text stringlengths 1 2.7k | source stringlengths 21 174 |
|---|---|
In the following table men's slalom World Cup podiums in the World Cup since first season in 1967. | Wikipedia - Slalom skiing - Men's slalom World Cup podiums |
In the following table of more recent triangle centers, no specific notations are mentioned for the various points. Also for each center only the first trilinear coordinate f(a,b,c) is specified. The other coordinates can be easily derived using the cyclicity property of trilinear coordinates. | Wikipedia - Triangle center function - Recent triangle centers |
In the following table the energy efficiency and energy consumption for different types of passenger land vehicles and modes of transport, as well as standard occupancy rates, are presented. The sources for these figures are in the correspondent section for each vehicle, in the following article. The conversions amongs... | Wikipedia - Fuel efficiency in transportation - Table Overview |
In the following table the ligands are sorted by field strength (weak field ligands first): The entries in the table are sorted by field strength, binding through the stated atom (i.e. as a terminal ligand). The 'strength' of the ligand changes when the ligand binds in an alternative binding mode (e.g., when it bridges... | Wikipedia - Bidentate ligand - Examples of common ligands (by field strength) |
In the following table the sizes of various just intervals are compared against their equal-tempered counterparts, given as a ratio as well as cents. Differences of less than six cents cannot be noticed by most people, and intervals that are more than a quarter of a step; which in this case is 25 cents, off sound out o... | Wikipedia - 12 equal temperament - Table |
In the following table women's giant slalom World Cup podiums from the World Cup first edition in 1967. | Wikipedia - Giant slalom - Women's World Cup podiums |
In the following table ψ ( x ) = Γ ′ ( x ) Γ ( x ) {\displaystyle \psi (x)={\frac {\Gamma '(x)}{\Gamma (x)}}} is the digamma function, K ( x ) = e ζ ′ ( − 1 , x ) − ζ ′ ( − 1 ) = e z − z 2 2 + z 2 ln ( 2 π ) − ψ ( − 2 ) ( z ) {\displaystyle K(x)=e^{\zeta ^{\prime }(-1,x)-\zeta ^{\prime }(-1)}=e^{{\frac {z-z^{2}}{2}}+... | Wikipedia - List of derivatives and integrals in alternative calculi - Table |
In the following table, "full sun" refers to occurrences of the full solar disk just above the horizon, while "half sun" refers to occurrences of the solar disk partially hidden below the horizon. | Wikipedia - Manhattanhenge - Occurrences |
In the following table, each row shows undisputed Greek cognates sharing the three ablaut grades of a root. The four sonorants and the two semivowels are represented as individual letters, other consonants as C and the vowel or its absence as (V). The reconstructed PIE e grade and zero grade of the above roots may be a... | Wikipedia - Laryngeal theory - Ablaut in the root |
In the following table, it is assumed that for β = v / c > 0 {\displaystyle \beta =v/c>0} the receiver and the source are moving away from each other, v {\displaystyle v} being the relative velocity and c {\displaystyle c} the speed of light, and γ = 1 / 1 − β 2 {\textstyle \gamma =1/{\sqrt {1-\beta ^{2}}}} . | Wikipedia - Transverse Doppler effect - Summary of major results |
In the following table, material data are given for standard pressure of 0.1 MPa (equivalent to 1 bar). Up to 99.63 °C (the boiling point of water at 0.1 MPa), at this pressure water exists as a liquid. Above that, it exists as water vapor. Note that the boiling point of 100.0 °C is at a pressure of 0.101325 MPa (1 atm... | Wikipedia - Water (data page) - Standard conditions |
In the following table, material data are given with a pressure of 611.7 Pa (equivalent to 0.006117 bar). Up to a temperature of 0.01 °C, the triple point of water, water normally exists as ice, except for supercooled water, for which one data point is tabulated here. At the triple point, ice can exist together with bo... | Wikipedia - Water (data page) - Triple point |
In the following table, ploidy, copy number and chromosome/chromatid counts listed are for a single cell, generally prior to DNA synthesis and division (in G1 if applicable). Primary spermatocytes are arrested after DNA synthesis and prior to division. | Wikipedia - Secondary spermatocytes - Cell type summary |
In the following table, sizes are shown for the silver-oxide IEC number; types and capacity are identified as "(L)" for alkaline, "(M)" for mercury (no longer manufactured), and "(S)" for silver-oxide. Some sizes may be interchangeably used in battery holders. For example, the 189/389 cell is 3.1 mm high and was design... | Wikipedia - LR44 battery - Silver oxide and alkaline cells |
