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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...
Relativizer
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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...
Fuzzy clustering
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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.
Fuzzy clustering
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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 bla...
Equine coat color genetics
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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.
Equine coat color genetics
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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.
Equine coat color genetics
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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. Extens...
Equine coat color genetics
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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 ten...
Diffusion constant
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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 perf...
Diffusion constant
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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 unifo...
Diffusion constant
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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...
Gender
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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 langua...
Gender
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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 femini...
Gender
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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 h...
Theta rhythm
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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, rep...
Theta rhythm
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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 co...
Theta rhythm
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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 as...
Theta rhythm
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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.
Posterior cingulate
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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...
Posterior cingulate
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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 ci...
Posterior cingulate
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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...
Paternal care
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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 amou...
Paternal care
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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 conve...
Remdesivir
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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...
Parietal bone
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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 (d...
Kambo cleanse
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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 {\displayst...
Four-acceleration
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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 ...
Erythrocyte sedimentation rate
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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.
Key frame
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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 . {\dis...
Terrorist network analysis
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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...
Terrorist network analysis
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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 ...
Implant induction welding of thermoplastics
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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 ...
Squamosal bone
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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 dete...
Zygomaticotemporal foramen
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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.
Zygomaticotemporal foramen
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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 se...
Zygomaticotemporal foramen
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In non-medical press and literature, the movie-character Indiana Jones has been used as an example of someone with ophidiophobia. == References ==
Fear of snakes
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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...
Area formula
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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 qu...
Shaped charges
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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...
Actin cytoskeleton
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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 par...
Actin cytoskeleton
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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 ...
Organic fertiliser
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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 ...
Median slope
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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 p...
Median slope
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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 manife...
Neuro-Behçet's disease
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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 coun...
Respiratory burst
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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) stimulatio...
Respiratory burst
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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...
Respiratory burst
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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 cla...
Δ-aminolevulinic acid
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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 ac...
Porphyrin ring
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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 ...
Porphyrin ring
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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 OMI...
Porphyrin ring
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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 co...
Goto (command)
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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/f...
Second-generation antipsychotic
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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 sequen...
Database table
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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 we...
Time measurement
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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 t...
Probability flux
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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 ove...
Feynman propagator
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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 }^{\inf...
Feynman propagator
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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.
Relativistic quantum mechanics
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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 {...
Relativistic quantum mechanics
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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 al...
Relativistic quantum mechanics
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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 u...
Transmission factor
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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 {\...
Transmission factor
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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
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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 use...
Double tee
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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 ...
Hyperspectral imaging
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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 fiel...
Hyperspectral imaging
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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 Lig...
Hyperspectral imaging
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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 remain...
Vitiligo
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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 \lamb...
Unilateral contact
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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...
Unilateral contact
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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 ...
Unilateral contact
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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...
Limit (mathematics)
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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_{...
Limit (mathematics)
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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 {\display...
Uniform continuity
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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 ext...
Epsilon, delta
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In non-synapsids, such as reptiles and crocodiles, teeth similar to canines may be termed "caniniform" ("canine-shaped") teeth.
Canine teeth
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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 i...
Introduction to M-theory
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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.
Black-eyed pea
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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 t...
Black-eyed pea
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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 t...
Mathematical descriptions of opacity
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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 suppl...
Spectral triple
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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...
Cyclic cohomology
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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).
Fredholm module
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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 alge...
JLO cocycle
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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.
Christian Fundamentalism
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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...
Quantum communication complexity
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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 s...
Poiseuille equation
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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...
Poiseuille equation
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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 in...
Poiseuille equation
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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.
Tangent cone
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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 Popo...
Popov criterion
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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.
Circle criterion
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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.
Aizerman's conjecture
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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 transi...
Coherent effects in semiconductor optics
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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 construc...
Coherent effects in semiconductor optics
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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 whic...
Coherent effects in semiconductor optics
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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.
Coherent effects in semiconductor optics
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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 ...
B Integral
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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 obser...
Filament propagation