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It is said that unification is decidable for a theory, if a unification algorithm has been devised for it that terminates for any input problem. It is said that unification is semi-decidable for a theory, if a unification algorithm has been devised for it that terminates for any solvable input problem, but may keep sea... | Wikipedia - Robinson's unification algorithm | null | null | null |
It is significant that the name logic is etymologically connected with the Greek word logos, which denotes both 'thought' and 'word' or 'discourse'. The significance of this etymological connection can be adequately appreciated if it is remembered that logic, in its rise and development in the western world, particular... | Wikipedia - Nyaya | null | null | null |
The essential features of logic in the Western tradition are well captured in the following statement by a famous logician Alonzo Church: Logic is the systematic study of the structure of propositions and of the general conditions of valid inference by a method, which abstracts from the content or matter of the proposi... | Wikipedia - Nyaya | null | null | null |
Thus, the basic features of Western logic are: It deals with a study of ‘propositions’, specially their ‘logical form’ as abstracted from their ‘content’ or ‘matter’. It deals with ‘general conditions of valid inference’, wherein the truth or otherwise of the premises have no bearing on the ‘logical soundness or validi... | Wikipedia - Nyaya | null | null | null |
The main concern of Western logic, in its entire course of development, has been one of systematising patterns of mathematical reasoning, with the mathematical objects being thought of as existing either in an independent ideal world or in a formal domain. Indian logic however, does not deal with ideal entities, such a... | Wikipedia - Nyaya | null | null | null |
Thus Indian logic is not concerned merely with making arguments in formal mathematics rigorous and precise, but attends to the much larger issue of providing rigour to the arguments encountered in natural sciences (including mathematics, which in Indian tradition has the attributes of a natural science and not that of ... | Wikipedia - Nyaya | null | null | null |
Indian ‘formal logic’ is thus not ‘formal’, in the sense generally understood: in Indian logic ‘form’ cannot be entirely separated from ‘content’. In fact, great care is exercised to exclude from logical discourse terms, which have no referential content. No statement, which is known to be false, is admitted as a premi... | Wikipedia - Nyaya | null | null | null |
Thus, the ‘method of indirect proof’ (reductio ad absurdum) is not accepted as a valid method−neither in Indian philosophy nor in Indian mathematics−for proving the existence of an entity whose existence is not demonstrable (even in principle) by other (direct) means of proof. Indian logic does not make any attempt to ... | Wikipedia - Nyaya | null | null | null |
It is sited on Capital Park in the same building (CPC4) as Syngenta UK (former Zeneca then ICI) near the eastern edge of Cambridge in Fulbourn, South Cambridgeshire. The site is also known as Fulbourn Technology Park. It is just south of the boundary with Teversham and the main east-west railway line. Health Education ... | Wikipedia - Health Data Insight | null | null | null |
It is sometimes alleged that the Greeks had no algebra, but this is inaccurate. By the time of Plato, Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them, and with this n... | Wikipedia - Greek geometric algebra | null | null | null |
"The application of areas" is only a part of geometric algebra and it is thoroughly covered in Euclid's Elements. An example of geometric algebra would be solving the linear equation a x = b c . {\displaystyle ax=bc.} | Wikipedia - Greek geometric algebra | null | null | null |
The ancient Greeks would solve this equation by looking at it as an equality of areas rather than as an equality between the ratios a: b {\displaystyle a:b} and c: x . {\displaystyle c:x.} The Greeks would construct a rectangle with sides of length b {\displaystyle b} and c , {\displaystyle c,} then extend a side of th... | Wikipedia - Greek geometric algebra | null | null | null |
It is sometimes suggested, for example by Ovádi, that metabolite channeling decreases the concentration of metabolite in free solution. However, it has also been argued that there is no net effect on the free concentration in steady-state conditions, a claim disputed by others. More recent authors consider this and oth... | Wikipedia - Metabolic channeling | null | null | null |
