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89,400 | The Sibley–Ahlquist taxonomy is a bird taxonomy proposed by Charles Sibley and Jon E. Ahlquist. It is based on DNA–DNA hybridization studies conducted in the late 1970s and throughout the 1980s.DNA–DNA hybridization is among a class of comparative techniques in molecular biology that produce distance data (versus chara... | Sibley–Ahlquist taxonomy of birds | 0.781329 |
89,401 | Owing to its rapid growth rate, ability to grow on inexpensive carbon sources, and capacity to secrete proteins into the growth media, efforts are underway to leverage this species as a host for molecular biology and biotechnology applications. Recently, V. natriegens crude extract has been shown by multiple research g... | Vibrio natriegens | 0.781327 |
89,402 | In organic chemistry, nitroamines are organic compounds with the general chemical structure R2N−NO2. They consist of a nitro group (−NO2) bonded to an amine. The parent inorganic compound, where both R substituents are hydrogen, is nitramide, H2N−NO2. == References == | Nitroamine | 0.781326 |
89,403 | Risopatrón Base, also Luis Risopatrón Base, is a small Chilean Antarctic research base in the northwest of Robert Island in the South Shetland Islands, Antarctica situated on the isthmus linking Coppermine Peninsula to Alfatar Peninsula and bounded by Carlota Cove to the north and Coppermine Cove to the south. Establis... | Risopatrón Base | 0.781323 |
89,404 | Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to Kelly and Ulam. | Reconstruction conjecture | 0.781322 |
89,405 | In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, is an upper bound on the variance σ2 of any bounded probability distribution. Let M and m be upper and lower bounds on the values of any random variable with a particular probability distribution. Then Popoviciu's inequality states: σ 2 ≤ 1 4... | Popoviciu's inequality on variances | 0.781322 |
89,406 | Sony was reported to be a key licensee of Transmeta technology and approximately half of the remaining employees were to work on LongRun2 power optimization technology for Sony. On May 31, 2005, Transmeta announced the signing of asset purchase and license agreements with Hong Kong’s Culture.com Technology Limited. The... | Code Morphing Software | 0.781321 |
89,407 | The result was Stjerneborg ("castle of the stars"), a smaller site built entirely at ground level and dedicated purely to observations (there was no "house"). The basic layout was similar to Uraniborg, with a wall of similar shape surrounding the site, although the enclosed area was much smaller. The instruments were a... | Uraniborg | 0.781321 |
89,408 | Brahe and his many assistants began charting the positions of stars, planets, and other celestial bodies over time with unprecedented accuracy in this pursuit. While Brahe openly shared his findings in the field of astronomy and meteorology, he did not openly share his work in alchemy. Brahe's underground laboratory wa... | Uraniborg | 0.781321 |
89,409 | Paul Wittich visited Uraniborg for several months in 1580 and aided Brahe in the construction of the Tychonic system. Brahe had also researched meteorology for the King of Denmark, Frederick II, although Brahe did not put his name on the publications.During the period in which Uraniborg was actively used, astronomy and... | Uraniborg | 0.781321 |
89,410 | Uraniborg was a place for the study of astronomy, meteorology, astrology, and alchemy. Over the life span of Uraniborg it had upwards of thirty different assistants for Tycho Brahe, and visits from many other researchers and royalty; Martin Zeiler, Nicolaus Reimers, Erik Lange, and David Wunderer being some of the note... | Uraniborg | 0.781321 |
89,411 | Research was done in the fields of astronomy, alchemy, and meteorology by Tycho and his assistants. Brahe abandoned Uraniborg and Stjerneborg in 1597 after he fell out of favour with the Danish king, Christian IV of Denmark; Brahe left the country, and the institution was destroyed in 1601 after his death. Hven was lat... | Uraniborg | 0.781321 |
89,412 | In addition to being decorative, the gardens also supplied herbs for Brahe's medicinal chemistry experiments. The gardens are currently being re-created, using seeds found on-site or identified in Brahe's writings. At the gatehouses, Tycho incorporated his printing workshop and the island's prison.Extending beyond the ... | Uraniborg | 0.781321 |
