the case of creatures, such as dinosaurs in paleontology, whose entire skull has not been found. | https://en.wikipedia.org/wiki/Zygomaticotemporal_foramen |
In coelacanths and early tetrapods the bone is relatively large. Here, it is a plate-like bone forming the lower margin of the orbit and much of the side of the face. In ray-finned fishes it is reduced or absent, and the entire cheek region is generally small. | https://en.wikipedia.org/wiki/Zygomaticotemporal_foramen |
The bone is also absent in living amphibians.With the exception of turtles, the jugal bone in reptiles forms a relatively narrow bar separating the orbit from the inferior temporal fenestra, of which it may also form the lower boundary. The bone is similarly reduced in birds. In mammals, it takes on broadly the form seen in humans, with the bar between the orbit and fenestra vanishing entirely, and only the lower boundary of the fenestra remaining, as the zygomatic arch. | https://en.wikipedia.org/wiki/Zygomaticotemporal_foramen |
In non-medical press and literature, the movie-character Indiana Jones has been used as an example of someone with ophidiophobia. == References == | https://en.wikipedia.org/wiki/Fear_of_snakes |
In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units. 1 foot = 12 inches,the relationship between square feet and square inches is 1 square foot = 144 square inches,where 144 = 122 = 12 × 12. Similarly: 1 square yard = 9 square feet 1 square mile = 3,097,600 square yards = 27,878,400 square feetIn addition, conversion factors include: 1 square inch = 6.4516 square centimetres 1 square foot = 0.09290304 square metres 1 square yard = 0.83612736 square metres 1 square mile = 2.589988110336 square kilometres | https://en.wikipedia.org/wiki/Area_formula |
In non-military applications shaped charges are used in explosive demolition of buildings and structures, in particular for cutting through metal piles, columns and beams and for boring holes. In steelmaking, small shaped charges are often used to pierce taps that have become plugged with slag. They are also used in quarrying, breaking up ice, breaking log jams, felling trees, and drilling post holes.Shaped charges are used most extensively in the petroleum and natural gas industries, in particular in the completion of oil and gas wells, in which they are detonated to perforate the metal casing of the well at intervals to admit the influx of oil and gas.A 4.5 kg (9.9 lb) shaped charge was used on the Hayabusa2 mission on asteroid 162173 Ryugu. The spacecraft dropped the explosive device onto the asteroid and detonated it with the spacecraft behind cover. The detonation dug a crater about 10 meters wide, to provide access to a pristine sample of the asteroid. | https://en.wikipedia.org/wiki/Shaped_charges |
In non-muscle cells, actin filaments are formed proximal to membrane surfaces. Their formation and turnover are regulated by many proteins, including: Filament end-tracking protein (e.g., formins, VASP, N-WASP) Filament-nucleator known as the Actin-Related Protein-2/3 (or Arp2/3) complex Filament cross-linkers (e.g., α-actinin, fascin, and fimbrin) Actin monomer-binding proteins profilin and thymosin β4 Filament barbed-end cappers such as Capping Protein and CapG, etc. Filament-severing proteins like gelsolin. Actin depolymerizing proteins such as ADF/cofilin.The actin filament network in non-muscle cells is highly dynamic. The actin filament network is arranged with the barbed-end of each filament attached to the cell's peripheral membrane by means of clamped-filament elongation motors, the above-mentioned "actoclampins", formed from a filament barbed-end and a clamping protein (formins, VASP, Mena, WASP, and N-WASP). | https://en.wikipedia.org/wiki/Actin_cytoskeleton |
The primary substrate for these elongation motors is profilin-actin-ATP complex which is directly transferred to elongating filament ends. The pointed-end of each filament is oriented toward the cell's interior. In the case of lamellipodial growth, the Arp2/3 complex generates a branched network, and in filopodia a parallel array of filaments is formed. | https://en.wikipedia.org/wiki/Actin_cytoskeleton |
In non-organic farming, a compromise between the use of artificial and organic fertilizers is common, often using inorganic fertilizers supplemented with the application of organics that are readily available such as the return of crop residues or the application of manure. Cover crops are also grown to enrich soil as a green manure through nitrogen fixation from the atmosphere; as well as phosphorus (through nutrient mobilization) content of soils. Fertilizer trees aid organic farming by bringing nutrients from the depths of the soil, and by assisting in the regulation of water usage.Leguminous cover crops or fertilizer trees are also grown to enrich soil as a green manure through nitrogen fixation from the atmosphere; as well as phosphorus (through nutrient mobilization) content of soils. | https://en.wikipedia.org/wiki/Organic_fertiliser |
In non-parametric statistics, the Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane (simple linear regression) by choosing the median of the slopes of all lines through pairs of points. It has also been called Sen's slope estimator, slope selection, the single median method, the Kendall robust line-fit method, and the Kendall–Theil robust line. It is named after Henri Theil and Pranab K. Sen, who published papers on this method in 1950 and 1968 respectively, and after Maurice Kendall because of its relation to the Kendall tau rank correlation coefficient.Theil-Sen regression has several advantages over Ordinary least squares regression. It is insensitive to outliers. | https://en.wikipedia.org/wiki/Median_slope |
