id
int32
0
100k
text
stringlengths
21
3.54k
source
stringlengths
1
124
similarity
float32
0.78
0.88
96,700
The class of all semigroups forms a variety of algebras of signature (2), meaning that a semigroup has a single binary operation. A sufficient defining equation is the associative law: x ( y z ) = ( x y ) z . {\displaystyle x(yz)=(xy)z.} The class of groups forms a variety of algebras of signature (2,0,1), the three op...
Finitary algebraic category
0.778107
96,701
One direction of the equivalence mentioned above, namely that a class of algebras satisfying some set of identities must be closed under the HSP operations, follows immediately from the definitions. Proving the converse—classes of algebras closed under the HSP operations must be equational—is more difficult. Using the ...
Finitary algebraic category
0.778107
96,702
Given a class of algebraic structures of the same signature, we can define the notions of homomorphism, subalgebra, and product. Garrett Birkhoff proved that a class of algebraic structures of the same signature is a variety if and only if it is closed under the taking of homomorphic images, subalgebras and arbitrary p...
Finitary algebraic category
0.778107
96,703
The Ministry of Power and Energy (Sinhala: විදුලිබල හා බලශක්ති අමාත්‍යාංශය; Tamil: மின்சக்தி மற்றும் வலுசக்தி அமைச்சு) is a cabinet ministry of the Government of Sri Lanka responsible for power and renewable energy. The ministry is responsible for formulating and implementing national policy on power and renewable ener...
Ministry of Power and Energy
0.778106
96,704
For instance some genera such as Hyacinthus, previously placed in Liliaceae s.l., were reclassified in families within Asparagales (in this case Asparagaceae). In 1995 Chase et al. reviewed the understanding of the lilioids and equated them to Dahlgreen's Liliiflorae, which they designated as superorder Lilianae. They ...
Lilioid monocots
0.778105
96,705
The Steinitz exchange lemma is a basic result in computational mathematics, especially in linear algebra and in combinatorial algorithms.
Steinitz exchange lemma
0.778104
96,706
Inner sphere complex is a type of surface complex that refers to the surface chemistry changing a water-surface interface to one without water molecules bridging a ligand to the metal ion. Formation of inner sphere complexes occurs when ions bind directly to the surface with no intervening water molecules. These types ...
Inner sphere complex
0.778103
96,707
More generally, f ( z ) = ∫ 0 z sin ⁡ ( ζ ρ ) ζ ρ d ζ , {\displaystyle f(z)=\int _{0}^{z}{\frac {\sin(\zeta ^{\rho })}{\zeta ^{\rho }}}d\zeta ,} with ρ any positive integer, is of order ρ and has 2ρ asymptotic values. It is clear that the theorem applies to polynomials only if they are not constant. A constant polynomi...
Denjoy–Carleman–Ahlfors theorem
0.778102
96,708
The Denjoy–Carleman–Ahlfors theorem states that the number of asymptotic values attained by a non-constant entire function of order ρ on curves going outwards toward infinite absolute value is less than or equal to 2ρ. It was first conjectured by Arnaud Denjoy in 1907.Torsten Carleman showed that the number of asymptot...
Denjoy–Carleman–Ahlfors theorem
0.778102
96,709
In mathematics, the braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see § Introduction). Example applications of braid gro...
Braid length
0.778101
96,710
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, option pricing, and pattern theory and computational vision.
Jump-diffusion models
0.778101
96,711
A drainage basin's boundaries are determined by watershed delineation, a common task in environmental engineering and science. In a closed drainage basin, or endorheic basin, rather than flowing to the ocean, water converges toward the interior of the basin, known as a sink, which may be a permanent lake, a dry lake, o...
Drainage basin
0.778101
96,712
Those who are oriented toward science tend to regard their discipline as empirical and data-oriented, and to borrow their methods and ways of thinking from psychology, acoustics, psychoacoustics, physiology, cognitive science, and (empirical) sociology.More recently emerged areas of research which at least partially ar...
Systematic musicology
0.7781
96,713
These questions tend to be answered either by analysing empirical data (based on observation) or by developing theory – or better, by a combination of both. The 19th-century positivist dream of discovering "laws" of music (by analogy to "laws" in other disciplines such as physics; cf. Adler, 1885), and of defining the ...