89,413 | The building was dedicated to Urania, the Muse of Astronomy, and it was named Uraniborg, "The Castle of Urania". It was the first custom-built observatory in modern Europe, and the last to be built without a telescope as its primary instrument. The cornerstone was laid on August 8, 1576.The sandstone and limestone-fram... | Uraniborg | 0.781321 |
89,414 | The generating series of T over the binary field is the formal power series t ( Z ) = ∑ n = 0 ∞ T ( n ) Z n . {\displaystyle t(Z)=\sum _{n=0}^{\infty }T(n)Z^{n}\ .} This power series is algebraic over the field of rational functions, satisfying the equation Z + ( 1 + Z ) 2 t + ( 1 + Z ) 3 t 2 = 0 {\displaystyle Z+(1+Z)... | Thue-Morse Sequence | 0.781317 |
89,415 | The Prouhet–Tarry–Escott problem can be defined as: given a positive integer N and a non-negative integer k, partition the set S = { 0, 1, ..., N-1 } into two disjoint subsets S0 and S1 that have equal sums of powers up to k, that is: ∑ x ∈ S 0 x i = ∑ x ∈ S 1 x i {\displaystyle \sum _{x\in S_{0}}x^{i}=\sum _{x\in S_{1... | Thue-Morse Sequence | 0.781317 |
89,416 | Resemblances between two or more languages (whether in typology or in vocabulary) have been observed to result from several mechanisms, including lingual genealogical relation (descent from a common ancestor language, not principally related to biological genetics) ; borrowing between languages ; retention of features ... | Areal feature | 0.781317 |
89,417 | In theoretical physics the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten in 1996... | Hanany–Witten transition | 0.781316 |
89,418 | Solid VCl2 is prepared by thermal decomposition of VCl3, which leaves a residue of VCl2: 2 VCl3 → VCl2 + VCl4VCl2 dissolves in water to give the purple hexaaquo ion 2+. Evaporation of such solutions produces crystals of Cl2.Vanadium dichloride is used as a specialty reductant in organic chemistry. As an aqueous solutio... | VCl2 | 0.781316 |
89,419 | This allowed image guidance by displaying co-registered planning data over the real images of the patient seen by the video camera, so that the clinician had 'see-through' visualization on the patient's head, and helped plan the craniotomy and guide during the intervention. The DEX-Ray was clinically tested at the Sing... | Dextroscope | 0.781315 |
89,420 | Subharmonic functions make a convex cone, that is, a linear combination of subharmonic functions with positive coefficients is also subharmonic. The pointwise maximum of two subharmonic functions is subharmonic. If the pointwise maximum of a countable number of subharmonic functions is upper semi-continuous, then it is... | Subharmonic function | 0.781315 |
89,421 | In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory. Intuitively, subharmonic functions are related to convex functions of one variable as follows. If the graph of a convex function and a lin... | Subharmonic function | 0.781315 |
89,422 | The Witten conjecture is a special case of a more general relation between integrable systems of Hamiltonian PDEs and the geometry of certain families of 2D topological field theories (axiomatized in the form of the so-called cohomological field theories by Kontsevich and Manin), which was explored and studied systemat... | Witten conjecture | 0.781314 |
89,423 | = t 0 3 6 + t 1 24 + t 0 t 2 24 + t 1 2 24 + t 0 2 t 3 48 + ⋯ {\displaystyle F(t_{0},t_{1},\ldots )=\sum \langle \tau _{0}^{k_{0}}\tau _{1}^{k_{1}}\cdots \rangle \prod _{i\geq 0}{\frac {t_{i}^{k_{i}}}{k_{i}! }}={\frac {t_{0}^{3}}{6}}+{\frac {t_{1}}{24}}+{\frac {t_{0}t_{2}}{24}}+{\frac {t_{1}^{2}}{24}}+{\frac {t_{0}^{2}... | Witten conjecture | 0.781314 |
89,424 | In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper Witten (1991), and generalized in Witten (1993). Witten's original conjecture was proved by Maxim Kontsevich in the paper Kontsevich (1992). W... | Witten conjecture | 0.781314 |
89,425 | The actual function space used is often determined by the solutions of the eigenvalue problem of the differential operator; that is, by the solutions to L ψ n ( x ) = ω n ψ n ( x ) {\displaystyle L\psi _{n}(x)=\omega _{n}\psi _{n}(x)} where the ωn are the eigenvalues, and the ψn(x) are the eigenvectors. The set of eige... | Fredholm theory | 0.781313 |