It can be used for significance tests even when residuals are not normally distributed. It can be significantly more accurate than non-robust simple linear regression (least squares) for skewed and heteroskedastic data, and competes well against least squares even for normally distributed data in terms of statistical power. It has been called "the most popular nonparametric technique for estimating a linear trend". There are fast algorithms for efficiently computing the parameters. | https://en.wikipedia.org/wiki/Median_slope |
In non-parenchymal NBD, vascular complications such as cerebral venous thrombosis primarily occurs. Other distinct characteristics include intracranial aneurysm and extracranial aneurysm. In most cases, veins are much more likely to be affected than arteries. Venous sinus thrombosis is the most frequent vascular manifestation in NBD followed by cortical cerebral veins thrombosis. On the other hand, thrombosis and aneurysms of the large cerebral arteries are rarely reported. | https://en.wikipedia.org/wiki/Neuro-Behçet's_disease |
In non-phagocytic cells, oxidative burst products are used in intracellular signalling pathways. The generated ROS achieve this via shifting the cell redox state. This may be monitored by the ratio of the antioxidant enzyme glutathione to its oxidised product, glutathione disulphide (GSH:GSSG). Antioxidant enzymes counterbalance redox signalling by eliminating the involved molecules, importantly superoxide anion and nitric oxide. | https://en.wikipedia.org/wiki/Respiratory_burst |
Redox signalling is critical for normal processes such as proliferation, differentiation, as well as vascular function and neurotransmission. It is also involved in disease states such as cancer. The NADPH oxidase isoform NOX1 transiently produces a burst of superoxide in response to growth factor (e.g. EGF) stimulation of respective receptors. | https://en.wikipedia.org/wiki/Respiratory_burst |
Superoxide is dismutated to hydrogen peroxide at a rate close to the diffusion-limited rate. This spatial restriction for superoxide‘s dismutation allows for specificity of redox signalling. Specificity is also ensured by NOX1 localisation in specific microdomains in the cell’s plasma membrane. Through channels such as aquaporin or diffusion, hydrogen peroxide enters the cytosol. There, it oxidises the cysteine groups of redox-sensitive proteins, which can then transduce signals. | https://en.wikipedia.org/wiki/Respiratory_burst |
In non-photosynthetic eukaryotes such as animals, fungi, and protozoa, as well as the class Alphaproteobacteria of bacteria, it is produced by the enzyme ALA synthase, from glycine and succinyl-CoA. This reaction is known as the Shemin pathway, which occurs in mitochondria.In plants, algae, bacteria (except for the class Alphaproteobacteria) and archaea, it is produced from glutamic acid via glutamyl-tRNA and glutamate-1-semialdehyde. The enzymes involved in this pathway are glutamyl-tRNA synthetase, glutamyl-tRNA reductase, and glutamate-1-semialdehyde 2,1-aminomutase. This pathway is known as the C5 or Beale pathway. In most plastid-containing species, glutamyl-tRNA is encoded by a plastid gene, and the transcription, as well as the following steps of C5 pathway, take place in plastids. | https://en.wikipedia.org/wiki/Δ-aminolevulinic_acid |
In non-photosynthetic eukaryotes such as animals, insects, fungi, and protozoa, as well as the α-proteobacteria group of bacteria, the committed step for porphyrin biosynthesis is the formation of δ-aminolevulinic acid (δ-ALA, 5-ALA or dALA) by the reaction of the amino acid glycine with succinyl-CoA from the citric acid cycle. In plants, algae, bacteria (except for the α-proteobacteria group) and archaea, it is produced from glutamic acid via glutamyl-tRNA and glutamate-1-semialdehyde. The enzymes involved in this pathway are glutamyl-tRNA synthetase, glutamyl-tRNA reductase, and glutamate-1-semialdehyde 2,1-aminomutase. This pathway is known as the C5 or Beale pathway. | https://en.wikipedia.org/wiki/Porphyrin_ring |
Two molecules of dALA are then combined by porphobilinogen synthase to give porphobilinogen (PBG), which contains a pyrrole ring. Four PBGs are then combined through deamination into hydroxymethyl bilane (HMB), which is hydrolysed to form the circular tetrapyrrole uroporphyrinogen III. This molecule undergoes a number of further modifications. | https://en.wikipedia.org/wiki/Porphyrin_ring |
Intermediates are used in different species to form particular substances, but, in humans, the main end-product protoporphyrin IX is combined with iron to form heme. Bile pigments are the breakdown products of heme. The following scheme summarizes the biosynthesis of porphyrins, with references by EC number and the OMIM database. The porphyria associated with the deficiency of each enzyme is also shown: | https://en.wikipedia.org/wiki/Porphyrin_ring |
