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Note that the foregoing proof of analyticity derived an expression for a system of n different function elements fi (x), provided that x is not a critical point of p(x, y). A critical point is a point where the number of distinct zeros is smaller than the degree of p, and this occurs only where the highest degree term ... | Wikipedia - Algebraic function | null | null | null |
Thus the holomorphic extension of the fi has at worst algebraic poles and ordinary algebraic branchings over the critical points. Note that, away from the critical points, we have p ( x , y ) = a n ( x ) ( y − f 1 ( x ) ) ( y − f 2 ( x ) ) ⋯ ( y − f n ( x ) ) {\displaystyle p(x,y)=a_{n}(x)(y-f_{1}(x))(y-f_{2}(x))\cdots... | Wikipedia - Algebraic function | null | null | null |
Note that the method of transposition and contraposition should not be confused. Contraposition is a type of immediate inference in which from a given categorical proposition another categorical proposition is inferred which has as its subject the contradictory of the original predicate. Since nothing is said in the de... | Wikipedia - Transposition (logic) | null | null | null |
Note that the previous algorithm requires O ( W n 2 ) {\displaystyle O(Wn^{2})} space for storing the current packing of items for all m,w, which may not be able to handle large-size problems. In fact, this can be easily improved by dropping the index m from f ( m , w ) {\displaystyle f(m,w)} since all the computations... | Wikipedia - 0-1 quadratic knapsack problem | null | null | null |
That is, f ( w ) = max { ∑ i = 1 m p i x i + ∑ i = 1 m ∑ j = 1 , i ≠ j m P i j x i x j: ∑ i = 1 m w i = w , m ≤ n } . {\displaystyle f(w)=\max \left\{\sum _{i=1}^{m}p_{i}x_{i}+\sum _{i=1}^{m}\sum _{j=1,i\neq j}^{m}P_{ij}x_{i}x_{j}:\sum _{i=1}^{m}w_{i}=w,m\leq n\right\}.} Accordingly, by dynamic programming we have that... | Wikipedia - 0-1 quadratic knapsack problem | null | null | null |
Note that this classification structure is written from a Data Management perspective and therefore has a focus for text and text convertible binary data sources. Images, videos, and audio files are highly structured formats built for industry standard API's and do not readily fit within the classification scheme outli... | Wikipedia - Data classification (data management) | null | null | null |
Applications that produce structured data are usually database applications. This type of data usually brings complex procedures of data evaluation and migration between the storage tiers. To ensure adequate quality standards, the classification process has to be monitored by subject matter experts. | Wikipedia - Data classification (data management) | null | null | null |
Semi-structured or Poly-structured data (all other non-audio/video data that does not conform to a system or platform defined Relational or Tabular form). Generally describes data files that have a dynamic or non-relational semantic structure (e.g. documents, XML, JSON, Device or System Log output, Sensor Output, etc.)... | Wikipedia - Data classification (data management) | null | null | null |
Simple process of data migration between assigned segments of predefined storage tiers.There are different types of data classification used. Please note that this designation is entirely orthogonal to the application-centric designation outlined above. Regardless of structure inherited from application, data may be of... | Wikipedia - Data classification (data management) | null | null | null |
Geographical 2. Chronological 3. Qualitative 4. | Wikipedia - Data classification (data management) | null | null | null |
Quantitative It should also be evaluated across three dimensions: Identifiability: how easily can this data be used to identify an individual? Sensitivity: how much damage could be done if this data reached the wrong hands? Scarcity: how readily available is this data? | Wikipedia - Data classification (data management) | null | null | null |
Note that unlike in the original case, non-integer degrees of freedom are allowed, though the value must usually still be constrained between 0 and n.Consider, as an example, the k-nearest neighbour smoother, which is the average of the k nearest measured values to the given point. Then, at each of the n measured point... | Wikipedia - Degree of freedom (statistics) | null | null | null |
