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84,900 | {\displaystyle kX=X.} Otherwise the topology on k X {\displaystyle kX} is strictly finer than X {\displaystyle X} (i.e., there are more open sets). This construction is functorial. | Compactly-generated space | 0.783116 |
84,901 | Given any topological space X {\displaystyle X} we can define a possibly finer topology on X {\displaystyle X} that is compactly generated, sometimes called the k-ification of the topology. Let { K α } {\displaystyle \{K_{\alpha }\}} denote the family of compact subsets of X . {\displaystyle X.} We define the new topol... | Compactly-generated space | 0.783116 |
84,902 | For a concrete example, the Sierpiński space is not CG-3, but is homeomorphic to the quotient of the compact interval {\displaystyle } obtained by identifying ( 0 , 1 ] {\displaystyle (0,1]} to a point. More generally, any final topology on a set induced by a family of functions from CG-1 spaces is also CG-1. | Compactly-generated space | 0.783116 |
84,903 | {\displaystyle X.} The space X {\displaystyle X} is then compactly generated exactly when its topology is coherent with that family of subspaces; namely, a set A ⊆ X {\displaystyle A\subseteq X} is open (resp. closed) in X {\displaystyle X} exactly when the intersection A ∩ K {\displaystyle A\cap K} is open (resp. | Compactly-generated space | 0.783116 |
84,904 | The space X {\displaystyle X} together with the new topology T F {\displaystyle T_{\mathcal {F}}} is usually denoted k X . {\displaystyle kX.} The space X {\displaystyle X} is called compactly generated or a k-space (with respect to the family F {\displaystyle {\mathcal {F}}} ) if its topology is determined by all maps... | Compactly-generated space | 0.783116 |
84,905 | {\displaystyle T.} Since all the functions in F {\displaystyle {\mathcal {F}}} were continuous into ( X , T ) , {\displaystyle (X,T),} the k-ification of T {\displaystyle T} is finer than (or equal to) the original topology T {\displaystyle T} . The open sets in the k-ification are called the k-open sets in X ; {\displ... | Compactly-generated space | 0.783116 |
84,906 | {\displaystyle X.} The various definitions differ in their choice of the family F , {\displaystyle {\mathcal {F}},} as detailed below. The final topology T F {\displaystyle T_{\mathcal {F}}} on X {\displaystyle X} with respect to the family F {\displaystyle {\mathcal {F}}} is called the k-ification of T . | Compactly-generated space | 0.783116 |
84,907 | Let ( X , T ) {\displaystyle (X,T)} be a topological space, where T {\displaystyle T} is the topology, that is, the collection of all open sets in X . {\displaystyle X.} There are multiple (non-equivalent) definitions of compactly generated space or k-space in the literature. These definitions share a common structure,... | Compactly-generated space | 0.783116 |
84,908 | In mathematics, Kachurovskii's theorem is a theorem relating the convexity of a function on a Banach space to the monotonicity of its Fréchet derivative. | Kachurovskii's theorem | 0.783115 |
84,909 | The Appropedia Foundation is a non-profit organization running Appropedia, the largest wiki documenting schematics, ideas, observations, experimental data, deployment logs etc. about patent-free appropriate technology, permaculture and related subjects.At the university level, the use of open-source-appropriate technol... | Open-source-appropriate technology | 0.783114 |
84,910 | One of the key parameter which characterizes the gas flow over the droplet is the droplet Reynolds number based on the relative velocity, droplet diameter and gas phase properties. The features of the gas flow have a critical impact on the exchanges of mass, momentum and energy between the gas and the liquid phases and... | Droplet vaporization | 0.783114 |
84,911 | In this section we assume that there is no relative motion between the droplet and the gas, R e d = 0 {\displaystyle Re_{d}=0} , and that the temperature inside the droplet is uniform (models that account for the non-uniformity of the droplet temperature are presented in the next section). The time evolution of the dro... | Droplet vaporization | 0.783114 |
