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In this correspondence, an intermediate field E is assigned D e r E ( F , F ) ⊂ D e r K ( F , F ) {\displaystyle Der_{E}(F,F)\subset Der_{K}(F,F)} . Conversely, a subspace V ⊂ D e r K ( F , F ) {\displaystyle V\subset Der_{K}(F,F)} satisfying appropriate further conditions is mapped to { x ∈ F , f ( x ) = 0 ∀ f ∈ V } {... | Wikipedia - Galois group of a polynomial - Inseparable extensions |
In the form of "rocks all the way down", the saying dates to at least 1838, when it was printed in an unsigned anecdote in the New-York Mirror about a schoolboy and an old woman living in the woods: "The world, marm," said I, anxious to display my acquired knowledge, "is not exactly round, but resembles in shape a flat... | Wikipedia - Turtles all the way down - Modern form |
"Why, on another, to be sure!" "But what supports the last?" | Wikipedia - Turtles all the way down - Modern form |
"Lud! child, how stupid you are! There's rocks all the way down!" | Wikipedia - Turtles all the way down - Modern form |
A version of the saying in its "turtle" form appeared in an 1854 transcript of remarks by preacher Joseph Frederick Berg addressed to Joseph Barker: My opponent's reasoning reminds me of the heathen, who, being asked on what the world stood, replied, "On a tortoise." But on what does the tortoise stand? "On another tor... | Wikipedia - Turtles all the way down - Modern form |
With Mr. Barker, too, there are tortoises all the way down. (Vehement and vociferous applause.) Many 20th-century attributions claim that philosopher and psychologist William James is the source of the phrase. | Wikipedia - Turtles all the way down - Modern form |
James referred to the fable of the elephant and tortoise several times, but told the infinite regress story with "rocks all the way down" in his 1882 essay, "Rationality, Activity and Faith": Like the old woman in the story who described the world as resting on a rock, and then explained that rock to be supported by an... | Wikipedia - Turtles all the way down - Modern form |
"Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it's wrong. I've got a better theory," said the little old lady. "And what is that, madam?" | Wikipedia - Turtles all the way down - Modern form |
inquired James politely. "That we live on a crust of earth which is on the back of a giant turtle." Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of h... | Wikipedia - Turtles all the way down - Modern form |
"If your theory is correct, madam," he asked, "what does this turtle stand on?" "You're a very clever man, Mr. James, and that's a very good question," replied the little old lady, "but I have an answer to it. And it's this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under ... | Wikipedia - Turtles all the way down - Modern form |
"But what does this second turtle stand on?" persisted James patiently. To this, the little old lady crowed triumphantly, "It's no use, Mr. James—it's turtles all the way down." | Wikipedia - Turtles all the way down - Modern form |
In the form of fibers, PLA is used for monofilament fishing line and netting for vegetation and weed prevention. It is used for sandbags, planting pots, binding tape and ropes . | Wikipedia - Poly(lactic acid) - Agricultural |
In the form of pilocarpine, muscarinic receptor agonists have been used medically for a short time. M3 agonists Aceclidine, for glaucoma Arecoline, an alkaloid present in the Betel nut Pilocarpine is a drug that acts as a muscarinic receptor agonist that is used to treat glaucoma Cevimeline (AF102B) (Evoxac®) is a musc... | Wikipedia - Muscarinic agonists - M3 |
In the form of the Zimbabwe Bird, it is the national bird of Zimbabwe and appears on the Zimbabwean flag. The bird also figures in the coats of arms of Malawi, Namibia, Zambia, and South Sudan, and on the Zambian flag. | Wikipedia - African fish eagle - Heraldry |
In the form stated here, the splitting lemma does not hold in the full category of groups, which is not an abelian category. | Wikipedia - Splitting lemma - Non-abelian groups |
In the formal language of first-order logic, set A {\displaystyle A} has the property of being inhabited if ∃ z . ( z ∈ A ) . {\displaystyle \exists z. (z\in A).} | Wikipedia - Inhabited set - Definition |
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: ∀ A ∀ B ( ∀ X ( X ∈ A ⟺ X ∈ B ) ⟹ A = B ) {\displaystyle \forall A\,\forall B\,(\forall X\,(X\in A\iff X\in B)\implies A=B)} or in words: Given any set A and any set B, if for every set X, X is a member of A if and only if X is a member of B, then ... | Wikipedia - Axiom of extension - Formal statement |