In the following table, the chapter number (#), chapter name and original magazine date of publication, and a brief synopsis are given. The nine stories are grouped into three parts. | Wikipedia - Accelerando - Plot summary and breakdown by story |
In the following table, the commemorative coins were dedicated to anniversaries of life and activities of famous historical figures of Azerbaijan. The coins are worth of 50, 100 and 500 AZN. | Wikipedia - Commemorative coins of Azerbaijan - Commemorative Coins Dedicated to the Famous Historical Figures |
In the following table, the formula and the name of the anion refer to what remains of the acid when it loses all its hydrogen atoms as protons. Many of these acids, however, are polyprotic, and in such cases, there also exists one or more intermediate anions. In name of such anions, the prefix hydrogen- (in older nome... | Wikipedia - Oxyacid - Examples |
In the following table, the frequency parameter ω {\displaystyle \omega } is real. Notes An extensive table of Hilbert transforms is available. Note that the Hilbert transform of a constant is zero. | Wikipedia - Hilbert transforms - Table of selected Hilbert transforms |
In the following table, the leftmost column lists the route of administration. == References == | Wikipedia - Toxicity category rating - Acute toxicity categories for pesticide products |
In the following table, the rules for each busy beaver (maximizing Σ) are represented visually, with orange squares corresponding to a "1" on the tape, and white corresponding to "0". The position of the head is indicated by the black ovoid, with the orientation of the head representing the state. Individual tapes are ... | Wikipedia - Busy Beaver Number - Visualizations |
In the following table, the same particle can be named with the spectroscopic notation or with its mass. In some cases excitation series are used: ψ′ is the first excitation of ψ (which, for historical reasons, is called J/ψ particle); ψ″ is a second excitation, and so on. That is, names in the same cell are synonymous... | Wikipedia - Quarkonium - Charmonium |
The quantum numbers of the X(3872) particle have been measured recently by the LHCb experiment at CERN. This measurement shed some light on its identity, excluding the third option among the three envisioned, which are: a charmonium hybrid state a D0 D∗0 molecule a candidate for the 11D2 stateIn 2005, the BaBar experim... | Wikipedia - Quarkonium - Charmonium |
At first, Y(4260) was thought to be a charmonium state, but the evidence suggests more exotic explanations, such as a D "molecule", a 4-quark construct, or a hybrid meson. Notes: Needs confirmation. Interpretation as a 1−− charmonium state not favored. Predicted, but not yet identified. | Wikipedia - Quarkonium - Charmonium |
In the following table, the same particle can be named with the spectroscopic notation or with its mass. Some of the states are predicted, but have not been identified; others are unconfirmed. Notes: Preliminary results. Confirmation needed.The ϒ(1S) state was discovered by the E288 experiment team, headed by Leon Led... | Wikipedia - Quarkonium - Bottomonium |
In the following table, the temperature is given in kelvins. | Wikipedia - List of viscosities - Liquids (including liquid metals) |
In the following table, the years correspond to the date in which the award was given, rather than when the poem was first published. Each year links to the corresponding "year in poetry". Entries with a blue background and an asterisk (*) next to the writer's name have won the award, while those with a gray background... | Wikipedia - Dwarf stars - Winners and nominees |
In the following table, there is a description of the classical geometries, modeled as Klein geometries. | Wikipedia - Reductive homogeneous space - Examples |
In the following tables the month names used in each Greek-speaking city are laid out with Athenian Greek letters (not necessarily how they were spelled in the city they were used in) transliterated into English letters, and with a leading ordinal number column. The ordinal column is mostly for reference, and should no... | Wikipedia - Ancient Greek calendars - Calendars by region |
In the following tables there are seven tasks, labeled a through g. Some tasks can be done concurrently (a and b) while others cannot be done until their predecessor task is complete (c and d cannot begin until a is complete). Additionally, each task has three time estimates: the optimistic time estimate (O), the most ... | Wikipedia - Gantt chart - Example |
In the following tables, planetary satellites are indicated in bold type (e.g. Moon) while planets and dwarf planets, which directly circle the Sun, are in italic type (e.g. Earth). The Sun itself is indicated in roman type. The tables are sorted by publication/announcement date. Dates are annotated with the following ... | Wikipedia - Timeline of discovery of Solar System planets and their moons - Key info |
