id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
86,200 | Many believers in Young Earth creationism—a position held by the majority of proponents of 'flood geology'—accept biblical chronogenealogies (such as the Ussher chronology, which in turn is based on the Masoretic version of the Genealogies of Genesis). They believe that God created the universe approximately 6,000 year... | Creation–evolution controversy | 0.782624 |
86,201 | Society of Environmental Toxicology and Chemistry (SETAC). A nonprofit, worldwide society working to promote scientific research to further our understanding of environmental stressors, environmental education, and the use of science in environmental policy. EPA publishes guidance manuals outlining aquatic toxicity tes... | Aquatic toxicity | 0.782621 |
86,202 | In the United States, aquatic toxicology plays an important role in the NPDES wastewater permit program. While most wastewater dischargers typically conduct analytical chemistry testing for known pollutants, whole effluent toxicity tests have been standardized and are performed routinely as a tool for evaluating the po... | Aquatic toxicity | 0.782621 |
86,203 | The Lagrangian reorganizes itself as the Higgs boson acquires a non-vanishing vacuum expectation value dictated by the potential of the previous section. As a result of this rewriting, the symmetry breaking becomes manifest. In the history of the universe, this is believed to have happened shortly after the hot big ban... | Electroweak interaction | 0.782621 |
86,204 | It therefore follows that the laws of configuration of rigid bodies with respect to K' do not agree with the laws of configuration of rigid bodies that are in accordance with Euclidean geometry. If, further, we place two similar clocks (rotating with K'), one upon the periphery, and the other at the centre of the circl... | Ehrenfest paradox | 0.782619 |
86,205 | The rotating disc and its connection with rigidity was also an important thought experiment for Albert Einstein in developing general relativity. He referred to it in several publications in 1912, 1916, 1917, 1922 and drew the insight from it, that the geometry of the disc becomes non-Euclidean for a co-rotating observ... | Ehrenfest paradox | 0.782619 |
86,206 | Grøn states that the resolution of the paradox stems from the impossibility of synchronizing clocks in a rotating reference frame. If observers on the rotating circumference try to synchronise their clocks around the circumference to establish disc time, there is a time difference between the two end points where they ... | Ehrenfest paradox | 0.782619 |
86,207 | 1952: C. Møller attempts to study null geodesics from the point of view of rotating observers (but incorrectly tries to use slices rather than the appropriate quotient space) 1968: V. Cantoni provides a straightforward, purely kinematical explanation of the paradox by showing that "one of the assumptions implicitly con... | Ehrenfest paradox | 0.782619 |
86,208 | He asserts without proof that this geometry is in fact essentially just the geometry of the hyperbolic plane. 1911: Vladimir Varićak argued that the paradox only occurs in the Lorentz standpoint, where rigid bodies contract, but not if the contraction is "caused by the manner of our clock-regulation and length-measurem... | Ehrenfest paradox | 0.782619 |
86,209 | He suggests that resolving the first problem will require introducing some material model and employing the theory of elasticity. 1910: Theodor Kaluza points out that there is nothing inherently paradoxical about the static and disk-riding observers obtaining different results for the circumference. This does however i... | Ehrenfest paradox | 0.782619 |
86,210 | Citations to the papers mentioned below (and many which are not) can be found in a paper by Øyvind Grøn which is available on-line. 1909: Max Born introduces a notion of rigid motion in special relativity. 1909: After studying Born's notion of rigidity, Paul Ehrenfest demonstrated by means of a paradox about a cylinder... | Ehrenfest paradox | 0.782619 |
86,211 | However, since the radius is perpendicular to the direction of motion, it will not undergo any contraction. So c i r c u m f e r e n c e d i a m e t e r = 2 π R 1 − ( ω R ) 2 / c 2 2 R = π 1 − ( ω R ) 2 / c 2 . {\displaystyle {\frac {\mathrm {circumference} }{\mathrm {diameter} }}={\frac {2\pi R{\sqrt {1-(\omega R)^{2}... | Ehrenfest paradox | 0.782619 |