As another example, consider the existence of nearly duplicated observations. Naive application of classical formula, n − p, would lead to over-estimation of the residuals degree of freedom, as if each observation were independent. More realistically, though, the hat matrix H = X(X ' Σ−1 X)−1X ' Σ−1 would involve an ob... | Wikipedia - Degree of freedom (statistics) | null | null | null |
Note that, in the previous version of the GMD algorithm in step "3", we do not really need to use "fresh" randomness for each i {\displaystyle i} . Now we come up with another randomized version of the GMD algorithm that uses the same randomness for every i {\displaystyle i} . This idea follows the algorithm below. | Wikipedia - Generalized minimum-distance decoding | null | null | null |
Modified_Randomized_Decoder Given: y = ( y 1 , … , y N ) ∈ N {\displaystyle \mathbf {y} =(y_{1},\ldots ,y_{N})\in ^{N}} , pick θ ∈ {\displaystyle \theta \in } at random. Then every for every 1 ≤ i ≤ N {\displaystyle 1\leq i\leq N}: Set y i ′ = M L D C in ( y i ) {\displaystyle y_{i}'=MLD_{C_{\text{in}}}(y_{i})} . Com... | Wikipedia - Generalized minimum-distance decoding | null | null | null |
If θ < 2 ω i d {\displaystyle \theta <{\tfrac {2\omega _{i}}{d}}} , set y i ″ ← ? , {\displaystyle y_{i}''\leftarrow ?,} otherwise set y i ″ = y i ′ {\displaystyle y_{i}''=y_{i}'} . Run errors and erasure algorithm for C out {\displaystyle C_{\text{out}}} on y ″ = ( y 1 ″ , … , y N ″ ) {\displaystyle \mathbf {y} ''=(y_... | Wikipedia - Generalized minimum-distance decoding | null | null | null |
Note that, in the rule for spawn, Blumofe and Leiserson suggest that the "parent" thread execute its new thread, as if performing a function call (in the C-like program f(x); g(y);, the function call to f completes before the call to g is performed). This is called "continuation stealing", because the continuation of t... | Wikipedia - Work stealing | null | null | null |
Note the previous construction can be proven in algebraic geometry using the affine cone of a projective variety X {\displaystyle X} using Local cohomology. | Wikipedia - Local homology | null | null | null |
Note! The examples here describe an algorithm that is for finding the minimum of a function. For maximum, the comparison operators need to be reversed. | Wikipedia - Golden-section search | null | null | null |
Note. — If each vertex in a graph is to be traversed by a tree-based algorithm (such as DFS or BFS), then the algorithm must be called at least once for each connected component of the graph. This is easily accomplished by iterating through all the vertices of the graph, performing the algorithm on each vertex that is ... | Wikipedia - Graph search algorithm | null | null | null |
Note: % Died refers to 30-day mortality. | Wikipedia - Pneumonia severity index | null | null | null |
Note: All measurements given are in picometers (pm). For more recent data on covalent radii see Covalent radius. Just as atomic units are given in terms of the atomic mass unit (approximately the proton mass), the physically appropriate unit of length here is the Bohr radius, which is the radius of a hydrogen atom. The... | Wikipedia - Atomic radii of the elements (data page) | null | null | null |
Note: Any missing lines or empty entries do reflect some lack of information on that exact item. | Wikipedia - CUDA | null | null | null |
Note: Cloud-based PDSes are sometimes called personal data clouds or personal clouds. (HAT) Hub-of-All-Things Personium.io - open-source personal datastore SOLID Project - SOLID (Social Linked Data) is an open-source web decentralization project led by Tim Berners-Lee. Atsign - Open source end-to-end encrypted and publ... | Wikipedia - Personal data service | null | null | null |
Note: Financial data in billions of US dollars and employee data in thousands. For years 1998, 1999, and 2000 figures are combined for Chase Manhattan and J.P. Morgan & Co., for consistency, pre-dating their official merger in 2000. The data is sourced from the company's SEC Form 10-K from 1998 to 2020. | Wikipedia - Interbank Information Network | null | null | null |
