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86,400 | As he explained: "We were the designers of the bomb, like the tailor who tells you how much of the material is required to stitch a suit. We had to identify the fissile material, whether to use plutonium or...enriched uranium, which method of detonation, which explosive, which type of tampers and lenses to use, how mat... | Riazuddin (physicist) | 0.782521 |
86,401 | During the meeting, the word "bomb" was never used; instead academic scientists preferred to use the scientific research rationale. The Theoretical Physics Group began its research and directly reported to Abdus Salam.In 1977, both MPG and TPG scientists completed the design and calculation of an atomic bomb. Along wit... | Riazuddin (physicist) | 0.782521 |
86,402 | Later in his career, Qadir published a college text book on theory of special relativity. Shortly after the India surprise nuclear test — Pokhran-I, Munir Ahmad Khan called for a meeting to initiate the work on atomic bomb. Riazuddin and Salam represented the Theoretical Physics Group (TPG), and it was decided to devel... | Riazuddin (physicist) | 0.782521 |
86,403 | In 1974, he began to take research with the TPG, and began one of the pioneering member of the TPG. In 1973, Raziddin Siddiqui formed the Mathematical Physics Group (MPG) which closely collaborated with Theoretical Physics Group. Riazuddin called his mathematician friend Asghar Qadir, who specialised in special relativ... | Riazuddin (physicist) | 0.782521 |
86,404 | The Theoretical Physics Group took research in fast neutron calculations – how neutrons moved in a nuclear chain reaction – the theory simultaneity — how would fission weapon would detonated from several points at the same point during the detonation process – and hydrodynamics – how the explosion produced by a chain r... | Riazuddin (physicist) | 0.782521 |
86,405 | During his stay at PAEC, Riazuddin and Fayyazuddin were central figures of Pakistan's atomic program during the early and critical years. In December 1972, Riazuddin returned to Pakistan on the request of Salam. Salam asked Riazuddin to report to Munir Ahmad Khan – chairman of the Pakistan Atomic Energy Commission at t... | Riazuddin (physicist) | 0.782521 |
86,406 | In an experiment performed at the Synchrotron light source installed at the National Center for Physics (NCP), now the Abdus Salam Centre for Physics, Riazuddin observed the decay of the Tau particle, in which he theorised that hadronisation vector currents and axial vectors can be used to study the implicit properties... | Riazuddin (physicist) | 0.782521 |
86,407 | In 1972, Riazuddin and Fayyazuddin were the first to post mathematical frameworks of Current-algebra in neutrino scattering to determine the Scale invariance of Chiral symmetry breaking the Hamiltonian Quantum Mechanics. In 1987, Riazuddin and Fayyazuddin theorised that it is possible get light-neutrino masses in the r... | Riazuddin (physicist) | 0.782521 |
86,408 | In 1967, at the Fermi Institute, Riazuddin, with his brother Fayyazuddin, carried out research in the field of current algebra, where they applied the mathematical framework of current algebra in the applications of radiative decays of mesons.In 1982, Riazuddin and Fayyazuddin published a pioneering work on K mesons. R... | Riazuddin (physicist) | 0.782521 |
86,409 | During the 1960s, he associated himself with complex mathematical applications of nuclear physics. In 1960, Riazuddin used Nucleon-nucleon dispersion relation to discriminate proton-proton scattering in pseudoscalar mesons. In 1965, Riazuddin carried out the pioneering work on vector currents, in which he showed the di... | Riazuddin (physicist) | 0.782521 |
86,410 | During his post-graduate research, Riazuddin made contributions to mathematical physics, as he was highly interested in complex mathematical series, and its relation to modern physics. In 1959, Riazuddin was the first physicist to use the dispersion relation for Compton scattering of virtual photons on pions to analyse... | Riazuddin (physicist) | 0.782521 |
86,411 | Riazuddin, Riazuddin National Center for Physics. (SU) × U(1) model for electroweak unification and sterile neutrinos. Jointly written with Riazuddin and Fayyazuddin. | Riazuddin (physicist) | 0.782521 |
