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87,000 | Barth is a post doctoral researcher at the Harvard–Smithsonian Center for Astrophysics, and holds a PhD in Astronomy, 1998, from UC Berkeley. What he found initially were mathematical blunders and unjustified assumptions. | Blacklight Power | 0.78226 |
87,001 | By 2000, Park remained skeptical, stating: "Unlike most schemes for free energy, the hydrino process of Randy Mills is not without ample theory. Mills has written a 1000 page tome, entitled, "The Grand Unified Theory of Classical Quantum Mechanics", that takes the reader all the way from hydrinos to antigravity. Fortun... | Blacklight Power | 0.78226 |
87,002 | Applications were rejected by the UK patent office for similar reasons. The European Patent Office (EPO) rejected a similar BLP patent application due to lack of clarity on how the process worked. Reexamination of this European patent is pending.Robert L. Park, emeritus professor of physics at the University of Marylan... | Blacklight Power | 0.78226 |
87,003 | This caused the USPTO to withdraw from issue the patent application before it was granted and re-open it for review, and to withdraw four related applications, including one for a hydrino power plant.In 2000, a law firm engaged by BLP sent letters to four prominent physicists asking them to stop making what it called "... | Blacklight Power | 0.78226 |
87,004 | In 1999, the Nobel prize winning physicist Philip Warren Anderson said he is "sure that it's a fraud", and in the same year another Nobel prize winning physicist, Steven Chu, called it "extremely unlikely". The following year, a 2000 patent based on its hydrino-related technology was later withdrawn by the United State... | Blacklight Power | 0.78226 |
87,005 | It included a television set for display and a special keyboard for navigating the system's function menus; PLATO II, in 1961, featured two users at once, one of the first implementations of multi-user time-sharing.The PLATO system was re-designed, between 1963 and 1969; PLATO III allowed "anyone" to design new lesson ... | PLATO system | 0.78226 |
87,006 | These are not true for all functions, but are true under various conditions, which are the content of the various forms of the Fourier inversion theorem. This fourfold periodicity of the Fourier transform is similar to a rotation of the plane by 90°, particularly as the two-fold iteration yields a reversal, and in fact... | Fourier Transform | 0.782259 |
87,007 | With its natural group structure and the topology of uniform convergence on compact sets (that is, the topology induced by the compact-open topology on the space of all continuous functions from G {\displaystyle G} to the circle group), the set of characters Ĝ is itself a locally compact abelian group, called the Pontr... | Fourier Transform | 0.782259 |
87,008 | More precisely, defining the parity operator P {\displaystyle {\mathcal {P}}} such that ( P f ) ( x ) = f ( − x ) {\displaystyle ({\mathcal {P}}f)(x)=f(-x)} , we have: F 0 = i d , F 1 = F , F 2 = P , F 3 = F − 1 = P ∘ F = F ∘ P , F 4 = i d {\displaystyle {\begin{aligned}{\mathcal {F}}^{0}&=\mathrm {id} ,\\{\mathcal {F}... | Fourier Transform | 0.782258 |
87,009 | One might consider enlarging the domain of the Fourier transform from L1 + L2 by considering generalized functions, or distributions. A distribution on Rn is a continuous linear functional on the space Cc(Rn) of compactly supported smooth functions, equipped with a suitable topology. The strategy is then to consider th... | Fourier Transform | 0.782258 |
87,010 | The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature and National Center for Biotechnology Information. | Acidobacteriota | 0.782256 |
87,011 | Since they have only recently been discovered and the large majority have not been cultured, the ecology and metabolism of these bacteria is not well understood. However, these bacteria may be an important contributor to ecosystems, since they are particularly abundant within soils. Members of subdivisions 1, 4, and 6 ... | Acidobacteriota | 0.782256 |
87,012 | Thus, this is a growing field of microbiology. Some of this uncertainty can be attributed to the difficulty with which these bacteria are grown in the laboratory. There has been recent success in propagation by using low concentrations of nutrients in combination with high amounts of CO2, yet, progress is still quite s... | Acidobacteriota | 0.782256 |