In non-procedural paradigms, goto is less relevant or completely absent. One of the main alternatives is message passing, which is of particular importance in concurrent computing, interprocess communication, and object oriented programming. In these cases, the individual components do not have arbitrary transfer of control, but the overall control may be scheduled in complex ways, such as via preemption. The influential languages Simula and Smalltalk were among the first to introduce the concepts of messages and objects. By encapsulating state data, object-oriented programming reduced software complexity to interactions (messages) between objects. | https://en.wikipedia.org/wiki/Goto_(command) |
In non-psychotic major depressive disorder (MDD), some SGAs have demonstrated significant efficacy as adjunctive agents; and, such agents include: Aripiprazole Brexpiprazole Cariprazine Olanzapine Quetiapine Ziprasidonewhereas only quetiapine has demonstrated efficacy as a monotherapy in non-psychotic MDD. Olanzapine/fluoxetine is an efficacious treatment in both psychotic and non-psychotic MDD.Aripiprazole, brexpiprazole, cariprazine, olanzapine, and quetiapine have been approved as adjunct treatment for MDD by the FDA in the United States. Quetiapine, lurasidone, and lumateperone have been approved, as monotherapies, for bipolar depression, but as of present, lurasidone has not been approved for MDD. | https://en.wikipedia.org/wiki/Second-generation_antipsychotic |
In non-relational systems, hierarchical databases, the distant counterpart of a table is a structured file, representing the rows of a table in each row of the file and each column in a row. This structure implies that a row can have repeating information, generally in the child data segments. Data are stored in sequence of physical records. | https://en.wikipedia.org/wiki/Database_table |
In non-relativistic classical mechanics, Newton's concept of "relative, apparent, and common time" can be used in the formulation of a prescription for the synchronization of clocks. Events seen by two different observers in motion relative to each other produce a mathematical concept of time that works sufficiently well for describing the everyday phenomena of most people's experience. In the late nineteenth century, physicists encountered problems with the classical understanding of time, in connection with the behavior of electricity and magnetism. Einstein resolved these problems by invoking a method of synchronizing clocks using the constant, finite speed of light as the maximum signal velocity. This led directly to the conclusion that observers in motion relative to one another measure different elapsed times for the same event. | https://en.wikipedia.org/wiki/Time_measurement |
In non-relativistic quantum mechanics, the probability current j of the wave function Ψ of a particle of mass m in one dimension is defined as where ℏ {\displaystyle \hbar } is the reduced Planck constant; Ψ ∗ {\displaystyle \Psi ^{*}} denotes the complex conjugate of the wave function; ℜ {\displaystyle \Re } denotes the real part; ℑ {\displaystyle \Im } denotes the imaginary part.Note that the probability current is proportional to a Wronskian W ( Ψ , Ψ ∗ ) . {\displaystyle W(\Psi ,\Psi ^{*}).} In three dimensions, this generalizes to where ∇ {\displaystyle \nabla } denotes the del or gradient operator. This can be simplified in terms of the kinetic momentum operator, to obtain These definitions use the position basis (i.e. for a wavefunction in position space), but momentum space is possible. | https://en.wikipedia.org/wiki/Probability_flux |
The quantum-mechanical propagator may also be found by using a path integral: K ( x , t ; x ′ , t ′ ) = ∫ exp D , {\displaystyle K(x,t;x',t')=\int \exp \leftD,} where the boundary conditions of the path integral include q(t) = x, q(t′) = x′. Here L denotes the Lagrangian of the system. The paths that are summed over move only forwards in time and are integrated with the differential D {\displaystyle D} following the path in time. | https://en.wikipedia.org/wiki/Feynman_propagator |
In non-relativistic quantum mechanics, the propagator lets one find the wave function of a system, given an initial wave function and a time interval. The new wave function is specified by the equation ψ ( x , t ) = ∫ − ∞ ∞ ψ ( x ′ , t ′ ) K ( x , t ; x ′ , t ′ ) d x ′ . {\displaystyle \psi (x,t)=\int _{-\infty }^{\infty }\psi (x',t')K(x,t;x',t')\,dx'.} If K(x, t; x′, t′) only depends on the difference x − x′, this is a convolution of the initial wave function and the propagator. | https://en.wikipedia.org/wiki/Feynman_propagator |
In non-relativistic quantum mechanics, the square modulus of the wavefunction ψ gives the probability density function ρ = |ψ|2. This is the Copenhagen interpretation, circa 1927. In RQM, while ψ(r, t) is a wavefunction, the probability interpretation is not the same as in non-relativistic QM. | https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics |
Some RWEs do not predict a probability density ρ or probability current j (really meaning probability current density) because they are not positive-definite functions of space and time. The Dirac equation does: ρ = ψ † ψ , j = ψ † γ 0 γ ψ ⇌ J μ = ψ † γ 0 γ μ ψ {\displaystyle \rho =\psi ^{\dagger }\psi ,\quad \mathbf {j} =\psi ^{\dagger }\gamma ^{0}{\boldsymbol {\gamma }}\psi \quad \rightleftharpoons \quad J^{\mu }=\psi ^{\dagger }\gamma ^{0}\gamma ^{\mu }\psi } where the dagger denotes the Hermitian adjoint (authors usually write ψ = ψ†γ0 for the Dirac adjoint) and Jμ is the probability four-current, while the Klein–Gordon equation does not: ρ = i ℏ 2 m c 2 ( ψ ∗ ∂ ψ ∂ t − ψ ∂ ψ ∗ ∂ t ) , j = − i ℏ 2 m ( ψ ∗ ∇ ψ − ψ ∇ ψ ∗ ) ⇌ J μ = i ℏ 2 m ( ψ ∗ ∂ μ ψ − ψ ∂ μ ψ ∗ ) {\displaystyle \rho ={\frac {i\hbar }{2mc^{2}}}\left(\psi ^{*}{\frac {\partial \psi }{\partial t}}-\psi {\frac {\partial \psi ^{*}}{\partial t}}\right)\,,\quad \mathbf {j} =-{\frac {i\hbar }{2m}}\left(\psi ^{*}\nabla \psi -\psi \nabla \psi ^{*}\right)\quad \rightleftharpoons \quad J^{\mu }={\frac {i\hbar }{2m}}(\psi ^{*}\partial ^{\mu }\psi -\psi \partial ^{\mu }\psi ^{*})} where ∂μ is the four-gradient. Since the initial values of both ψ and ∂ψ/∂t may be freely chosen, the density can be negative. | https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics |
Instead, what appears look at first sight a "probability density" and "probability current" has to be reinterpreted as charge density and current density when multiplied by electric charge. Then, the wavefunction ψ is not a wavefunction at all, but reinterpreted as a field. The density and current of electric charge always satisfy a continuity equation: ∂ ρ ∂ t + ∇ ⋅ J = 0 ⇌ ∂ μ J μ = 0 , {\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {J} =0\quad \rightleftharpoons \quad \partial _{\mu }J^{\mu }=0\,,} as charge is a conserved quantity. Probability density and current also satisfy a continuity equation because probability is conserved, however this is only possible in the absence of interactions. | https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics |
In non-relativistic quantum mechanics, the transmission coefficient and related reflection coefficient are used to describe the behavior of waves incident on a barrier. The transmission coefficient represents the probability flux of the transmitted wave relative to that of the incident wave. This coefficient is often used to describe the probability of a particle tunneling through a barrier. | https://en.wikipedia.org/wiki/Transmission_factor |
The transmission coefficient is defined in terms of the incident and transmitted probability current density J according to: T = J → t r a n s ⋅ n ^ J → i n c ⋅ n ^ , {\displaystyle T={\frac {{\vec {J}}_{\mathrm {trans} }\cdot {\hat {n}}}{{\vec {J}}_{\mathrm {inc} }\cdot {\hat {n}}}},} where J → i n c {\displaystyle {\vec {J}}_{\mathrm {inc} }} is the probability current in the wave incident upon the barrier with normal unit vector n ^ {\displaystyle {\hat {n}}} and J → t r a n s {\displaystyle {\vec {J}}_{\mathrm {trans} }} is the probability current in the wave moving away from the barrier on the other side. The reflection coefficient R is defined analogously: R = J → r e f l ⋅ ( − n ^ ) J → i n c ⋅ n ^ = | J r e f l | | J i n c | {\displaystyle R={\frac {{\vec {J}}_{\mathrm {refl} }\cdot \left(-{\hat {n}}\right)}{{\vec {J}}_{\mathrm {inc} }\cdot {\hat {n}}}}={\frac {|J_{\mathrm {refl} }|}{|J_{\mathrm {inc} }|}}} Law of total probability requires that T + R = 1 {\displaystyle T+R=1} , which in one dimension reduces to the fact that the sum of the transmitted and reflected currents is equal in magnitude to the incident current. For sample calculations, see rectangular potential barrier. | https://en.wikipedia.org/wiki/Transmission_factor |
In non-relativistic treatment, l {\displaystyle l} and s {\displaystyle s} are good quantum numbers but in relativistic quantum mechanics they are no longer good quantum numbers as L {\displaystyle L} and S {\displaystyle S} do not commute with H {\displaystyle H} (in Dirac theory). J = L + S {\displaystyle J=L+S} is a good quantum number in relativistic quantum mechanics as J {\displaystyle J} commutes with H {\displaystyle H} . | https://en.wikipedia.org/wiki/Good_quantum_number |
In non-residential buildings, the roof structure may be flat. Structural concrete is an alternative for flat roof construction. There are three main categories for such method: precast/prestressed, cast-in-place and shell. Within the precast/prestressed concrete roofing, the double tees are the most common products used for roof span up to 60 feet (18 m). | https://en.wikipedia.org/wiki/Double_tee |
In non-scanning, a single 2-D sensor output contains all spatial (x, y) and spectral (λ) data. HSI devices for non-scanning yield the full datacube at once, without any scanning. Figuratively speaking, a single snapshot represents a perspective projection of the datacube, from which its three-dimensional structure can be reconstructed. | https://en.wikipedia.org/wiki/Hyperspectral_imaging |
The most prominent benefits of these snapshot hyperspectral imaging systems are the snapshot advantage (higher light throughput) and shorter acquisition time. A number of systems have been designed, including computed tomographic imaging spectrometry (CTIS), fiber-reformatting imaging spectrometry (FRIS), integral field spectroscopy with lenslet arrays (IFS-L), multi-aperture integral field spectrometer (Hyperpixel Array), integral field spectroscopy with image slicing mirrors (IFS-S), image-replicating imaging spectrometry (IRIS), filter stack spectral decomposition (FSSD), coded aperture snapshot spectral imaging (CASSI), image mapping spectrometry (IMS), and multispectral Sagnac interferometry (MSI). However, computational effort and manufacturing costs are high. | https://en.wikipedia.org/wiki/Hyperspectral_imaging |