84,912 | Mass-analyzed ion kinetic-energy spectrometry (MIKES) is a mass spectrometry technique by which mass spectra are obtained from a sector instrument that incorporates at least one magnetic sector plus one electric sector in reverse geometry (the beam first enters the magnetic sector). The accelerating voltage V, and the ... | Mass-analyzed ion kinetic energy spectrometry | 0.783113 |
84,913 | The MIKES Schematic shows that the ion species in the source goes into the magnetic field. After which, the chemistry is later studied in the second field-free region (FFR) by scanning the electric sector which defines the nature of the fragments by measuring their kinetic energy. This causes competitive unimolecular f... | Mass-analyzed ion kinetic energy spectrometry | 0.783113 |
84,914 | MIKES is a powerful technique used for structural studies of organic compounds, gaseous ions, and also for direct analysis of complex mixtures without separation of the components. In other words, it is used for molecular structure studies. The reason why MIKES is good for molecular structure studies is due to the reve... | Mass-analyzed ion kinetic energy spectrometry | 0.783113 |
84,915 | Plateau type minimization problems from calculus of variationsThe following theorems and concepts are also central: The area formula, which generalizes the concept of change of variables in integration. The coarea formula, which generalizes and adapts Fubini's theorem to geometric measure theory. The isoperimetric ineq... | Geometric measure theory | 0.783113 |
84,916 | The following objects are central in geometric measure theory: Hausdorff measure and Hausdorff dimension Rectifiable sets (or Radon measures), which are sets with the least possible regularity required to admit approximate tangent spaces. Characterization of rectifiability through existence of approximate tangents, den... | Geometric measure theory | 0.783113 |
84,917 | The Brunn–Minkowski inequality for the n-dimensional volumes of convex bodies K and L, v o l ( ( 1 − λ ) K + λ L ) 1 / n ≥ ( 1 − λ ) v o l ( K ) 1 / n + λ v o l ( L ) 1 / n , {\displaystyle \mathrm {vol} {\big (}(1-\lambda )K+\lambda L{\big )}^{1/n}\geq (1-\lambda )\mathrm {vol} (K)^{1/n}+\lambda \,\mathrm {vol} (L)^{1... | Geometric measure theory | 0.783113 |
84,918 | In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth. | Geometric measure theory | 0.783113 |
84,919 | Biological robots are not officially neurorobots in that they are not neurologically inspired AI systems, but actual neuron tissue wired to a robot. This employs the use of cultured neural networks to study brain development or neural interactions. These typically consist of a neural culture raised on a multielectrode ... | Neurorobotics | 0.783112 |
84,920 | Neuroscientists benefit from neurorobotics because it provides a blank slate to test various possible methods of brain function in a controlled and testable environment. While robots are more simplified versions of the systems they emulate, they are more specific, allowing more direct testing of the issue at hand. They... | Neurorobotics | 0.783112 |
84,921 | This includes robots, prosthetic or wearable systems but also, at smaller scale, micro-machines and, at the larger scales, furniture and infrastructures. Neurorobotics is that branch of neuroscience with robotics, which deals with the study and application of science and technology of embodied autonomous neural systems... | Neurorobotics | 0.783112 |
84,922 | Neurorobotics is the combined study of neuroscience, robotics, and artificial intelligence. It is the science and technology of embodied autonomous neural systems. Neural systems include brain-inspired algorithms (e.g. connectionist networks), computational models of biological neural networks (e.g. artificial spiking ... | Neurorobotics | 0.783112 |
84,923 | This is a II1,1-graded algebra with a bilinear form and carries an action of the Virasoro algebra. Let P 1 {\displaystyle P^{1}} be the subspace of the vertex algebra V ⊗ V I I 1 , 1 {\displaystyle V\otimes V_{II_{1,1}}} consisting of vectors v {\displaystyle v} such that L 0 ⋅ v = v , L n ⋅ v = 0 {\displaystyle L_{0}\... | No-ghost theorem | 0.783112 |