Note: Refer to 29 CFR 1910.1200 for the most current and updated information (https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=standards&p_id=10099) SDSs information is required by EPA, OSHA, DOT, and/or DOE regulations depending upon the type of hazardous substance. The Safety Data Sheet includes the fol... | Wikipedia - Hazard Communication | null | null | null |
Physical hazards, such as fire and explosion. Health hazards, including symptoms. Primary routes of entry of the chemical into the body. | Wikipedia - Hazard Communication | null | null | null |
Legal exposure limits (OSHA and other recommended limits). Whether the chemical can cause cancer. | Wikipedia - Hazard Communication | null | null | null |
Precautions for safe handling and use. Control measures, including ventilation, personal protective equipment, etc. Emergency and first aid procedures. The date the SDS was prepared. | Wikipedia - Hazard Communication | null | null | null |
Name, address, and phone number of the manufacturer. Regulatory agencies, such as United States Environmental Protection Agency EPA SARA Title III rules EPCRAChemical manufacturers may legally withhold the specific chemical identity of a material from the SDS and label in the case of bona fide trade secrets. In such ca... | Wikipedia - Hazard Communication | null | null | null |
The SDS must disclose information concerning the properties and effects of the hazardous chemical, even if the actual chemical identity is withheld. The trade secret information must be disclosed to a doctor or nurse in a medical emergency. In non-emergency cases health professionals can obtain a trade secret chemical ... | Wikipedia - Hazard Communication | null | null | null |
Note: Statistics are correct through the end of the 2018 American Arena League season. | Wikipedia - Triangle Torch | null | null | null |
Note: The 'topics' are a selection of related articles provided by Wiley Online Library. The number (#) indicates that, for example, 15 articles relate to the main branch of agrochemicals. The numbers do not exactly sum up to the total number of articles (1,050), but its sole purpose is for organizing and categorizing ... | Wikipedia - Ullmann's Encyclopedia of Industrial Chemistry | null | null | null |
Note: The Liberty metadata schema are listed verbatim in the specification documents listed below. Since the direct link to the Version 1.1 XSD document on the Liberty web site is broken, a copy of the XSD document for Liberty Metadata Version 1.1 has been uploaded to the web. That document is also included in the lega... | Wikipedia - SAML metadata | null | null | null |
Note: The MINRES method is more complicated than the algebraically equivalent Conjugate Residual method. The Conjugate Residual (CR) method was therefore produced below as a substitute. It differs from MINRES in that in MINRES, the columns of a basis of the Krylov space (denoted below by p k {\displaystyle p_{k}} ) can... | Wikipedia - Minimal residual method | null | null | null |
There are more efficient and preconditioned variants with fewer AXPYs. Compare with the article. First you choose x 0 ∈ R n {\displaystyle x_{0}\in \mathbb {R} ^{n}} arbitrary and compute Then we iterate for k = 1 , 2 , … {\displaystyle k=1,2,\dots } in the following steps: | Wikipedia - Minimal residual method | null | null | null |
Note: There is no scientific consensus about terrestrial composition of most of the planets in the list. Sources in the "Main source" column confirm the possibility of terrestrial composition. In September 2012, the discovery of two planets orbiting Gliese 163 was announced. One of the planets, Gliese 163 c, about 6.9 ... | Wikipedia - List of nearest terrestrial exoplanet candidates | null | null | null |
Note: These conjectures are about models of Zermelo-Frankel set theory with choice, and may not be able to be expressed in models of other set theories such as the various constructive set theories or non-wellfounded set theory. (Woodin) Does the generalized continuum hypothesis below a strongly compact cardinal imply ... | Wikipedia - Open problem in mathematics | null | null | null |
If ℵω is a strong limit cardinal, is 2 ℵ ω < ℵ ω 1 {\displaystyle 2^{\aleph _{\omega }}<\aleph _{\omega _{1}}} (see Singular cardinals hypothesis)? The best bound, ℵω4, was obtained by Shelah using his PCF theory. The problem of finding the ultimate core model, one that contains all large cardinals. | Wikipedia - Open problem in mathematics | null | null | null |