Systematic musicology
0.7781
96,714
In the Springer Handbook of Systematic Musicology, "(the) sections follow the main topics in the field, Musical Acoustics, Signal Processing, Music Psychology, Psychophysics/Psychoacoustics, and Music Ethnology while also taking recent research trends into consideration, like Embodied Music Cognition and Media Applicat...
Systematic musicology
0.7781
96,715
Systematic musicology is an umbrella term, used mainly in Central Europe, for several subdisciplines and paradigms of musicology. "Systematic musicology has traditionally been conceived of as an interdisciplinary science, whose aim it is to explore the foundations of music from different points of view, such as acousti...
Systematic musicology
0.7781
96,716
The Journal of Structural Engineering is the principal professional peer-reviewed journal of the American Society of Civil Engineers, the oldest professional civil engineering society in the United States. The journal is one of the flagship journals of the Society. It is sponsored by its division, the ASCE Structural E...
Journal of Structural Engineering
0.778097
96,717
The Journal of Structural Engineering is indexed in Scopus, Web of Science, and Engineering Index, Civil engineering database, OCLC (WorldCat). It is available on ProQuest and EbscoNet.
Journal of Structural Engineering
0.778097
96,718
Kurzweil then explains that a computer version of this design could be used to create an artificial intelligence more capable than the human brain. It would employ techniques such as hidden Markov models and genetic algorithms, strategies Kurzweil used successfully in his years as a commercial developer of speech recog...
How to Create a Mind
0.778097
96,719
In the first case it is tempting to say the clone is not the original person, because the original person still exists. Kurzweil instead concludes both versions are equally the same person. He explains that an advantage of nonbiological systems is "the ability to be copied, backed up, and re-created" and this is just s...
How to Create a Mind
0.778097
96,720
Kurzweil holds a pragmatic belief in free will because he feels society needs it to function. He also suggests that quantum mechanics may provide "a continual source of uncertainty at the most basic level of reality" such that determinism does not exist. Finally Kurzweil addresses identity with futuristic scenarios inv...
How to Create a Mind
0.778097
96,721
Simson Garfinkel, an entrepreneur and professor of computer science at the Naval Postgraduate School, says Kurzweil's pattern recognition theory of mind (PRTM) is misnamed because of the word "theory", he feels it is not a theory since it cannot be tested. Garfinkel rejects Kurzweil's one-algorithm approach instead say...
How to Create a Mind
0.778097
96,722
Kurzweil next writes about creating a digital brain inspired by the biological brain he has been describing. One existing effort he points to is Henry Markram's Blue Brain Project, which is attempting to create a full brain simulation by 2023. Kurzweil says the full molecular modeling they are attempting will be too sl...
How to Create a Mind
0.778097
96,723
He says "There will be no distinction, post-Singularity, between human and machine...".Kurzweil himself plans to "stick around" for the Singularity. He has written two health and nutrition books aimed at living longer, the subtitle of one is "Live Long Enough to Live Forever". One month after How to Create a Mind was p...
How to Create a Mind
0.778097
96,724
As computational power continues to grow, machine intelligence will represent an ever-larger percentage of total intelligence on the planet. Ultimately it will lead to the Singularity, a merger between biology and technology, which Kurzweil predicts will occur in 2045.
How to Create a Mind
0.778097
96,725
The Z machine's origins can be traced to the Department of Energy needing to replicate the fusion reactions of a thermonuclear bomb in a lab environment to better understand the physics involved. Since the 1970s the DoE had been looking into ways to generate electricity from fusion reactions, with continuous reactions ...
Z Pulsed Power Facility
0.778096
96,726
Wideband audio codingLinear predictive coding (LPC) AMR-WB for WCDMA networks VMR-WB for CDMA2000 networks Speex, IP-MR, SILK (part of Opus), and USAC/xHE-AAC for voice-over-IP (VoIP) and videoconferencing Modified discrete cosine transform (MDCT) AAC-LD, G.722.1, G.729.1, CELT and Opus for VoIP and videoconferencing A...
Speech coder
0.778094
96,727
Speech coders are of two classes: Waveform coders Time-domain: PCM, ADPCM Frequency-domain: sub-band coding, ATRAC Vocoders Linear predictive coding (LPC) Formant coding Machine learning, i.e. neural vocoder
Speech coder
0.778094
96,728
In the geometry of hyperbolic 3-space, the order-6 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,6}. It has six icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around ...
Order-4 icosahedral honeycomb
0.778094
96,729
In the geometry of hyperbolic 3-space, the infinite-order icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,∞}. It has infinitely many icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahed...