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: ∀ A ∀ B ∃ C ∀ D {\displaystyle \forall A\,\forall B\,\exists C\,\forall D\,} In words: Given any object A and any object B, there is a set C such that, given any object D, D is a member of C if and only if D is equal to A or D is equal to B.Or in ... | Wikipedia - Axiom of pairing - Formal statement |
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: ∀ A ∃ B ∀ c ( c ∈ B ⟺ ∃ D ( c ∈ D ∧ D ∈ A ) ) {\displaystyle \forall A\,\exists B\,\forall c\,(c\in B\iff \exists D\,(c\in D\land D\in A)\,)} or in words: Given any set A, there is a set B such that, for any element c, c is a member of B if and onl... | Wikipedia - Axiom of union - Formal statement |
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: ∃ I ( ∅ ∈ I ∧ ∀ x ∈ I ( ( x ∪ { x } ) ∈ I ) ) . {\displaystyle \exists \mathbf {I} \,(\emptyset \in \mathbf {I} \,\land \,\forall x\in \mathbf {I} \,(\,(x\cup \{x\})\in \mathbf {I} )).} In words, there is a set I (the set that is postulated to be i... | Wikipedia - Inductive set (axiom of infinity) - Formal statement |
In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: ∃ x ∀ y ¬ ( y ∈ x ) {\displaystyle \exists x\,\forall y\,\lnot (y\in x)} or in words: There is a set such that no element is a member of it. | Wikipedia - Axiom of empty set - Formal statement |
In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the fact that it decomposes into a string from that same language (on the left) and a suffix (on the right). For instance, 1 + 2 + 3 {\displaystyle 1+2+3} can be recogni... | Wikipedia - Left recursion - Summary |
In the formal limit where μ → 0, the equations of motion approach Born–Oppenheimer molecular dynamics. | Wikipedia - Car–Parrinello molecular dynamics - Born–Oppenheimer limit |
In the formal rules of mourning dress in Georgian, Victorian, and Edwardian Britain, lavender was one of the few colors generally considered acceptable for women's clothing during the period of half-mourning, during which the bereaved was considered to still be in mourning and required to dress in sober, muted tones, b... | Wikipedia - Lavender blush - Fashion |
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. | Wikipedia - Universe of discourse - Summary |
In the formalism of particle theories, charge-like quantum numbers can sometimes be inverted by means of a charge conjugation operator called C. Charge conjugation simply means that a given symmetry group occurs in two inequivalent (but still isomorphic) group representations. It is usually the case that the two charge... | Wikipedia - Charge (physics) - Charge conjugation |
{\displaystyle 2\otimes {\overline {2}}=3\oplus 1.\ } That is, the product of two (Lorentz) spinors is a (Lorentz) vector and a (Lorentz) scalar. Note that the complex Lie algebra sl(2,C) has a compact real form su(2) (in fact, all Lie algebras have a unique compact real form). The same decomposition holds for the comp... | Wikipedia - Charge (physics) - Charge conjugation |
The decomposition is given by the Clebsch–Gordan coefficients. A similar phenomenon occurs in the compact group SU(3), where there are two charge-conjugate but inequivalent fundamental representations, dubbed 3 {\displaystyle 3} and 3 ¯ {\displaystyle {\overline {3}}} , the number 3 denoting the dimension of the repres... | Wikipedia - Charge (physics) - Charge conjugation |
The Kronecker product of the two gives 3 ⊗ 3 ¯ = 8 ⊕ 1. {\displaystyle 3\otimes {\overline {3}}=8\oplus 1.\ } That is, an eight-dimensional representation, the octet of the eight-fold way, and a singlet. | Wikipedia - Charge (physics) - Charge conjugation |
The decomposition of such products of representations into direct sums of irreducible representations can in general be written as Λ ⊗ Λ ′ = ⨁ i L i Λ i {\displaystyle \Lambda \otimes \Lambda '=\bigoplus _{i}{\mathcal {L}}_{i}\Lambda _{i}} for representations Λ {\displaystyle \Lambda } . The dimensions of the represent... | Wikipedia - Charge (physics) - Charge conjugation |
In the formation of a glass-ceramic-to-metal seal, the parts to be joined are first heated, normally under inert atmosphere, in order to melt the glass and allow it to wet and flow into the metal parts, in much the same way as when preparing a more conventional glass-to-metal seal. The temperature is then normally redu... | Wikipedia - Glass-ceramic-to-metal seal - Process |
In the formation of gene families, four levels of duplication exist: 1) exon duplication and shuffling, 2) entire gene duplication, 3) multigene family duplication, and 4) whole genome duplication. Exon duplication and shuffling gives rise to variation and new genes. Genes are then duplicated to form multigene families... | Wikipedia - Multigene family - Duplication |