89,426 | Much of Fredholm theory concerns itself with the following integral equation for f when g and K are given: g ( x ) = ∫ a b K ( x , y ) f ( y ) d y . {\displaystyle g(x)=\int _{a}^{b}K(x,y)f(y)\,dy.} This equation arises naturally in many problems in physics and mathematics, as the inverse of a differential equation. Th... | Fredholm theory | 0.781313 |
89,427 | Given the collection of eigenvectors and eigenvalues of K, the resolvent may be given a concrete form as R ( ω ; x , y ) = ∑ n ψ n ( y ) ψ n ( x ) ω n − ω {\displaystyle R(\omega ;x,y)=\sum _{n}{\frac {\psi _{n}(y)\psi _{n}(x)}{\omega _{n}-\omega }}} with the solution being φ ( x ) = ∫ R ( ω ; x , y ) f ( y ) d y . {\d... | Fredholm theory | 0.781313 |
89,428 | The classical results of the theory are Fredholm's theorems, one of which is the Fredholm alternative. One of the important results from the general theory is that the kernel is a compact operator when the space of functions are equicontinuous. A related celebrated result is the Atiyah–Singer index theorem, pertaining ... | Fredholm theory | 0.781313 |
89,429 | It was designed to provide a general systems language affording quantitative accounting and mathematical simulation of qualitative energy relationships between ecological entities: "that science in which are treated the forms or formulas of things in general, that is, quality in general". A general algebra known as the... | Universal characteristic | 0.78131 |
89,430 | Connections with the Jewish Cabbala, and the International auxiliary language policy of the Baháʼí Faith have also been made. The characteristic has also been claimed as an ancestor of the pictographic Energy Systems Language and associated Emergy Synthesis of Odum's Systems Ecology (Cevolatti and Maud, 2004). The Ener... | Universal characteristic | 0.78131 |
89,431 | Otto Neurath's isotype pictogram system, and "international picture language." The following attempts to recast parts of theoretical science as axiomatic first-order theories can be viewed as attempts to develop parts of the characteristica: Special relativity, by Hans Reichenbach, Rudolf Carnap, and others during the ... | Universal characteristic | 0.78131 |
89,432 | Even though Charles Sanders Peirce, a founder of semiotics, believed that all reasoning was diagrammatic, the relation, if any, of the characteristica to his existential graphs and to semiotics has yet to be explored in the English literature. Several aspects of logical positivism, specifically: The first-order theorie... | Universal characteristic | 0.78131 |
89,433 | Some people other than Fearnley-Sander working in the area of "universal algebra," the study of the mathematical and logical properties of algebraic structures generally, do not believe that universal algebra has anything to do with the characteristica. Palko, Gy Bulcsu (1986) considered structured analysis for analyzi... | Universal characteristic | 0.78131 |
89,434 | But these approaches have yet to result in any pictographic notations. Fearnley-Sander (1986) went one step further, defining Leibniz's characteristica as a combination of the algebra of logic (which Fearnley-Sander defined as the calculus ratiocinator) and the algebra of geometry (defined as the characteristica geomet... | Universal characteristic | 0.78131 |
89,435 | Adsorptive membranes are available in a variety of geometries and chemistry which allows them to be used for purification and also fractionation, concentration, and clarification in an efficiency that is 10 fold that of using beads. Membranes can be prepared through isolation of the membrane itself, where membranes are... | Ion chromatography | 0.78131 |
89,436 | Likewise, it also has great uses in the semiconductor industry. Because of the abundant separating columns, elution systems, and detectors available, chromatography has developed into the main method for ion analysis.When this technique was initially developed, it was primarily used for water treatment. Since 1935, ion... | Ion chromatography | 0.78131 |
89,437 | Because Leibniz never described the characteristica universalis in operational detail, many philosophers have deemed it an absurd fantasy. In this vein, Parkinson wrote: Leibniz's views about the systematic character of all knowledge are linked with his plans for a universal symbolism, a Characteristica Universalis. Th... | Universal characteristic | 0.78131 |