Order-4 icosahedral honeycomb
0.778094
96,730
The Wagner-Jauregg reaction is a classic organic reaction in organic chemistry, named after Theodor Wagner-Jauregg (son of Julius Wagner-Jauregg), describing the double Diels–Alder reaction of 2 equivalents of maleic anhydride with a 1,1-diarylethylene. After aromatization of the bis-adduct, the ultimate reaction produ...
Wagner-Jauregg reaction
0.778091
96,731
and Elpida Memory Inc. will produce its new memory technology, known as XDR DRAM. The memory technology is capable of running at 3.2 GHz and is said to be faster than any memory technology available in consumer entertainment devices and PCs at the time.Rambus purchased Cryptography Research on June 6, 2011, for $342.5M...
Rambus
0.778091
96,732
Proof of the Higgs field (by observing the associated particle) validates the final unconfirmed part of the Standard Model as essentially correct, avoiding the need for alternative sources for the Higgs mechanism. Evidence of its properties is likely to greatly affect human understanding of the universe and open up "ne...
Search for the Higgs boson
0.77809
96,733
The search for the Higgs boson was a 40-year effort by physicists to prove the existence or non-existence of the Higgs boson, first theorised in the 1960s. The Higgs boson was the last unobserved fundamental particle in the Standard Model of particle physics, and its discovery was described as being the "ultimate verif...
Search for the Higgs boson
0.77809
96,734
In 2012, the "5-sigma" criterion required by the scientists at the LHC, and its underlying frequentist interpretation of probability, triggered the interest of some statisticians, especially Bayesians: "five standard deviations, assuming normality, means a p-value of around 0.0000005 Are the particle physics community...
Search for the Higgs boson
0.77809
96,735
All of the above confidence intervals were derived using the CLs method. As of December 2011 the search had narrowed to the approximate region to 115–130 GeV, with a specific focus around 125 GeV, where both the ATLAS and CMS experiments had independently reported an excess of events, meaning that a higher than expecte...
Search for the Higgs boson
0.77809
96,736
During the early 1970s there were only few constraints on the existence of the Higgs boson. The limits that did exist came from the absence of the observation of Higgs related effects in nuclear physics, neutron stars, and neutron scattering experiments. This resulted in the conclusion that the Higgs—if it existed—was ...
Search for the Higgs boson
0.77809
96,737
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positiv...
Search for the Higgs boson
0.77809
96,738
Planning for a new powerful collider to explore new physics at the >1 TeV scale had already started in 1983. The Superconducting Super Collider was to accelerate protons in an underground 87.1 km circular tunnel just outside Dallas, Texas to energies of 20 TeV each. One of the primary goals of this megaproject was find...
Search for the Higgs boson
0.77809
96,739
In their final analyses, the collaborations of the two detectors at Tevatron (CDF and DØ) report that based on their data they can exclude the possibility of a Higgs boson with a mass between 100 GeV/c2 and 103 GeV/c2 and between 147 GeV/c2 and 180 GeV/c2 at a 95% confidence level. In addition, they found an excess of ...
Search for the Higgs boson
0.77809
96,740
If it were too light (<140 GeV), then the Higgs would predominantly decay to pairs of bottom quarks—a signal that would be swamped by background events, and the Tevatron would not produce enough collisions to filter out the statistics. Nonetheless, the Tevatron was at the time the only operational particle collider tha...
Search for the Higgs boson
0.77809
96,741
These observables are sensitive to the value of the Higgs mass through contributions of processes containing loops of virtual Higgs bosons. This allowed for the first time a direct estimate of the Higgs mass of about 100±30 GeV/c2. This estimate however is subject to the condition that the Standard Model is all there i...
Search for the Higgs boson
0.77809
96,742
Using χ = h 0 , 0 − h 0 , 1 + h 0 , 2 c 2 = 2 − 2 b 1 + b 2 {\displaystyle {\begin{aligned}\chi &=h^{0,0}-h^{0,1}+h^{0,2}\\c_{2}&=2-2b_{1}+b_{2}\end{aligned}}} we arrive at: 10 + 12 h 0 , 2 = 8 h 0 , 1 + 2 ( 2 h 0 , 1 − b 1 ) + b 2 {\displaystyle 10+12h^{0,2}=8h^{0,1}+2\left(2h^{0,1}-b_{1}\right)+b_{2}} Moreover since ...