Whole genome duplication doubles the number of copies of every gene and gene family. Whole genome duplication or polyploidization can be either autopolyploidization or alloploidization. Autopolyploidization is the duplication of the same genome and allopolyploidization is the duplication of two closely related genomes ... | Wikipedia - Multigene family - Duplication |
In the formation of general principles of intelligent behavior, Pfeifer intended to be contrary to older principles given in traditional artificial intelligence. The most dramatic difference is that the principles are applicable only to situated robotic agents in the real world, a domain where traditional artificial in... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
The internal processing needed for some bad architectures can grow out of proportion to new tasks needed of an agent. One of the primary reasons for scalability problems is that the amount of programming and knowledge engineering that the robot designers have to perform grows very rapidly with the complexity of the rob... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
The proposed solutions are to have the agent exploit the inherent physics of its environment, to exploit the constraints of its niche, and to have agent morphology based on parsimony and the principle of Redundancy. Redundancy reflects the desire for the error-correction of signals afforded by duplicating like channels... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
(See redundant modalities). In terms of design, this implies that redundancy should be introduced with respect not only to one sensory modality but to several. | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
: 448 It has been suggested that the fusion and transfer of knowledge between modalities can be the basis of reducing the size of the sense data taken from the real world. This again addresses the scalability problem. Principle of parallel, loosely-coupled processes: An alternative to hierarchical methods of knowledge ... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
This design principle differs most importantly from the Sense-Think-Act cycle of traditional AI. Since it does not involve this famous cycle, it is not affected by the frame problem. | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
Principle of sensory-motor coordination: Ideally, internal mechanisms in an agent should give rise to things like memory and choice-making in an emergent fashion, rather than being prescriptively programmed from the beginning. These kinds of things are allowed to emerge as the agent interacts with the environment. The ... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
Principle of ecological balance: This is more a theory than a principle, but its implications are widespread. Its claim is that the internal processing of an agent cannot be made more complex unless there is a corresponding increase in complexity of the motors, limbs, and sensors of the agent. In other words, the extra... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
The robot's morphology must already contain the complexity in itself to allow enough "breathing room" for more internal processing to develop. Value principle: This was the architecture developed in the Darwin III robot of Gerald Edelman. It relies heavily on connectionism. | Wikipedia - Embodied cognitive science - General principles of intelligent behavior |
In the formation of quasicrystals, a 15-site truncated pentagonal bipyramid structure may form the nucleus of larger structures with five-fold or icosahedral symmetry. == References == | Wikipedia - Pentagonal bifrustum - Application |
In the former AFL (North American Arena Football League), a drop-kicked extra point was worth two points, rather than one point, while a drop-kicked field goal counted for four points rather than three. The most recent conversion of a drop kick was by Geoff Boyer of the Pittsburgh Power on June 16, 2012; it was the fir... | Wikipedia - Drop kick - Arena football |
In the former Federal District of Mexico, an area that is officially equivalent to Mexico City, 323 Septimus of the Civil Code prohibited a family member from transforming the conscience of a minor so as to prevent, hinder or interfere with the minor's relationship with one of the minor's parents. If a court found that... | Wikipedia - Parental alienation - Mexico |
In the former German capital Berlin, surrounded by Soviet-occupied Germany, Stalin instituted the Berlin Blockade on 24 June 1948, preventing food, materials and supplies from arriving in West Berlin. The blockade was caused, in part, by early local elections of October 1946 in which the Socialist Unity Party of German... | Wikipedia - Eastern Bloc - Berlin blockade and airlift |