* Note: Moons marked by an asterisk (*) had complicated discoveries. Some took years to be confirmed, and in several cases were actually lost and rediscovered. Others were found in Voyager photographs years after they were taken. | Wikipedia - Timeline of discovery of Solar System planets and their moons - Key info |
Color legendThe Sun, the planets, dwarf planets, and their natural satellites are marked in the following colors: It is not known precisely how many objects in the Solar System are dwarf planets; the nine objects listed in the third column are those agreed on by most astronomers, corresponding to a threshold of about 9... | Wikipedia - Timeline of discovery of Solar System planets and their moons - Key info |
DesignationsOther designations are synonyms or periphrases sometimes encountered for the object. Permanent designations (of planetary satellites) are explained here. Temporary designations are explained here.If a satellite is named, its name is bolded; if it is unnamed, but has a permanent designation, then its permane... | Wikipedia - Timeline of discovery of Solar System planets and their moons - Key info |
In the following tables, values are temperature-dependent and to a lesser degree pressure-dependent, and are arranged by state of aggregation (s = solid, lq = liquid, g = gas), which are clearly a function of temperature and pressure. All of the data were computed from data given in "Formulation of the Thermodynamic Pr... | Wikipedia - Water (data page) - Physical and thermodynamic tables |
In the following text, ( R ) {\displaystyle ({\mathfrak {R}})} indicates "Ramanujan summation". This formula originally appeared in one of Ramanujan's notebooks, without any notation to indicate that it exemplified a novel method of summation. For example, the ( R ) {\displaystyle ({\mathfrak {R}})} of 1 − 1 + 1 − ⋯ is... | Wikipedia - Ramanujan summation - Ramanujan summation of divergent series |
In the following the Copeland winner for the first group of voters is determined. The results would be tabulated as follows: indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption indicates voters who preferred the candidate listed in the row caption to th... | Wikipedia - Consistency criterion - First group of voters |
In the following the Kemeny-Young winner for the first group of voters is determined. The Kemeny–Young method arranges the pairwise comparison counts in the following tally table: The ranking scores of all possible rankings are: Result: The ranking A > B > C has the highest ranking score. Thus, A wins ahead of B and C. | Wikipedia - Consistency criterion - First group of voters |
In the following the Majority Judgment winner for the normal ballots is determined. The sorted ratings would be as follows: Result: The median of A is between "Good" and "Poor" and thus is rounded down to "Poor". The median of B is "Fair". Thus, B is elected Majority Judgment winner. | Wikipedia - Reversal symmetry - Normal order |
In the following the Majority Judgment winner for the reversed ballots is determined. For reversing, the higher ratings are considered to be mirror-inverted to the lower ratings ("Good" is exchanged with "Poor", "Fair" stays as is). The sorted ratings would be as follows: Result: Still, the median of A is between "Good... | Wikipedia - Reversal symmetry - Reversed order |
In the following the Minimax winner for the ballots in normal order is determined. The results would be tabulated as follows: indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption indicates voters who preferred the candidate listed in the row caption to t... | Wikipedia - Reversal symmetry - Normal order |
In the following the Minimax winner for the ballots in reversed order is determined. The results would be tabulated as follows: Result: Still, the candidates A, B, and C form a cycle with clear defeats and D benefits from that. Therefore D's biggest defeat is the closest of all candidates. Thus, D is elected Minimax wi... | Wikipedia - Reversal symmetry - Reversed order |
In the following the Ranked pairs winner for the first group of voters is determined. The results would be tabulated as follows: indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption indicates voters who preferred the candidate listed in the row caption t... | Wikipedia - Consistency criterion - First group of voters |
In the following the Schulze winner for the first group of voters is determined. The pairwise preferences would be tabulated as follows: Now, the strongest paths have to be identified, e.g. the path A > B > C is stronger than the direct path A > C (which is nullified, since it is a loss for A). Result: A > B, A > C and... | Wikipedia - Consistency criterion - First group of voters |