In an effort to reduce the computational demands and potentially the high cost of non-scanning hyperspectral instrumentation, prototype devices based on Multivariate Optical Computing have been demonstrated. These devices have been based on the Multivariate Optical Element spectral calculation engine or the Spatial Light Modulator spectral calculation engine. In these platforms, chemical information is calculated in the optical domain prior to imaging such that the chemical image relies on conventional camera systems with no further computing. As a disadvantage of these systems, no spectral information is ever acquired, i.e. only the chemical information, such that post processing or reanalysis is not possible. | https://en.wikipedia.org/wiki/Hyperspectral_imaging |
In non-segmental vitiligo (NSV), there is usually some form of symmetry in the location of the patches of depigmentation. New patches also appear over time and can be generalized over large portions of the body or localized to a particular area. Extreme cases of vitiligo, to the extent that little pigmented skin remains, are referred to as vitiligo universalis. NSV can come about at any age (unlike segmental vitiligo, which is far more prevalent in teenage years).Classes of non-segmental vitiligo include the following: Generalized vitiligo: the most common pattern, wide and randomly distributed areas of depigmentation Universal vitiligo: depigmentation encompasses most of the body Focal vitiligo: one or a few scattered macules in one area, most common in children Acrofacial vitiligo: fingers and periorificial areas Mucosal vitiligo: depigmentation of only the mucous membranes | https://en.wikipedia.org/wiki/Vitiligo |
In non-smooth method, unilateral interactions between bodies are fundamentally modelled by the Signorini condition for non-penetration, and impact laws are used to define the impact process. The Signorini condition can be expressed as the complementarity problem: g ≥ 0 , λ ≥ 0 , λ ⊥ g {\displaystyle g\geq 0,\quad \lambda \geq 0,\quad \lambda \perp g} , where g {\displaystyle g} denotes the distance between two bodies and λ {\displaystyle \lambda } denotes the contact force generated by the unilateral constraints, as shown in the figure below. Moreover, in terms of the concept of proximal point of convex theory, the Signorini condition can be equivalently expressed as: λ = p r o j R + ( λ − ρ g ) {\displaystyle \lambda ={\rm {proj}}_{\mathbb {R} ^{+}}(\lambda -\rho g)} , where ρ > 0 {\displaystyle \rho >0} denotes an auxiliary parameter, and p r o j C ( x ) {\displaystyle {\rm {proj}}_{\bf {C}}(x)} represents the proximal point in the set C {\displaystyle C} to the variable x {\displaystyle x} , defined as: p r o j C ( x ) = a r g m i n y ∈ C ‖ y − x ‖ {\displaystyle {\rm {proj}}_{\bf {C}}(x)={\rm {argmin}}_{y\in C}\|y-x\|} . Both the expressions above represent the dynamic behaviour of unilateral constraints: on the one hand, when the normal distance g N {\displaystyle g_{\rm {N}}} is above zero, the contact is open, which means that there is no contact force between bodies, λ = 0 {\displaystyle \lambda =0} ; on the other hand, when the normal distance g N {\displaystyle g_{\rm {N}}} is equal to zero, the contact is closed, resulting in λ ≥ 0 {\displaystyle \lambda \geq 0} . | https://en.wikipedia.org/wiki/Unilateral_contact |
When implementing non-smooth theory based methods, the velocity Signorini condition or the acceleration Signorini condition are actually employed in most cases. The velocity Signorini condition is expressed as: U N + ≥ 0 , λ ≥ 0 , U + λ = 0 {\displaystyle U_{\rm {N}}^{+}\geq 0,\quad \lambda \geq 0,\quad U^{+}\lambda =0} , where U N + {\displaystyle U_{\rm {N}}^{+}} denotes the relative normal velocity after impact. The velocity Signorini condition should be understood together with the previous conditions g ≥ 0 , λ ≥ 0 , λ ⊥ g {\displaystyle g\geq 0,\;\lambda \geq 0,\;\lambda \perp g} . | https://en.wikipedia.org/wiki/Unilateral_contact |
The acceleration Signorini condition is considered under closed contact ( g = 0 , U N + = 0 {\displaystyle g=0,U_{\rm {N}}^{+}=0} ), as: g ¨ ≥ 0 , λ ≥ 0 , g ¨ λ = 0 {\displaystyle {\ddot {g}}\geq 0,\quad \lambda \geq 0,\quad {\ddot {g}}\lambda =0} , where the overdots denote the second-order derivative with respect to time. When using this method for unilateral constraints between two rigid bodies, the Signorini condition alone is not enough to model the impact process, so impact laws, which give the information about the states before and after the impact, are also required. For example, when the Newton restitution law is employed, a coefficient of restitution will be defined as: e = − U N + / U N − {\displaystyle e=-{U_{\rm {N}}^{+}}/{U_{\rm {N}}^{-}}} , where U N − {\displaystyle U_{\rm {N}}^{-}} denotes the relative normal velocity before impact. | https://en.wikipedia.org/wiki/Unilateral_contact |
In non-standard analysis (which involves a hyperreal enlargement of the number system), the limit of a sequence ( a n ) {\displaystyle (a_{n})} can be expressed as the standard part of the value a H {\displaystyle a_{H}} of the natural extension of the sequence at an infinite hypernatural index n=H. Thus, lim n → ∞ a n = st ( a H ) . {\displaystyle \lim _{n\to \infty }a_{n}=\operatorname {st} (a_{H}).} Here, the standard part function "st" rounds off each finite hyperreal number to the nearest real number (the difference between them is infinitesimal). | https://en.wikipedia.org/wiki/Limit_(mathematics) |