87,013 | Most of these microbes are aerobes, and they are all heterotrophic. Subdivision 1 contains 11 of the known genera in addition to the majority of the species that have been able to be cultivated thus far.Within the 22 known genera, there are 40 conclusive species. The genera are divided amongst subdivisions 3, 4, 8, 10,... | Acidobacteriota | 0.782256 |
87,014 | For low levels of doping, the relevant energy states are populated sparsely by electrons (conduction band) or holes (valence band). It is possible to write simple expressions for the electron and hole carrier concentrations, by ignoring Pauli exclusion (via Maxwell–Boltzmann statistics): n e = N C ( T ) exp ( ( E F −... | Doping (Semiconductors) | 0.782255 |
87,015 | This is a key concept in the physics of a diode. A very heavily doped semiconductor behaves more like a good conductor (metal) and thus exhibits more linear positive thermal coefficient. Such effect is used for instance in sensistors. Lower dosage of doping is used in other types (NTC or PTC) thermistors. | Doping (Semiconductors) | 0.782255 |
87,016 | Differential inclusions can be used to understand and suitably interpret discontinuous ordinary differential equations, such as arise for Coulomb friction in mechanical systems and ideal switches in power electronics. An important contribution has been made by A. F. Filippov, who studied regularizations of discontinuou... | Differential inclusion | 0.782255 |
87,017 | In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form d x d t ( t ) ∈ F ( t , x ( t ) ) , {\displaystyle {\frac {dx}{dt}}(t)\in F(t,x(t)),} where F is a multivalued map, i.e. F(t, x) is a set rather than a single point in R d {\displaystyle \mathbb {R}... | Differential inclusion | 0.782255 |
87,018 | Note that a "break" is any attack that requires less than 2128 operations; the 6-round attack requires 264 known plaintexts and 2126.8 operations. Bruce Schneier thought highly of IDEA in 1996, writing: "In my opinion, it is the best and most secure block algorithm available to the public at this time." (Applied Crypto... | International Data Encryption Algorithm | 0.782253 |
87,019 | The designers analysed IDEA to measure its strength against differential cryptanalysis and concluded that it is immune under certain assumptions. No successful linear or algebraic weaknesses have been reported. As of 2007, the best attack applied to all keys could break IDEA reduced to 6 rounds (the full IDEA cipher us... | International Data Encryption Algorithm | 0.782253 |
87,020 | IDEA operates on 64-bit blocks using a 128-bit key and consists of a series of 8 identical transformations (a round, see the illustration) and an output transformation (the half-round). The processes for encryption and decryption are similar. IDEA derives much of its security by interleaving operations from different g... | International Data Encryption Algorithm | 0.782253 |
87,021 | The CEC concept was conceived by Johns Hopkins applied physics laboratory in the early 1970s. The concept was originally called Battle Group Anti-Air Warfare (AAW) Coordination. The first critical at-sea experiment with a system prototype occurred in 1990. The CEC became a Navy acquisition program in 1992. | Cooperative Engagement Capability | 0.782252 |
87,022 | The Gregory–Laflamme instability (after Ruth Gregory and Raymond Laflamme) is a result in theoretical physics which states that certain black strings and branes are unstable in dimensions higher than four.In their seminal papers in 1993 and 1994, Gregory and Laflamme showed that certain branes and Higher-dimensional Ei... | Gregory–Laflamme instability | 0.782251 |
87,023 | The dienone–phenol rearrangement is a reaction in organic chemistry first reported in 1921 by Karl von Auwers and Karl Ziegler. A common example of dienone–phenol rearrangement is 4,4-disubstituted cyclohexadienone converting into a stable 3,4-disubstituted phenol in presence of acid. A similar rearrangement is possibl... | Dienone–phenol rearrangement | 0.782251 |
87,024 | The Shlaer–Mellor method is one of a number of software development methodologies which arrived in the late 1980s. Most familiar were object-oriented analysis and design (OOAD) by Grady Booch, object modeling technique (OMT) by James Rumbaugh, object-oriented software engineering by Ivar Jacobson and object-oriented an... | Shlaer–Mellor method | 0.782251 |