Woodin's Ω-conjecture: if there is a proper class of Woodin cardinals, then Ω-logic satisfies an analogue of Gödel's completeness theorem.Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal? Does there exist a Jónsson algebra on ℵω? Is OCA (the ... | Wikipedia - Open problem in mathematics | null | null | null |
Note: This section contains an excerpt from 'Computer Algebra in Particle Physics' by Stefan Weinzierl Particle physics is an important field of application for computer algebra and exploits the capabilities of Computer Algebra Systems (CAS). This leads to valuable feed-back for the development of CAS. Looking at the h... | Wikipedia - Computational particle physics | null | null | null |
LISP is an interpreted language and, as the name already indicates, designed for the manipulation of lists. Its importance for symbolic computer programs in the early days has been compared to the importance of FORTRAN for numerical programs in the same period. Already in this first period, the program REDUCE had some ... | Wikipedia - Computational particle physics | null | null | null |
An exception to the LISP-based programs was SCHOONSHIP, written in assembler language by Martinus J. G. Veltman and specially designed for applications in particle physics. The use of assembler code lead to an incredible fast program (compared to the interpreted programs at that time) and allowed the calculation of mor... | Wikipedia - Computational particle physics | null | null | null |
Also the program MACSYMA deserves to be mentioned explicitly, since it triggered important development with regard to algorithms. In the 1980s new computer algebra systems started to be written in C. This enabled the better exploitation of the resources of the computer (compared to the interpreted language LISP) and at... | Wikipedia - Computational particle physics | null | null | null |
In addition, also a few dedicated programs appeared, an example relevant to particle physics is the program FORM by J. Vermaseren as a (portable) successor to SCHOONSHIP. More recently issues of the maintainability of large projects became more and more important and the overall programming paradigma changed from proce... | Wikipedia - Computational particle physics | null | null | null |
Following this change of paradigma, the library GiNaC was developed. The GiNac library allows symbolic calculations in C++. Code generation for computer algebra can also be used in this area. | Wikipedia - Computational particle physics | null | null | null |
Note: in most cases the composition of the atmosphere and atmosphere pressure of exoplanets are unknown, so surface temperatures are estimates based on computer models and expert opinions. | Wikipedia - List of nearest terrestrial exoplanet candidates | null | null | null |
Note: the presentation here is informal and simplified. A more accurate presentation is given in the book. Use a near-exact division procedure on X and get a partition which all n players view as ε-near-exact with weights w1, …, wm. | Wikipedia - Robertson–Webb protocol | null | null | null |
Let one of the active players (e.g. A1) cut the pieces such that the division is exact for him, i.e. for every j: V1(Xj)/V1(X) = wj. If all other active players agree with the cutter, then just give piece Xi to active player Ai. This division is envy-free among the active players, so we are done. | Wikipedia - Robertson–Webb protocol | null | null | null |
Otherwise, there is some piece P on which there is disagreement among the active players. By cutting P to smaller pieces if necessary, we may bound the disagreement such that all players agree that: V(P)/V(X) < ε. Split the active players to two camps: the "optimists" who think that P is more valuable, and the "pessimi... | Wikipedia - Robertson–Webb protocol | null | null | null |
Assign P ∪ Q to the optimists. Because they believe that P is valuable, they necessarily believe that P ∪ Q is sufficiently valuable to more than cover their due share. Assign R to the pessimists. | Wikipedia - Robertson–Webb protocol | null | null | null |