86,212 | This indicates that geometry is non-Euclidean for rotating observers, and was important for Einstein's development of general relativity.Any rigid object made from real material that is rotating with a transverse velocity close to that material's speed of sound must exceed the point of rupture due to centrifugal force,... | Ehrenfest paradox | 0.782619 |
86,213 | Space and time, therefore, cannot be defined with respect to K' as they were in the special theory of relativity with respect to inertial systems. But, according to the principle of equivalence, K' is also to be considered as a system at rest, with respect to which there is a gravitational field (field of centrifugal f... | Ehrenfest paradox | 0.782619 |
86,214 | The first significant (submicrograms) amounts of einsteinium were produced in 1961 by Cunningham and colleagues, but this has not been done for fermium yet.The first isotope of mendelevium, 256Md (half-life 87 min), was synthesized by Albert Ghiorso, Glenn T. Seaborg, Gregory R. Choppin, Bernard G. Harvey and Stanley G... | Actinide elements | 0.782617 |
86,215 | Organic farming encourages crop diversity. The science of Agroecology has revealed the benefits of polyculture (multiple crops in the same space), which is often employed in organic farming. Planting a variety of vegetable crops supports a wider range of beneficial insects, soil microorganisms, and other factors that a... | Organic production | 0.782617 |
86,216 | Naturally, there are a great number of examples for concepts that are dual: Greatest elements and least elements Maximal elements and minimal elements Least upper bounds (suprema, ∨) and greatest lower bounds (infima, ∧) Upper sets and lower sets Ideals and filters Closure operators and kernel operators.Examples of not... | Duality (order theory) | 0.782612 |
86,217 | Ambitious climate policy would see a doubling of energy share consumed as electricity by 2050, from 20% in 2020.One of the challenges in providing universal access to electricity is distributing power to rural areas. Off-grid and mini-grid systems based on renewable energy, such as small solar PV installations that gen... | Low-carbon energy | 0.782612 |
86,218 | Over one-third of energy use is by industry. Most of that energy is deployed in thermal processes: generating heat, drying, and refrigeration. The share of renewable energy in industry was 14.5% in 2017—mostly low-temperature heat supplied by bioenergy and electricity. The most energy-intensive activities in industry h... | Low-carbon energy | 0.782612 |
86,219 | Given a closed, convex subset K of a Hilbert space X and a vector field -F which takes elements from K into X, the projected differential equation associated with K and -F is defined to be d x ( t ) d t = Π K ( x ( t ) , − F ( x ( t ) ) ) . {\displaystyle {\frac {dx(t)}{dt}}=\Pi _{K}(x(t),-F(x(t))).} On the interior of... | Projected dynamical systems | 0.782612 |
86,220 | Projected dynamical systems have evolved out of the desire to dynamically model the behaviour of nonstatic solutions in equilibrium problems over some parameter, typically take to be time. This dynamics differs from that of ordinary differential equations in that solutions are still restricted to whatever constraint se... | Projected dynamical systems | 0.782612 |
86,221 | Sky & Telescope (S&T) is a monthly American magazine covering all aspects of amateur astronomy, including the following: current events in astronomy and space exploration; events in the amateur astronomy community; reviews of astronomical equipment, books, and computer software; amateur telescope making; and astrophoto... | Sky & Telescope | 0.782611 |
86,222 | The original impulse to develop the "derived" formalism came from the need to find a suitable formulation of Grothendieck's coherent duality theory. Derived categories have since become indispensable also outside of algebraic geometry, for example in the formulation of the theory of D-modules and microlocal analysis. R... | Derived category | 0.782611 |
86,223 | The development of the derived category, by Alexander Grothendieck and his student Jean-Louis Verdier shortly after 1960, now appears as one terminal point in the explosive development of homological algebra in the 1950s, a decade in which it had made remarkable strides. The basic theory of Verdier was written down in ... | Derived category | 0.782611 |