86,412 | Riazuddin also played an important role in education in Pakistan, contributing to the rise of science in Pakistan. Riazuddin authored several scientific books on particle physics and quantum mechanics. Later in his life, he joined the National University of Sciences and Technology (NUST) as a visiting professor of theo... | Riazuddin (physicist) | 0.782521 |
86,413 | Riazuddin, also spelled as Riaz-Ud-Din (Urdu: رياض الدين; 10 November 1930 – 9 September 2013), was a Pakistani theoretical physicist, specialising in high-energy physics and nuclear physics. Starting his scientific research in physics in 1958, Riazuddin was considered one of the early pioneers of Pakistan's nuclear w... | Riazuddin (physicist) | 0.782521 |
86,414 | At Cambridge, he was awarded his PhD in Theoretical physics in 1959. Riazuddin's dissertation was written on "Charge Radius of Pion" which also covered many issues relevant to the field of quantum theory. Riazuddin returned to Pakistan where he joined Punjab University as an Associate professor. In 1968, Riazuddin was ... | Riazuddin (physicist) | 0.782521 |
86,415 | In 1953, Salam supervised his MSc in applied mathematics where his master's dissertation dealt with fundamental concepts of mathematical physics. By the time he published his thesis in 1953, he received a Gold medal from the Punjab University for post-graduate contributions to physics and mathematics.With the help of S... | Riazuddin (physicist) | 0.782521 |
86,416 | Riazuddin also studied under the supervision of Abdus Salam at the Postgraduate level at Cambridge University. As a student of mathematics, he learned the advanced course on quantum mechanics under Abdus Salam, as he had made the course of quantum mechanics outside the regular curriculum. In 1951, Salam funded his scho... | Riazuddin (physicist) | 0.782521 |
86,417 | He was most famous for his TPG Group work Riazuddin and his team of theoretical physicists are widely credited to have developed and designed Pakistan's nuclear weapon devices. On 26 April 2009, a day-long conference was held in Islamabad to pay tribute to an eminent research scientist and theoretical physicist, Riazud... | Riazuddin (physicist) | 0.782521 |
86,418 | At PAEC, Riazuddin had closely worked with another noted Pakistani theoretical physicist Masud Ahmad (late). Later in life, he worked as a professor of theoretical physics and neutrino physics at the National University of Sciences and Technology, in Islamabad. He had also been the director of the Riazuddin National Ce... | Riazuddin (physicist) | 0.782521 |
86,419 | In 1983, Riazuddin, along with Asghar Qadir, went to Trieste, Italy, to join the International Centre for Theoretical Physics. Both scientists joined Salam where they continued research in their fields. In 1998, Riazuddin left King Fahd University of Petroleum and Minerals and returned to Pakistan to rejoin PAEC. | Riazuddin (physicist) | 0.782521 |
86,420 | At Daresbury, he trained British scientists in the field of nuclear physics.In 1981, he became visiting professor of physics and mathematics at the University of Iowa and Virginia Polytechnic Institute and State University, now Virginia Tech. In 1982, Riazuddin came back to Pakistan where he joined Quaid-e-Azam Univers... | Riazuddin (physicist) | 0.782521 |
86,421 | In 1971, Riazuddin traveled to the United Kingdom to join the Daresbury Nuclear Physics Laboratory where he was joined by Michael Duff. At Daresbury, he became senior research associate. There, Riazuddin gained expertise and specialised in nuclear physics. | Riazuddin (physicist) | 0.782521 |
86,422 | In 1970, he returned to the United States where he became Professor of Mathematics at the University of Maryland. Riazuddin left the United States for Italy as he was asked by Salam to join the International Centre for Theoretical Physics in 1970. He was joined by other students of Salam where they created a Theoretica... | Riazuddin (physicist) | 0.782521 |
86,423 | In 1968, Riazuddin returned to Pakistan on the request of Salam, and joined Quaid-i-Azam University's Institute of Physics. He was the founding director of the Institute of Physics (IP) where he engaged in research on string theory, the theory of relativity, particle physics and nuclear physics. Later, the scientists o... | Riazuddin (physicist) | 0.782521 |
86,424 | The same year, he joined the University of Pennsylvania where he taught physics until 1966. Later, he went to Chicago, Illinois where he joined his brother Fayyazuddin, and theoretical physicists Faheem Hussain and Peter Rottoli. Riazuddin joined University of Chicago's Enrico Fermi Institute where they created the "Re... | Riazuddin (physicist) | 0.782521 |