Because they believe that P is less valuable, they necessarily believe that the remainder, R, is sufficiently valuable to more than cover their due share. At this point we have partitioned the active players to two camps, each collectively claiming complementary portions of the cake and each camp is more than satisfied... | Wikipedia - Robertson–Webb protocol | null | null | null |
This is done by two recursive applications of the procedure: Recursively partition P ∪ Q among the optimists (i.e. the optimists are active and all other players are only watching). Recursively partition R among the pessimists.In both applications, the near-exactness factor should be at most δ. Because the resulting pa... | Wikipedia - Robertson–Webb protocol | null | null | null |
Note: this section tracks the calculations by referring to or similar. This is to align with the notation stated in the CIA archive description. | Wikipedia - VIC cipher | null | null | null |
Note: ¬(A→¬B)→A (TH4), ¬(A→¬B)→B (TH6), and A→(B→¬(A→¬B)) (TH10), so ¬(A→¬B) behaves just like A∧B (compare with axioms AND-1, AND-2, and AND-3). TH11 is axiom NOT-1 of standard PC, called "reductio ad absurdum". Theorem TH15 is the converse of axiom THEN-2. | Wikipedia - Frege's propositional calculus | null | null | null |
Compare TH17 with theorem TH5. Note: A→((A→B)→B) (TH8), B→((A→B)→B) (TH9), and (A→C)→((B→C)→(((A→B)→B)→C)) (TH19), so ((A→B)→B) behaves just like A∨B. (Compare with axioms OR-1, OR-2, and OR-3.) | Wikipedia - Frege's propositional calculus | null | null | null |
TH20 corresponds to axiom NOT-3 of standard PC, called "tertium non datur". TH21 corresponds to axiom NOT-2 of standard PC, called "ex contradictione quodlibet". All the axioms of standard PC have been derived from Frege's PC, after having let A∧B := ¬(A→¬B) and A∨B := (A→B)→B. | Wikipedia - Frege's propositional calculus | null | null | null |
These expressions are not unique, e.g. A∨B could also have been defined as (B→A)→A, ¬A→B, or ¬B→A. Notice, though, that the definition A∨B := (A→B)→B contains no negations. On the other hand, A∧B cannot be defined in terms of implication alone, without using negation. | Wikipedia - Frege's propositional calculus | null | null | null |
In a sense, the expressions A∧B and A∨B can be thought of as "black boxes". Inside, these black boxes contain formulas made up only of implication and negation. The black boxes can contain anything, as long as when plugged into the AND-1 through AND-3 and OR-1 through OR-3 axioms of standard PC the axioms remain true. | Wikipedia - Frege's propositional calculus | null | null | null |
These axioms provide complete syntactic definitions of the conjunction and disjunction operators. The next set of theorems will aim to find the remaining four axioms of Frege's PC within the "theorem-space" of standard PC, showing that the theory of Frege's PC is contained within the theory of standard PC. ST2 is axiom... | Wikipedia - Frege's propositional calculus | null | null | null |
ST4 is axiom FRG-2 of Frege's PC. Prove ST5: (A→(B→C))→(B→(A→C)) ST5 is axiom THEN-3 of Frege's PC. ST6 is axiom FRG-1 of Frege's PC. | Wikipedia - Frege's propositional calculus | null | null | null |
Each of Frege's axioms can be derived from the standard axioms, and each of the standard axioms can be derived from Frege's axioms. This means that the two sets of axioms are interdependent and there is no axiom in one set that is independent from the other set. Therefore, the two sets of axioms generate the same theor... | Wikipedia - Frege's propositional calculus | null | null | null |
(For if the theories should be different, then one of them should contain theorems not contained by the other theory. These theorems can be derived from their own theory's axiom set: but as has been shown this entire axiom set can be derived from the other theory's axiom set, which means that the given theorems can act... | Wikipedia - Frege's propositional calculus | null | null | null |
Note: ρ is density, n is refractive index at 589 nm, and η is viscosity, all at 20 °C; Teq is the equilibrium temperature between two phases: ice/liquid solution for Teq < 0–0.1 °C and NaCl/liquid solution for Teq above 0.1 °C. | Wikipedia - Water (data page) | null | null | null |
Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4 | Wikipedia - Homotopical algebraic geometry | null | null | null |