86,224 | In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such c... | Derived category | 0.782611 |
86,225 | 2010: The first solar sail based spacecraft, IKAROS. 2010: The first synthetic organism, Mycoplasma laboratorium is created by the J. Craig Venter Institute. 2010: ASML releases the first prototype of an extreme ultraviolet lithography machine. 2014: The first known "NFT", Quantum, was created by Kevin McCoy and Anil D... | Timeline of historic inventions | 0.78261 |
86,226 | 1977: Dr. Walter Gilbert and Frederick Sanger invented a new DNA sequencing method for which they won the Nobel Prize. 1977: The first self-driving car that did not rely upon rails or wires under the road is designed by the Tsukuba Mechanical Engineering Laboratory. 1978: The Global Positioning System (GPS) enters serv... | Timeline of historic inventions | 0.78261 |
86,227 | 1970s: Public-key cryptography is invented and developed by James H. Ellis, Clifford Cocks, Malcolm J. Williamson, Whitfield Diffie, Martin Hellman, Ralph Merkle, Ron Rivest, Adi Shamir, Leonard Adleman, et al. 1970: The pocket calculator is invented. 1971: The first single-chip microprocessor, the Intel 4004, is inven... | Timeline of historic inventions | 0.78261 |
86,228 | Modern detectors in particle physics combine several of the above elements in layers much like an onion. | Radiation Detector | 0.78261 |
86,229 | Shortly after, Bryce DeWitt proposed a simplification of the model, giving rise to the Unruh-DeWitt detector model. Beyond their applications to theoretical physics, particle detector models are related to experimental fields such as quantum optics, where atoms can be used as detectors for the quantum electromagnetic f... | Radiation Detector | 0.78261 |
86,230 | Beyond their experimental implementations, theoretical models of particle detectors are also of great importance to theoretical physics. These models consider localized non-relativistic quantum systems coupled to a quantum field. They receive the name of particle detectors because when the non-relativistic quantum syst... | Radiation Detector | 0.78261 |
86,231 | In algebraic topology, simplices are used as building blocks to construct an interesting class of topological spaces called simplicial complexes. These spaces are built from simplices glued together in a combinatorial fashion. Simplicial complexes are used to define a certain kind of homology called simplicial homology... | Singular simplices functor | 0.782608 |
86,232 | An "orthogonal corner" means here that there is a vertex at which all adjacent edges are pairwise orthogonal. It immediately follows that all adjacent faces are pairwise orthogonal. Such simplices are generalizations of right triangles and for them there exists an n-dimensional version of the Pythagorean theorem: The s... | Singular simplices functor | 0.782608 |
86,233 | In geometric design and computer graphics, many methods first perform simplicial triangulations of the domain and then fit interpolating polynomials to each simplex. In chemistry, the hydrides of most elements in the p-block can resemble a simplex if one is to connect each atom. Neon does not react with hydrogen and as... | Singular simplices functor | 0.782608 |
86,234 | In statistics, simplices are sample spaces of compositional data and are also used in plotting quantities that sum to 1, such as proportions of subpopulations, as in a ternary plot. In industrial statistics, simplices arise in problem formulation and in algorithmic solution. In the design of bread, the producer must co... | Singular simplices functor | 0.782608 |
86,235 | Similarly, the National Institute of Health, in 2021, looked at a wide range of depressive models. It highlights the learned helplessness model. The model allows one to predict depressive symptoms because of its high rates of overlap with post-traumatic stress disorder and major depressive disorder, which is the leadin... | Learned helplessness | 0.782607 |
86,236 | The article also discusses the neurocircuitry of learned helplessness, the role of serotonin (or 5-HT), and the exercise-associated neural adaptations that may contribute to the stress-resistant brain. However, the authors finally conclude that "The underlying neurobiological mechanisms of this effect, however, remain ... | Learned helplessness | 0.782607 |