In the former Portuguese territory of Macau, Fok Lei and its successor Transmac used second-hand double-deckers widely from the early 1970s until the late 1980s. | Wikipedia - Double decker bus - Macau |
In the former Soviet Union and other countries-members of OIRT, frequencies from 76 MHz to 100 MHz were designated for broadcast television usage. Considering 8 MHz channel bandwidth used by the Russian analog television system (System D), the following television channels had been defined: Broadcast television channel... | Wikipedia - Band II - Usage in Russia and in other former members of OIRT |
In the former Soviet Union many patients with negligible radioactive exposure after the Chernobyl disaster displayed extreme anxiety about low level radiation exposure, and therefore developed many psychosomatic problems, with an increase in fatalistic alcoholism also being observed. As Japanese health and radiation sp... | Wikipedia - Radiophobia - Radiophobia and Chernobyl |
We must not only track those problems, but also treat them. Otherwise people will feel they are just guinea pigs in our research. The term "radiation phobia syndrome" was introduced in 1987. by L. A. Ilyin and O. A. Pavlovsky in their report "Radiological consequences of the Chernobyl accident in the Soviet Union and m... | Wikipedia - Radiophobia - Radiophobia and Chernobyl |
Perhaps rather—a fear of wars? Perhaps—the dread of betrayal, Cowardice, stupidity, lawlessness? The term has been criticized by Adolph Kharash, Science Director at the Moscow State University because, he writes, It treats the normal impulse to self-protection, natural to everything living, your moral suffering, your a... | Wikipedia - Radiophobia - Radiophobia and Chernobyl |
Radiophobia refers only to a display of anxiety disproportionate to the actual quantity of radiation one is exposed to, with, in many cases, radiation exposure values equal to, or not much higher than, that which individuals are naturally exposed to every day from background radiation. Anxiety following a response to a... | Wikipedia - Radiophobia - Radiophobia and Chernobyl |
In the former Soviet Union these schools were sometimes known as Internat-schools (Russian: Школа-интернат) (from Latin: internet). They varied in their organization. Some schools were a type of specialized schools with a specific focus in a particular field or fields such as mathematics, physics, language, science, sp... | Wikipedia - Boarding schools - Russia and former Soviet Union |
Those schools were parts of some major universities and prepared students to study there. Now, only a few exist in Russia - in Moscow, Novosibirsk, and Yekaterinburg, though several boarding schools still operate in former Soviet republics, and even some new ones are being opened (e.g. MSU Gymnasium in Moscow, Russia, ... | Wikipedia - Boarding schools - Russia and former Soviet Union |
Also, separate boarding schools were established for children with special needs (schools for the blind, deaf, and others). General schools offered "extended stay" programs (Russian: Группа продленного дня) featuring cheap meals for children and preventing them from coming home too early before parents were back from w... | Wikipedia - Boarding schools - Russia and former Soviet Union |
In the former Soviet Union, defamatory insults can "only constitute a criminal offence, not a civil wrong". | Wikipedia - Character defamation - Former Soviet Union |
In the former Soviet Union, many patients with negligible radioactive exposure after the Chernobyl disaster displayed extreme anxiety about radiation exposure. They developed many psychosomatic problems, including radiophobia along with an increase in fatalistic alcoholism. As Japanese health and radiation specialist S... | Wikipedia - Fukushima nuclear disaster - Effects on evacuees |
Relocation is not easy, the stress is very big. We must not only track those problems, but also treat them. | Wikipedia - Fukushima nuclear disaster - Effects on evacuees |
Otherwise people will feel they are just guinea pigs in our research. A survey by the Iitate local government obtained responses from approximately 1,743 evacuees within the evacuation zone. The survey showed that many residents are experiencing growing frustration, instability, and an inability to return to their earl... | Wikipedia - Fukushima nuclear disaster - Effects on evacuees |
Sixty percent of respondents stated that their health and the health of their families had deteriorated after evacuating, while 39.9% reported feeling more irritated compared to before the disaster. Summarizing all responses to questions related to evacuees' current family status, one-third of all surveyed families liv... | Wikipedia - Fukushima nuclear disaster - Effects on evacuees |