87,025 | Information causality is a physical principle suggested in 2009. Information Causality states that information gain that a receiver (Bob) can reach about data, previously unknown to him, from a sender (Alice), by using all his local resources and n {\displaystyle n} classical bits communicated by the sender, is at most... | Information causality | 0.782248 |
87,026 | The Stöber process is a chemical process used to prepare silica (SiO2) particles of controllable and uniform size for applications in materials science. It was pioneering when it was reported by Werner Stöber and his team in 1968, and remains today the most widely used wet chemistry synthetic approach to silica nanopar... | Stöber process | 0.782245 |
87,027 | One major advantage of the Stöber process is that it can produce silica particles that are nearly monodisperse, and thus provides an ideal model for use in studying colloidal phenomena. It was a pioneering discovery when first published, allowing synthesis of spherical monodisperse silica particles of controlled sizes,... | Stober process | 0.782245 |
87,028 | The nacre from the shell of the abalone has become one of the more intensively studied biological structures in materials science. Clearly visible in these images are the neatly stacked (or ordered) mineral tiles separated by thin organic sheets along with a macrostructure of larger periodic growth bands which collecti... | Ceramic Engineering | 0.782244 |
87,029 | Understanding the processes in which living organisms control the growth of crystalline minerals such as silica could lead to significant advances in the field of materials science, and open the door to novel synthesis techniques for nanoscale composite materials, or nanocomposites. High-resolution scanning electron mi... | Ceramic Engineering | 0.782244 |
87,030 | Ceramic engines do not require a cooling system and hence allow a major weight reduction and therefore greater fuel efficiency. Fuel efficiency of the engine is also higher at high temperature, as shown by Carnot's theorem. In a conventional metallic engine, much of the energy released from the fuel must be dissipated ... | Ceramic Engineering | 0.782244 |
87,031 | Some pores and other structural defects associated with density variations have been shown to play a detrimental role in the sintering process by growing and thus limiting end-point densities. Differential stresses arising from inhomogeneous densification have also been shown to result in the propagation of internal cr... | Ceramic Engineering | 0.782244 |
87,032 | The usual rules of elementary arithmetic form an abstract rewriting system. For example, the expression (11 + 9) × (2 + 4) can be evaluated starting either at the left or at the right parentheses; however, in both cases the same result is eventually obtained. If every arithmetic expression evaluates to the same result ... | Confluence (abstract rewriting) | 0.782243 |
87,033 | In a Church–Rosser system, an object has at most one normal form; that is the normal form of an object is unique if it exists, but it may well not exist. In lambda calculus for instance, the expression (λx.xx)(λx.xx) does not have a normal form because there exists an infinite sequence of β-reductions (λx.xx)(λx.xx) → ... | Confluence (abstract rewriting) | 0.782243 |
87,034 | A rewriting system is said to possess the Church–Rosser property if and only if x ↔ ∗ y {\displaystyle x{\stackrel {*}{\leftrightarrow }}y} implies x ↓ y {\displaystyle x{\mathbin {\downarrow }}y} for all objects x, y. Alonzo Church and J. Barkley Rosser proved in 1936 that lambda calculus has this property; hence the ... | Confluence (abstract rewriting) | 0.782243 |
87,035 | Reduction of polynomials modulo an ideal is a confluent rewrite system provided one works with a Gröbner basis. Matsumoto's theorem follows from confluence of the braid relations. β-reduction of λ-terms is confluent by the Church–Rosser theorem. | Confluence (abstract rewriting) | 0.782243 |
87,036 | They can be described as a RNC version of the S60R/V70R B5254T4 engine. Lower compression (different pistons), stronger connecting rods, and same geometry camshafts as B5254T4 but different (dual) VVT units. These engines use a slightly larger Borg-Warner K16 turbo, the K16 turbo is an integrated manifold turbocharger,... | Volvo Modular engine | 0.782243 |