Notes that sound well together to a Western ear are sounds whose fundamental frequencies of vibration are in simple ratios. For example, an octave doubles the frequency and a perfect fifth multiplies it by 3 2 {\displaystyle {\frac {3}{2}}} .This link between frequencies and harmony was discussed in Traité de l'harmoni... | Wikipedia - Fields of mathematics | null | null | null |
The harmonic frequencies, which are integer multiples of the fundamental frequency.Humans, as well as some other animals, find symmetric patterns to be more beautiful. Mathematically, the symmetries of an object form a group known as the symmetry group.For example, the group underlying mirror symmetry is the cyclic gro... | Wikipedia - Fields of mathematics | null | null | null |
A Rorschach test is a figure invariant by this symmetry, as well as a butterfly, and animal bodies more generally (at least on the surface). Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea. Furthermore, fractals poss... | Wikipedia - Fields of mathematics | null | null | null |
Notes: 1.^ – For reference to compare with the HRP-1. 2.^ - The external appearances of HRP-2 and HRP-3 were designed by Yutaka Izubuchi. 3.^ – "C" means "Cybernetic Human". | Wikipedia - Humanoid Robotics Project | null | null | null |
Notes: All speeds are theoretical maximums and will vary by a number of factors, including the use of external antennas, distance from the tower and the ground speed (e.g. communications on a train may be poorer than when standing still). Usually the bandwidth is shared between several terminals. The performance of eac... | Wikipedia - Comparison of wireless data standards | null | null | null |
Notes^4 Excluding the Aeroflot-Group Airlines Rossyia, Donavia, Aurora, Orenair и Pobeda ^5 Excluding UTair-Group Airlines UTair Express and other airlines ^6 Excluding an S7-Group Airline Globus The airlines mentioned with cursive letters, are the airlines, which ceased their operations currently | Wikipedia - List of biggest airlines of Russia | null | null | null |
Nothing is known about the Cayenne nightjar's biology. Its feeding, breeding, and other behaviors are assumed to be similar to those of other nightjars. | Wikipedia - Cayenne nightjar | null | null | null |
Nothrotheriops behaved like all typical ground sloths of North and South America, feeding on various plants like the desert globemallow, cacti, and yucca. It was hunted by various local predators, like dire wolves and Smilodon, from which the sloths may have defended themselves by standing upright on hindlegs and tail ... | Wikipedia - Shasta ground sloth | null | null | null |
Notice however, the case of a rotating frame that happens to have the same angular rate as the particle, so that Ω = dθ/dt at some particular moment (that is, the polar coordinates are set up in the instantaneous, non-inertial co-rotating frame of Figure 3). In this case, at this moment, dθ'/dt = 0. In this co-rotating... | Wikipedia - Mechanics of planar particle motion | null | null | null |
Notice that a Proposer in Paxos could propose "I am the leader," (or, for example, "Proposer X is the leader"). Because of the agreement and validity guarantees of Paxos, if accepted by a Quorum, then the Proposer is now known to be the leader to all other nodes. This satisfies the needs of leader election because ther... | Wikipedia - Paxos algorithm | null | null | null |
Notice that as addressed in Behavior of Atomic DEVS, depending on the value of b {\displaystyle b} return by δ e x t {\displaystyle \delta _{ext}} , last event time, t l {\displaystyle t_{l}} , and next event time, t n {\displaystyle t_{n}} ,consequently, elapsed time, t e {\displaystyle t_{e}} , and lifespan t n {\dis... | Wikipedia - Simulation algorithms for atomic DEVS | null | null | null |
Notice that the above solution takes O ( n k 2 ) {\displaystyle O(nk^{2})} time with a DP solution. This can be improved to O ( n k log k ) {\displaystyle O(nk\log k)} time by binary searching on the optimal x {\displaystyle x} in the above recurrence, since W ( n − 1 , x − 1 ) {\displaystyle W(n-1,x-1)} is increasin... | Wikipedia - Dynamic Programming | null | null | null |