A total of 36.8% reported a lack of sleep, while 17.9% reported smoking or drinking more than before they evacuated. Stress often manifests in physical ailments, including behavioral changes such as poor dietary choices, lack of exercise, and sleep deprivation. Survivors, including some who lost homes, villages, and fa... | Wikipedia - Fukushima nuclear disaster - Effects on evacuees |
Much of the stress came from lack of information and from relocation.A 2014 metareview of 48 articles indexed by PubMed, PsycINFO, and EMBASE, highlighted several psychophysical consequences among the residents in Miyagi, Iwate, Ibaraki, Tochigi and Tokyo. The resulting outcomes included depressive symptoms, anxiety, s... | Wikipedia - Fukushima nuclear disaster - Effects on evacuees |
In the former Soviet Union, subbotniks were days of voluntary unpaid labor. | Wikipedia - Working Saturday - Subbotnik |
In the former Soviet Union, the Simmental was the most important cattle breed. Russian Simmental (Симментальская корова) accounted for one-quarter of all cattle in the USSR. Through extensive crossbreeding, six strains were developed: Steppe Simmental (Russian cattle × Simmental bulls) Ukrainian Simmental (Grey steppe ... | Wikipedia - Simmental cattle - Soviet Union |
In the former Soviet Union, under the 1961 Fundamentals, copyrights held by legal entities such as companies were defined to be perpetual; if a company was reorganized, its legal successor entity took over the copyrights, and if a company ceased to exist, the copyrights passed to the state. | Wikipedia - Perpetual copyright - Former Soviet Union |
In the former Yugoslavia, and originally in Serbia, there is a local version of the hamburger known as the pljeskavica. It is often served as a patty but may also have a bun. | Wikipedia - Hamburger bun - Yugoslavia and Serbia |
In the former Yugoslavia, cheek kissing is also very commonplace, with your ethnicity being ascertainable by the number of kisses on each cheek. Typically, Croats and Bosniaks will kiss once on each cheek, for two total kisses, whereas Serbs will kiss once, but three times as a traditional greeting, typically starting ... | Wikipedia - Cheek kissing - Southeastern Europe |
Kissing is usually performed by people of the opposite sex and between two women. Men kissing is rare even between close friends and is usually considered unnatural and awkward. Male relatives are more likely to initiate kissing if there is a significant age gap, such as between uncles and nephews, or if both men are e... | Wikipedia - Cheek kissing - Southeastern Europe |
In Romania, cheek kissing is commonly used as a greeting between a man and a woman or two women, once on each cheek. Men usually prefer handshakes among themselves, though sometimes close male relatives may also practice cheek kissing.In Albania, cheek kissing is used as a greeting between the opposite sex and also the... | Wikipedia - Cheek kissing - Southeastern Europe |
Males usually slightly bump their heads or just touch their cheeks (no kissing) so to masculinize the act. Females practice the usual left to right cheek kissing. Albanian old women often kiss four times, so two times on each cheek. | Wikipedia - Cheek kissing - Southeastern Europe |
{\displaystyle G={\frac {\pi }{8}}\ln(2)+\sum _{n=0}^{\infty }(-1)^{n}{\frac {H_{2n+1}}{2n+1}}.} If the measure ρ is reducible and let φ be the associated reducer, one has the equality ∫ I φ 2 ( x ) ρ ( x ) d x = 4 π 2 3 ∫ I ρ 3 ( x ) d x . {\displaystyle \int _{I}\varphi ^{2}(x)\rho (x)\,dx={\frac {4\pi ^{2}}{3}}\int ... | Wikipedia - Secondary measure - A few beautiful applications |
If the measure ρ is reducible with μ the associated reducer, then if f is square integrable for μ, and if g is square integrable for ρ and is orthogonal with P0 = 1 one has equivalence: f ( x ) = ∫ I g ( t ) − g ( x ) t − x ρ ( t ) d t ⇔ g ( x ) = ( x − c 1 ) f ( x ) − T μ ( f ( x ) ) = φ ( x ) μ ( x ) ρ ( x ) f ( x ) ... | Wikipedia - Secondary measure - A few beautiful applications |
In addition, the sequence of secondary measures has applications in Quantum Mechanics. The sequence gives rise to the so-called sequence of residual spectral densities for specialized Pauli-Fierz Hamiltonians. This also provides a physical interpretation for the sequence of secondary measures. | Wikipedia - Secondary measure - A few beautiful applications |
In the formulas for energy of electrons at various levels given below in an atom, the zero point for energy is set when the electron in question has completely left the atom, i.e. when the electron's principal quantum number n = ∞. When the electron is bound to the atom in any closer value of n, the electron's energy i... | Wikipedia - Energy level - Intrinsic energy levels |