Enriques–Kodaira classification
0.778089
96,743
These are the complex surfaces such that q = 0 and the canonical line bundle is non-trivial, but has trivial square. Enriques surfaces are all algebraic (and therefore Kähler). They are quotients of K3 surfaces by a group of order 2 and their theory is similar to that of algebraic K3 surfaces. Invariants: The plurigene...
Enriques–Kodaira classification
0.778089
96,744
These are never algebraic, though they have non-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite groups of orders 2, 3, 4, or 6, and which have non-trivial canonical b...
Enriques–Kodaira classification
0.778089
96,745
The two-dimensional complex tori include the abelian surfaces. One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic. The algebraic ones are exactly the 2-dimensional abelian varieties. Most of their theory is a specia...
Enriques–Kodaira classification
0.778089
96,746
Algebraic surfaces of Kodaira dimension − ∞ {\displaystyle -\infty } can be classified as follows. If q > 0 then the map to the Albanese variety has fibers that are projective lines (if the surface is minimal) so the surface is a ruled surface. If q = 0 this argument does not work as the Albanese variety is a point, bu...
Enriques–Kodaira classification
0.778089
96,747
Federigo Enriques (1914, 1949) described the classification of complex projective surfaces. Kunihiko Kodaira (1964, 1966, 1968a, 1968b) later extended the classification to include non-algebraic compact surfaces. The analogous classification of surfaces in positive characteristic was begun by David Mumford (1969) and c...
Enriques–Kodaira classification
0.778089
96,748
In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli spaces are well understood, but for the class of surfaces of general type t...
Enriques–Kodaira classification
0.778089
96,749
The system would then look for oxygen given off as metabolic byproduct and report results to a Mars-orbiting relay satellite.If this experiment works on Mars, they will propose to build several large and sealed structures called biodomes, to produce and harvest oxygen for a future human mission to Mars life support sys...
Terraforming of Mars
0.778087
96,750
Mars doesn't have an intrinsic global magnetic field, but the solar wind directly interacts with the atmosphere of Mars, leading to the formation of a magnetosphere from magnetic field tubes. This poses challenges for mitigating solar radiation and retaining an atmosphere. The lack of a magnetic field, its relatively s...
Terraforming of Mars
0.778087
96,751
SYSTEMCONFIG.GBX – Launcher info. TRACKMANIAVEHICLE.GBX – Info about a certain car type. VEHICLETUNINGS.GBX – Vehicle physics.
List of file formats
0.778087
96,752
Electronic design automation (EDA), or electronic computer-aided design (ECAD), is specific to the field of electrical engineering. BRD – Board file for EAGLE Layout Editor, a commercial PCB design tool BSDL – Description language for testing through JTAG CDL – Transistor-level netlist format for IC design CPF – Power-...
List of file formats
0.778087
96,753
ASC – ASCII point of interest (POI) text file APR – ESRI ArcView 3.3 and earlier project file DEM – USGS DEM file format E00 – ARC/INFO interchange file format GeoJSON – Geographically located data in object notation TopoJSON – Extension of GeoJSON with topology encoded in arcs for web development GeoTIFF – Geographica...
List of file formats
0.778087
96,754
Sometimes also given as QUAL. GCPROJ – The Genome Compiler project. Advanced format for genetic data to be designed, shared and visualized. GenBank – The flatfile format used by the NCBI to represent database records for nucleotide and peptide sequences from the GenBank and RefSeq databases GFF – The General feature fo...
List of file formats
0.778087
96,755
Molecular biology and bioinformatics: AB1 – In DNA sequencing, chromatogram files used by instruments from Applied Biosystems ACE – A sequence assembly format ASN.1 – Abstract Syntax Notation One, is an International Standards Organization (ISO) data representation format used to achieve interoperability between platfo...
List of file formats
0.778087
96,756
Other calendars count from various other events, and different schools of astronomy give the years different names. The Theocracy of Muntab has a calendar that counts down, rather than up. The reason for this is unknown, though it is agreed that waiting around for it to reach zero is unwise.
Counterweight Continent
0.778086
96,757
The Discworld is the fictional setting for all of Terry Pratchett's Discworld fantasy novels. It consists of a large disc (complete with edge-of-the-world drop-off and consequent waterfall) resting on the backs of four huge elephants which are in turn standing on the back of an enormous turtle, named Great A'Tuin (simi...