84,924 | This statement is that of Borcherds (1992). Suppose that V {\displaystyle V} is a unitary representation of the Virasoro algebra V i r {\displaystyle \mathrm {Vir} } , so V {\displaystyle V} is equipped with a non-degenerate bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} and there is an algebra homomorphism ρ:... | No-ghost theorem | 0.783112 |
84,925 | The Goddard–Thorn theorem amounts to the assertion that this quantization functor more or less cancels the addition of two free bosons, as conjectured by Lovelace in 1971. Lovelace's precise claim was that at critical dimension 26, Virasoro-type Ward identities cancel two full sets of oscillators. Mathematically, this ... | No-ghost theorem | 0.783112 |
84,926 | There are two naturally isomorphic functors that are typically used to quantize bosonic strings. In both cases, one starts with positive-energy representations of the Virasoro algebra of central charge 26, equipped with Virasoro-invariant bilinear forms, and ends up with vector spaces equipped with bilinear forms. Here... | No-ghost theorem | 0.783112 |
84,927 | The bosonic string quantization functors described here can be applied to any conformal vertex algebra of central charge 26, and the output naturally has a Lie algebra structure. The Goddard–Thorn theorem can then be applied to concretely describe the Lie algebra in terms of the input vertex algebra. Perhaps the most s... | No-ghost theorem | 0.783112 |
84,928 | In mathematics, and in particular in the mathematical background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem describing properties of a functor that quantizes bosonic strings. It is named after Peter Goddard and Charles Thorn. The name "no-ghost theorem" stems from the fa... | No-ghost theorem | 0.783112 |
84,929 | A nitronate (IUPAC: azinate) in organic chemistry is a functional group with the general structure R1R2C=NO−2. It is the anion of nitronic acid (sometimes also called an aci, or an azinic acid), a tautomeric form of a nitro compound. Just as ketones and aldehydes can exist in equilibrium with their enol tautomer, nitro... | Nitronic acid | 0.78311 |
84,930 | The stronger version of Fermat's little theorem, which a Wieferich prime satisfies, is usually expressed as a congruence relation 2p -1 ≡ 1 (mod p2). From the definition of the congruence relation on integers, it follows that this property is equivalent to the definition given at the beginning. Thus if a prime p satisf... | Generalized Wieferich prime | 0.78311 |
84,931 | In 1902, Meyer proved a theorem about solutions of the congruence ap − 1 ≡ 1 (mod pr). : 930 Later in that decade Arthur Wieferich showed specifically that if the first case of Fermat's last theorem has solutions for an odd prime exponent, then that prime must satisfy that congruence for a = 2 and r = 2. In other words... | Generalized Wieferich prime | 0.78311 |
84,932 | In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem,... | Generalized Wieferich prime | 0.78311 |
84,933 | A Wieferich number is an odd natural number n satisfying the congruence 2φ(n) ≡ 1 (mod n2), where φ denotes the Euler's totient function (according to Euler's theorem, 2φ(n) ≡ 1 (mod n) for every odd natural number n). If Wieferich number n is prime, then it is a Wieferich prime. The first few Wieferich numbers are: 1,... | Generalized Wieferich prime | 0.78311 |
84,934 | In statistics, burstiness is the intermittent increases and decreases in activity or frequency of an event. One measure of burstiness is the Fano factor—a ratio between the variance and mean of counts. Burstiness is observable in natural phenomena, such as natural disasters, or other phenomena, such as network/data/ema... | Burstiness | 0.78311 |
84,935 | Unified neutral theory is a hypothesis proposed by Stephen P. Hubbell in 2001. The hypothesis aims to explain the diversity and relative abundance of species in ecological communities, although like other neutral theories in ecology, Hubbell's hypothesis assumes that the differences between members of an ecological com... | Theoretical ecologist | 0.783106 |
84,936 | If e is zero, the dynamics of the system favor the species that is better at colonizing (i.e. has the higher m value). This leads to a very important result in theoretical ecology known as the Intermediate Disturbance Hypothesis, where the biodiversity (the number of species that coexist in the population) is maximized... | Theoretical ecologist | 0.783106 |