86,425 | Riazuddin National Center for Physics, Quaid-e-Azam University, in Islamabad. | Riazuddin (physicist) | 0.782521 |
86,426 | The Role of Great Equations in Life by Riazuddin, Riazuddin National Center of Physics. Tribimaximal mixing and leptogenesis in a seesaw model, Riazuddin, Islamabad. Dirac equation in (1+2) dimensions for quasi-particles in graphene and quantum field theory of their Coulomb interaction. | Riazuddin (physicist) | 0.782521 |
86,427 | In the conference, Masud Ahmad, who is also the student of his, said: "Prof. Riaz always put in his best efforts to obtain original results while working on various issues related to science and technology". NUST Rector, Engr. Muhammad Asghar also paid tributes to him and said: "Prof. Riazuddin has a very strong and pr... | Riazuddin (physicist) | 0.782521 |
86,428 | For opening of any productive layer it is necessary to open the casing, cement sheath and productive layer formation. Geophysics and mining geo-mechanics dictated the next requirements: Zone of cement sheath should be opened completely and not have cracks (to prevent possible overflows of water); Productive layer forma... | Hydro-slotted perforation | 0.78252 |
86,429 | At the end of the cutting process of a continuous slot the engine is set up to the initial position and ready for the next cutting interval. Hydro-slotting perforation sets the perfect geometry for the subsequent fracturing. Hydro-slotting perforation can be applied in any formation: shale, carbonates, sandstone and so... | Hydro-slotted perforation | 0.78252 |
86,430 | The first mention regarding the hydro-slotting perforation in America, was in 1987 at the oil and gas conference in Texas. The first use of hydro-slotting perforation in the United States dates back to 1996, when together with Shell E & P Technology Company, discovered two wells (Abrasive Hydro jet Technology in Albert... | Hydro-slotted perforation | 0.78252 |
86,431 | The geometry and depth of the slots creates the conditions for occurrence of the effect of unloading the circular stress conditions in the near wellbore zone (from 50 to 100 percent) and accordingly the increase of permeability (up to 30 to 50 percent) in this zone. In addition to this it forms a large area of the pene... | Hydro-slotted perforation | 0.78252 |
86,432 | Having three congruent angles and two sides does not guarantee triangle congruence in taxicab geometry. Therefore, the only triangle congruence theorem in taxicab geometry is SASAS, where all three corresponding sides must be congruent and at least two corresponding angles must be congruent. This result is mainly due t... | Manhattan shape | 0.782519 |
86,433 | Two triangles are congruent if and only if three corresponding sides are equal in distance and three corresponding angles are equal in measure. There are several theorems that guarantee triangle congruence in Euclidean geometry, namely Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), Side-Angle-Side (SAS), and Side-Side... | Manhattan shape | 0.782519 |
86,434 | As the size of the city blocks diminishes, the points become more numerous and become a rotated square in a continuous taxicab geometry. While each side would have length 2 r {\displaystyle {\sqrt {2}}r} using a Euclidean metric, where r is the circle's radius, its length in taxicab geometry is 2r. Thus, a circle's cir... | Manhattan shape | 0.782519 |
86,435 | A topological ball is a set of points with a fixed distance, called the radius, from a point called the center. In n-dimensional Euclidean geometry, the balls are spheres. In taxicab geometry, distance is determined by a different metric than in Euclidean geometry, and the shape of the ball changes as well. In n dimens... | Manhattan shape | 0.782519 |
86,436 | Thus, the value of a geometric analog to π {\displaystyle \pi } is 4 in this geometry. The formula for the unit circle in taxicab geometry is | x | + | y | = 1 {\displaystyle |x|+|y|=1} in Cartesian coordinates andin polar coordinates. A circle of radius 1 (using this distance) is the von Neumann neighborhood of its ce... | Manhattan shape | 0.782519 |
86,437 | Taxicab distance depends on the rotation of the coordinate system, but does not depend on its reflection about a coordinate axis or its translation. Taxicab geometry satisfies all of Hilbert's axioms (a formalization of Euclidean geometry) except for the side-angle-side axiom, as two triangles with equally "long" two s... | Manhattan shape | 0.782519 |