In the following the elements used in event-driven process chain diagram will be described: Event Events are passive elements in event-driven process chains. They describe under what circumstances a function or a process works or which state a function or a process results in. Examples of events are "requirement captur... | Wikipedia - Event-driven Process Chain - Elements |
They model the tasks or activities within the company. Functions describe transformations from an initial state to a resulting state. | Wikipedia - Event-driven Process Chain - Elements |
If different resulting states can occur, the selection of the respective resulting state can be modeled explicitly as a decision function using logical connectors. Functions can be refined into another EPC. In this case it is called a hierarchical function. | Wikipedia - Event-driven Process Chain - Elements |
Examples of functions are "capture requirement", "check material in stock", etc. In the event-driven process chain graph a function is represented as rounded rectangle.Process owner Process owner is responsible for a function (i.e. a booking clerk is responsible for booking journeys). The process owner is usually part ... | Wikipedia - Event-driven Process Chain - Elements |
Examples are "sales department", "procurement department", etc. It is represented as an ellipse with a vertical line.Information, material, or resource object In the event-driven process chain, the information, material, or resource objects portray objects in the real world, for example business objects, entities, etc.... | Wikipedia - Event-driven Process Chain - Elements |
A branch may have one incoming control flow and two or more outgoing control flows. When the condition is fulfilled, a branch activates exactly only one of the outgoing control flows and deactivates the others. The counterpart of a branch is a merge. | Wikipedia - Event-driven Process Chain - Elements |
A merge may have two or more incoming flows and one outgoing control flow. A merge synchronizes an activated and the deactivated alternatives. The control will then be passed to the next element after the merge. | Wikipedia - Event-driven Process Chain - Elements |
A branch in the EPC is represented by an opening XOR, whereas a merge is represented as a closing XOR connectors.Fork/Join: Fork and join correspond to activating all paths in the control flow concurrently. A fork may have one incoming control flow and two or more outgoing control flows. When the condition is fulfilled... | Wikipedia - Event-driven Process Chain - Elements |
A join may have two or more incoming control flows and one outgoing control flow. A join synchronizes all activated incoming control flows. In the Event-driven Process Chain diagram how the concurrency achieved is not a matter. | Wikipedia - Event-driven Process Chain - Elements |
In reality the concurrency can be achieved by true parallelism or by virtual concurrency achieved by interleaving. A fork in the EPC is represented by an opening 'AND', whereas a join is represented as a closing 'AND' connectors. OR: An 'OR' relationship corresponds to activating one or more paths among control flows. | Wikipedia - Event-driven Process Chain - Elements |
An opening 'OR' connector may have one incoming control flow and two or more outgoing control flows. When the condition is fulfilled, an opening 'OR' connector activates one or more control flows and deactivates the rest of them. The counterpart of this is the closing 'OR' connector. | Wikipedia - Event-driven Process Chain - Elements |
When at least one of the incoming control flows is activated, the closing 'OR' connector will pass the control to the next element after it.Control flow A control flow connects events with functions, process paths, or logical connectors creating chronological sequence and logical interdependencies between them. A contr... | Wikipedia - Event-driven Process Chain - Elements |
In the following the instant-runoff winner for the first group of voters is determined. B has only 2 votes and is eliminated first. Its votes are transferred to A. Now, A has 6 votes and wins against C with 4 votes. Result: A wins against C, after B has been eliminated. | Wikipedia - Consistency criterion - First group of voters |
In the following the majority judgment winner for the first group of voters is determined. The sorted ratings would be as follows: Result: With the votes of the first group of voters, A has the median rating of "Excellent" and B has the median rating of "Fair". Thus, A is elected majority judgment winner by the first g... | Wikipedia - Consistency criterion - First group of voters |
In the following the minimax winner for the first group of voters is determined. The results would be tabulated as follows: indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption indicates voters who preferred the candidate listed in the row caption to the... | Wikipedia - Consistency criterion - First group of voters |