In the formulation of Chevalley and Mostow, the additive decomposition states that an element X in a real semisimple Lie algebra g with Iwasawa decomposition g = k ⊕ a ⊕ n can be written as the sum of three commuting elements of the Lie algebra X = S + D + N, with S, D and N conjugate to elements in k, a and n respecti... | Wikipedia - Jordan–Chevalley decomposition - Real semisimple Lie algebras |
In the formulation of Kant, who wrote some of the most influential modern treatises on the subject, the great achievement of reason (German: Vernunft) is that it is able to exercise a kind of universal law-making. Kant was able therefore to reformulate the basis of moral-practical, theoretical and aesthetic reasoning, ... | Wikipedia - Method of reasoning - Substantive and formal reason |
He formulated such a principle, called the "categorical imperative", which would justify an action only if it could be universalized: Act only according to that maxim whereby you can, at the same time, will that it should become a universal law. In contrast to Hume then, Kant insists that reason itself (German Vernunft... | Wikipedia - Method of reasoning - Substantive and formal reason |
Instead, the unity of reason has to be strictly formal, or "procedural". He thus described reason as a group of three autonomous spheres (on the model of Kant's three critiques): Cognitive–instrumental reason is the kind of reason employed by the sciences. It is used to observe events, to predict and control outcomes, ... | Wikipedia - Method of reasoning - Substantive and formal reason |
In the formulation of the de Broglie–Bohm theory, there is only a wavefunction for the entire universe (which always evolves by the Schrödinger equation). Here, the "universe" is simply the system limited by the same boundary conditions used to solve the Schrödinger equation. However, once the theory is formulated, it ... | Wikipedia - Bohmian Mechanics - The conditional wavefunction of a subsystem |
Let us write the wavefunction of the universe as ψ ( t , q I , q II ) {\displaystyle \psi (t,q^{\text{I}},q^{\text{II}})} , where q I {\displaystyle q^{\text{I}}} denotes the configuration variables associated to some subsystem (I) of the universe, and q II {\displaystyle q^{\text{II}}} denotes the remaining configurat... | Wikipedia - Bohmian Mechanics - The conditional wavefunction of a subsystem |
The conditional wavefunction of subsystem (I) is defined by ψ I ( t , q I ) = ψ ( t , q I , Q II ( t ) ) . {\displaystyle \psi ^{\text{I}}(t,q^{\text{I}})=\psi (t,q^{\text{I}},Q^{\text{II}}(t)).} It follows immediately from the fact that Q ( t ) = ( Q I ( t ) , Q II ( t ) ) {\displaystyle Q(t)=(Q^{\text{I}}(t),Q^{\text... | Wikipedia - Bohmian Mechanics - The conditional wavefunction of a subsystem |
Also, the fact that Q ( t ) {\displaystyle Q(t)} is random with probability density given by the square modulus of ψ ( t , ⋅ ) {\displaystyle \psi (t,\cdot )} implies that the conditional probability density of Q I ( t ) {\displaystyle Q^{\text{I}}(t)} given Q II ( t ) {\displaystyle Q^{\text{II}}(t)} is given by the s... | Wikipedia - Bohmian Mechanics - The conditional wavefunction of a subsystem |
If, in addition, the Hamiltonian does not contain an interaction term between subsystems (I) and (II), then ψ I {\displaystyle \psi ^{\text{I}}} does satisfy a Schrödinger equation. More generally, assume that the universal wave function ψ {\displaystyle \psi } can be written in the form ψ ( t , q I , q II ) = ψ I ( t ... | Wikipedia - Bohmian Mechanics - The conditional wavefunction of a subsystem |
In the formulations of Larmor's formula given above, the acceleration is given at the retarded time. This means that any acceleration in the earlier motion of the charged particle could be used in the formula, which makes it essentially undetermined. This difficulty has been resolved by a recent derivation that gives t... | Wikipedia - Larmor formula - Radiation at the present time |
In the fortnight prior to the announcement of the PNG solution, Rudd visited Indonesia for regular annual talks with Indonesian president Susilo Bambang Yudhoyono where they discussed asylum seeker issues, but played down expectations of a policy announcement. On 15 July, he and Immigration Minister Tony Burke visited ... | Wikipedia - PNG solution - Announcement |
The announcement also outlined plans to expand the Manus Island detention facility, from 600 occupants to 3,000. All refugees found to be legitimate will be resettled in Papua New Guinea. | Wikipedia - PNG solution - Announcement |
Any asylum seekers found to be non-genuine refugees will either be repatriated, moved to a third country other than Australia if it is unsafe to be repatriated, or remain in detention indefinitely. Australia will bear the full cost of the setup of the policy, as well as provide funding for reforms of Papua New Guinea's... | Wikipedia - PNG solution - Announcement |