86,438 | Let X disc {\displaystyle X_{\text{disc}}} be the set X with the discrete topology. Let p: X disc → X {\displaystyle p\colon X_{\text{disc}}\to X} be the continuous map induced by the identity. | Godement resolution | 0.782519 |
86,439 | The Godement resolution of a sheaf is a construction in homological algebra that allows one to view global, cohomological information about the sheaf in terms of local information coming from its stalks. It is useful for computing sheaf cohomology. It was discovered by Roger Godement. | Godement resolution | 0.782519 |
86,440 | Such limitations in compatibility contribute to lock-in, and more subtly, to design compromises for independently developed products, if they attempt to be compatible. Also see embrace, extend and extinguish. In socioeconomic systems, commercial fisheries' harvest rates and conservation consequences are found to be pat... | Path dependence | 0.782517 |
86,441 | The ability to produce chemical state information, i.e. the local bonding environment of an atomic species in question from the topmost few nanometers of the sample makes XPS a unique and valuable tool for understanding the chemistry of the surface. The local bonding environment is affected by the formal oxidation stat... | X-ray photoelectron emission microscopy | 0.782515 |
86,442 | SnBr4 occurs in form of crystals. The compound crystallises in a monoclinic crystal system with molecular SnBr4 units that have distorted tetrahedral geometry, with mean Sn-Br bond lengths of 242.3 pm. | SnBr4 | 0.782514 |
86,443 | Bottom-up modeling focuses on processes to develop system behavior, whilst top-down modeling focuses on system outcomes and try to look for correlations to determine system behavior.There can also be other differences between models. Models could be physics-based, data-based or conceptual. Another difference between mo... | Socio-hydrology | 0.782513 |
86,444 | Most of the socio-hydrological efforts to date have focused on investigating recurring social behavior and societal development resulting from their coevolution with hydrological systems. The majority of these studies have explained coupled human and water systems through quantitative approaches and dedicated efforts t... | Socio-hydrology | 0.782513 |
86,445 | ( cos θ , sin θ ) {\displaystyle (\cos \theta ,\sin \theta )} is the solution ( x ( θ ) , y ( θ ) ) {\displaystyle (x(\theta ),y(\theta ))} to the two-dimensional system of differential equations y ′ ( θ ) = x ( θ ) {\displaystyle y'(\theta )=x(\theta )} and x ′ ( θ ) = − y ( θ ) {\displaystyle x'(\theta )=-y(\thet... | Cosine (trigonometric function) | 0.782513 |
86,446 | In 2009, the regeneration of hollow organs and tissues with a long diffusion distance, was a little more challenging. Therefore, to regenerate hollow organs and tissues with a long diffusion distance, the tissue had to be regenerated inside the lab, via the use of a 3D printer.Various tissues that have been regenerated... | Regeneration in humans | 0.782512 |
86,447 | By 2016, regeneration had been operationalised and induced by four main techniques: regeneration by instrument; regeneration by materials; regeneration by 3d printing; and regeneration by drugs. By 2016, regeneration by instrument, regeneration by materials and by regeneration drugs had been generally operationalised i... | Regeneration in humans | 0.782512 |
86,448 | Other organs and body parts that have been procured to regenerate include: penis, fats, vagina, brain tissue, thymus, and a scaled down human heart. One goal of scientists is to induce full regeneration in more human organs. There are various techniques that can induce regeneration. By 2016, regeneration of tissue had ... | Regeneration in humans | 0.782512 |
86,449 | Detector construction, algorithm development and Monte Carlo simulation for the ATLAS experiment at the Large Hadron Collider (LHC) under construction at the CERN; Experiment design and construction of the MAGIC high energy gamma-ray telescope, under operation since 2004 in the Canary Islands, Spain; Design of the Cher... | IFAE | 0.782511 |
86,450 | The IFAE has its own Titular Personnel as well as Associated Personnel consisting on members of the Physics Department of UAB working on Particle Physics. It has also an agreement with Universitat de Barcelona (dated 8/7/1992) which also allows the faculty of that university working on Particle Physics to be Associated... | IFAE | 0.782511 |