84,937 | However, most models work with the Lagrangian approach, which is an agent-based model following the individual agents (points or particles) that make up the swarm. Individual particle models can follow information on heading and spacing that is lost in the Eulerian approach. Examples include ant colony optimization, se... | Theoretical ecologist | 0.783106 |
84,938 | In mathematics, endoscopic groups of reductive algebraic groups were introduced by Robert Langlands (1979, 1983) in his work on the stable trace formula. Roughly speaking, an endoscopic group H of G is a quasi-split group whose L-group is the connected component of the centralizer of a semisimple element of the L-group... | Endoscopic group | 0.783106 |
84,939 | This decision was informed partly by the Science Council of Japan. The Japanese government sought monetary support from other countries to help fund this project.In 2022, the Japanese plan for the ILC was "shelved" by a panel for Japan’s Ministry of Education, Culture, Sports, Science and Technology (MEXT) Several reas... | International Linear Collider | 0.783105 |
84,940 | The information presented above is a summary of that contained in the International Workshop on Linear Colliders 2010 (ECFA-CLIC-ILC Joint Meeting) at CERN.The 2008 economic crisis led the United States and United Kingdom to cut funds to the collider project, leading to Japan's position as the most likely host for the ... | International Linear Collider | 0.783105 |
84,941 | Originally, three sites for the International Linear Collider were leading contenders at established High Energy Physics centers in Europe. At CERN in Geneva the tunnel is located deep underground in non-permeable bedrock. This site was considered favorable for a number of practical reasons but due to the LHC the site ... | International Linear Collider | 0.783105 |
84,942 | In this sense, this promise problem belongs to the complexity class UP (which is usually only defined for languages). The proof of the Valiant–Vazirani theorem consists of a probabilistic reduction from SAT to SAT such that, with probability at least Ω ( 1 / n ) {\displaystyle \Omega (1/n)} , the output formula has at ... | Valiant–Vazirani theorem | 0.783105 |
84,943 | The Valiant–Vazirani theorem is a theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT, then NP = RP. It was proven by Leslie Valiant and Vijay Vazirani in their paper titled NP is as easy as detecting unique solutions published in 1986. The proof is based ... | Valiant–Vazirani theorem | 0.783105 |
84,944 | In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier results of Henri Poincaré. | Rational Hurewicz theorem | 0.783103 |
84,945 | The Center for Nanotechnology is one of the first centers for nanotechnology. It is located in Münster, North Rhine-Westphalia, Germany. It offers many possibilities for research, education, start-ups and companies in nanotechnology. Hence it works together with the University of Münster (WWU), the Max Planck Institute... | CeNTech | 0.783103 |
84,946 | The Hopf construction, viewed as a fiber bundle p: S3 → CP1, admits several generalizations, which are also often known as Hopf fibrations. First, one can replace the projective line by an n-dimensional projective space. Second, one can replace the complex numbers by any (real) division algebra, including (for n = 1) t... | Hopf map | 0.783102 |
84,947 | Signature blocks are also used in the Usenet discussion system. ...orist it's an unnecessary optimization and a (to use your words) "performance hack", but I'm interested in a Real operating system --- not a research toy. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Theodore Ts'o bloom-beacon!m... | Signature block | 0.783102 |
84,948 | Mars is named after the Roman god of war. This association between Mars and war dates back at least to Babylonian astronomy, in which the planet was named for the god Nergal, deity of war and destruction. It persisted into modern times, as exemplified by Gustav Holst's orchestral suite The Planets, whose famous first m... | Fourth planet | 0.783101 |