In the fortunate situation that the experimental arm is shown to be undeniably superior to the control arm, the DMC may recommend termination of the trial. This would allow the company sponsoring the trial to get regulatory approval earlier and to allow the superior treatment to get to the patient population earlier. T... | Wikipedia - Data Monitoring Committees - Overwhelming benefit |
In the forward problem of electrocardiography, the torso is seen as a passive conductor and its model can be derived starting from the Maxwell's equations under quasi-static assumption.The standard formulation consists of a partial differential equation with one unknown scalar field, the torso potential u T {\displayst... | Wikipedia - Forward problem of electrocardiology - Torso tissue model |
In the forward to a book on the Power of peer learning by Jean-H. Guilmette, Maureen O'Neil, then president of Canada's International Development Research Centre, states that Our experience has proven that is an efficient way to transmit knowledge across a wide range of groups or regions. Peer learning, based on joint... | Wikipedia - Peer learning - Applications in development |
In essence, the dominant management approach for companies and institutions rests on cybernetics, with the view of keeping communications and accountability simple and clear. Managing methods that are successful in such a context counterproductive when managing networks.Guilmette cites Anne K. Bernard, who in a report... | Wikipedia - Peer learning - Applications in development |
In the forward, Keyhoe charges that the Air Force began refusing to share information with public in December 1953. Keyhoe 'conspiracy' is not a sinister one, as he explains: "In revealing this censorship, I am not attacking the Air Force as a whole. Most of the officers and officials I hae encountered are simply obeyi... | Wikipedia - The Flying Saucer Conspiracy - A benevolent conspiracy |
In the foundational approach of André Weil, developed in his Foundations of Algebraic Geometry, generic points played an important role, but were handled in a different manner. For an algebraic variety V over a field K, generic points of V were a whole class of points of V taking values in a universal domain Ω, an alge... | Wikipedia - Generic fiber - History |
Oscar Zariski, a colleague of Weil's at São Paulo just after World War II, always insisted that generic points should be unique. (This can be put back into topologists' terms: Weil's idea fails to give a Kolmogorov space and Zariski thinks in terms of the Kolmogorov quotient.) | Wikipedia - Generic fiber - History |
In the rapid foundational changes of the 1950s Weil's approach became obsolete. In scheme theory, though, from 1957, generic points returned: this time à la Zariski. For example for R a discrete valuation ring, Spec(R) consists of two points, a generic point (coming from the prime ideal {0}) and a closed point or speci... | Wikipedia - Generic fiber - History |
For morphisms to Spec(R), the fiber above the special point is the special fiber, an important concept for example in reduction modulo p, monodromy theory and other theories about degeneration. The generic fiber, equally, is the fiber above the generic point. Geometry of degeneration is largely then about the passage f... | Wikipedia - Generic fiber - History |
(For a discrete valuation ring the topological space in question is the Sierpinski space of topologists. Other local rings have unique generic and special points, but a more complicated spectrum, since they represent general dimensions. The discrete valuation case is much like the complex unit disk, for these purposes.... | Wikipedia - Generic fiber - History |
In the foundations of mathematics, Aczel's anti-foundation axiom is an axiom set forth by Peter Aczel (1988), as an alternative to the axiom of foundation in Zermelo–Fraenkel set theory. It states that every accessible pointed directed graph corresponds to exactly one set. In particular, according to this axiom, the gr... | Wikipedia - Aczel's anti-foundation axiom - Summary |
In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays... | Wikipedia - Morse–Kelley set theory - Summary |
Morse's own version appeared later in his book A Theory of Sets (1965). While von Neumann–Bernays–Gödel set theory is a conservative extension of Zermelo–Fraenkel set theory (ZFC, the canonical set theory) in the sense that a statement in the language of ZFC is provable in NBG if and only if it is provable in ZFC, Mors... | Wikipedia - Morse–Kelley set theory - Summary |
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