89,438 | Based on the work of its over 250 technical committees, the ISO has issued over 20,000 standards for scientific terminology, names and abbreviations, weights and measures, and safety-related and other pictographs. The Unified Modeling Language (UML) is a general-purpose, developmental modeling language in the field of ... | Universal characteristic | 0.78131 |
89,439 | If this ancestral claim is granted, then simulation software like EXTEND and Valyi's Emergy Simulator can be seen as combining the characteristica and the calculus ratiocinator, if and only if the digital computer is interpreted as a physical embodiment of the calculus ratiocinator. The work of Mario Bunge on the borde... | Universal characteristic | 0.78131 |
89,440 | Specifically, the members of the universal set of a Boolean algebra or group need not be numbers. Moreover, a fair bit of philosophy and theoretical science can be formalized as axiomatic theories embodying first-order logic and set theory. Note also how model theory has been employed to formalize and reason about such... | Universal characteristic | 0.78131 |
89,441 | A wide variety of constructed languages have emerged over the past 150 years which may be seen as supporting some of Leibniz's intuitions. Raymond F. Piper (1957; 432–433) claimed that O.L. Reiser's Unified Symbolism for World Understanding in Science (1955), an expansion of his A Philosophy for World Unification (1946... | Universal characteristic | 0.78131 |
89,442 | Couturat wrote that Leibniz gave Egyptian and Chinese hieroglyphics and chemical signs as examples of real characteristics writing: This shows that the real characteristic was for him an ideography, that is, a system of signs that directly represent things (or, rather, ideas) and not words, in such a way that each nati... | Universal characteristic | 0.78131 |
89,443 | Leibniz said that his goal was an alphabet of human thought, a universal symbolic language (characteristic) for science, mathematics, and metaphysics. According to Couturat, "In May 1676, he once again identified the universal language with the characteristic and dreamed of a language that would also be a calculus—a so... | Universal characteristic | 0.78131 |
89,444 | Inconsistency, vagueness, and a lack of specifics in both English language translations and modern English language interpretations of Leibniz's writings render a clear exposition difficult. As with Leibniz's calculus ratiocinator two different schools of philosophical thought have come to emphasise two different aspec... | Universal characteristic | 0.78131 |
89,445 | It was first reported in 1930 by Ruff and Krug who prepared it by fluorination of chlorine; this also produced Chlorine monofluoride (ClF) and the mixture was separated by distillation. 3 F2 + Cl2 → 2 ClF3The molecular geometry of ClF3 is approximately T-shaped, with one short bond (1.598 Å) and two long bonds (1.698 Å... | ClF3 | 0.781309 |
89,446 | In molecular biology, this protein domain has been termed SRA-YDG, which is the abbreviation for SET and Ring finger Associated, YDG motif. Additional characteristics of the domain include conservation of up to 13 evenly spaced glycine residues and a VRV(I/V)RG motif. The protein domain is mainly found in plants and an... | YDG SRA protein domain | 0.781308 |
89,447 | Over the real and complex numbers, the topology of PGL and PSL can be determined from the fiber bundles that define them: Z ≅ K ∗ → G L → P G L S Z ≅ μ n → S L → P S L {\displaystyle {\begin{matrix}\mathrm {Z} &\cong &K^{*}&\to &\mathrm {GL} &\to &\mathrm {PGL} \\\mathrm {SZ} &\cong &\mu _{n}&\to &\mathrm {SL} &\to &\m... | Projective general linear group | 0.781308 |
89,448 | Over the real and complex numbers, the projective special linear groups are the minimal (centerless) Lie group realizations for the special linear Lie algebra s l ( n ): {\displaystyle {\mathfrak {sl}}(n)\colon } every connected Lie group whose Lie algebra is s l ( n ) {\displaystyle {\mathfrak {sl}}(n)} is a cover of ... | Projective general linear group | 0.781308 |
89,449 | The name comes from projective geometry, where the projective group acting on homogeneous coordinates (x0:x1: ... :xn) is the underlying group of the geometry. Stated differently, the natural action of GL(V) on V descends to an action of PGL(V) on the projective space P(V). The projective linear groups therefore genera... | Projective general linear group | 0.781308 |