84,949 | It was not until the findings were confirmed by W. S. Adams in 1925 that the myth of the Earth-like habitability of Mars was finally broken. However, even in the 1960s, articles were published on Martian biology, putting aside explanations other than life for the seasonal changes on Mars. Detailed scenarios for the met... | Fourth planet | 0.783101 |
84,950 | Dozens of crewless spacecraft, including orbiters, landers, and rovers, have been sent to Mars by the Soviet Union, the United States, Europe, India, the United Arab Emirates, and China to study the planet's surface, climate, and geology. NASA's Mariner 4 was the first spacecraft to visit Mars; launched on 28 November ... | Fourth planet | 0.783101 |
84,951 | Ptolemy, a Greek living in Alexandria, attempted to address the problem of the orbital motion of Mars. Ptolemy's model and his collective work on astronomy was presented in the multi-volume collection later called the Almagest (from the Arabic for "greatest"), which became the authoritative treatise on Western astronom... | Fourth planet | 0.783101 |
84,952 | With the arrival of spring, sunlight warms the subsurface and pressure from subliming CO2 builds up under a slab, elevating and ultimately rupturing it. This leads to geyser-like eruptions of CO2 gas mixed with dark basaltic sand or dust. This process is rapid, observed happening in the space of a few days, weeks or mo... | Fourth planet | 0.783101 |
84,953 | Quantum suicide is a thought experiment in quantum mechanics and the philosophy of physics. Purportedly, it can falsify any interpretation of quantum mechanics other than the Everett many-worlds interpretation by means of a variation of the Schrödinger's cat thought experiment, from the cat's point of view. Quantum imm... | Quantum immortality | 0.783101 |
84,954 | Hugh Everett did not mention quantum suicide or quantum immortality in writing; his work was intended as a solution to the paradoxes of quantum mechanics. Eugene Shikhovtsev's biography of Everett states that "Everett firmly believed that his many-worlds theory guaranteed him immortality: his consciousness, he argued, ... | Quantum immortality | 0.783101 |
84,955 | The RXNO Ontology is a formal ontology of chemical named reactions. It was originally developed at the Royal Society of Chemistry (RSC) and is associated with the Open Biomedical Ontologies Foundry. The RXNO ontology unifies several previous attempts to systematize chemical reactions including the Merck Index and the h... | RXNO Ontology | 0.7831 |
84,956 | In a theological work, On the Creation of the World (De opificio mundi), he denied that the heavens are moved by either a soul or by angels, proposing that "it is not impossible that God, who created all these things, imparted a motive force to the Moon, the Sun, and other stars – just as the inclination to heavy and l... | Dynamics of the celestial spheres | 0.783099 |
84,957 | In considering the physics of the celestial spheres, scholars followed two different views about the material composition of the celestial spheres. For Plato, the celestial regions were made "mostly out of fire" on account of fire's mobility. Later Platonists, such as Plotinus, maintained that although fire moves natur... | Dynamics of the celestial spheres | 0.783099 |
84,958 | As early as Plato, philosophers considered the heavens to be moved by immaterial agents. Plato believed the cause to be a world-soul, created according to mathematical principles, which governed the daily motion of the heavens (the motion of the Same) and the opposed motions of the planets along the zodiac (the motion ... | Dynamics of the celestial spheres | 0.783099 |
84,959 | Although Nicolaus Copernicus (1473–1543) transformed Ptolemaic astronomy and Aristotelian cosmology by moving the Earth from the center of the universe, he retained both the traditional model of the celestial spheres and the medieval Aristotelian views of the causes of its motion. Copernicus follows Aristotle to mainta... | Dynamics of the celestial spheres | 0.783099 |
84,960 | Avicenna maintained that besides an intelligence and its soul, each sphere was also moved by a natural inclination (mayl).An interpreter of Aristotle from Muslim Spain, al-Bitruji (d. c. 1024), proposed a radical transformation of astronomy that did away with epicycles and eccentrics, in which the celestial spheres wer... | Dynamics of the celestial spheres | 0.783099 |