Let m {\displaystyle m} be the minimum floor from which the egg must be dropped to be broken. Let f ( t , n ) {\displaystyle f(t,n)} be the maximum number of values of m {\displaystyle m} that are distinguishable using t {\displaystyle t} tries and n {\displaystyle n} eggs. Then f ( t , 0 ) = f ( 0 , n ) = 1 {\displays... | Wikipedia - Dynamic Programming | null | null | null |
Let a {\displaystyle a} be the floor from which the first egg is dropped in the optimal strategy. If the first egg broke, m {\displaystyle m} is from 1 {\displaystyle 1} to a {\displaystyle a} and distinguishable using at most t − 1 {\displaystyle t-1} tries and n − 1 {\displaystyle n-1} eggs. If the first egg did not ... | Wikipedia - Dynamic Programming | null | null | null |
Therefore, f ( t , n ) = f ( t − 1 , n − 1 ) + f ( t − 1 , n ) {\displaystyle f(t,n)=f(t-1,n-1)+f(t-1,n)} . Then the problem is equivalent to finding the minimum x {\displaystyle x} such that f ( x , n ) ≥ k {\displaystyle f(x,n)\geq k} . | Wikipedia - Dynamic Programming | null | null | null |
To do so, we could compute { f ( t , i ): 0 ≤ i ≤ n } {\displaystyle \{f(t,i):0\leq i\leq n\}} in order of increasing t {\displaystyle t} , which would take O ( n x ) {\displaystyle O(nx)} time. Thus, if we separately handle the case of n = 1 {\displaystyle n=1} , the algorithm would take O ( n k ) {\displaystyle O(n{\... | Wikipedia - Dynamic Programming | null | null | null |
Notice that the condition for transforming DFT ω n {\displaystyle {\text{DFT}}_{\omega _{n}}} into η ′ ∘ ⨂ d DFT ω n d ∘ η ∗ {\displaystyle \eta '\circ \bigotimes _{d}{\text{DFT}}_{\omega _{n_{d}}}\circ \eta ^{*}} relies on "an" additive group isomorphism η {\displaystyle \eta } from ( Z n , + , 0 ) {\displaystyle (\ma... | Wikipedia - Prime-factor FFT algorithm | null | null | null |
Since ( Z n , + , 0 ) {\displaystyle (\mathbb {Z} _{n},+,0)} is cyclic, any automorphism can be written as 1 ↦ g {\displaystyle 1\mapsto g} where g {\displaystyle g} is a generator of ( Z n , + , 0 ) {\displaystyle (\mathbb {Z} _{n},+,0)} . By the definition of ( Z n , + , 0 ) {\displaystyle (\mathbb {Z} _{n},+,0)} , g... | Wikipedia - Prime-factor FFT algorithm | null | null | null |
Notions or order can be defined using strict, non-strict or second-order formulations. Additional properties such as commutativity simplify the axioms. Given a strict total order (also sometimes called linear order, or pseudo-order in a constructive formulation), then by definition, the positive and negative elements f... | Wikipedia - Boolean semiring | null | null | null |
Nototheniidae species have no swim bladder, however, they have other depth-related adaptations, such as increased fatty tissues and reduced mineralization of the bones, resulting in a body density approaching neutral, to fill a variety of niches. The spleen may be used to remove ice crystals from circulating blood. As ... | Wikipedia - Cod icefish | null | null | null |
Nouns and adjectives inflect for case and gender. In Russian, nominals occur when: Adjectives and non-personal pronouns take the same agreement as their referent Personal pronouns agree with the natural gender of the referentCases Nominative: expresses the subject Accusative: expresses the direct object Genitive: expre... | Wikipedia - Nominal (linguistics) | null | null | null |
Novaro et al. (2000) assessed the potential ecological extinction of guanacos (Lama guanicoe) and lesser rheas (Pterocnemia pennata) as a prey source for native omnivores and predators in the Argentine Patagonia. These native species are being replaced by introduced species such as the European rabbit, red deer, and do... | Wikipedia - Ecological extinction | null | null | null |
They also suggested that the lesser rhea and guanaco had already passed their ecological effective density as a prey species, and thus were ecological extinct. It is possible that the niches of introduced species as herbivores too closely mirrored those of the natives, and thus competition was the primary cause of ecol... | Wikipedia - Ecological extinction | null | null | null |
Guanacos and rheas have been classified as a low risk for global extinction, but this simplistic view of their demography doesn't take into account that they have already become functionally extinct in the Argentine Patagonia. Novaro and his colleagues suggest "this loss could have strong effects on plant-animal intera... | Wikipedia - Ecological extinction | null | null | null |