89,450 | The zeta function can be rewritten as: ζ ( z ; Λ ) = 1 z − ∑ k = 1 ∞ G 2 k + 2 ( Λ ) z 2 k + 1 {\displaystyle \operatorname {\zeta } {(z;\Lambda )}={\frac {1}{z}}-\sum _{k=1}^{\infty }{\mathcal {G}}_{2k+2}(\Lambda )z^{2k+1}} where G 2 k + 2 {\displaystyle {\mathcal {G}}_{2k+2}} is the Eisenstein series of weight 2k +... | Weierstrass functions | 0.781307 |
89,451 | The Statistical Analysis System (SAS) began as a project at North Carolina State University's agricultural department. It was originally led by Anthony James Barr in 1966, then joined by NCSU graduate student James Goodnight in 1967 and John Sall in 1973. In the early 1970s, the software was primarily leased to other a... | SAS Institute | 0.781307 |
89,452 | This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at the end of this article. | Stable cohomotopy theory | 0.781303 |
89,453 | Spectrum: BP Coefficient ring: π*(BP) is a polynomial algebra over Z(p) on generators vn of dimension 2(pn − 1) for n ≥ 1. Brown–Peterson cohomology BP is a summand of MUp, which is complex cobordism MU localized at a prime p. In fact MU(p) is a sum of suspensions of BP. | Stable cohomotopy theory | 0.781303 |
89,454 | A nitrenium ion (also called: aminylium ion or imidonium ion (obsolete)) in organic chemistry is a reactive intermediate based on nitrogen with both an electron lone pair and a positive charge and with two substituents (R2N+). Nitrenium ions are isoelectronic with carbenes, and can exist in either a singlet or a triple... | Nitrenium ion | 0.781303 |
89,455 | The regiochemistry and energetics of the reaction of phenylnitrenium ion with guanine has been investigated using density functional theory computations.Nitrenium species have been exploited as intermediates in organic reactions. They are typically generated via heterolysis of N–X (X = N, O, Halogen) bonds. | Nitrenium ion | 0.781303 |
89,456 | Within the C* formalism this non-unitary process is equivalent to the algebra gaining a non-trivial centre or centre of its centralizer corresponding to classical observables.The significance ascribed to the wave function varies from interpretation to interpretation, and varies even within an interpretation (such as th... | Collapse of the wave function | 0.781298 |
89,457 | Mathematically it can be shown that collapse is equivalent to interaction with a classical system modeled within quantum theory as systems with Boolean algebras of observables and equivalent to a conditional expectation value.Everett's many-worlds interpretation deals with it by discarding the collapse-process, thus re... | Collapse of the wave function | 0.781298 |
89,458 | However, he did not prove the necessity of such a collapse. Although von Neumann's projection postulate is often presented as a normative description of quantum measurement, it was conceived by taking into account experimental evidence available during the 1930s (in particular the Compton-Simon experiment was paradigma... | Collapse of the wave function | 0.781298 |
89,459 | The concept of wavefunction collapse was introduced by Werner Heisenberg in his 1927 paper on the uncertainty principle, "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik", and incorporated into the mathematical formulation of quantum mechanics by John von Neumann, in his 1932 treatise Math... | Collapse of the wave function | 0.781298 |
89,460 | Written out, this means that P must be true if there is a proposition Q such that the truth of P follows from the truth of "if P then Q". In particular, when Q is taken to be a false formula, the law says that if P must be true whenever it implies falsity, then P is true. In this way Peirce's law implies the law of exc... | Peirce's law | 0.781296 |
89,461 | In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. It can be thought of as the law of excluded middle written in a form that involves only one sort of connective, namely implication. In propositional cal... | Peirce's law | 0.781296 |
89,462 | From that and P→Z, we get P→Q. Then we apply modus ponens with (P→Q)→Z as the major premise to get Z. Applying the deduction theorem, we get that (Z→Q)→Z follows from the original premises. Then we use Peirce's law in the form ((Z→Q)→Z)→Z and modus ponens to derive Z from the original premises. Then we can finish off p... | Peirce's law | 0.781296 |
89,463 | Peirce's law allows one to enhance the technique of using the deduction theorem to prove theorems. Suppose one is given a set of premises Γ and one wants to deduce a proposition Z from them. With Peirce's law, one can add (at no cost) additional premises of the form Z→P to Γ. For example, suppose we are given P→Z and (... | Peirce's law | 0.781296 |