It is standard practice in physics to perform blinded data analysis. After data analysis is complete, one is allowed to unblind the data. A prior agreement to publish the data regardless of the results of the analysis may be made to prevent publication bias. | Wikipedia - Blinded study | null | null | null |
It is standard practice to refer to a statistical model, e.g., a linear or logistic models, when analyzing data from randomized experiments. However, the randomization scheme guides the choice of a statistical model. It is not possible to choose an appropriate model without knowing the randomization scheme. Seriously m... | Wikipedia - Inferential statistics | null | null | null |
It is still not fully understood why neurons die in ALS, but this neurodegeneration is thought to involve many different cellular and molecular processes. The genes known to be involved in ALS can be grouped into three general categories based on their normal function: protein degradation, the cytoskeleton, and RNA pro... | Wikipedia - Motor neurone disease | null | null | null |
It is thought that misfolded mutant SOD1 can cause misfolding and aggregation of wild-type SOD1 in neighboring neurons in a prion-like manner. Other protein degradation genes that can cause ALS when mutated include VCP, OPTN, TBK1, and SQSTM1. Three genes implicated in ALS that are important for maintaining the cytoske... | Wikipedia - Motor neurone disease | null | null | null |
The first to be discovered was TDP-43 protein, a nuclear protein that aggregates in the cytoplasm of motor neurons in almost all cases of ALS; however, mutations in TARDBP, the gene that codes for TDP-43, are a rare cause of ALS. FUS codes for FUS, another RNA-binding protein with a similar function to TDP-43, which ca... | Wikipedia - Motor neurone disease | null | null | null |
Once these mutant RNA-binding proteins are misfolded and aggregated, they may be able to misfold normal proteins both within and between cells in a prion-like manner. This also leads to decreased levels of RNA-binding protein in the nucleus, which may mean that their target RNA transcripts do not undergo normal process... | Wikipedia - Motor neurone disease | null | null | null |
The pathogenic mutation is a hexanucleotide repeat expansion (a series of six nucleotides repeated over and over); people with up to 30 repeats are considered normal, while people with hundreds or thousands of repeats can have familial ALS, frontotemporal dementia, or sometimes sporadic ALS. The three mechanisms of dis... | Wikipedia - Motor neurone disease | null | null | null |
Motor neurons are more sensitive to excitotoxicity than other types of neurons because they have a lower calcium-buffering capacity and a type of glutamate receptor (the AMPA receptor) that is more permeable to calcium. In ALS, there are decreased levels of excitatory amino acid transporter 2 (EAAT2), which is the main... | Wikipedia - Motor neurone disease | null | null | null |
It is straightforward to compute the components of a finite graph in linear time (in terms of the numbers of the vertices and edges of the graph) using either breadth-first search or depth-first search. In either case, a search that begins at some particular vertex v {\displaystyle v} will find the entire component con... | Wikipedia - Component (graph theory) | null | null | null |
Hopcroft & Tarjan (1973) describe essentially this algorithm, and state that it was already "well known".Connected-component labeling, a basic technique in computer image analysis, involves the construction of a graph from the image and component analysis on the graph. The vertices are the subset of the pixels of the i... | Wikipedia - Component (graph theory) | null | null | null |
Identifying the connected components of this graph allows additional processing to find more structure in those parts of the image or identify what kind of object is depicted. Researchers have developed component-finding algorithms specialized for this type of graph, allowing it to be processed in pixel order rather th... | Wikipedia - Component (graph theory) | null | null | null |
These algorithms take amortized time O ( α ( n ) ) {\displaystyle O(\alpha (n))} per operation, where adding vertices and edges and determining the component in which a vertex falls are both operations, and α {\displaystyle \alpha } is a very slowly growing inverse of the very quickly growing Ackermann function. One ap... | Wikipedia - Component (graph theory) | null | null | null |