Ants disperse up to 30% of the flora in the shrublands and are vital to the survival of fynbos plants because they bury the large seeds away from the dangers of predation and fire damage. It is also crucial for seeds to be buried, because nearly all seed germination takes place in the first season after a fire. Argenti... | Wikipedia - Ecological extinction | null | null | null |
Christian tested whether the invasion of the Argentine ant differentially effected small and large-seeded fauna. He found that post-fire recruitment of large-seeded flora was reduced disproportionately for large seeds in sites already invaded by Argentine ants. These initial low large-seed density recruitments will eve... | Wikipedia - Ecological extinction | null | null | null |
Novel or enhanced synthetic techniques can often provide improved environmental performance or enable better adherence to the principles of green chemistry. For example, the 2005 Nobel Prize for Chemistry was awarded to Yves Chauvin, Robert H. Grubbs and Richard R. Schrock, for the development of the metathesis method ... | Wikipedia - Green Chemistry | null | null | null |
A number of important process chemicals can be synthesized in engineered organisms, such as shikimate, a Tamiflu precursor which is fermented by Roche in bacteria. Click chemistry is often cited as a style of chemical synthesis that is consistent with the goals of green chemistry. The concept of 'green pharmacy' has re... | Wikipedia - Green Chemistry | null | null | null |
Novel treatments for autoimmune disorders: Edward Roberts and his team designed and synthesized a selective and bitopic S1P1 agonist, RPC1063. This compound showed promise as a safe treatment for autoimmune diseases such as multiple sclerosis, ulcerative colitis, and Crohn's disease. Ozanimod (RPC1063), now marketed as... | Wikipedia - Edward Roberts (chemist) | null | null | null |
One such antagonist, Navacaprant (formerly CYM-53093, BTRX-335140), exhibited robust efficacy in early clinical trials and is currently in multiple phase 3 trials for major depressive diseases. Compounds for use in the treatment of autistic spectrum disorders and/or post-traumatic stress disorders: Roberts' team design... | Wikipedia - Edward Roberts (chemist) | null | null | null |
Novelist Vanna Bonta claimed to have coined the term quantum fiction in 1996, when she published her novel Flight: A Quantum Fiction Novel. In the story, the protagonist struggles to tell real life from elements in a novel he is writing, as people and events from his novel begin to appear in reality. The first line of ... | Wikipedia - Quantum fiction | null | null | null |
"Bonta defined quantum fiction as stories in which consciousness affects physics and determines reality; in her words, "the genre is broad and includes life." Bonta further explained her development of this new genre: "I don't write science fiction. Science fiction is a niche genre, defined by Ray Bradbury as depiction... | Wikipedia - Quantum fiction | null | null | null |
Novelist Wilson Harris stated he realized what he was writing was quantum fiction, and further described it as giving witness to "realities hidden from the world you see." He describes, "The quantum concept is that if one fires out an object, it breaks into particles and waves. Conventional novelists go along a linear ... | Wikipedia - Quantum fiction | null | null | null |
In 2003, when interviewed by British-Guyanese poet, novelist and playwright Fred D'Aguiar, Harris describes: "'Quantum' brings a hand in fiction that challenges all conventional fixtures of control within the psyche of art." Harris explains that an awareness of the "mystery of consciousness" as actuated by quantum theo... | Wikipedia - Quantum fiction | null | null | null |
Novolaks are produced by reacting phenol with methanal (formaldehyde). The reaction of epichlorohydrin and novolaks produces novolaks with glycidyl residues, such as epoxyphenol novolak (EPN) or epoxycresol novolak (ECN). These highly viscous to solid resins typically carry 2 to 6 epoxy groups per molecule. By curing, ... | Wikipedia - Epoxy adhesive | null | null | null |
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