84,961 | In the Early Middle Ages, Plato's picture of the heavens was dominant among European philosophers, which led Christian thinkers to question the role and nature of the world-soul. With the recovery of Aristotle's works in the twelfth and thirteenth centuries, Aristotle's views supplanted the earlier Platonism, and a new... | Dynamics of the celestial spheres | 0.783099 |
84,962 | Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin.Ronald Kaplan, former mana... | Powerset (company) | 0.783098 |
84,963 | Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge Un... | Powerset (company) | 0.783098 |
84,964 | ", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the pro... | Powerset (company) | 0.783098 |
84,965 | The theorem has particular use in algebraic graph theory. The "underlying graph" of a nonnegative n-square matrix is the graph with vertices numbered 1, ..., n and arc ij if and only if Aij ≠ 0. If the underlying graph of such a matrix is strongly connected, then the matrix is irreducible, and thus the theorem applies.... | Frobenius-Perron eigenvector | 0.783097 |
84,966 | A row (column) stochastic matrix is a square matrix each of whose rows (columns) consists of non-negative real numbers whose sum is unity. The theorem cannot be applied directly to such matrices because they need not be irreducible. If A is row-stochastic then the column vector with each entry 1 is an eigenvector corre... | Frobenius-Perron eigenvector | 0.783097 |
84,967 | Therefore, many of the spectral properties of A may be deduced by applying the theorem to the irreducible Bi. For example, the Perron root is the maximum of the ρ(Bi). While there will still be eigenvectors with non-negative components it is quite possible that none of these will be positive. | Frobenius-Perron eigenvector | 0.783097 |
84,968 | The Perron–Frobenius theorem does not apply directly to non-negative matrices. Nevertheless, any reducible square matrix A may be written in upper-triangular block form (known as the normal form of a reducible matrix) PAP−1 = ( B 1 ∗ ∗ ⋯ ∗ 0 B 2 ∗ ⋯ ∗ ⋮ ⋮ ⋮ ⋮ 0 0 0 ⋯ ∗ 0 0 0 ⋯ B h ) {\displaystyle \left({\begin{smallma... | Frobenius-Perron eigenvector | 0.783097 |
84,969 | For a non-negative A, this is also a sufficient condition. Wielandt's theorem. If |B| | Frobenius-Perron eigenvector | 0.783097 |
84,970 | The key point is that a positive projection always has rank one. This means that if A is an irreducible non-negative square matrix then the algebraic and geometric multiplicities of its Perron root are both one. Also if P is its Perron projection then AP = PA = ρ(A)P so every column of P is a positive right eigenvector... | Frobenius-Perron eigenvector | 0.783097 |
84,971 | The proof now proceeds using spectral decomposition. The trick here is to split the Perron root from the other eigenvalues. The spectral projection associated with the Perron root is called the Perron projection and it enjoys the following property: The Perron projection of an irreducible non-negative square matrix is ... | Frobenius-Perron eigenvector | 0.783097 |
84,972 | Let A = ( a i j ) {\displaystyle A=(a_{ij})} be an n × n {\displaystyle n\times n} positive matrix: a i j > 0 {\displaystyle a_{ij}>0} for 1 ≤ i , j ≤ n {\displaystyle 1\leq i,j\leq n} . Then the following statements hold. There is a positive real number r, called the Perron root or the Perron–Frobenius eigenvalue (als... | Frobenius-Perron eigenvector | 0.783097 |
84,973 | Despite the differences between the AGM and bone marrow, both are subjected to the circulation, and it is entirely possible that these same forces exist in this adult stem cell niche. Other characteristics, such as strain, geometry, and ligand profiles of the extracellular matrix (ECM) have been suggested as important ... | Hematopoietic stem cell niche | 0.783096 |
84,974 | Betweenness is an algorithmic problem in order theory about ordering a collection of items subject to constraints that some items must be placed between others. It has applications in bioinformatics and was shown to be NP-complete by Opatrný (1979). | Betweenness | 0.783096 |