It is straightforward to obtain quantitative expressions for time dilation and length contraction. Fig. 3-3 is a composite image containing individual frames taken from two previous animations, simplified and relabeled for the purposes of this section. To reduce the complexity of the equations slightly, there are a var... | Wikipedia - Invariant interval | null | null | null |
{\displaystyle c=1.} In Fig. 3-3a, segments OA and OK represent equal spacetime intervals. | Wikipedia - Invariant interval | null | null | null |
Time dilation is represented by the ratio OB/OK. The invariant hyperbola has the equation w = √x2 + k2 where k = OK, and the red line representing the world line of a particle in motion has the equation w = x/β = xc/v. A bit of algebraic manipulation yields O B = O K / 1 − v 2 / c 2 . | Wikipedia - Invariant interval | null | null | null |
{\textstyle OB=OK/{\sqrt {1-v^{2}/c^{2}}}.} The expression involving the square root symbol appears very frequently in relativity, and one over the expression is called the Lorentz factor, denoted by the Greek letter gamma γ {\displaystyle \gamma }: γ = 1 1 − v 2 / c 2 = 1 1 − β 2 {\displaystyle \gamma ={\frac {1}{\sqr... | Wikipedia - Invariant interval | null | null | null |
In Fig. 3-3b, segments OA and OK represent equal spacetime intervals. Length contraction is represented by the ratio OB/OK. The invariant hyperbola has the equation x = √w2 + k2, where k = OK, and the edges of the blue band representing the world lines of the endpoints of a rod in motion have slope 1/β = c/v. Event A h... | Wikipedia - Invariant interval | null | null | null |
It is straightforward to test whether a graph may be edge colored with one or two colors, so the first nontrivial case of edge coloring is testing whether a graph has a 3-edge-coloring. As Kowalik (2009) showed, it is possible to test whether a graph has a 3-edge-coloring in time O(1.344n), while using only polynomial ... | Wikipedia - Edge coloring | null | null | null |
Because edge coloring is NP-complete even for three colors, it is unlikely to be fixed parameter tractable when parametrized by the number of colors. However, it is tractable for other parameters. | Wikipedia - Edge coloring | null | null | null |
In particular, Zhou, Nakano & Nishizeki (1996) showed that for graphs of treewidth w, an optimal edge coloring can be computed in time O(nw(6w)w(w + 1)/2), a bound that depends superexponentially on w but only linearly on the number n of vertices in the graph. Nemhauser & Park (1991) formulate the edge coloring problem... | Wikipedia - Edge coloring | null | null | null |
It is synthesized in two chemical steps starting from 3'-chloro-propiophenone. The alpha position adjacent to the ketone is first brominated followed by nucleophilic displacement of the resulting alpha-bromoketone with t-butylamine and treated with hydrochloric acid to give bupropion as the hydrochloride salt in 75–85%... | Wikipedia - Bupropion | null | null | null |
It is tempting to simplify the recursive version given above by reducing the instances of recursive calls. For example, as: This implementation will succeed in producing all permutations but does not minimize movement. As the recursive call-stacks unwind, it results in additional swaps at each level. Half of these will... | Wikipedia - Heap's algorithm | null | null | null |
It is tempting to think that every non-convex polyhedron must have some vertices whose defect is negative, but this need not be the case. Two counterexamples to this are the small stellated dodecahedron and the great stellated dodecahedron, which have twelve convex points each with positive defects. A counterexample wh... | Wikipedia - Angular deficiency | null | null | null |
It is theoretically allowed, but the multiplet structure becomes automatically the same with that of an N=4 supersymmetric theory. So it is less often discussed compared to N=1,2,4 version. | Wikipedia - Super Poincaré algebra | null | null | null |
It is theorized that certain biological features of the Homo lineage have evolved over time as a means to mitigate injury from hand-to-hand combat. Facial robusticity, which includes traits such as jaw adductor muscle strength and brow ridge size, may offer a protective effect against combat. The jaw adductors stretch ... | Wikipedia - Street fighting | null | null | null |