This formalizes the natural intuition that for "very large" values of the index, the terms in the sequence are "very close" to the limit value of the sequence. Conversely, the standard part of a hyperreal a = {\displaystyle a=} represented in the ultrapower construction by a Cauchy sequence ( a n ) {\displaystyle (a_{n})} , is simply the limit of that sequence: st ( a ) = lim n → ∞ a n . {\displaystyle \operatorname {st} (a)=\lim _{n\to \infty }a_{n}.} In this sense, taking the limit and taking the standard part are equivalent procedures. | https://en.wikipedia.org/wiki/Limit_(mathematics) |
In non-standard analysis, a real-valued function f {\displaystyle f} of a real variable is microcontinuous at a point a {\displaystyle a} precisely if the difference f ∗ ( a + δ ) − f ∗ ( a ) {\displaystyle f^{*}(a+\delta )-f^{*}(a)} is infinitesimal whenever δ {\displaystyle \delta } is infinitesimal. Thus f {\displaystyle f} is continuous on a set A {\displaystyle A} in R {\displaystyle \mathbb {R} } precisely if f ∗ {\displaystyle f^{*}} is microcontinuous at every real point a ∈ A {\displaystyle a\in A} . Uniform continuity can be expressed as the condition that (the natural extension of) f {\displaystyle f} is microcontinuous not only at real points in A {\displaystyle A} , but at all points in its non-standard counterpart (natural extension) ∗ A {\displaystyle ^{*}A} in ∗ R {\displaystyle ^{*}\mathbb {R} } . Note that there exist hyperreal-valued functions which meet this criterion but are not uniformly continuous, as well as uniformly continuous hyperreal-valued functions which do not meet this criterion, however, such functions cannot be expressed in the form f ∗ {\displaystyle f^{*}} for any real-valued function f {\displaystyle f} . (see non-standard calculus for more details and examples). | https://en.wikipedia.org/wiki/Uniform_continuity |
In non-standard calculus the limit of a function is defined by: if and only if for all x ∈ R ∗ , {\displaystyle x\in \mathbb {R} ^{*},} f ∗ ( x ) − L {\displaystyle f^{*}(x)-L} is infinitesimal whenever x − a is infinitesimal. Here R ∗ {\displaystyle \mathbb {R} ^{*}} are the hyperreal numbers and f* is the natural extension of f to the non-standard real numbers. Keisler proved that such a hyperreal definition of limit reduces the quantifier complexity by two quantifiers. On the other hand, Hrbacek writes that for the definitions to be valid for all hyperreal numbers they must implicitly be grounded in the ε-δ method, and claims that, from the pedagogical point of view, the hope that non-standard calculus could be done without ε-δ methods cannot be realized in full. Bŀaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize Hrbacek's criticism as a "dubious lament". | https://en.wikipedia.org/wiki/Epsilon,_delta |
In non-synapsids, such as reptiles and crocodiles, teeth similar to canines may be termed "caniniform" ("canine-shaped") teeth. | https://en.wikipedia.org/wiki/Canine_teeth |
In non-technical terms, M-theory presents an idea about the basic substance of the universe. As of 2023, science has produced no experimental evidence to support the conclusion that M-theory is a description of the real world. Although a complete mathematical formulation of M-theory is not known, the general approach is the leading contender for a universal "Theory of Everything" that unifies gravity with other forces such as electromagnetism. M-theory aims to unify quantum mechanics with general relativity's gravitational force in a mathematically consistent way. In comparison, other theories such as loop quantum gravity are considered by physicists and researchers/students to be less elegant, because they posit gravity to be completely different from forces such as the electromagnetic force. | https://en.wikipedia.org/wiki/Introduction_to_M-theory |
In non-tropical climates, this heat-loving crop should be sown after all danger of frost has passed and the soil is warm. Seeds sown too early will rot before germination. Black-eyed peas are extremely drought tolerant, so excessive watering should be avoided.The crop is relatively free of pests and disease. | https://en.wikipedia.org/wiki/Black-eyed_pea |
Root-knot nematodes can be a problem, especially if crops are not rotated. As a nitrogen-fixing legume, fertilization can exclude nitrogen three weeks after germination. The blossom produces nectar plentifully, and large areas can be a source of honey. Because the bloom attracts a variety of pollinators, care must be taken in the application of insecticides to avoid label violations. After planting the pea, it should start to grow after 2–5 days. | https://en.wikipedia.org/wiki/Black-eyed_pea |
In nonattenuating media, the electric permittivity and refractive index are related by: where μ is the magnetic permeability of the medium; ε is the electric permittivity of the medium. "SI" refers to the SI system of units, while "cgs" refers to Gaussian-cgs units.In attenuating media, the same relation is used, but the permittivity is allowed to be a complex number, called complex electric permittivity: where ε is the complex electric permittivity of the medium. Squaring both sides and using the results of the previous section gives: | https://en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity |
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain Connes who was motivated by the Atiyah-Singer index theorem and sought its extension to 'noncommutative' spaces. Some authors refer to this notion as unbounded K-cycles or as unbounded Fredholm modules. | https://en.wikipedia.org/wiki/Spectral_triple |
In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independently introduced by Boris Tsygan (homology) and Alain Connes (cohomology) in the 1980s. These invariants have many interesting relationships with several older branches of mathematics, including de Rham theory, Hochschild (co)homology, group cohomology, and the K-theory. Contributors to the development of the theory include Max Karoubi, Yuri L. Daletskii, Boris Feigin, Jean-Luc Brylinski, Mariusz Wodzicki, Jean-Louis Loday, Victor Nistor, Daniel Quillen, Joachim Cuntz, Ryszard Nest, Ralf Meyer, and Michael Puschnigg. | https://en.wikipedia.org/wiki/Cyclic_cohomology |
In noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial changes, the same as the abstract elliptic operator introduced by Atiyah (1970). | https://en.wikipedia.org/wiki/Fredholm_module |
In noncommutative geometry, the JLO cocycle is a cocycle (and thus defines a cohomology class) in entire cyclic cohomology. It is a non-commutative version of the classic Chern character of the conventional differential geometry. In noncommutative geometry, the concept of a manifold is replaced by a noncommutative algebra A {\displaystyle {\mathcal {A}}} of "functions" on the putative noncommutative space. The cyclic cohomology of the algebra A {\displaystyle {\mathcal {A}}} contains the information about the topology of that noncommutative space, very much as the de Rham cohomology contains the information about the topology of a conventional manifold. The JLO cocycle is associated with a metric structure of non-commutative differential geometry known as a θ {\displaystyle \theta } -summable spectral triple (also known as a θ {\displaystyle \theta } -summable Fredholm module). | https://en.wikipedia.org/wiki/JLO_cocycle |
In nondenominational Christianity of the evangelical variety, the word "biblical" or "independent" often appears in the name of the church or denomination. The independence of the church is claimed and affiliation with a Christian denomination is infrequent, although there are fundamentalist denominations. | https://en.wikipedia.org/wiki/Christian_Fundamentalism |
In nondeterministic communication complexity, Alice and Bob have access to an oracle. After receiving the oracle's word, the parties communicate to deduce f ( x , y ) {\displaystyle f(x,y)} . The nondeterministic communication complexity is then the maximum over all pairs ( x , y ) {\displaystyle (x,y)} over the sum of number of bits exchanged and the coding length of the oracle word. Viewed differently, this amounts to covering all 1-entries of the 0/1-matrix by combinatorial 1-rectangles (i.e., non-contiguous, non-convex submatrices, whose entries are all one (see Kushilevitz and Nisan or Dietzfelbinger et al.)). The nondeterministic communication complexity is the binary logarithm of the rectangle covering number of the matrix: the minimum number of combinatorial 1-rectangles required to cover all 1-entries of the matrix, without covering any 0-entries. Nondeterministic communication complexity occurs as a means to obtaining lower bounds for deterministic communication complexity (see Dietzfelbinger et al.), but also in the theory of nonnegative matrices, where it gives a lower bound on the nonnegative rank of a nonnegative matrix. | https://en.wikipedia.org/wiki/Quantum_communication_complexity |
In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840–41 and 1846. | https://en.wikipedia.org/wiki/Poiseuille_equation |
The theoretical justification of the Poiseuille law was given by George Stokes in 1845.The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen–Poiseuille equation. Poiseuille's equation describes the pressure drop due to the viscosity of the fluid; other types of pressure drops may still occur in a fluid (see a demonstration here). | https://en.wikipedia.org/wiki/Poiseuille_equation |
For example, the pressure needed to drive a viscous fluid up against gravity would contain both that as needed in Poiseuille's law plus that as needed in Bernoulli's equation, such that any point in the flow would have a pressure greater than zero (otherwise no flow would happen). Another example is when blood flows into a narrower constriction, its speed will be greater than in a larger diameter (due to continuity of volumetric flow rate), and its pressure will be lower than in a larger diameter (due to Bernoulli's equation). However, the viscosity of blood will cause additional pressure drop along the direction of flow, which is proportional to length traveled (as per Poiseuille's law). Both effects contribute to the actual pressure drop. | https://en.wikipedia.org/wiki/Poiseuille_equation |
In nonlinear analysis, there are many definitions for a tangent cone, including the adjacent cone, Bouligand's contingent cone, and the Clarke tangent cone. These three cones coincide for a convex set, but they can differ on more general sets. | https://en.wikipedia.org/wiki/Tangent_cone |
In nonlinear control and stability theory, the Popov criterion is a stability criterion discovered by Vasile M. Popov for the absolute stability of a class of nonlinear systems whose nonlinearity must satisfy an open-sector condition. While the circle criterion can be applied to nonlinear time-varying systems, the Popov criterion is applicable only to autonomous (that is, time invariant) systems. | https://en.wikipedia.org/wiki/Popov_criterion |