86,451 | The Institute for High Energy Physics (Institut de Fisica d'Altes Energies, IFAE) of Barcelona, Spain, is a Public Consortium between the Generalitat de Catalunya (Government of the Autonomous Community of Catalonia) and the Universitat Autònoma de Barcelona (UAB). It was formally created on July 16, 1991, by Act numbe... | IFAE | 0.782511 |
86,452 | The graphical user interface, called the Pipeline Pilot Professional Client, allows users to drag and drop discrete data processing units called "components". Components can load, filter, join or manipulate data. Components can also perform much more advanced data manipulations, such as building regression models, trai... | Pipeline Pilot | 0.782511 |
86,453 | The product expanded from an initial focus on chemistry to include general extract, transform and load (ETL) capabilities. Beyond the base product, Dassault has added analytical and data processing collections for report generation, data visualization and a number of scientific and engineering sectors. Currently, the p... | Pipeline Pilot | 0.782511 |
86,454 | Pipeline Pilot is a desktop software program sold by Dassault Systèmes for processing and analyzing data. Originally used in the natural sciences, the product's basic ETL (Extract, transform, load) and analytics capabilities have broadened over time. The product is now used for data science, ETL, reporting, prediction,... | Pipeline Pilot | 0.782511 |
86,455 | Pipeline Pilot features a number of add-ons called "collections". Collections are groups of specialized functions like processing genetic information or analyzing polymers offered to end users for an additional licensing fee. Currently, there are a number of these collections. Given the number of different add-ons now ... | Pipeline Pilot | 0.782511 |
86,456 | Let G be a locally compact abelian group, and Ĝ the dual group of G. Then L 1 ( G ^ ) {\displaystyle L_{1}({\hat {\mathit {G}}})} is the space of all functions on Ĝ which are integrable with respect to the Haar measure on Ĝ, and it has a Banach algebra structure where the product of two functions is convolution. We def... | Fourier algebra | 0.782509 |
86,457 | It is a closed sub-algebra of C B ( G ) {\displaystyle CB(G)} , the space of bounded continuous complex-valued functions on G with pointwise multiplication. We call B ( G ) {\displaystyle B(G)} the Fourier-Stieltjes algebra of G. Equivalently, B ( G ) {\displaystyle B(G)} can be defined as the linear span of the set P ... | Fourier algebra | 0.782509 |
86,458 | The generalized Bochner theorem states that a measurable function on G {\displaystyle {\mathit {G}}} is equal, almost everywhere, to the Fourier–Stieltjes transform of a non-negative finite measure on G ^ {\displaystyle {\widehat {G}}} if and only if it is positive definite. Thus, B ( G ) {\displaystyle B({\mathit {G}}... | Fourier algebra | 0.782509 |
86,459 | Fourier and related algebras occur naturally in the harmonic analysis of locally compact groups. They play an important role in the duality theories of these groups. The Fourier–Stieltjes algebra and the Fourier–Stieltjes transform on the Fourier algebra of a locally compact group were introduced by Pierre Eymard in 19... | Fourier algebra | 0.782509 |
86,460 | Let A(G) be the Fourier algebra of a compact group G. Building upon the work of Wiener, Lévy, Gelfand, and Beurling, in 1959 Helson, Kahane, Katznelson, and Rudin proved that, when G is compact and abelian, a function f defined on a closed convex subset of the plane operates in A(G) if and only if f is real analytic. I... | Fourier algebra | 0.782509 |
86,461 | The software architecture of LIONsolver permits interactive multi-objective optimization, with a user interface for visualizing the results and facilitating the solution analysis and decision making process. The architecture allows for problem-specific extensions, and it is applicable as a post-processing tool for all ... | Reactive business intelligence | 0.782508 |
86,462 | Version 2.0 of the software was released on Oct 1, 2011, covering also the Unix and Mac OS X operating systems in addition to Windows. The modeling components include neural networks, polynomials, locally weighted Bayesian regression, k-means clustering, and self-organizing maps. A free academic license for non-commerc... | Reactive business intelligence | 0.782508 |