It is thought that there are significant neuroanatomical differences among congenitally deaf humans versus those who become deaf later in life. Therefore, it is widely thought that research into the differences in connections and projections of neurons in deaf humans must block into two groups—congenitally deaf and dea... | Wikipedia - Sign language in the brain | null | null | null |
This heightened ratio is thought to exist due to less overall white matter in Heschl's gyrus and the Superior Temoral gyrus among deaf humans. Overall, the auditory cortices of deaf humans have an increased gray-white matter ratio as a result of the lack of auditory stimuli which is commonly thought to lead to less mye... | Wikipedia - Sign language in the brain | null | null | null |
Congenitally deaf humans have measurably higher volume of Calcarine cortex than hearing humans. The increased volume and size of visual cortices of deaf individuals can lead to heightened visual processing. Deaf humans have demonstrated, via event-related potential, an increased sensitivity and reactivity to new visual... | Wikipedia - Sign language in the brain | null | null | null |
It is thought to be polyestrous, with individuals capable of becoming pregnant throughout the year and no clearly defined breeding season. Females are capable of becoming pregnant at approximately one year of age. Pregnancy lasts a relatively long time considering the small body size of the species, at gestation length... | Wikipedia - Hairy-legged vampire bat | null | null | null |
Pups are born with their eyes open and a set of deciduous teeth. There are fewer deciduous teeth than permanent teeth (20 compared to 26), with a deciduous dental formula of 2.1.2.02.1.2.0 Females who have lost their pups will continue to lactate, and females have been observed nursing the young of unrelated females. P... | Wikipedia - Hairy-legged vampire bat | null | null | null |
Caves and mines are preferred roosts, though hollow trees may also be used. It is generally solitary, but may be found roosting in small groups of twelve or fewer individuals. | Wikipedia - Hairy-legged vampire bat | null | null | null |
Groups of up to 50 individuals have been reported, though. It will share its roosts with the common vampire bat, as well as other leaf-nosed bats. It was originally described to have a diploid karyotype of 28 chromosomes, but it actually has 32.It is sanguivorous, feeding on the blood of vertebrates. | Wikipedia - Hairy-legged vampire bat | null | null | null |
It was formerly believed to feed exclusively on birds. However, it has since been documented that it will feed on the blood of mammals, including humans and cattle. Previously thought to have not been a vector species for rabies due to exclusively feeding on bird blood, it is now a possibility that it can transmit rabi... | Wikipedia - Hairy-legged vampire bat | null | null | null |
It is to be decided whether a found improvement is to work only by the better fitness (Baldwinian learning) or whether also the individual is adapted accordingly (lamarckian learning). In the case of an EA, this would mean an adjustment of the genotype. This question has been controversially discussed for EAs in the li... | Wikipedia - Hybrid genetic algorithm | null | null | null |
It is topped by four silver-white clock faces with gilded hands and numerals. The animated sculpture underneath consists of a sunflower with 36 copper petals, partially obscuring an orchestra of six 'jewelled' players; three squirrels and three birds. At fifteen-minute intervals, a bell strikes followed by a performanc... | Wikipedia - Aqua Horological Tintinnabulator | null | null | null |
A two-metre diameter cobweb wheel carrying 'jewelled' butterflies and frogs rotates continuously during the daytime as does the 'Top Feature' which consists of three arms with 'jewelled' pendants: one is a flying fish ridden by a squirrel, the second is a squirrel pushing a pram with a bird's nest and birds above, the ... | Wikipedia - Aqua Horological Tintinnabulator | null | null | null |
Motive power is provided by four 230 Volt AC Parvalux geared motors (cobweb wheel, Top Feature, petals and orchestra) and two 230 Volt AC Crouzet synchronous motors (going and strike trains). The bell solenoid is powered by 240 Volt DC pulses. Electrical control of the motors is via 12 Volt DC relays. == References == | Wikipedia - Aqua Horological Tintinnabulator | null | null | null |
It is typically found at depths of 0–30 metres (0–98 ft), but may occur up to 150 m (490 ft), seen singly or in small groups near seagrass or over sandy bottoms, but sometimes in estuaries during the spring.It mainly feeds on shellfish, but also some plant material.Gilt-head bream are protandrous sequential hermaphrodi... | Wikipedia - Gilt-head bream | null | null | null |