87,037 | In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behav... | Stopping time | 0.782243 |
87,038 | Grothendieck saw that it would be possible to use Serre's idea to define a cohomology theory that he suspected would be the Weil cohomology. To define this cohomology theory, Grothendieck needed to replace the usual, topological notion of an open covering with one that would use étale coverings instead. Grothendieck al... | Grothendieck topologies | 0.782242 |
87,039 | In the early 1960s, Alexander Grothendieck introduced étale maps into algebraic geometry as algebraic analogues of local analytic isomorphisms in analytic geometry. He used étale coverings to define an algebraic analogue of the fundamental group of a topological space. Soon Jean-Pierre Serre noticed that some propertie... | Grothendieck topologies | 0.782242 |
87,040 | André Weil's famous Weil conjectures proposed that certain properties of equations with integral coefficients should be understood as geometric properties of the algebraic variety that they define. His conjectures postulated that there should be a cohomology theory of algebraic varieties that gives number-theoretic inf... | Grothendieck topologies | 0.782242 |
87,041 | The conditions we impose on a Grothendieck topology are: (T 1) (Base change) If S is a covering sieve on X, and f: Y → X is a morphism, then the pullback f ∗ {\displaystyle \ast } S is a covering sieve on Y. (T 2) (Local character) Let S be a covering sieve on X, and let T be any sieve on X. Suppose that for each objec... | Grothendieck topologies | 0.782242 |
87,042 | Let Spc be the category of all topological spaces. Given any family of functions {uα: Vα → X}, we say that it is a surjective family or that the morphisms uα are jointly surjective if ∪ {\displaystyle \cup } uα(Vα) equals X. We define a pretopology on Spc by taking the covering families to be surjective families all of... | Grothendieck topologies | 0.782242 |
87,043 | We can also define this topology using the same pretopology we used above. Notice that to satisfy (PT 0), we need to check that for any continuous map of manifolds X → Y and any open subset U of Y, the fibered product U ×Y X is in Mfd/M. This is just the statement that the preimage of an open set is open. Notice, howev... | Grothendieck topologies | 0.782242 |
87,044 | Let Mfd be the category of all manifolds and continuous maps. (Or smooth manifolds and smooth maps, or real analytic manifolds and analytic maps, etc.) Mfd is a subcategory of Spc, and open immersions are continuous (or smooth, or analytic, etc.), so Mfd inherits a topology from Spc. This lets us construct the big site... | Grothendieck topologies | 0.782242 |
87,045 | Let M be a manifold. M has a category of open sets O(M) because it is a topological space, and it gets a topology as in the above example. For two open sets U and V of M, the fiber product U ×M V is the open set U ∩ V, which is still in O(M). This means that the topology on O(M) is defined by a pretopology, the same pr... | Grothendieck topologies | 0.782242 |
87,046 | Let C be any category. To define the discrete topology, we declare all sieves to be covering sieves. If C has all fibered products, this is equivalent to declaring all families to be covering families. To define the indiscrete topology, also known as the coarse or chaotic topology, we declare only the sieves of the for... | Grothendieck topologies | 0.782242 |
87,047 | Using the Yoneda lemma, it is possible to show that a presheaf on the category O(X) is a sheaf on the topology defined above if and only if it is a sheaf in the classical sense. Sheaves on a pretopology have a particularly simple description: For each covering family {Xα → X}, the diagram F ( X ) → ∏ α ∈ A F ( X α ) ⟶ ... | Grothendieck topologies | 0.782242 |
87,048 | Let C be a category and let J be a Grothendieck topology on C. The pair (C, J) is called a site. A presheaf on a category is a contravariant functor from C to the category of all sets. Note that for this definition C is not required to have a topology. A sheaf on a site, however, should allow gluing, just like sheaves ... | Grothendieck topologies | 0.782242 |
87,049 | Judd–Ofelt theory is a theory in physical chemistry describing the intensity of electron transitions within the 4f shell of rare-earth ions in solids and solutions.The theory was introduced independently in 1962 by Brian R. Judd of the University of California, Berkeley, and PhD candidate George S. Ofelt at Johns Hopki... | Judd–Ofelt theory | 0.78224 |