86,463 | LIONsolver originates from research principles in Reactive Search Optimization advocating the use of self-tuning schemes acting while a software system is running. Learning and Intelligent OptimizatioN refers to the integration of online machine learning schemes into the optimization software, so that it becomes capabl... | Reactive business intelligence | 0.782508 |
86,464 | Speech is a major area of study for acoustical engineering, including the production, processing and perception of speech. This can include physics, physiology, psychology, audio signal processing and linguistics. Speech recognition and speech synthesis are two important aspects of the machine processing of speech. Ens... | Acoustic engineering | 0.782508 |
86,465 | The theorem was proved by Prigogine in 1947 from the Onsager relations. Prigogine's theorem is valid if the kinetic coefficients in the Onsager relations are constant (do not depend on driving forces and flows); for real systems, it is valid only approximately, so the minimum entropy production for a stationary state i... | Prigogine's theorem | 0.782508 |
86,466 | Prigogine's theorem is a theorem of non-equilibrium thermodynamics, originally formulated by Ilya Prigogine. The formulation of Prigogine's theorem is: In a stationary state, the production of entropy inside a thermodynamic system with constant external parameters is minimal and constant. If the system is not in a stat... | Prigogine's theorem | 0.782508 |
86,467 | Quantum photoelectrochemistry is the investigation of the quantum mechanical nature of photoelectrochemistry, the subfield of study within physical chemistry concerned with the interaction of light with electrochemical systems, typically through the application of quantum chemical calculations. Quantum photoelectrochem... | Quantum photoelectrochemistry | 0.782506 |
86,468 | Then the range of h {\textstyle h} omits all complex numbers of the form 2 π n ± i cosh − 1 ( m ) {\textstyle 2\pi n\pm i\cosh ^{-1}(m)} , where n {\textstyle n} is an integer and m {\textstyle m} is a nonnegative integer. By Landau's theorem, if h ′ ( w ) ≠ 0 {\textstyle h'(w)\neq 0} , then for all R > 0 {\textstyle... | Picard's theorem | 0.782503 |
86,469 | As with the little theorem, the (at most two) points that are not attained are lacunary values of the function. The following conjecture is related to "Great Picard's Theorem": Conjecture: Let {U1, ..., Un} be a collection of open connected subsets of C that cover the punctured unit disk D \ {0}. Suppose that on each U... | Picard's theorem | 0.782503 |
86,470 | Great Picard's theorem is true in a slightly more general form that also applies to meromorphic functions: Great Picard's Theorem (meromorphic version): If M is a Riemann surface, w a point on M, P1(C) = C ∪ {∞} denotes the Riemann sphere and f: M\{w} → P1(C) is a holomorphic function with essential singularity at w, t... | Picard's theorem | 0.782503 |
86,471 | In order to prove they are the same, it is then only necessary to check they are the same on a set of generators of this ring. Thom's cobordism theory gives a set of generators; for example, complex vector spaces with the trivial bundle together with certain bundles over even dimensional spheres. So the index theorem c... | Index theory | 0.782503 |
86,472 | The initial proof was based on that of the Hirzebruch–Riemann–Roch theorem (1954), and involved cobordism theory and pseudodifferential operators. The idea of this first proof is roughly as follows. Consider the ring generated by pairs (X, V) where V is a smooth vector bundle on the compact smooth oriented manifold X, ... | Index theory | 0.782503 |
86,473 | Abstract elliptic operators became protagonists in Kasparov's theory and Connes's noncommutative differential geometry. 1971: Isadore Singer proposes a comprehensive program for future extensions of index theory. 1972: Gennadi G. Kasparov publishes his work on the realization of K-homology by abstract elliptic operator... | Index theory | 0.782503 |
86,474 | Robion Kirby and Laurent C. Siebenmann's results, combined with René Thom's paper proved the existence of rational Pontryagin classes on topological manifolds. The rational Pontryagin classes are essential ingredients of the index theorem on smooth and topological manifolds. 1969: Michael Atiyah defines abstract ellipt... | Index theory | 0.782503 |