It is uncertain how effective any solar geoengineering technique would be, due to the difficulties modeling their impacts and the complex nature of the global climate system. Certain efficacy issues are specific to stratospheric aerosols. Lifespan of aerosols: Tropospheric sulfur aerosols are short-lived. | Wikipedia - Stratospheric aerosol layer | null | null | null |
Delivery of particles into the lower stratosphere in the arctic will typically ensure that they remain aloft only for a few weeks or months, as air in this region is predominantly descending. To ensure endurance, higher-altitude delivery is needed, ensuring a typical endurance of several years by enabling injection int... | Wikipedia - Stratospheric aerosol layer | null | null | null |
Aerosol delivery: There are two proposals for how to create a stratospheric sulfate aerosol cloud, either through the release of a precursor gas (SO2) or the direct release of sulfuric acid (H2SO4) and these face different challenges. If SO2 gas is released it will oxidize to form H2SO4 and then condense to form drople... | Wikipedia - Stratospheric aerosol layer | null | null | null |
Simulations suggest that as the SO2 release rate is increased there would be diminishing returns on the cooling effect, as larger particles would be formed which have a shorter lifetime and are less effective scatterers of light. If H2SO4 is released directly then the aerosol particles would form very quickly and in pr... | Wikipedia - Stratospheric aerosol layer | null | null | null |
Strength of cooling: The magnitude of the effect of forcing from aerosols by decreasing insolation received at the surface is not completely certain, as its scientific modelling involves complex calculations due to different confounding factors and parameters such as optical properties, spatial and temporal distributio... | Wikipedia - Stratospheric aerosol layer | null | null | null |
It is unclear how long data on flash memory will persist under archival conditions (i.e., benign temperature and humidity with infrequent access with or without prophylactic rewrite). Datasheets of Atmel's flash-based "ATmega" microcontrollers typically promise retention times of 20 years at 85 °C (185 °F) and 100 year... | Wikipedia - Program-erase cycle | null | null | null |
It is undecidable whether a given first-order sentence can be realized by a finite undirected graph. This means that no algorithm can correctly answer this question for all sentences.Some first-order sentences are modeled by infinite graphs but not by any finite graph. For instance, the property of having exactly one v... | Wikipedia - Logic of graphs | null | null | null |
It is understood in the market, by both the sales engineer and his or her wary industrial client, that the sales portion of the sales engineering role inherently involves a conflict of interest (COI), because it is always possible that the ideal solutions could involve recommending a competitor's products or services. ... | Wikipedia - Sales engineering | null | null | null |
Nevertheless, sales engineers do usually provide real value to customers, which is why the role endures despite customers' apprehension. The customer's only motivation to participate in the encounter is to achieve return on investment (ROI) in one way or another. Toward that end, sales engineering increasingly relies o... | Wikipedia - Sales engineering | null | null | null |
It is unknown how long the rai stones have been used in Yap. Flat rocks up to 2000 years old have been found there, but the oldest does not resemble today's rai stones, and how they were used is not known.An alternative hypothesis for the origin of rai stones is that they may have evolved from smaller carved beads. Two... | Wikipedia - Rai stones | null | null | null |
However, there are small veins of marble, a crystalline calcite rocks of metamorphic origin, that has a sparkling appearance similar to that of the Palau flowstones. It has been conjectured that the Yapese originally came to value crystalline calcite from these sources before discovering the much more abundant deposits... | Wikipedia - Rai stones | null | null | null |
Excavations were carried out at the quarries of Omis Cave on the island of Oreor, Chelechol ra Orrak and Upper Orrak on the island of Orrak, and Metuker ra Bisech on the island of the same name. The first two sites, caves/coves that open on the beach, appear to have been exploited before contact with Europeans, althoug... | Wikipedia - Rai stones | null | null | null |