87,050 | Donald Price and James Barrell write that, according to reflexive monism, experience and matter are two complementary (first- and third-person viewable) sides of the same reality, and neither can be reduced to the other. That brain states are causes and correlates of consciousness, they write, does not mean that they a... | Reflexive monism | 0.78224 |
87,051 | A Q-machine is a device that is used in experimental plasma physics. The name Q-machine stems from the original intention of creating a quiescent plasma that is free from the fluctuations that are present in plasmas created in electric discharges. The Q-machine was first described in a publication by Rynn and D'Angelo.... | Q-machine | 0.782236 |
87,052 | The Rhizobiales-2 RNA motif is a set of RNAs found in certain bacteria that are presumed to be homologous because they conserve a common primary and secondary structure (see diagram). The motif was discovered using bioinformatics, and is found only within bacteria that belong to the order Hyphomicrobiales (formerly Rhi... | Rhizobiales-2 RNA motif | 0.782234 |
87,053 | The last of NASA's three High Energy Astronomy Observatories, HEAO 3 was launched 20 September 1979 on an Atlas-Centaur launch vehicle, into a nearly circular, 43.6 degree inclination low Earth orbit with an initial perigeum of 486.4 km. The normal operating mode was a continuous celestial scan, spinning approximately ... | High Energy Astronomy Observatory 3 | 0.782234 |
87,054 | The HEAO 3 Project was the final mission in the High Energy Astronomy Observatory series, which was managed by the NASA Marshall Space Flight Center (MSFC), where the project scientist was Dr. Thomas A. Parnell, and the project manager was Dr. John F. Stone. The prime contractor was TRW. | High Energy Astronomy Observatory 3 | 0.782234 |
87,055 | The experiment was capable of measuring gamma-ray energies falling within the energy interval from 0.045 to 10 MeV. The Ge detector system had an initial energy resolution better than 2.5 keV at 1.33 MeV and a line sensitivity from 1.E-4 to 1.E-5 photons/cm2-s, depending on the energy. Key experimental parameters were ... | High Energy Astronomy Observatory 3 | 0.782234 |
87,056 | It is not straightforward to translate the condition geology d σ > 0 {\displaystyle d\sigma >0} to three dimensions, particularly for rock plasticity which is dependent not only on the deviatoric stress but also on the mean stress. However, during loading f ≥ 0 {\displaystyle f\geq 0} and it is assumed that the directi... | Rock mass plasticity | 0.782233 |
87,057 | Over a period of 40 years, psychiatrist Ian Stevenson, from the University of Virginia, recorded case studies of young children who claimed to remember past lives. He published twelve books, including Twenty Cases Suggestive of Reincarnation, Reincarnation and Biology: A Contribution to the Etiology of Birthmarks and B... | Reincarnation research | 0.782233 |
87,058 | Four-legged robots also benefit from a lower center of gravity than two-legged systems.Four legged robots include: The TITAN series, developed since the 1980s by the Hirose-Yoneda Laboratory. The dynamically stable BigDog, developed in 2005 by Boston Dynamics, NASA's Jet Propulsion Laboratory, and the Harvard Universit... | Legged robot | 0.782229 |
87,059 | In general, optimizing any of these quantities may be a hard combinatorial optimization problem, and can indeed be NP-hard fairly easily. Therefore, sophisticated optimization algorithms are often required and it may be practical to use approximation algorithms or heuristics in some cases. Additionally, most SoC design... | Computer on a chip | 0.782225 |
87,060 | SoCs must optimize power use, area on die, communication, positioning for locality between modular units and other factors. Optimization is necessarily a design goal of SoCs. If optimization was not necessary, the engineers would use a multi-chip module architecture without accounting for the area use, power consumptio... | Computer on a chip | 0.782225 |
87,061 | SYSTAT is a statistics and statistical graphics software package, developed by Leland Wilkinson in the late 1970s, who was at the time an assistant professor of psychology at the University of Illinois at Chicago. Systat Software Inc. was incorporated in 1983 and grew to over 50 employees. In 1995, SYSTAT was sold to S... | SYSTAT (statistics package) | 0.782224 |