In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion for linear time-invariant (LTI) systems. | https://en.wikipedia.org/wiki/Circle_criterion |
In nonlinear control, Aizerman's conjecture or Aizerman problem states that a linear system in feedback with a sector nonlinearity would be stable if the linear system is stable for any linear gain of the sector. This conjecture was proven false but led to the (valid) sufficient criteria on absolute stability. | https://en.wikipedia.org/wiki/Aizerman's_conjecture |
In nonlinear optics it is possible to reverse the destructive interference of so-called inhomogeneously broadened systems which contain a distribution of uncoupled subsystems with different resonance frequencies. For example, consider a four-wave-mixing experiment in which the first short laser pulse excites all transitions at t = 0 {\displaystyle t=0} . As a result of the destructive interference between the different frequencies the overall polarization decays to zero. A second pulse arriving at t = τ > 0 {\displaystyle t=\tau >0} is able to conjugate the phases of the individual microscopic polarizations, i.e., p → p ⋆ {\displaystyle p\rightarrow p^{\star }} , of the inhomogeneously broadened system. | https://en.wikipedia.org/wiki/Coherent_effects_in_semiconductor_optics |
The subsequent unperturbed dynamical evolution of the polarizations leads to rephasing such that all polarization are in phase at t = 2 τ {\displaystyle t=2\tau } which results in a measurable macroscopic signal. Thus, this so-called photon echo occurs since all individual polarizations are in phase and add up constructively at t = 2 τ {\displaystyle t=2\tau } . Since the rephasing is only possible if the polarizations remain coherent, the loss of coherence can be determined by measuring the decay of the photon echo amplitude with increasing time delay. | https://en.wikipedia.org/wiki/Coherent_effects_in_semiconductor_optics |
When photon echo experiments are performed in semiconductors with exciton resonances, it is essential to include many-body effects in the theoretical analysis since they may qualitatively alter the dynamics. For example, numerical solutions of the SBEs have demonstrated that the dynamical reduction of the band gap which originates from the Coulomb interaction among the photoexcited electrons and holes is able to generate a photon echo even for resonant excitation of a single discrete exciton resonance with a pulse of sufficient intensity.Besides the rather simple effect of inhomogeneous broadening, spatial fluctuations of the energy, i.e., disorder, which in semiconductor nanostructure may, e.g., arise from imperfection of the interfaces between different materials, can also lead to a decay of the photon echo amplitude with increasing time delay. | https://en.wikipedia.org/wiki/Coherent_effects_in_semiconductor_optics |
To consistently treat this phenomenon of disorder induced dephasing the SBEs need to be solved including biexciton correlations. As shown in Ref. such a microscopic theoretical approach is able to describe disorder induced dephasing in good agreement with experimental results. | https://en.wikipedia.org/wiki/Coherent_effects_in_semiconductor_optics |
In nonlinear optics, B-Integral is a measure of the nonlinear phase shift of light. It calculates the exponential growth of the least stable spatial frequency in a laser beam, and is the numerical equivalent of the nonlinear phase shift along the laser system's optical axis. In a multipass laser system as a cumulative measure of the nonlinear interaction, this integral is given by: B = 2 π λ ∫ n 2 I ( z ) d z {\displaystyle B={\frac {2\pi }{\lambda }}\int \!n_{2}I(z)\,dz\,} where I ( z ) {\displaystyle I(z)} is the optical intensity along the beam axis, z {\displaystyle z} the position in beam direction, and n 2 {\displaystyle n_{2}} the nonlinear index quantifying the Kerr nonlinearity. As n 2 I ( z ) {\displaystyle n_{2}I(z)} is the nonlinear change in the refractive index, one easily recognizes the B integral to be the total on-axis nonlinear phase shift accumulated in a passage through the device. The B integral is frequently used in the context of ultrafast amplifiers, e.g. for optical components such as the Pockels cell of a regenerative amplifier. | https://en.wikipedia.org/wiki/B_Integral |
In nonlinear optics, filament propagation is propagation of a beam of light through a medium without diffraction. This is possible because the Kerr effect causes an index of refraction change in the medium, resulting in self-focusing of the beam.Filamentary damage tracks in glass caused by laser pulses were first observed by Michael Hercher in 1964. Filament propagation of laser pulses in the atmosphere was observed in 1994 by Gérard Mourou and his team at University of Michigan. The balance between the self-focusing refraction and self-attenuating diffraction by ionization and rarefaction of a laser beam of terawatt intensities, created by chirped pulse amplification, in the atmosphere creates "filaments" which act as waveguides for the beam thus preventing divergence. | https://en.wikipedia.org/wiki/Filament_propagation |
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