86,237 | In the context of software engineering and software architecture, service granularity is a key design concern when applying the paradigm of service-orientation for instance during service-oriented modeling. Service granularity specifies the scope of business functionality and the structure of the message payload in a s... | Service granularity principle | 0.782607 |
86,238 | There are no known bioluminescent stygobites to date, despite this adaptation's popularity in other dark systems.Outside of light availability, there are a wide variety of geochemical parameters that affect the biology and ecology within these systems. Possibly the most notable and universal in these systems is the str... | Anchialine system | 0.782605 |
86,239 | Anchialine systems are a feature of coastal aquifers which are density stratified, with water near the surface being fresh or brackish, and saline water intruding from the coast at depth. Depending on the site, it is sometimes possible to access the deeper saline water directly in the anchialine pool, or sometimes it m... | Anchialine system | 0.782605 |
86,240 | An anchialine system (, from Greek ankhialos, "near the sea") is a landlocked body of water with a subterranean connection to the ocean. Depending on its formation, these systems can exist in one of two primary forms: pools or caves. The primary differentiating characteristics between pools and caves is the availabilit... | Anchialine system | 0.782605 |
86,241 | The complicated geometry of anchialine systems limits the understanding of hydrologic processes involved, requiring many studies to estimate or model the processes thought to be contributing to the physical and chemical properties of the system. More recent studies look at categorizing changes in biodiversity and physi... | Anchialine system | 0.782605 |
86,242 | Several countries are conducting extensive research and development programs around renewable energy sources like solar, wind, water, and nuclear energy in hopes to achieve energy independence. However, because solar, wind, and water cannot always be derived as an energy source, nuclear energy is seen as a near-univers... | Energy independence | 0.782604 |
86,243 | Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the 3⁄4 power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M is the animal's mass, then Kleiber's law states th... | Kleiber's law | 0.782604 |
86,244 | Kleiber's law, as many other biological allometric laws, is a consequence of the physics and/or geometry of animal circulatory systems. Max Kleiber first discovered the law when analyzing a large number of independent studies on respiration within individual species. Kleiber expected to find an exponent of 2⁄3 (for rea... | Kleiber's law | 0.782604 |
86,245 | One method is to keep the logical design normalized, but allow the database management system (DBMS) to store additional redundant information on disk to optimize query response. In this case it is the DBMS software's responsibility to ensure that any redundant copies are kept consistent. This method is often implement... | Database denormalization | 0.7826 |
86,246 | Some third-generation solar cells boost efficiency through the integration of concentrator and/or multi-junction device geometry. This can lead to efficiencies larger than the Shockley–Queisser limit of approximately 42% efficiency for a single-junction semiconductor solar cell under one-sun illumination.A multi-juncti... | Thin-film photovoltaic cell | 0.782597 |
86,247 | In order to meet international renewable energy goals, the worldwide solar capacity must increase significantly. For example, to keep up with the International Energy Agency's goal of 4674 GW of solar capacity installed globally by 2050, significant expansion is required from the 1185 GW installed globally as of 2022. ... | Thin-film photovoltaic cell | 0.782597 |
86,248 | The HSW theorem states that the classical capacity of a quantum channel Ψ {\displaystyle \Psi } can be characterized as its regularized Holevo information: lim n → ∞ 1 n χ ( Ψ ⊗ n ) {\displaystyle \lim _{n\to \infty }{\frac {1}{n}}\chi \left(\Psi ^{\otimes n}\right)} This quantity is difficult to compute and this refle... | Quantum depolarizing channel | 0.782597 |