In the following theorems A , P , Q ∈ R n × n {\displaystyle A,P,Q\in \mathbb {R} ^{n\times n}} , and P {\displaystyle P} and Q {\displaystyle Q} are symmetric. The notation P > 0 {\displaystyle P>0} means that the matrix P {\displaystyle P} is positive definite. Theorem (continuous time version). Given any Q > 0 {\dis... | Wikipedia - Lyapunov equation - Application to stability |
The quadratic function V ( x ) = x T P x {\displaystyle V(x)=x^{T}Px} is a Lyapunov function that can be used to verify stability. Theorem (discrete time version). Given any Q > 0 {\displaystyle Q>0} , there exists a unique P > 0 {\displaystyle P>0} satisfying A T P A − P + Q = 0 {\displaystyle A^{T}PA-P+Q=0} if and on... | Wikipedia - Lyapunov equation - Application to stability |
In the following there are lists of sites of notable radio transmitters. During the early history of radio many countries had only a few high power radio stations, operated either by the government or large corporations, which broadcast to the population or to other countries. Because of the large number of transmissio... | Wikipedia - List of transmission sites - Summary |
In the following thermodynamical equilibrium is assumed, as well as for simplicity (2) should be a vaporous phase. The first (1) and the second (2) phase are always divided by some form of interface, what results in an interfacial energy γ 1 − 2 {\displaystyle \gamma _{1-2}} . One can now ask whether this energy can be... | Wikipedia - Premelting - Thermodynamical picture for solid gas interface |
The only possibility for the system to form such a layer is to take material of the solid and "melt" it to a quasi-liquid. In further notation there will be no distinction between quasi-liquid and liquid but one should always keep in mind that there is a difference. This difference to a real liquid becomes clear when l... | Wikipedia - Premelting - Thermodynamical picture for solid gas interface |
As, due to the long range forces of the molecules of the solid material the liquid very near the solid still "feels" the order of crystalline solid and hence itself is in a state providing a not liquid like amount of order. As considering a very thin layer at the moment it is clear that the whole separating layer (l) i... | Wikipedia - Premelting - Thermodynamical picture for solid gas interface |
Now, looking closer at the thermodynamics of the newly introduced phase (l), its Gibbs energy can be written as: where T {\displaystyle T} is the temperature, P {\displaystyle P} the pressure, d {\displaystyle d} the thickness of (l) corresponding to the number or particles N {\displaystyle N} in this case. n l {\displ... | Wikipedia - Premelting - Thermodynamical picture for solid gas interface |
In the following transcriptions, diacritics may be used to distinguish between apical and laminal . | Wikipedia - Voiced retroflex lateral approximant - Occurrence |
In the following transcriptions, diacritics may be used to distinguish between apical and laminal . The commonality of cross-linguistically is 2% in a phonological analysis of 2155 languages | Wikipedia - Voiced retroflex non-sibilant fricative - Occurrence |
In the following transcriptions, diacritics may be used to distinguish between apical and laminal . The commonality of cross-linguistically is 6% in a phonological analysis of 2155 languages. | Wikipedia - Voiceless retroflex non-sibilant fricative - Occurrence |
In the following transcriptions, the undertack diacritic may be used to indicate an approximant . Danish is actually a velarized alveolar approximant. | Wikipedia - Voiced dental fricative - Occurrence |
In the following two examples, we always assume it is difficult to factorize a large composite number (see Integer factorization). | Wikipedia - Trapdoor function - Examples |
In the following variants, the entries for the server ns.target.example would be poisoned and redirected to the attacker's name server at IP address w.x.y.z. These attacks assume that the name server for target.example is ns.target.example.To accomplish the attacks, the attacker must force the target DNS server to make... | Wikipedia - DNS cache poisoning - Variants |
In the following we assume all manifolds are differentiable manifolds of class Cr for a fixed r ≥ 1, and all morphisms are differentiable of class Cr. | Wikipedia - Immersed submanifold - Formal definition |
In the following we formally extend the range of p {\displaystyle p} to {\displaystyle } with the convention that ‖ ⋅ ‖ ∞ {\displaystyle \|\cdot \|_{\infty }} is the operator norm. The dual index to p = ∞ {\displaystyle p=\infty } is then q = 1 {\displaystyle q=1} . The Schatten norms are unitarily invariant: for unit... | Wikipedia - Schatten norm - Properties |