Counterweight Continent
0.778086
96,758
Discworld witches often employ narrative in their magic, but consider it ethically tricky since it interferes with free will. Discworld wizards avoid doing so because narrative that severely strains credibility requires outright sources of magic to feed on, sometimes indiscriminately. Knowledge of stories, their use an...
Counterweight Continent
0.778086
96,759
The Chalk is an area of rolling chalk downland near Lancre, bearing a great resemblance to Pratchett's native Wiltshire. The "soft" geology of the area is, according to some mountain witches, not conducive to the channelling of magic. In fact this is a misconception (the bones of the hills are flint), and powerful witc...
Counterweight Continent
0.778086
96,760
These concepts of Discworld physics are also exploited in both wizard and witch magic. For example, when a character wishes to turn a cat into a human, the easiest way is to convince the cat, on a deep level, that he is a human. In fact, the main reason the Auditors of Reality dislike sentient beings in the Discworld u...
Counterweight Continent
0.778086
96,761
Reality is spread thinly on the Disc, so events may be affected by expectations, especially those of 'intelligent' species such as humans, dwarves, etc. As such, the Discworld is not governed by real-world physics or logic but by belief and narrative resolution. Essentially, if something is believed strongly enough, or...
Counterweight Continent
0.778086
96,762
Susan Sto Helit describes it as "an education in, well, education" (Hogfather). It appears that those students who do not marry upon leaving school generally go into the teaching profession themselves, or become governesses. Staff include Miss Butts, the Headmistress; Miss Delcross, the Biology mistress; and "Iron Lily...
Counterweight Continent
0.778086
96,763
The school's strong emphasis on decency reportedly makes it rather difficult to teach certain areas of Biology; students come out of that class "with the vague idea that they were supposed to marry a rabbit" (Soul Music). Students at the school do not seem to be preparing for any particular profession. As the known uni...
Counterweight Continent
0.778086
96,764
Featured in Unseen Academicals. (Other definitions) Trolls Trolls on the Discworld are large lifeforms best described as living rock, composed of silicon with carbon; they survive on minerals and are named after geology. Trolls are not known to die natural deaths: while they can be killed, as they grow several centurie...
Counterweight Continent
0.778086
96,765
The Low King, whose authority extends over all dwarfish communities, is the final arbiter in cases where disputes where the kruk is unclear. Dwarfs consider their culture more important than genetics, and can consider other species to be Dwarfs, such as in the case of Carrot Ironfoundersson. Dwarfs believe the universe...
Counterweight Continent
0.778086
96,766
The thaum also appears to be a particle, the Discworld physics equivalent of the atom. "Splitting the thaum" revealed that it was in fact composed of numerous sub-particles, called resons ("thingies") which in turn are created from a combination of up to five "flavours": up, down, sideways, sex appeal, and peppermint (...
Counterweight Continent
0.778086
96,767
Areas with larger than normal quantities of background magic tend to display unusual qualities, even for the Disc. Very high quantities of magic can knock a hole in Discworld reality, leading to an invasion by Lovecraftian monstrosities from the Dungeon Dimensions, or, almost as bad, the world of the Elves. In the Disc...
Counterweight Continent
0.778086
96,768
On the Discworld, where magic has more in common with particle physics than Houdini, high-level background magic (most likely a reference to real-world background radiation) occurs when a very powerful spell hits, creating myriad sub-astral particles that severely distort local reality. Building a house in (or even wal...
Counterweight Continent
0.778086
96,769
This eventually led the way to the creation of the U.S. Atomic Energy Commission in 1947. From 1946 to 1957, he worked as a senior physicist at the Brookhaven National Laboratory on Long Island, and wrote a textbook titled Nuclear Physics. Kaplan visited MIT in 1957, and became a professor in 1958 to participate in the...
Irving Kaplan (chemist)
0.778085
96,770
Kaplan received a BA from Columbia University in 1933, an MA in 1934 and a PhD in chemistry in 1937. Before coming to MIT, he was a researcher in chemistry at the Michael Reese Hospital in Chicago from 1937 to 1941. He participated in the Manhattan Project to do research on isotope separation. Kaplan was also a lead fo...
Irving Kaplan (chemist)
0.778085
96,771
In the geometry of hyperbolic 3-space, the order-3-infinite hexagonal honeycomb or (6,3,∞ honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,3,∞}. It has infinitely many hexagonal tiling {6,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with...