86,249 | Software update systems allow for updates to be managed by users and software developers. In the 2017 Petya cyberpandemic, the financial software "MeDoc"'s update system is said to have been compromised to spread malware via its updates. On the Tor Blog, cybersecurity expert Mike Perry states that deterministic, distri... | Live patching | 0.782596 |
86,250 | HCII offers Human Computer Interaction (HCI) as an additional major for undergraduates, as well as a master's degree and PhDs in HCI. Students from various academic backgrounds come together from around the world to participate in this program. Students hold undergraduate degrees in psychology, design, and computer sci... | Human–Computer Interaction Institute | 0.782594 |
86,251 | The Human–Computer Interaction Institute (HCII) is a department within the School of Computer Science at Carnegie Mellon University (CMU) in Pittsburgh, Pennsylvania. It is considered one of the leading centers of human–computer interaction research, and was named one of the top ten most innovative schools in informati... | Human–Computer Interaction Institute | 0.782594 |
86,252 | Some fields in which notable research is currently being done at the HCII are Learning Technologies, Tools and Technology, Human Assistance, Robotics, Arts and Entertainment, and the Entertainment Technology Center (ETC). == References == | Human–Computer Interaction Institute | 0.782594 |
86,253 | She started the OHLab, along with Amy Ogan and associated students, staff, and colleagues. Amy Ogan is an assistant professor at the HCII department with interests in emerging technologies for education. She graduated from Carnegie Mellon two times, first as undergraduate with degrees in Spanish, Computer Science, and ... | Human–Computer Interaction Institute | 0.782594 |
86,254 | His interests lie with social computing, design, and information technology. In 2016 he received the Carnegie Mellon School of Computer Science – SCS Allen Newell Research Award for his research on "Designing Online Communities." Jessica Hammer is an assistant professor, jointly appointed between the HCI Institute and ... | Human–Computer Interaction Institute | 0.782594 |
86,255 | He is known for his pioneering work on scratch input and for developing Skinput and Omnitouch. He is also the CTO and co-founder of Qeexo, a machine learning and interaction technology startup. Robert Kraut is a Herbert A. Simon Professor of Human–Computer Interaction. | Human–Computer Interaction Institute | 0.782594 |
86,256 | Randy Pausch was a professor of computer science, human-computer interaction and design. Pausch was also a best-selling author, who became known around the world after he gave "The Last Lecture" speech on September 18, 2007, at Carnegie Mellon. Pausch was instrumental in the development of Alice, a computer teaching to... | Human–Computer Interaction Institute | 0.782594 |
86,257 | In mathematics, Tsen's theorem states that a function field K of an algebraic curve over an algebraically closed field is quasi-algebraically closed (i.e., C1). This implies that the Brauer group of any such field vanishes, and more generally that all the Galois cohomology groups H i(K, K*) vanish for i ≥ 1. This resul... | Tsen's theorem | 0.782594 |
86,258 | Depending on the relative orientations of the two components the linking number of the Hopf link is ±1.The Hopf link is a (2,2)-torus link with the braid word σ 1 2 . {\displaystyle \sigma _{1}^{2}.\,} The knot complement of the Hopf link is R × S1 × S1, the cylinder over a torus. This space has a locally Euclidean geo... | Hopf link | 0.782593 |
86,259 | The Hopf link is also present in some proteins. It consists of two covalent loops, formed by pieces of protein backbone, closed with disulfide bonds. The Hopf link topology is highly conserved in proteins and adds to their stability. | Hopf link | 0.782593 |
86,260 | Practices include recycling as much farm waste as possible and adding composted material from sources outside the farm. Regenerative agriculture on small farms and gardens is often based on philosophies like permaculture, agroecology, agroforestry, restoration ecology, keyline design, and holistic management. Large far... | Regenerative farming | 0.782593 |
86,261 | Practices and principles used in regenerative farming include: Alternative food networks (AFNs), commonly defined by attributes such as the spatial proximity between farmers and consumers. AquacultureEcological aquaculture Regenerative ocean farming Agroecology Agroforestry Biochar/terra preta Use of biostimulants Bord... | Regenerative farming | 0.782593 |