89,464 | In mathematics and information theory, Sanov's theorem gives a bound on the probability of observing an atypical sequence of samples from a given probability distribution. In the language of large deviations theory, Sanov's theorem identifies the rate function for large deviations of the empirical measure of a sequence... | Sanov's theorem | 0.781294 |
89,465 | On May 19, 1998, all seven members of L0pht (Brian Oblivion, Kingpin, Mudge, Space Rogue, Stefan Von Neumann, John Tan, Weld Pond) famously testified before the Congress of the United States that they could shut down the entire Internet in 30 minutes. The Washington Post referred to the response as "a tragedy of missed... | L0pht | 0.781294 |
89,466 | Symmetry breaking can cover any of the following scenarios: The breaking of an exact symmetry of the underlying laws of physics by the apparently random formation of some structure; A situation in physics in which a minimal energy state has less symmetry than the system itself; Situations where the actual state of the ... | Broken symmetry | 0.781293 |
89,467 | This is not invariant under the action of G {\displaystyle G} . It is often proportional to a small, perturbative parameter. This is essentially the paradigm for perturbation theory in quantum mechanics. An example of its use is in finding the fine structure of atomic spectra. | Broken symmetry | 0.781293 |
89,468 | Frequently and variably, other common symptoms occur involving numerous body systems, and chronic pain is very common. The often incapacitating fatigue in CFS is different from that caused by normal strenuous exertion, is not significantly relieved by rest, and is not due to a previous medical condition. Diagnosis is b... | Myalgic encephalitis | 0.781291 |
89,469 | Autoimmunity has been proposed as a cause, but evidence is scant. People with ME/CFS may have abnormal gut microbiota, which has been proposed to affect mitochondria or nervous system function.Several small studies have investigated the genetics of ME/CFS, but none of their findings have been replicated. A larger study... | Myalgic encephalitis | 0.781291 |
89,470 | Boston University's student-run "Rocket Propulsion Group", which in the past has launched only solid motor rockets, is attempting to design and build a single-stage hybrid sounding rocket to launch into sub-orbital space by July 2015.Brigham Young University (BYU), the University of Utah, and Utah State University laun... | Hybrid-propellant rocket | 0.78129 |
89,471 | POSTECH was established in 1986 in Pohang, Korea by POSCO, a steel company.POSTECH hosted POSCO's Research Institute of Science and Technology (RIST) on campus. In 1994, POSTECH set up the Pohang Accelerator Laboratory (PAL), a 3rd-generation synchrotron light source and now a national facility. PAL-XFEL, a 4th-generat... | Pohang University of Science and Technology | 0.781289 |
89,472 | Asteroid mining within the Solar System is also a detectable technosignature of the first kind.Individual extrasolar planets can be analyzed for signs of technology. Avi Loeb of the Center for Astrophysics | Harvard & Smithsonian has proposed that persistent light signals on the night side of an exoplanet can be an ind... | Search for extraterrestrial intelligence | 0.781287 |
89,473 | Released on June 7, 2022, 0.6.0 defined a new level for ELKS, as indicated by the much shorter than usual release cycle. The speed at which the system evolves and improves, combined with its recently acquired reliability and usability created a demand for 'updated packaged releases' from new users. 0.6.0 included lots ... | Embeddable Linux Kernel Subset | 0.781287 |
89,474 | Chemically analogous cyclic thiacyclols have also been obtained. Classic azacyclols have been observed in small molecules and tripeptides. Peptides are naturally produced from the reversion of azacylols, a key prediction of the cyclol model. Hundreds of cyclol molecules have now been identified, despite Linus Pauling's... | Cyclol reaction | 0.781285 |
89,475 | The physics governing Jupiter's radio emissions is similar to that of radio pulsars. They differ only in the scale, and Jupiter can be considered a very small radio pulsar too. In addition, Jupiter's radio emissions strongly depend on solar wind pressure and, hence, on solar activity.In addition to relatively long-wave... | Magnetosphere of Jupiter | 0.781285 |