84,975 | One application of betweenness arises in bioinformatics, as part of the process of gene mapping. Certain types of genetic experiments can be used to determine the ordering of triples of genetic markers, but do not distinguish a genetic sequence from its reversal, so the information yielded from such an experiment deter... | Betweenness | 0.783096 |
84,976 | Crew members during the 2017 expedition will carry outreach in field geology, microbiology, lichen ecology, and small crew dynamics. The research will be similar to that conducted during the MDRS portion of the Mars 160 mission, to gauge how different locations affect the data collected. Dr. Shannon Rupert is serving a... | Flashline Mars Arctic Research Station | 0.783095 |
84,977 | The arctic portion of the Mars 160 mission concluded on September 3, 2017. Principal Investigators Dr. Shannon Rupert and Dr. Paul Sokoloff acquired permission for research on Inuit-owned land for the first time in FMARS history, allowing for more wide-reaching geology studies than have been done in the past. Dr. Alexa... | Flashline Mars Arctic Research Station | 0.783095 |
84,978 | Robert Zubrin – Commander John Blitch – Robotics Expert Brent Bos – Planetary Scientist Steve Braham – Engineer Cathrine Frandsen – Physicist & Planetary Scientist Charles Frankel – Geologist Christine Jayarajah – Chemist | Flashline Mars Arctic Research Station | 0.783095 |
84,979 | Pascal Lee John Blitch – Robotics Expert Charles Cockell Larry Lemke Peter Smith Carol Stoker | Flashline Mars Arctic Research Station | 0.783095 |
84,980 | Jason Held – Commander Blazej Blazejowski – Paleontologist Akos Kereszturi – Geologist Judd Reed – Engineer Joan Roch – Journalist Shannon Rupert – Biologist Louise Wynn – Planetary Geology, Health and Safety Officer (HSO), and Journalist | Flashline Mars Arctic Research Station | 0.783095 |
84,981 | FMARS sponsors in 2009 included the Mars Society, 4Frontiers Corporation, Florida Space Grant Consortium, NASA, Florida's Space Coast, Georgia Space Grant Consortium, Prioria Robotics, AUVSI, Procerus Technologies, Nikon, Lighthouse Technical Innovations, Nanometrics, Geonics Limited, Del Mar College, First Air, E. Bar... | Flashline Mars Arctic Research Station | 0.783095 |
84,982 | FMARS Crew 7, with seven personnel, occupied the station from July 9, 2002 through July 26, 2002.The crew operated under full Mars simulation constraints between July 11 and July 24. In addition to conducting a systematic program of field geology and microbiology under simulated Mars mission conditions, the crew worked... | Flashline Mars Arctic Research Station | 0.783095 |
84,983 | Steklov Institute of Mathematics or Steklov Mathematical Institute (Russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 found... | Steklov Institute of Mathematics | 0.783095 |
84,984 | The converse is also true: if α(A) = 0, then A must be precompact, and indeed compact if A is closed. Also, if A is a subset of B, then α(A) ≤ α(B). In some sense, the quantity α(A) is a numerical description of "how non-compact" the set A is. Now consider a sequence of sets An ⊆ X, one for each natural number n. Kurat... | Kuratowski's intersection theorem | 0.783094 |
84,985 | In mathematics, Kuratowski's intersection theorem is a result in general topology that gives a sufficient condition for a nested sequence of sets to have a non-empty intersection. Kuratowski's result is a generalisation of Cantor's intersection theorem. Whereas Cantor's result requires that the sets involved be compact... | Kuratowski's intersection theorem | 0.783094 |
84,986 | It is possible to study the number of integer points in a polytope P if we dilate some facets of P but not others. In other words, one would like to know the number of integer points in semi-dilated polytopes. It turns out that such a counting function will be what is called a multivariate quasi-polynomial. An Ehrhart-... | Ehrhart polynomial | 0.783093 |
84,987 | In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane. ... | Ehrhart polynomial | 0.783093 |
84,988 | Von Neumann algebras have found applications in diverse areas of mathematics like knot theory, statistical mechanics, quantum field theory, local quantum physics, free probability, noncommutative geometry, representation theory, differential geometry, and dynamical systems. For instance, C*-algebra provides an alternat... | Commutative von Neumann algebras | 0.78309 |