86,262 | Mwnci extension can import data from Wikidata to LibreOffice Calc spreadsheets There are (at October 2019) discussions about using QID items in relation to what is being called QID emoji Wiki Explorer – Android application to discover things around you and micro editing Wikidata KDE Itinerary – a privacy conscious open... | Wikidata | 0.782593 |
86,263 | The creation of the project was funded by donations from the Allen Institute for Artificial Intelligence, the Gordon and Betty Moore Foundation, and Google, Inc., totaling €1.3 million. The development of the project is mainly driven by Wikimedia Deutschland under the management of Lydia Pintscher, and was originally s... | Wikidata | 0.782593 |
86,264 | In molecular biology, ADF-H domain (actin-depolymerising factor homology domain) is an approximately 150 amino acid motif that is present in three phylogenetically distinct classes of eukaryotic actin-binding proteins. ADF/cofilins, which include ADF, cofilin, destrin, actophorin, coactosin, depactin and glia maturatio... | ADF-H domain | 0.782591 |
86,265 | The LogSumExp (LSE) (also called RealSoftMax or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms. It is defined as the logarithm of the sum of the exponentials of the arguments: | LogSumExp | 0.78259 |
86,266 | LSE is convex but not strictly convex. We can define a strictly convex log-sum-exp type function by adding an extra argument set to zero: This function is a proper Bregman generator (strictly convex and differentiable). It is encountered in machine learning, for example, as the cumulant of the multinomial/binomial fami... | LogSumExp | 0.78259 |
86,267 | (This is Mordell's Theorem, later generalized to the Mordell–Weil theorem.) Moreover, Mazur's torsion theorem restricts the structure of the torsion subgroup. When g > 1 {\displaystyle g>1} , according to Faltings's theorem, C {\displaystyle C} has only a finite number of rational points. | Mordell conjecture | 0.782589 |
86,268 | Let C {\displaystyle C} be a non-singular algebraic curve of genus g {\displaystyle g} over Q {\displaystyle \mathbb {Q} } . Then the set of rational points on C {\displaystyle C} may be determined as follows: When g = 0 {\displaystyle g=0} , there are either no points or infinitely many. In such cases, C {\displaystyl... | Mordell conjecture | 0.782589 |
86,269 | Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field Q {\displaystyle \mathbb {Q} } of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by G... | Mordell conjecture | 0.782589 |
86,270 | Because of the Mordell–Weil theorem, Faltings's theorem can be reformulated as a statement about the intersection of a curve C {\displaystyle C} with a finitely generated subgroup Γ {\displaystyle \Gamma } of an abelian variety A {\displaystyle A} . Generalizing by replacing A {\displaystyle A} by a semiabelian variety... | Mordell conjecture | 0.782589 |
86,271 | He served as a regional editor of the Journal of Non-Crystalline Solids, an associate editor of Materials Research Bulletin, and an editorial board member of the publication Semiconductors & Insulators. Adler was also well known in the physics community for his love and knowledge of fine food and world travel. Adler wa... | David Adler (physicist) | 0.782587 |
86,272 | Since Adler was “regarded as one of his department’s most outstanding teachers of undergraduates” and headed up its undergraduate thesis program, MIT established in his honor the yearly David Adler Memorial Thesis Prize for Outstanding Undergraduate Thesis. This honor has since been reconfigured as the David Adler Memo... | David Adler (physicist) | 0.782587 |
86,273 | He then became a research associate at the Massachusetts Institute of Technology (MIT) in 1965, advancing to full professor in the department of electrical engineering and computer science in 1975. During his relatively short career, Adler published almost 300 papers in technical journals and presented over 80 invited ... | David Adler (physicist) | 0.782587 |
86,274 | from Rensselaer Polytechnic Institute (RPI) in 1956 and his doctorate in physics from Harvard University in 1964. At Harvard, Adler started a dissertation on quantum field theory advised by Julian Schwinger at a time when Prof. Schwinger was revolutionizing theoretical physics. | David Adler (physicist) | 0.782587 |