{\displaystyle \|UTV\|_{p}=\|T\|_{p}.} They satisfy Hölder's inequality: for all p ∈ {\displaystyle p\in } and q {\displaystyle q} such that 1 p + 1 q = 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1} , and operators S ∈ L ( H 2 , H 3 ) , T ∈ L ( H 1 , H 2 ) {\displaystyle S\in {\mathcal {L}}(H_{2},H_{3}),T\in {\mat... | Wikipedia - Schatten norm - Properties |
If p , q , r ∈ {\displaystyle p,q,r\in } satisfy 1 p + 1 q = 1 r {\displaystyle {\tfrac {1}{p}}+{\tfrac {1}{q}}={\tfrac {1}{r}}} , then we have ‖ S T ‖ r ≤ ‖ S ‖ p ‖ T ‖ q {\displaystyle \|ST\|_{r}\leq \|S\|_{p}\|T\|_{q}} .The latter version of Hölder's inequality is proven in higher generality (for noncommutative L p... | Wikipedia - Schatten norm - Properties |
{\displaystyle \|T\|_{1}\geq \|T\|_{p}\geq \|T\|_{p'}\geq \|T\|_{\infty }.} Duality: Let H 1 , H 2 {\displaystyle H_{1},H_{2}} be finite-dimensional Hilbert spaces, p ∈ {\displaystyle p\in } and q {\displaystyle q} such that 1 p + 1 q = 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1} , then ‖ S ‖ p = sup { | ⟨ S , T... | Wikipedia - Schatten norm - Properties |
In the following we shall use imaginary time ( t ′ = i t {\displaystyle t'=it} ) so that space-time is Euclidean and the equations are simpler. The Poincaré transformations are given by the coordinate transformation on space-time parametrized by the 4-vectors V V μ ′ = O μ ν V ν + P μ {\displaystyle V_{\mu }^{\prime }=... | Wikipedia - Inversion transformations - Transformation on coordinates |
{\displaystyle r=|x-y|.\,} These transformations are subgroups of general 1-1 conformal transformations on space-time. It is possible to extend these transformations to include all 1-1 conformal transformations on space-time V μ ′ = ( A τ ν V ν + B τ ) ( C τ μ ν V ν + D τ μ ) − 1 . {\displaystyle V_{\mu }^{\prime }=\le... | Wikipedia - Inversion transformations - Transformation on coordinates |
We must also have an equivalent condition to the orthogonality condition of the Poincaré transformations: A A T + B C = D D T + C B {\displaystyle AA^{T}+BC=DD^{T}+CB\,} Because one can divide the top and bottom of the transformation by D , {\displaystyle D,} we lose no generality by setting D {\displaystyle D} to the ... | Wikipedia - Inversion transformations - Transformation on coordinates |
{\displaystyle V_{\mu }^{\prime }=\left(O_{\mu }^{\nu }V_{\nu }+P_{\tau }\right)\left(\delta _{\tau \mu }+Q_{\tau \mu }^{\nu }V_{\nu }\right)^{-1}.\,} Applying this transformation twice on a 4-vector gives a transformation of the same form. The new symmetry of 'inversion' is given by the 3-tensor Q . {\displaystyle Q.} | Wikipedia - Inversion transformations - Transformation on coordinates |
This symmetry becomes Poincaré symmetry if we set Q = 0. {\displaystyle Q=0.} When Q = 0 {\displaystyle Q=0} the second condition requires that O {\displaystyle O} is an orthogonal matrix. This transformation is 1-1 meaning that each point is mapped to a unique point only if we theoretically include the points at infin... | Wikipedia - Inversion transformations - Transformation on coordinates |
In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usu... | Wikipedia - Frobenius solution to the hypergeometric equation - Summary |
For instance, Legendre's differential equation can be shown to be a special case of the hypergeometric differential equation. Hence, by solving the hypergeometric differential equation, one may directly compare its solutions to get the solutions of Legendre's differential equation, after making the necessary substituti... | Wikipedia - Frobenius solution to the hypergeometric equation - Summary |
We shall prove that this equation has three singularities, namely at x = 0, x = 1 and around x = infinity. However, as these will turn out to be regular singular points, we will be able to assume a solution on the form of a series. Since this is a second-order differential equation, we must have two linearly independen... | Wikipedia - Frobenius solution to the hypergeometric equation - Summary |
In the following we use the probabilistic framework, but regardless of the finiteness of the measure, by adding the boundedness condition on the chosen subset of L 1 ( μ ) {\displaystyle L^{1}(\mu )} . Dunford–Pettis theoremA class of random variables X n ⊂ L 1 ( μ ) {\displaystyle X_{n}\subset L^{1}(\mu )} is uniforml... | Wikipedia - Uniformly integrable - Relevant theorems |
In the following x represents the string xi, ..., xn.The bounded μ-operator can be expressed rather simply in terms of two primitive recursive functions (hereafter "prf") that also are used to define the CASE function—the product-of-terms Π and the sum-of-terms Σ (cf Kleene #B page 224). (As needed, any boundary for th... | Wikipedia - Μ operator - Example 1: The bounded μ-operator is a primitive recursive function |