It is unknown how the body gets rid of cicutoxin. There is evidence that it has a long half-life in the body, because of a patient who was submitted in a hospital after eating a root of a Cicuta plant. The man was in the hospital for two days and still had a fuzzy feeling in his head two days after leaving the hospital... | Wikipedia - Cicutoxin | null | null | null |
It is unknown if, in the case of the disappearance of the "pure" dingo, the then-existing hybrids will alter the predation pressure on other species. It is also not clear what kind of place these dogs will have in the Australian ecosystem and research results on this topic are rare. However, it is considered probable t... | Wikipedia - Dingo–dog hybrid | null | null | null |
In addition these dogs also showed a preference for living prey, which lessened the efficacy of the baits. During studies in the Blue Mountains from March 2005 to April 2006 the main prey of the studied dogs consisted of red-necked wallabies, swamp wallabies, grey kangaroos, common wombats, common brushtail possums and... | Wikipedia - Dingo–dog hybrid | null | null | null |
The results indicated at a big hybrid population that exerted significant pressure on swamp wallabies and controlled outbreaks of the rabbit populations. According to David Jenkins, studies on wild dogs from the Kosciuszko National Park proofed that these dogs had about 75-80% content of dingo genes and filled in the r... | Wikipedia - Dingo–dog hybrid | null | null | null |
It is unknown whether or not men’s willingness and desire to perform oral sex on their female partners is an adaptation. Oral sex is not unique to humans, and it is proposed to serve a number of purposes relating to sperm competition risk. Some researchers have proposed that oral sex may serve to assess the reproductiv... | Wikipedia - Human sperm competition | null | null | null |
It is used as a binder of the sand when doing sand casting of all common metals. It allows for the rapid production of a strong mold or core by three main methods. Method 1 requires passing carbon dioxide gas through the mixture of sand and sodium silicate in the sand molding box or core box. The carbon dioxide gas rea... | Wikipedia - Soluble glass | null | null | null |
This provides adequate strength to remove the now hardened sand shape from the forming tool. Additional strength occurs as any unreacted sodium silicate in the sand shape dehydrates. Method 2 requires adding an ester (reaction product of an acid and an alcohol) to the mixture of sand and sodium silicate before it is pl... | Wikipedia - Soluble glass | null | null | null |
As the ester hydrolyzes from the water in the liquid sodium silicate, an acid is released which causes the liquid sodium silicate to gel. Once the gel has formed, it will dehydrate to a glassy phase due to syneresis. Commonly used esters include acetate esters of glycerol and ethylene glycol as well as carbonate esters... | Wikipedia - Soluble glass | null | null | null |
The higher the water solubility of the ester, the faster the hardening of the sand. Method 3 requires microwave energy to heat and dehydrate the mixture of sand and sodium silicate in the sand molding box or core box. The forming tools must be microwave transparent for this to work well. | Wikipedia - Soluble glass | null | null | null |
Because sodium silicate has a high dielectric constant, it absorbs microwave energy very rapidly. Fully dehydrated sand shapes can be produced in less than 1 minute of exposure to microwaves. | Wikipedia - Soluble glass | null | null | null |
This method produces the highest strength of sand shapes bonded with sodium silicate. Since the sodium silicate does not burn during casting (it can actually melt at pouring temperatures above 1800 degrees F.) it is common to add organic materials to provide for enhanced sand breakdown after casting. The additives incl... | Wikipedia - Soluble glass | null | null | null |
It is used in detergent auxiliaries such as complex sodium disilicate and modified sodium disilicate. The detergent granules gain their ruggedness from a coating of silicates. | Wikipedia - Soluble glass | null | null | null |
It is used to index fields that are neither ordering fields nor key fields (there is no assurance that the file is organized on key field or primary key field). One index entry for every tuple in the data file (dense index) contains the value of the indexed attribute and pointer to the block or record. | Wikipedia - Clustered index | null | null | null |