86,475 | The Atiyah–Singer theorem was announced in 1963. The proof sketched in this announcement was never published by them, though it appears in Palais's book. It appears also in the "Séminaire Cartan-Schwartz 1963/64" that was held in Paris simultaneously with the seminar led by Richard Palais at Princeton University. | Index theory | 0.782503 |
86,476 | The index problem for elliptic differential operators was posed by Israel Gel'fand. He noticed the homotopy invariance of the index, and asked for a formula for it by means of topological invariants. Some of the motivating examples included the Riemann–Roch theorem and its generalization the Hirzebruch–Riemann–Roch the... | Index theory | 0.782503 |
86,477 | Then the kernel is the space of multiples of exp(λx) if λ is an integral multiple of 2πi and is 0 otherwise, and the kernel of the adjoint is a similar space with λ replaced by its complex conjugate. So D has index 0. This example shows that the kernel and cokernel of elliptic operators can jump discontinuously as the ... | Index theory | 0.782503 |
86,478 | advisor Roman Jackiw, used the axial anomaly to derive this index theorem on spaces equipped with a Hermitian matrix called the Higgs field. The index of the Dirac operator is a topological invariant which measures the winding of the Higgs field on a sphere at infinity. If U is the unit matrix in the direction of the H... | Index theory | 0.782503 |
86,479 | The Callias index theorem is an index theorem for a Dirac operator on a noncompact odd-dimensional space. The Atiyah–Singer index is only defined on compact spaces, and vanishes when their dimension is odd. In 1978 Constantine Callias, at the suggestion of his Ph.D. | Index theory | 0.782503 |
86,480 | The kernel of the elliptic operator is in general infinite dimensional in this case, but it is possible to get a finite index using the dimension of a module over a von Neumann algebra; this index is in general real rather than integer valued. This version is called the L2 index theorem, and was used by Atiyah & Schmid... | Index theory | 0.782503 |
86,481 | If there is a group action of a group G on the compact manifold X, commuting with the elliptic operator, then one replaces ordinary K-theory with equivariant K-theory. Moreover, one gets generalizations of the Lefschetz fixed-point theorem, with terms coming from fixed-point submanifolds of the group G. See also: equiv... | Index theory | 0.782503 |
86,482 | This point of view is adopted in the proof of Melrose (1993) of the Atiyah–Patodi–Singer index theorem. Instead of just one elliptic operator, one can consider a family of elliptic operators parameterized by some space Y. In this case the index is an element of the K-theory of Y, rather than an integer. If the operator... | Index theory | 0.782503 |
86,483 | In the case when there are just two non-zero bundles in the complex this implies that the symbol is an isomorphism off the zero section, so an elliptic complex with 2 terms is essentially the same as an elliptic operator between two vector bundles. Conversely the index theorem for an elliptic complex can easily be redu... | Index theory | 0.782503 |
86,484 | The Atiyah–Singer theorem applies to elliptic pseudodifferential operators in much the same way as for elliptic differential operators. In fact, for technical reasons most of the early proofs worked with pseudodifferential rather than differential operators: their extra flexibility made some steps of the proofs easier.... | Index theory | 0.782503 |
86,485 | Suppose that M {\displaystyle M} is a compact oriented manifold of dimension n = 2 r {\displaystyle n=2r} . If we take Λ even {\displaystyle \Lambda ^{\text{even}}} to be the sum of the even exterior powers of the cotangent bundle, and Λ odd {\displaystyle \Lambda ^{\text{odd}}} to be the sum of the odd powers, define ... | Index theory | 0.782503 |
86,486 | 1986: Alain Connes publishes his fundamental paper on noncommutative geometry. 1989: Simon K. Donaldson and Sullivan study Yang–Mills theory on quasiconformal manifolds of dimension 4. They introduce the signature operator S defined on differential forms of degree two. 1990: Connes and Henri Moscovici prove the local i... | Index theory | 0.782503 |
86,487 | 1983: Nicolae Teleman proves that the analytical indices of signature operators with values in vector bundles are topological invariants. 1984: Teleman establishes the index theorem on topological manifolds. | Index theory | 0.782503 |