86,275 | David Adler (April 13, 1935 – March 31, 1987) was an American physicist and MIT professor. In condensed matter physics, Adler made significant contributions to the understanding of transition-metal oxides, the electronic properties of low-mobility materials, transport phenomena in amorphous materials, metal-insulator t... | David Adler (physicist) | 0.782587 |
86,276 | The improved resolution permitted better study to be made as to the area of the brain activated by a particular task. The biggest drawback of PET scanning is that because the radioactivity decays rapidly, it is limited to monitoring short tasks. : 60 Before fMRI technology came online, PET scanning was the preferred me... | Brain imaging | 0.782587 |
86,277 | Neuroimaging is the use of quantitative (computational) techniques to study the structure and function of the central nervous system, developed as an objective way of scientifically studying the healthy human brain in a non-invasive manner. Increasingly it is also being used for quantitative research studies of brain d... | Brain imaging | 0.782587 |
86,278 | This idea gained him international fame and led to the establishment of the Glacial Theory. In time, thanks to the refinement of geology, it has been demonstrated that there were several periods of glacial advance and retreat and that past temperatures on Earth were very different from today. In particular, the Milanko... | Quaternary | 0.782586 |
86,279 | For the same Calabi-Yau manifold X {\displaystyle X} in the A-model subsection, there is a dual superconformal field theory which has states in the eigenspace H 1 ( X , T X ) {\displaystyle H^{1}(X,T_{X})} of the operator Q ¯ {\displaystyle {\overline {Q}}} . Its three-point correlation function is defined as where Ω ∈... | Mirror symmetry conjecture | 0.782586 |
86,280 | Using the Euler characteristic and the Euler class, which is the top Chern class, the dimension of this group is 204 {\displaystyle 204} . This is because Using the Hodge structure we can find the dimensions of each of the components. First, because X {\displaystyle X} is Calabi-Yau, ω X ≅ O X {\displaystyle \omega _{X... | Mirror symmetry conjecture | 0.782586 |
86,281 | The set U smooth {\displaystyle U_{\text{smooth}}} corresponds to the equivalence classes of polynomials which define smooth Calabi-Yau quintic threefolds in P 4 {\displaystyle \mathbb {P} ^{4}} , giving a moduli space of Calabi-Yau quintics. Now, using Serre duality and the fact each Calabi-Yau manifold has trivial ca... | Mirror symmetry conjecture | 0.782586 |
86,282 | First, polynomials under scaling by the algebraic torus G m {\displaystyle \mathbb {G} _{m}} (non-zero scalers of the base field) given equivalent spaces. Second, projective equivalence is given by the automorphism group of P 4 {\displaystyle \mathbb {P} ^{4}} , PGL ( 5 ) {\displaystyle {\text{PGL}}(5)} which is 24 {\d... | Mirror symmetry conjecture | 0.782586 |
86,283 | The space X {\displaystyle X} has a complex structure, which is an integrable almost-complex structure J ∈ End ( T X ) {\displaystyle J\in {\text{End}}(TX)} , and because it is a Kähler manifold it necessarily has a symplectic structure ω {\displaystyle \omega } called the Kähler form which can be complexified to a com... | Mirror symmetry conjecture | 0.782586 |
86,284 | Also, in physics terminology, these theories are ( 2 , 2 ) {\displaystyle (2,2)} heterotic string theories because they have N = 2 {\displaystyle N=2} supersymmetry that comes in a pair, so really there are four supersymmetries. This is important because it implies there is a pair of operators acting on the Hilbert spa... | Mirror symmetry conjecture | 0.782586 |
86,285 | In string theory there is a class of models called non-linear sigma models which study families of maps ϕ: Σ → X {\displaystyle \phi :\Sigma \to X} where Σ {\displaystyle \Sigma } is a genus g {\displaystyle g} algebraic curve and X {\displaystyle X} is Calabi-Yau. These curves Σ {\displaystyle \Sigma } are called worl... | Mirror symmetry conjecture | 0.782586 |
86,286 | In mathematics, mirror symmetry is a conjectural relationship between certain Calabi–Yau manifolds and a constructed "mirror manifold". The conjecture allows one to relate the number of rational curves on a Calabi-Yau manifold (encoded as Gromov–Witten invariants) to integrals from a family of varieties (encoded as per... | Mirror symmetry conjecture | 0.782586 |