It is used to make inferences about an unknown population, by estimation and/or hypothesis testing. In other words, it is desirable to obtain parameters to describe the population of interest, but since the data is limited, it is necessary to make use of a representative sample in order to estimate them. With that, it ... | Wikipedia - Biostatistics | null | null | null |
Hypothesis testingHypothesis testing is essential to make inferences about populations aiming to answer research questions, as settled in "Research planning" section. Authors defined four steps to be set: The hypothesis to be tested: as stated earlier, we have to work with the definition of a null hypothesis (H0), that... | Wikipedia - Biostatistics | null | null | null |
But they must be defined before the experiment implementation. Significance level and decision rule: A decision rule depends on the level of significance, or in other words, the acceptable error rate (α). It is easier to think that we define a critical value that determines the statistical significance when a test stat... | Wikipedia - Biostatistics | null | null | null |
So, α also has to be predefined before the experiment. Experiment and statistical analysis: This is when the experiment is really implemented following the appropriate experimental design, data is collected and the more suitable statistical tests are evaluated. Inference: Is made when the null hypothesis is rejected or... | Wikipedia - Biostatistics | null | null | null |
It is pointed that the failure to reject H0 just means that there is not enough evidence to support its rejection, but not that this hypothesis is true.Confidence intervalsA confidence interval is a range of values that can contain the true real parameter value in given a certain level of confidence. The first step is ... | Wikipedia - Biostatistics | null | null | null |
It is usual for there to be some variation in the MPhys schemes, to allow for students to study the area of physics which most interests them. For example, Lancaster University's physics department offer the following schemes: MPhys Physics MPhys Physics, Astrophysics and Cosmology MPhys Physics with Particle Physics a... | Wikipedia - Master of Physics | null | null | null |
It is usually a simple matter to gain permission to perform a cultural field survey, especially a non-intrusive one. If the area is privately owned, the local laws may or may not require the landowners' co-operation. Permission for an intrusive form of survey may be more difficult to acquire, due to the fear of destroy... | Wikipedia - Archaeological survey | null | null | null |
It is usually assumed that the register consists of qubits. It is also generally assumed that registers are not density matrices, but that they are pure, although the definition of "register" can be extended to density matrices. An n {\displaystyle n} size quantum register is a quantum system comprising n {\displaystyl... | Wikipedia - Quantum register | null | null | null |
Qubits are 2-dimensional complex spaces ( C 2 {\displaystyle \mathbb {C} ^{2}} ), while qutrits are 3-dimensional complex spaces ( C 3 {\displaystyle \mathbb {C} ^{3}} ), et.c. For a register composed of N number of d-dimensional (or d-level) quantum systems we have the Hilbert space H = ( C d ) ⊗ N = C d ⊗ C d ⊗ ⋯ ⊗ C... | Wikipedia - Quantum register | null | null | null |
{\displaystyle {\mathcal {H}}=(\mathbb {C} ^{d})^{\otimes N}=\underbrace {\mathbb {C} ^{d}\otimes \mathbb {C} ^{d}\otimes \dots \otimes \mathbb {C} ^{d}} _{N{\text{ times}}}\cong \mathbb {C} ^{d^{N}}.} The registers quantum state can in the bra-ket notation be written | ψ ⟩ = ∑ k = 0 d N − 1 a k | k ⟩ = a 0 | 0 ⟩ + a 1... | Wikipedia - Quantum register | null | null | null |
The values a k {\displaystyle a_{k}} are probability amplitudes. Because of the Born rule and the 2nd axiom of probability theory, ∑ k = 0 d N − 1 | a k | 2 = 1 , {\displaystyle \sum _{k=0}^{d^{N}-1}|a_{k}|^{2}=1,} so the possible state space of the register is the surface of the unit sphere in C d N . {\displaystyle \... | Wikipedia - Quantum register | null | null | null |
Examples: The quantum state vector of a 5-qubit register is a unit vector in C 2 5 = C 32 . {\displaystyle \mathbb {C} ^{2^{5}}=\mathbb {C} ^{32}.} A register of four qutrits similarly is a unit vector in C 3 4 = C 81 . {\displaystyle \mathbb {C} ^{3^{4}}=\mathbb {C} ^{81}.} | Wikipedia - Quantum register | null | null | null |