89,476 | In organic chemistry an enol ether is an alkene with an alkoxy substituent. The general structure is R2C=CR-OR where R = H, alkyl or aryl. A common subfamily of enol ethers are vinyl ethers, with the formula ROCH=CH2. Important enol ethers include the reagent 3,4-dihydropyran and the monomers methyl vinyl ether and eth... | Enol ether | 0.781285 |
89,477 | Skinner's view of behavior is most often characterized as a "molecular" view of behavior; that is, behavior can be decomposed into atomistic parts or molecules. This view is inconsistent with Skinner's complete description of behavior as delineated in other works, including his 1981 article "Selection by Consequences".... | Behavioural psychology | 0.781284 |
89,478 | Pentacyanocyclopentadiene is synthesised by coupling carbon disulfide and sodium cyanide in dimethylformamide before oxidation using ammonium persulfate and final purification generates the ammonium pentacyanocyclopentadiene salt. Further reaction with sodium hydride generates NaC5(CN)5 which is a starting point for it... | Pentacyanocyclopentadiene | 0.781283 |
89,479 | The anion was first synthesised by Webster in the 1960s and its conjugate acid much later on. More recently Wright has discovered its extensive coordination chemistry. By virtue of a combination of mesomeric and aromatic stabilization of its anion, pentacyanocyclopentadiene is a superacid, with an estimated aqueous pKa... | Pentacyanocyclopentadiene | 0.781283 |
89,480 | SAE Aero Design, also called the SAE Aero Design Collegiate Design Series, is a series of competitive aerospace and mechanical engineering events held in the United States and Brazil every year. It is conducted by SAE International. It is generally divided into three categories: Regular class, Advanced class and Micro ... | SAE Aerodesign | 0.781282 |
89,481 | SMM has been adopted as a regulatory approach to manage materials by the U.S. Environmental Protection Agency (EPA) and many other governments around the world. Sustainable Materials Management is a broad approach that overlaps and supplements many programs and concepts being adopted by governments and business around ... | Sustainable materials management | 0.78128 |
89,482 | A strengthened version of Kirchberger's theorem fixes one of the given points, and only considers subsets of d + 2 {\displaystyle d+2} points that include the fixed point. If the red and blue points in each of these subsets are linearly separable, then all the red points and all the blue points are linearly separable. ... | Kirchberger's theorem | 0.78128 |
89,483 | The theorem is named after German mathematician Paul Kirchberger, a student of David Hilbert at the University of Göttingen who proved it in his 1902 dissertation, and published it in 1903 in Mathematische Annalen, as an auxiliary theorem used in his analysis of Chebyshev approximation. A report of Hilbert on the disse... | Kirchberger's theorem | 0.78128 |
89,484 | Kirchberger's theorem is a theorem in discrete geometry, on linear separability. The two-dimensional version of the theorem states that, if a finite set of red and blue points in the Euclidean plane has the property that, for every four points, there exists a line separating the red and blue points within those four, t... | Kirchberger's theorem | 0.78128 |
89,485 | Erdős and Hajnal (1966) showed that for every ordinal λ there is an ω-Jónsson function for λ. Kunen's proof of Kunen's inconsistency theorem uses a Jónsson function for cardinals λ such that 2λ = λℵ0, and Kunen observed that for this special case there is a simpler proof of the existence of Jónsson functions. Galvin an... | Jónsson function | 0.781279 |
89,486 | The assignment u ↦ t u {\displaystyle u\mapsto {}^{t}u} produces an injective linear map between the space of linear operators from X {\displaystyle X} to Y {\displaystyle Y} and the space of linear operators from Y # {\displaystyle Y^{\#}} to X # . {\displaystyle X^{\#}.} If X = Y {\displaystyle X=Y} then the space of... | Transpose of a linear map | 0.781279 |
89,487 | Let M {\displaystyle M} be a closed vector subspace of a Hausdorff locally convex space X {\displaystyle X} and denote the canonical quotient map by Assume X / M {\displaystyle X/M} is endowed with the quotient topology induced by the quotient map π: X → X / M . {\displaystyle \pi :X\to X/M.} Then the transpose of the ... | Transpose of a linear map | 0.781279 |