87,062 | Since 2012, Reis Robotics has also been developing mold casting machines and automation equipment for the post-processing of cast parts for foundry technology. In 2013, KUKA, an industrial robots-manufacturing company acquired 51% shares of Reis Robotics. In 2016, KUKA took over the remaining shares and became the sole... | Reis Robotics | 0.782224 |
87,063 | A major field of activity of Reis Robotics was the development and implementation of complex automation systems for all areas of industrial production. The group also included other high-tech development companies in Germany which focused on specific areas of robot application and supplied their products to both Reis R... | Reis Robotics | 0.782224 |
87,064 | Reis Robotics was founded in 1957 in Obernburg, Bavaria, Germany by Walter Reis who received the Rudolf Diesel Medal in 2006 and the German Mechanical Engineering Prize in 2011. In 2010, 18 companies in the Reis Group were combined as the Reis Group Holding GmbH & Co KG. The largest company within the Reis Group was Re... | Reis Robotics | 0.782224 |
87,065 | Reis Robotics is a German industrial robot manufacturer and systems integrator. In addition to robots and peripheral modules, Reis Robotics produces spotting and trimming presses and trimming tools. Reis Robotics comprises three German subsidiaries and eight international subsidiaries and several representative agencie... | Reis Robotics | 0.782224 |
87,066 | The Office works to investigate how drugs are absorbed, distributed, metabolized, and excreted, and how different drugs impact the immunology or physiology of animals. This office also helps develop screening tests for foodborne diseases and screens for drug residues in food products. The Office is involved in many sci... | Center for Veterinary Medicine | 0.782224 |
87,067 | In other scientific contexts, the term "calorie" and the symbol "cal" almost always refers to the small unit; the "large" unit being generally called "kilocalorie" with symbol "kcal". It is mostly used to express the amount of energy released in a chemical reaction or phase change, typically per mole of substance, as i... | Caloric intake | 0.782223 |
87,068 | The capacitance of the gap of the LGR is given by C = ε 0 w ℓ t , {\displaystyle C=\varepsilon _{0}{\frac {w\,\ell }{t}}\,,} where ε 0 {\displaystyle \varepsilon _{0}} is the permittivity of free space, w {\displaystyle w} is the thickness of the bore wall, t {\displaystyle t} is the gap width, and ℓ {\displaystyle \el... | Loop-gap resonator | 0.782223 |
87,069 | In some applications requiring high quality factors, the electromagnetic shielding provided by a concentric circular waveguide surrounding a cylindrical LGR can be bulky and awkward to work. A toroidal LGR can be used for high- Q {\displaystyle Q} measurements without requiring additional electromagnetic shielding. In ... | Loop-gap resonator | 0.782223 |
87,070 | The Research, Innovation, and Dissemination Center for Neuromathematics (RIDC NeuroMat, or simply NeuroMat) is a Brazilian research center established in 2013 at the University of São Paulo that is dedicated to integrating mathematical modeling and theoretical neuroscience. Among the core missions of NeuroMat are the c... | NeuroMat | 0.782222 |
87,071 | Thus the correlation coefficient is positive if Xi and Yi tend to be simultaneously greater than, or simultaneously less than, their respective means. The correlation coefficient is negative (anti-correlation) if Xi and Yi tend to lie on opposite sides of their respective means. Moreover, the stronger either tendency i... | Pearson product-moment correlation coefficient | 0.782222 |
87,072 | Exosomes contain RNA, proteins, lipids and metabolites that is reflective of the cell type of origin. As exosomes contain numerous proteins, RNA and lipids, large scale analysis including proteomics and transcriptomics is often performed. Currently, to analyse these data, non-commercial tools such as FunRich can be use... | Exosome (vesicle) | 0.78222 |
87,073 | Since the diameter of exosomes is typically below 100 nm and because they have a low refractive index, exosomes are below the detection range of many currently used techniques. A number of miniaturized systems, exploiting nanotechnology and microfluidics, have been developed to expedite exosome analyses. These new syst... | Exosome (vesicle) | 0.78222 |