Order-7 hexagonal tiling honeycomb
0.778085
96,772
The bottleneck mechanism occurs when the first stimulus is being processed, any other stimuli cannot be processed. The processing of the second stimulus is postponed which slows down reaction time. Neurons that take in information send this information to specific neural networks in different locations. However, when s...
Psychological refractory period
0.778085
96,773
In chemistry, a retort stand, also called a clamp stand, a ring stand, or a support stand, is a piece of scientific equipment intended to support other pieces of equipment and glassware — for instance, burettes, test tubes and flasks.The typical ring stand consists of a heavy base and a vertical rod, both usually made ...
Retort stand
0.778085
96,774
Retort stands are often used in the chemistry laboratory. For instance, they are used for distillation experiments (such as organic distillations) and titrations (where they hold a burette). They are also used as supports in filtration.
Retort stand
0.778085
96,775
He thus intended the term to mean a change in the timing of the embryonic development of one organ with respect to the rest of the same animal, whereas it is now used, following the work of the British evolutionary embryologist Gavin de Beer in 1930, to mean a change with respect to the development of the same organ in...
Heterochrony
0.778084
96,776
In evolutionary developmental biology, heterochrony is any genetically controlled difference in the timing, rate, or duration of a developmental process in an organism compared to its ancestors or other organisms. This leads to changes in the size, shape, characteristics and even presence of certain organs and features...
Heterochrony
0.778084
96,777
IT operations analytics (ITOA) (also known as advanced operational analytics, or IT data analytics) technologies are primarily used to discover complex patterns in high volumes of often "noisy" IT system availability and performance data. Forrester Research defined IT analytics as "The use of mathematical algorithms an...
IT operations analytics
0.778083
96,778
Operations research as a discipline emerged from the Second World War to improve military efficiency and decision-making on the battlefield. However, only with the emergence of machine learning tech in the early 2000s could an artificially intelligent operational analytics platform actually begin to engage in the high-...
IT operations analytics
0.778083
96,779
There is also a prevalence (as opposed to incidence) based calculation for YLD. Number of years lost due to premature death is calculated by YLL = N × Lwhere N = number of deaths due to condition, L = standard life expectancy at age of death. Life expectancies are not the same at different ages. For example, in Paleoli...
Disability adjusted life years
0.778083
96,780
Rigorously, a subderivative of a convex function f: I → R {\displaystyle f:I\to \mathbb {R} } at a point x 0 {\displaystyle x_{0}} in the open interval I {\displaystyle I} is a real number c {\displaystyle c} such that for all x ∈ I {\displaystyle x\in I} . By the converse of the mean value theorem, the set of subderiv...
Subderivative
0.778077
96,781
In mathematics, the subderivative, subgradient, and subdifferential generalize the derivative to convex functions which are not necessarily differentiable. Subderivatives arise in convex analysis, the study of convex functions, often in connection to convex optimization. Let f: I → R {\displaystyle f:I\to \mathbb {R} }...
Subderivative
0.778077
96,782
Noether's formula is the first case of the Riemann-Roch theorem for surfaces. The Noether inequality is one of the main restrictions on the possible discrete invariants of a surface. The Noether-Lefschetz theorem (proved by Lefschetz) says that the Picard group of a very general surface of degree at least 4 in P3 is ge...
Max Noether
0.778073
96,783
Brill and Max Noether developed alternative proofs using algebraic methods for much of Riemann's work on Riemann surfaces. Brill–Noether theory went further by estimating the dimension of the space of maps of given degree d from an algebraic curve to projective space Pn. In birational geometry, Noether introduced the f...
Max Noether
0.778073
96,784
In 1883 they had a son named Alfred, who later studied chemistry before dying in 1918. Their third child, Fritz Noether, was born in 1884, and like Emmy, found prominence as a mathematician; he was executed in the Soviet Union in 1941. Little is known about their fourth child, Gustav Robert, born in 1889; he suffered f...
Max Noether
0.778073
96,785
While there, he helped to found the field of algebraic geometry.In 1880 he married Ida Amalia Kaufmann, the daughter of another wealthy Jewish merchant family. Two years later they had their first child, named Amalia ("Emmy") after her mother. Emmy Noether went on to become a central figure in abstract algebra.
Max Noether
0.778073
96,786
Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of Emmy Noether.