89,488 | A is diagonalizable if and only if, for every eigenvalue λ of A, its geometric and algebraic multiplicities coincide. In particular, the Jordan blocks in this case are 1 × 1 matrices; that is, scalars. | Jordan canonical form | 0.781279 |
89,489 | Assuming this result, we can deduce the following properties: Counting multiplicities, the eigenvalues of J, and therefore of A, are the diagonal entries. Given an eigenvalue λi, its geometric multiplicity is the dimension of ker(A − λi I), where I is the identity matrix, and it is the number of Jordan blocks correspon... | Jordan canonical form | 0.781279 |
89,490 | It can be shown that the Jordan normal form of a given matrix A is unique up to the order of the Jordan blocks. Knowing the algebraic and geometric multiplicities of the eigenvalues is not sufficient to determine the Jordan normal form of A. Assuming the algebraic multiplicity m(λ) of an eigenvalue λ is known, the stru... | Jordan canonical form | 0.781279 |
89,491 | More generally, for a complex number λ, its index can be defined as the least non-negative integer ν(λ) such that ker ( A − λ I ) ν ( λ ) = ker ( A − λ I ) m , ∀ m ≥ ν ( λ ) . {\displaystyle \ker(A-\lambda I)^{\nu (\lambda )}=\ker(A-\lambda I)^{m},\;\forall m\geq \nu (\lambda ).} So ν(v) > 0 if and only if λ is an ... | Jordan canonical form | 0.781279 |
89,492 | See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion. Comparing the two decompositions, notice that, in general, l ≤ k. When A is normal, the subspaces Xi's in the first decomposition are one-dimensional and mutually orthogonal. This is the spectral ... | Jordan canonical form | 0.781279 |
89,493 | The Cayley–Hamilton theorem asserts that every matrix A satisfies its characteristic equation: if p is the characteristic polynomial of A, then p A ( A ) = 0 {\displaystyle p_{A}(A)=0} . This can be shown via direct calculation in the Jordan form, since if λ i {\displaystyle \lambda _{i}} is an eigenvalue of multiplici... | Jordan canonical form | 0.781279 |
89,494 | The assumption that σ(T) lie in the inside of Γ ensures f(T) is well defined; it does not depend on the choice of Γ. The functional calculus is the mapping Φ from Hol(T) to L(X) given by Φ ( f ) = f ( T ) . {\displaystyle \;\Phi (f)=f(T).} We will require the following properties of this functional calculus: Φ extends ... | Jordan canonical form | 0.781279 |
89,495 | Let X be a Banach space, L(X) be the bounded operators on X, and σ(T) denote the spectrum of T ∈ L(X). The holomorphic functional calculus is defined as follows: Fix a bounded operator T. Consider the family Hol(T) of complex functions that is holomorphic on some open set G containing σ(T). Let Γ = {γi} be a finite col... | Jordan canonical form | 0.781279 |
89,496 | Consider the annular region A centered at the eigenvalue λ with sufficiently small radius ε such that the intersection of the open disc Bε(λ) and σ(T) is {λ}. The resolvent function RT is holomorphic on A. Extending a result from classical function theory, RT has a Laurent series representation on A: R T ( z ) = ∑ − ∞ ... | Jordan canonical form | 0.781279 |
89,497 | Jordan reduction can be extended to any square matrix M whose entries lie in a field K. The result states that any M can be written as a sum D + N where D is semisimple, N is nilpotent, and DN = ND. This is called the Jordan–Chevalley decomposition. Whenever K contains the eigenvalues of M, in particular when K is alge... | Jordan canonical form | 0.781279 |
89,498 | This can be used to show the uniqueness of the Jordan form. Let J1 and J2 be two Jordan normal forms of A. Then J1 and J2 are similar and have the same spectrum, including algebraic multiplicities of the eigenvalues. The procedure outlined in the previous paragraph can be used to determine the structure of these matric... | Jordan canonical form | 0.781279 |
89,499 | The relation ∑ i e i = 1 {\displaystyle \sum _{i}e_{i}=1} implies C n = ⨁ i Ran e i ( T ) = ⨁ i ker ( T − λ i ) ν i {\displaystyle \mathbb {C} ^{n}=\bigoplus _{i}\;\operatorname {Ran} e_{i}(T)=\bigoplus _{i}\ker(T-\lambda _{i})^{\nu _{i}}} where the index i runs through the distinct eigenvalues of T. This is the in... | Jordan canonical form | 0.781279 |
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