87,074 | {f(x+ty)-f(x) \over t}\right|_{t=0}.} The theorem follows from this. | Ring of polynomial functions | 0.782218 |
87,075 | Let deg f = n {\displaystyle \deg f=n} and let t 0 , t 1 , … , t n {\displaystyle t_{0},t_{1},\dots ,t_{n}} be n +1 distinct elements of K. Then f ( t i ) = 0 {\displaystyle f(t_{i})=0} for 0 ≤ i ≤ n {\displaystyle 0\leq i\leq n} and by Lagrange interpolation we have f = 0 {\displaystyle f=0} . Hence the mapping f ↦ ... | Ring of polynomial functions | 0.782218 |
87,076 | p is a nonzero polynomial in K, however p ( t ) = 0 {\displaystyle p(t)=0} for all t in K, so p ^ = 0 {\displaystyle {\hat {p}}=0} is the zero function and our homomorphism is not an isomorphism (and, actually, the algebras are not isomorphic, since the algebra of polynomials is infinite while that of polynomial functi... | Ring of polynomial functions | 0.782218 |
87,077 | Let A = K {\displaystyle A=K} be the set of all polynomials over a field K and B be the set of all polynomial functions in one variable over K. Both A and B are algebras over K given by the standard multiplication and addition of polynomials and functions. We can map each f {\displaystyle f} in A to f ^ {\displaystyle... | Ring of polynomial functions | 0.782218 |
87,078 | The Broad Institute has 11 core faculty and 195 associate members from Harvard, MIT, and the Harvard-affiliated hospitals.The Broad Institute is made up of three types of organizational units: core member laboratories, research programs, and platforms. The institute's scientific research programs include: Cancer Progra... | Broad Institute | 0.782217 |
87,079 | Another cornerstone was the Institute of Chemistry and Cell Biology established by Harvard Medical School in 1998 to pursue chemical genetics as an academic discipline. Its screening facility was one of the first high-throughput resources opened in an academic setting. It facilitated small molecule screening projects f... | Broad Institute | 0.782217 |
87,080 | The Broad Institute evolved from a decade of research collaborations among MIT and Harvard scientists. One cornerstone was the Center for Genome Research of Whitehead Institute at MIT. Founded in 1982, the Whitehead became a major center for genomics and the Human Genome Project. As early as 1995, scientists at the Whi... | Broad Institute | 0.782217 |
87,081 | Since 2010, the Broad Institute has been listed on The Boston Globe's Top Places to Work. The 2014 report from Thomson Reuters' ScienceWatch entitled "The World's Most Influential Scientific Minds" recognized that 12 out of the 17 "hottest" researchers in science belonged to genomics, and 4 out of the top 5 were affili... | Broad Institute | 0.782217 |
87,082 | He has developed systematic ways to explore biology, especially disease biology, using small molecules toward the development of therapeutic drugs. Edward Scolnick is the former President of Merck Research Laboratories, former Director and current Chief Scientist of the Stanley Center for Psychiatric Research. Feng Zha... | Broad Institute | 0.782217 |
87,083 | Aviv Regev is a computational biologist with interests in biological networks, gene regulation and evolution. Stuart Schreiber is director of the Chemical Biology program. | Broad Institute | 0.782217 |
87,084 | Myriam Heiman combines genetics, biochemistry, and cell biology to study the features that define different types of neurons and their vulnerability to disease. Deborah Hung is a chemical biologist and an infectious disease physician who studies the interactions between pathogens and their hosts, with the goal of disco... | Broad Institute | 0.782217 |
87,085 | Between 2009 and 2012, the operating revenue of the institute was approximately $200 million, with 55% of that coming from federal grants. The Broad Foundation (Eli and Edythe Broad) has provided $700 million in funding to the Broad Institute as of February 2014.The Klarman Family Foundation provided a $32.5 million gr... | Broad Institute | 0.782217 |
87,086 | was giving $50 million to the Broad Institute of MIT and Harvard to support biology research.Dr. Richard Merkin has been donating since 2009 in support of research, founding the Merkin Institute for Transformative Technologies in Healthcare. Dedicated on October 6, 2021, The Broad Institute's new building at 415 Main S... | Broad Institute | 0.782217 |