Max Noether
0.778073
96,787
To solve the partial differential equation P ( D ) u = f {\displaystyle P(D)\,u=f} we (formally) apply the Fourier transform on both sides and obtain the algebraic equation P ( ξ ) u ^ ( ξ ) = f ^ ( ξ ) . {\displaystyle P(\xi )\,{\hat {u}}(\xi )={\hat {f}}(\xi ).} If the symbol P(ξ) is never zero when ξ ∈ Rn, then it i...
Pseudodifferential operator
0.778072
96,788
Differential operators are local in the sense that one only needs the value of a function in a neighbourhood of a point to determine the effect of the operator. Pseudo-differential operators are pseudo-local, which means informally that when applied to a distribution they do not create a singularity at points where the...
Pseudodifferential operator
0.778072
96,789
Linear differential operators of order m with smooth bounded coefficients are pseudo-differential operators of order m. The composition PQ of two pseudo-differential operators P, Q is again a pseudo-differential operator and the symbol of PQ can be calculated by using the symbols of P and Q. The adjoint and transpose o...
Pseudodifferential operator
0.778072
96,790
The study of pseudo-differential operators began in the mid 1960s with the work of Kohn, Nirenberg, Hörmander, Unterberger and Bokobza.They played an influential role in the second proof of the Atiyah–Singer index theorem via K-theory. Atiyah and Singer thanked Hörmander for assistance with understanding the theory of ...
Pseudodifferential operator
0.778072
96,791
The James Gregory Telescope was constructed in 1962 by the University of St Andrews. It is of a Schmidt-Cassegrain design and is fitted with a CCD camera. The telescope has very large field of view, compared even to regular 'wide field' designs, and can view 5 square degrees.The James Gregory Telescope is the largest w...
James Gregory Telescope
0.778072
96,792
Isolated molecules of BeH2 (sometimes called dihydridoberyllium and written to emphasize the differences with the solid state) are only stable as a dilute gas. When condensed, unsolvated BeH2 will spontaneously autopolymerise. Free molecular BeH2 produced by high-temperature electrical discharge has been confirmed to ...
Beryllium hydride
0.778071
96,793
A 1,2-Wittig rearrangement is a categorization of chemical reactions in organic chemistry, and consists of a 1,2-rearrangement of an ether with an alkyllithium compound. The reaction is named for Nobel Prize winning chemist Georg Wittig. The intermediate is an alkoxy lithium salt, and the final product an alcohol. When...
1,2-Wittig rearrangement
0.778068
96,794
Most formalised systems engineering processes recognise that the cost of correcting a fault increases as it progresses through the development process. Additional effort spent in the early stages of development to discover and correct errors is therefore likely to be worthwhile. Design reviews are example of such an ef...
Design review
0.778067
96,795
The Canadian Undergraduate Technology Conference (CUTC) is a Canadian student-organized conference. It concerns itself with all sorts of technology-related fields, such as: engineering, programming, interactive design, electronics, biology, and chemistry. It aims to introduce undergraduate students to the future of tec...
Canadian Undergraduate Technology Conference
0.778066
96,796
In the academic year 2019/2020 approximately 600 students visited lectures and lab exercises of the Institute of Electron Microscopy and Nanoanalysis. The courses offered are on the topics of fundamental physics, material analysis, electron microscopy and nano-manufacturing. In addition apprenticeships for both lab-tec...
Austrian Centre for Electron Microscopy and Nanoanalysis
0.778065
96,797
In 2011 a streamlined Blackbird reached close to 3 times the speed of wind. Upwind—In 2012, Blackbird set the world's first certified record for going directly upwind faster than the wind, using only wind power. The vehicle achieved a dead upwind speed of about 2.1 times the speed of the wind.Blackbird has been analyze...
Wind-powered land vehicle
0.778062
96,798
The James Webb Space Telescope (JWST) is a space telescope designed primarily to conduct infrared astronomy. Its complex launch and commissioning process lasted from late 2021 until mid-2022. The U.S. National Aeronautics and Space Administration (NASA) led JWST's development in collaboration with the European Space Ag...
Launch and commissioning of the James Webb Space Telescope
0.778062
96,799
In organic chemistry, the Baker–Nathan effect is observed with reaction rates for certain chemical reactions with certain substrates where the order in reactivity cannot be explained solely by an inductive effect of substituents.This effect was described in 1935 by John W. Baker and W. S. Nathan. They examined the chem...
Baker–Nathan effect
0.778061