86,287 | Stimulated emission was a theoretical discovery by Albert Einstein within the framework of the old quantum theory, wherein the emission is described in terms of photons that are the quanta of the EM field. Stimulated emission can also occur in classical models, without reference to photons or quantum-mechanics. (See al... | Stimulated Emission | 0.782584 |
86,288 | Electrons and their interactions with electromagnetic fields are important in our understanding of chemistry and physics. In the classical view, the energy of an electron orbiting an atomic nucleus is larger for orbits further from the nucleus of an atom. However, quantum mechanical effects force electrons to take on d... | Stimulated Emission | 0.782584 |
86,289 | The Dor procedure is a medical technique used as part of heart surgery and originally introduced by the French cardiac surgeon Vincent Dor (b.1932). It is also known as endoventricular circular patch plasty (EVCPP). In 1985, Dor introduced EVCPP as a viable method for restoring a dilated left ventricle (LV) to its norm... | Dor procedure | 0.782583 |
86,290 | Petersburg paradox.In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing is proportional to the population. This terminological confusion between logarithmic growth and exponential gro... | Logarithmic growth | 0.782581 |
86,291 | Even in the 19th century, a treatise by Lord Kelvin and Peter Guthrie Tait, which helped define much of modern physics, was titled Treatise on Natural Philosophy (1867). Greek philosophers defined it as the combination of beings living in the universe, ignoring things made by humans. The other definition refers to huma... | Natural philosopher | 0.782579 |
86,292 | The term gained its modern meaning when experimental science and the scientific method became a specialized branch of study apart from natural philosophy.From the mid-19th century, when it became increasingly unusual for scientists to contribute to both physics and chemistry, "natural philosophy" came to mean just phys... | Natural philosopher | 0.782579 |
86,293 | Even in the 19th century, the work that helped define much of modern physics bore the title Treatise on Natural Philosophy (1867). In the German tradition, Naturphilosophie (philosophy of nature) persisted into the 18th and 19th centuries as an attempt to achieve a speculative unity of nature and spirit, after rejectin... | Natural philosopher | 0.782579 |
86,294 | Natural philosophy or philosophy of nature (from Latin philosophia naturalis) is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science. From the ancient world (at least since Aristotle) until the 19th century, natural philosophy was the c... | Natural philosopher | 0.782579 |
86,295 | Let {e1, ..., en} be an Auerbach basis of V and {e1, ..., en} corresponding dual basis. By Hahn–Banach theorem each ei extends to f i ∈ X* such that ||f i|| = 1.Now set P(x) = Σ f i(x) ei.It's easy to check that P is indeed a projection onto V and that ||P|| ≤ n (this follows from triangle inequality). | Auerbach's lemma | 0.782578 |
86,296 | In mathematics, Auerbach's lemma, named after Herman Auerbach, is a theorem in functional analysis which asserts that a certain property of Euclidean spaces holds for general finite-dimensional normed vector spaces. | Auerbach's lemma | 0.782578 |
86,297 | This product really is the best solution for this security issue. It's protecting the end-point from a ransomware threat.”In October 2018, ICSA Labs released a report, stating Nyotron's Paranoid was ICSA Labs certified in Advanced Threat Defense. The report goes on to say that Nyotron detected 100% of the 441 malicious... | Nyotron | 0.782578 |
86,298 | The language used for describing these “maps” is called Behavior Patterns Mapping (BPM). This patented language does not require machine learning/artificial intelligence or any other statistical or math-based algorithm. Instead, it is deterministic. | Nyotron | 0.782578 |
86,299 | If the system of polynomials consists of the single polynomial ƒ1(x) = x, then the values n for which ƒ1(n) is prime are themselves the prime numbers, and the conjecture becomes a restatement of the prime number theorem. If the system of polynomials consists of the two polynomials ƒ1(x) = x and ƒ2(x) = x + 2, then the ... | Bateman-Horn conjecture | 0.782577 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.