87,087 | In mathematics, the Hadamard derivative is a concept of directional derivative for maps between Banach spaces. It is particularly suited for applications in stochastic programming and asymptotic statistics. | Hadamard derivative | 0.782214 |
87,088 | This allows the active solar-cell surface to be reduced, lowering cost and allowing the use of more efficient cells that would otherwise be too expensive. In the early 21st century, Fresnel reflectors began to be used in concentrating solar power (CSP) plants to concentrate solar energy. One application was to preheat ... | First order Fresnel lens | 0.782213 |
87,089 | There are several problems with defining relations for C*-algebras. One is, as previously mentioned, due to the non-existence of free C*-algebras, not every set of relations defines a C*-algebra. Another problem is that one would often want to include order relations, formulas involving continuous functional calculus, ... | Universal C*-algebra | 0.782212 |
87,090 | The noncommutative torus can be defined as a universal C*-algebra generated by two unitaries with a commutation relation. The Cuntz algebras, graph C*-algebras and k-graph C*-algebras are universal C*-algebras generated by partial isometries. The universal C*-algebra generated by a unitary element u has presentation ⟨ ... | Universal C*-algebra | 0.782212 |
87,091 | Alternatively, one can use a more concrete characterization of universal C*-algebras that more closely resembles the construction in abstract algebra. Unfortunately, this restricts the types of relations that are possible. Given a set G, a relation on G is a set R consisting of pairs (p, η) where p is a *-polynomial on... | Universal C*-algebra | 0.782212 |
87,092 | In mathematics, a universal C*-algebra is a C*-algebra described in terms of generators and relations. In contrast to rings or algebras, where one can consider quotients by free rings to construct universal objects, C*-algebras must be realizable as algebras of bounded operators on a Hilbert space by the Gelfand-Naimar... | Universal C*-algebra | 0.782212 |
87,093 | The Lie algebra of the conformal group has the following representation: M μ ν ≡ i ( x μ ∂ ν − x ν ∂ μ ) , P μ ≡ − i ∂ μ , D ≡ − i x μ ∂ μ , K μ ≡ i ( x 2 ∂ μ − 2 x μ x ν ∂ ν ) , {\displaystyle {\begin{aligned}&M_{\mu \nu }\equiv i(x_{\mu }\partial _{\nu }-x_{\nu }\partial _{\mu })\,,\\&P_{\mu }\equiv -i\partial _{\mu ... | Conformal symmetry | 0.782212 |
87,094 | The model of the structural fracture mechanics is similar to the cusp catastrophe behavior. The model predicts reserve ability of a complex system. Other applications include the outer sphere electron transfer frequently encountered in chemical and biological systems, modelling the dynamics of cloud condensation nuclei... | Catastrophe theory | 0.782207 |
87,095 | V = x 4 + a x 2 + b x {\displaystyle V=x^{4}+ax^{2}+bx\,} The cusp geometry is very common when one explores what happens to a fold bifurcation if a second parameter, b, is added to the control space. Varying the parameters, one finds that there is now a curve (blue) of points in (a,b) space where stability is lost, wh... | Catastrophe theory | 0.782207 |
87,096 | However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures. In the late 1970s, applications of catastrophe theory to areas outside its scope began to be criticized, especially in biology and social scien... | Catastrophe theory | 0.782207 |
87,097 | In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circum... | Catastrophe theory | 0.782207 |
87,098 | {\displaystyle q>{\frac {1}{10}}.} This is an example of linear optimization. In more complex cases, where more than one resource f is devoted to more than two areas, multivariate optimization is often used, through the simplex algorithm or its derivatives. | Mark and recapture | 0.782207 |
87,099 | The capture probability refers to the probability of a detecting an individual animal or person of interest, and has been used in both ecology and epidemiology for detecting animal or human diseases, respectively. The capture probability is often defined as a two-variable model, in which f is defined as the fraction of... | Mark and recapture | 0.782207 |
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