In the following year he was promoted from clinical fellow to attending physician at the Memorial Hospital for Cancer and also received a promotion from research fellow to full member at the Chief Division Virology/Immunology. He joined the faculty of Cornell's medical college in 1951 and was eventually promoted to ful... | Wikipedia - Chester M. Southam - Career |
In the following year, Jacobites started uprisings in Scotland and Cornwall aimed at putting "James III and VIII" on the throne. On 22 December 1715, James reached Scotland after the Jacobite defeats at the Battle of Sheriffmuir (13 November 1715) and Battle of Preston (1715). He landed at Peterhead and soon fell ill w... | Wikipedia - Warming Pan Baby - The Fifteen |
In January 1716, he set up court at Scone Palace. Reputedly Jane Stuart, a half-sister, came from Wisbech in England to visit him. Learning of the approach of government forces, he returned to France, sailing from Montrose on 5 February 1716. | Wikipedia - Warming Pan Baby - The Fifteen |
The abandonment of his rebel allies caused ill-feeling against him in Scotland; nor was he welcomed on his return to France. His patron, Louis XIV, had died on 1 September 1715, and the French government found him a political embarrassment. When France, hitherto his main protector, allied with Britain, this effectively... | Wikipedia - Warming Pan Baby - The Fifteen |
In the following years, Beaumont worked to develop Windows on Multinationals (1984–87), Toxic Imaging (1987) and El Otro Sendero (1988). These ambitious and extensively researched combined-media installations deal with the poisoning of mental and physical health, the uprooting of social structures, economic and politic... | Wikipedia - Betty Beaumont - Works 1984-Present |
Beaumont created a list of over 150 personally significant books and collected replicas from bookstores. The books were treated, burned, displayed, and arranged in over thirty feet of floor to ceiling shelving. Through the metaphor of fire and the social horror of book burning, the project grieves the irretrievable los... | Wikipedia - Betty Beaumont - Works 1984-Present |
For the first anniversary of the Velvet Revolution in Prague, Beaumont created the installation Voices (Whose What Which) (1990) at the Stalinov Pomnik. The opening was attended by Vaclav Havel. | Wikipedia - Betty Beaumont - Works 1984-Present |
This work invites the viewer to participate in a visual dialogue questioning the origins and location of voice by exploring public language in a public place. A founding member of REPOhistory, she coordinated and produced, with other artists, the medical section of Choice Histories (1992) installation at Artists Space.... | Wikipedia - Betty Beaumont - Works 1984-Present |
She seeks to examine the extent in which greenwashing exhibits itself throughout natural environments and a reconsideration of preconceptions. In 2006 Beaumont created Boxed In/Boxed Out: The Mobile Studio Project, an ambitious solo installation pointing to the suburbanization of Manhattan following the displacement of... | Wikipedia - Betty Beaumont - Works 1984-Present |
The colors for the four chair-arranged geometries relate directly to the flag colors of nations with the fastest explosion or implosion of population change: USA, Africa, China, and India, while Children's XO laptops display world clock counters. A related work, Way (2009), contains 21 variations of the word Way paired... | Wikipedia - Betty Beaumont - Works 1984-Present |
As each sheet is torn, the work is changed to reveal one of the permutations challenging the viewer to re-examine their beliefs, actions or inactions, tolerance of misinformation and potential to effect change- while the pile reflects viewer participation. With the Great Recession in 2008, Beaumont began an ongoing scu... | Wikipedia - Betty Beaumont - Works 1984-Present |
A related work, the sculptural assemblage Prêt-à-Porter, is a societal construct of identity. The work consists of a collection of international shopping bags, a rolling double clothes rack, and hangers. The branded shopping bags are hung with tags naming the individual who contributed the bag. | Wikipedia - Betty Beaumont - Works 1984-Present |
The highly designed and produced bags are surrogates for both garment and identity, while each nametag labels a person with a specific branded identity. In June 2012, the entire Alexandria... series was presented together for the first time at the Library of Alexandria in Egypt (the physical installation having been pr... | Wikipedia - Betty Beaumont - Works 1984-Present |
Four prints plus a 148-page digital catalog are now in the permanent archives of the Bibliotheca Alexandrina. Inspired by her experience in Egypt during the country's 2012 election week and of demonstrations at Cairo's Tahrir Square, she created Arab Voices in 2012. Four words—Whose, What, Which, and My—were translated... | Wikipedia - Betty Beaumont - Works 1984-Present |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.