84,989 | The tensor product of two von Neumann algebras, or of a countable number with states, is a von Neumann algebra as described in the section above. The crossed product of a von Neumann algebra by a discrete (or more generally locally compact) group can be defined, and is a von Neumann algebra. Special cases are the group... | Commutative von Neumann algebras | 0.78309 |
84,990 | The double commutant G′′ of G is also a von Neumann algebra. The von Neumann group algebra of a discrete group G is the algebra of all bounded operators on H = l2(G) commuting with the action of G on H through right multiplication. One can show that this is the von Neumann algebra generated by the operators correspondi... | Commutative von Neumann algebras | 0.78309 |
84,991 | The essentially bounded functions on a σ-finite measure space form a commutative (type I1) von Neumann algebra acting on the L2 functions. For certain non-σ-finite measure spaces, usually considered pathological, L∞(X) is not a von Neumann algebra; for example, the σ-algebra of measurable sets might be the countable-co... | Commutative von Neumann algebras | 0.78309 |
84,992 | All amenable factors can be constructed using the group-measure space construction of Murray and von Neumann for a single ergodic transformation. In fact they are precisely the factors arising as crossed products by free ergodic actions of Z or Z/nZ on abelian von Neumann algebras L∞(X). Type I factors occur when the m... | Commutative von Neumann algebras | 0.78309 |
84,993 | M has property E or the Hakeda–Tomiyama extension property: this means that there is a projection of norm 1 from bounded operators on H to M '. M is injective: any completely positive linear map from any self adjoint closed subspace containing 1 of any unital C*-algebra A to M can be extended to a completely positive m... | Commutative von Neumann algebras | 0.78309 |
84,994 | Connes (1976) and others proved that the following conditions on a von Neumann algebra M on a separable Hilbert space H are all equivalent: M is hyperfinite or AFD or approximately finite dimensional or approximately finite: this means the algebra contains an ascending sequence of finite dimensional subalgebras with de... | Commutative von Neumann algebras | 0.78309 |
84,995 | Subsequently, Sorin Popa showed that the fundamental group can be trivial for certain groups, including the semidirect product of Z2 by SL(2,Z). An example of a type II1 factor is the von Neumann group algebra of a countable infinite discrete group such that every non-trivial conjugacy class is infinite. McDuff (1969) ... | Commutative von Neumann algebras | 0.78309 |
84,996 | The tensor product of a factor of type II1 and an infinite type I factor has type II∞, and conversely any factor of type II∞ can be constructed like this. The fundamental group of a type II1 factor is defined to be the fundamental group of its tensor product with the infinite (separable) factor of type I. For many year... | Commutative von Neumann algebras | 0.78309 |
84,997 | A factor is said to be of type I if there is a minimal projection E ≠ 0, i.e. a projection E such that there is no other projection F with 0 < F < E. Any factor of type I is isomorphic to the von Neumann algebra of all bounded operators on some Hilbert space; since there is one Hilbert space for every cardinal number, ... | Commutative von Neumann algebras | 0.78309 |
84,998 | GHC is written in Haskell, but the runtime system for Haskell, essential to run programs, is written in C and C--. GHC's front end, incorporating the lexer, parser and typechecker, is designed to preserve as much information about the source language as possible until after type inference is complete, toward the goal o... | Glasgow Haskell Compiler | 0.783089 |
84,999 | Essentially, a polymorphic function or datatype constructor may require that one of its arguments is itself polymorphic. Generalized algebraic data types. Each constructor of a polymorphic datatype can encode information into the resulting type. | Glasgow Haskell Compiler | 0.783089 |
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