It is very common in many fields, including engineering, physics and the study of differential equations, to use a notation that makes the flow implicit. Thus, x(t) is written for φ t ( x 0 ) , {\displaystyle \varphi ^{t}(x_{0}),} and one might say that the variable x depends on the time t and the initial condition x =... | Wikipedia - Flow (geometry) | null | null | null |
In the case of a flow of a vector field V on a smooth manifold X, the flow is often denoted in such a way that its generator is made explicit. For example, Φ V: X × R → X ; ( x , t ) ↦ Φ V t ( x ) . {\displaystyle \Phi _{V}\colon X\times \mathbb {R} \to X;\qquad (x,t)\mapsto \Phi _{V}^{t}(x).} | Wikipedia - Flow (geometry) | null | null | null |
It is very common that in an experimentally acquired set of data the values of some components of a given data point are missing. Rather than discarding the whole data point, it is common to "fill in" values for the missing components, a process called "imputation". | Wikipedia - Redundancy analysis | null | null | null |
It is very difficult to measure the absolute amount of any thermodynamic quantity involving the internal energy (e.g. enthalpy), since the internal energy of a substance can take many forms, each of which has its own typical temperature at which it begins to become important in thermodynamic reactions. It is therefore ... | Wikipedia - Enthalpy of transition | null | null | null |
All of these terms mean the molar heat content for a substance in its normal standard state above a reference temperature of 298.15 K. Data for gases is for the hypothetical ideal gas at the designated standard pressure. The SI unit for enthalpy is J/mol, and is a positive number above the reference temperature. The he... | Wikipedia - Enthalpy of transition | null | null | null |
The heat content of an ideal gas is independent of pressure (or volume), but the heat content of real gases varies with pressure, hence the need to define the state for the gas (real or ideal) and the pressure. Note that for some thermodynamic databases such as for steam, the reference temperature is 273.15 K (0 °C). T... | Wikipedia - Enthalpy of transition | null | null | null |
It is very difficult to reuse the heat which comes from air-cooled data centers. For this reason, data center infrastructures are more often equipped with heat pumps. An alternative to heat pumps is the adoption of liquid cooling throughout a data center. Different liquid cooling techniques are mixed and matched to all... | Wikipedia - Data centers | null | null | null |
It is very easy to misconstruct hardware or software devices which attempt to generate random numbers. Also, most 'break' silently, often producing decreasingly random numbers as they degrade. A physical example might be the rapidly decreasing radioactivity of the smoke detectors mentioned earlier, if this source were ... | Wikipedia - Quantum random number generator | null | null | null |
Methods that combine multiple sources of entropy are more robust. Because many entropy sources are often quite fragile, and fail silently, statistical tests on their output should be performed continuously. Many, but not all, such devices include some such tests into the software that reads the device. | Wikipedia - Quantum random number generator | null | null | null |
It is very probable there were planetary dials, as the complicated motions and periodicities of all planets are mentioned in the manual of the mechanism. The exact position and mechanisms for the gears of the planets is unknown. There is no coaxial system but only for the Moon. Fragment D that is an epicycloidal system... | Wikipedia - Antikythera mechanism | null | null | null |
The Sun gear is operated from the hand-operated crank (connected to gear a1, driving the large four-spoked mean Sun gear, b1) and in turn drives the rest of the gear sets. The Sun gear is b1/b2 and b2 has 64 teeth. It directly drives the date/mean sun pointer (there may have been a second, "true sun" pointer that displ... | Wikipedia - Antikythera mechanism | null | null | null |
In this discussion, reference is to modelled rotational period of various pointers and indicators; they all assume the input rotation of the b1 gear of 360 degrees, corresponding with one tropical year, and are computed solely on the basis of the gear ratios of the gears named.The Moon train starts with gear b1 and pro... | Wikipedia - Antikythera mechanism | null | null | null |
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