86,488 | 1973: Atiyah, Raoul Bott, and Vijay Patodi gave a new proof of the index theorem using the heat equation, described in a paper by Melrose. 1977: Dennis Sullivan establishes his theorem on the existence and uniqueness of Lipschitz and quasiconformal structures on topological manifolds of dimension different from 4. 1983... | Index theory | 0.782503 |
86,489 | In statistical genetics, Haseman–Elston (HE) regression is a form of statistical regression originally proposed for linkage analysis of quantitative traits for sibling pairs. It was first developed by Joseph K. Haseman and Robert C. Elston in 1972. A much earlier source of sib-pair linkage implementation was, in 1935 a... | Haseman–Elston regression | 0.782502 |
86,490 | Railway engineering is a multi-faceted engineering discipline dealing with the design, construction and operation of all types of rail transport systems. It encompasses a wide range of engineering disciplines, including civil engineering, computer engineering, electrical engineering, mechanical engineering, industrial ... | Railway engineering | 0.7825 |
86,491 | Mechanical engineering Command, control & railway signalling Office systems design Data center design SCADA Network design Electrical engineering Energy electrification Third rail Fourth rail Overhead contact system Civil engineering Permanent way engineering Light rail systems On-track plant Rail systems integration T... | Railway engineering | 0.7825 |
86,492 | The hardware for the rover is being designed by the Johnson Space Center, while the instruments are provided by Ames Research Center, Kennedy Space Center, and Honeybee Robotics. As of March 2021, the estimated cost of the mission is US$433.5 million.The VIPER rover will operate near the lunar south pole at Nobile Crat... | Artemis program | 0.782499 |
86,493 | They will include technology demonstrators to advance lunar science or the commercial development of the Moon.In November 2019, NASA added five contractors to the group of companies who are eligible to bid to send large payloads to the surface of the Moon under the CLPS program: Blue Origin, Ceres Robotics, Sierra Neva... | Artemis program | 0.782499 |
86,494 | Constellation was subsequently put on hold.On 15 April 2010, Obama spoke at the Kennedy Space Center, announcing the administration's plans for NASA and cancelling the non-Orion elements of Constellation on the premise that the program had become nonviable. He instead proposed US$6 billion in additional funding and cal... | Artemis program | 0.782499 |
86,495 | A previous organisation of the same name existed between July 1910 and circa 1922. It was founded to promote astronomy following an appearance of Halley’s Comet. Initially there was strong support for such a society and by 30 September 1911 there were 239 members (192 original and a net 47 added during the first sessio... | Astronomical Society of India | 0.782499 |
86,496 | It organises meetings, supports and tries to popularise Astronomy and related subjects and publishes the Bulletin of the Astronomical Society of India.Prof. Dipankar Banerjee, Director of Aryabhatta Research Institute of Observational Sciences , Nainital, is the Society's President.The Society makes a series of awards,... | Astronomical Society of India | 0.782499 |
86,497 | The Astronomical Society of India (ASI) is an Indian society of professional astronomers and other professionals from related disciplines. It was founded in 1972, with Vainu Bappu being the founder President of the Society, and as of 2010 has a membership of approximately 1000. Its registered office is at the Astronomy... | Astronomical Society of India | 0.782499 |
86,498 | For the static events, each team could score a maximum of 300 points and for the dynamic (racing) events, each team could score a maximum of 700 points. The official results of the 2009 competition are as follows:1st Place Overall – Hybrid: Texas A&M University 981 out of 1000 points 2nd Place Overall – Hybrid: Colorad... | Formula Hybrid | 0.782496 |
86,499 | The total points possible were a 1000 (per team). For the static events, each team could score a maximum of 300 points and for the dynamic (racing) events, each team could score a maximum of 700 points. The official results of the 2010 competition are as follows:1st Place Overall – Hybrid: Politecnico di Torino 943 out... | Formula Hybrid | 0.782496 |
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