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98,000 | Mark Howard Kryder (born October 7, 1943 in Portland, Oregon) was Seagate Corp. 's senior vice president of research and chief technology officer. Kryder holds a Bachelor of Science degree in electrical engineering from Stanford University and a Ph.D. in electrical engineering and physics from the California Institute ... | Kryder's Law | 0.777478 |
98,001 | Monterey cypresses are often visited by tourists and photographers, particularly a tree known as the Lone Cypress.The fleshy cones of Juniperus communis are used to flavour gin. Native Americans and early European explorers used Thuja leaves as a cure for scurvy. Distillation of Fokienia roots produces an essential oil... | Cupressoideae | 0.777478 |
98,002 | If the vector norm is an inner product norm, as in a Hilbert space, then the logarithmic norm is the smallest number μ ( A ) {\displaystyle \mu (A)} such that for all x {\displaystyle x} ℜ ⟨ x , A x ⟩ ≤ μ ( A ) ⋅ ‖ x ‖ 2 {\displaystyle \Re \langle x,Ax\rangle \leq \mu (A)\cdot \|x\|^{2}} Unlike the original definition,... | Logarithmic norm | 0.777477 |
98,003 | In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for square matrices. It has since been extended to... | Logarithmic norm | 0.777477 |
98,004 | As an operator satisfying ⟨ u , A u ⟩ > 0 {\displaystyle \langle u,Au\rangle >0} is called elliptic, the logarithmic norm quantifies the (strong) ellipticity of − d 2 / d x 2 {\displaystyle -\mathrm {d} ^{2}/\mathrm {d} x^{2}} . Thus, if A {\displaystyle A} is strongly elliptic, then μ ( − A ) < 0 {\displaystyle \mu (-... | Logarithmic norm | 0.777477 |
98,005 | This extension offers many connections to fixed point theory, and critical point theory. The theory becomes analogous to that of the logarithmic norm for matrices, but is more complicated as the domains of the operators need to be given close attention, as in the case with unbounded operators. Property 8 of the logarit... | Logarithmic norm | 0.777477 |
98,006 | In stratiform anvil regions, aggregation into graupel was the main growth mechanism. The speed of the updraft determines if warm rain processes, riming, or aggregation are the primary mechanism of growth in updraft regions.Heymsfield et al. (2002) also looked at the microphysics of tropical convection, but they limited... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,007 | During the weakest simulated storm, the fall speed of the snow and graupel particles was increased. The increased rate of fallout also increased the evaporation, leading to weakened convection. Changes in the intercept parameter showed little change. This implies that the total number of particles does not matter as mu... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,008 | They note that modifications to the microphysics scheme dramatically impacted the hurricane intensity. The most intense hurricanes were when melting was suppressed, or when no evaporation was allowed. They interpret this as meaning that the energy needed to either melt or evaporate the particles could instead be used t... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,009 | Their study attempts to show how fall speed and intercept parameters can influence the tropical cyclone intensity. The size distribution of precipitation particles is parametrized as: N(D)=N0e−λDdDwhere N is the number of precipitation particles between a given diameter D and D + dD, N0 is the intercept parameter, λ is... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,010 | They report that their control run was successful in simulating the track, intensity, speed and precipitation. They used the microphysics scheme from NASA Goddard Space Flight Center. | Hurricane dynamics and cloud microphysics | 0.777477 |
98,011 | They used the Betts-Miller-Janjic cumulus parameterization scheme in two ways: one with the parameters set for midlatitude systems and the other for tropical systems. They note that when the parameterization scheme is set for midlatitude systems the simulation produces a more realistic track and storm intensity. Howeve... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,012 | Later, the peak winds decreased along with the central pressure.Zhu and Zhang (2006) used a mesoscale model to simulate the 1998 Hurricane Bonnie. They report that their control run was reasonably able to simulate the observed hurricane. They then ran a series of sensitivity experiments to examine how changes in the mi... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,013 | There have been several in-situ observations of cloud microphysics in tropical clouds which will be discussed here. Cloud microphysics are the physical processes that describe the growth, decay, and fallout of precipitation particles. In terms of models, cloud microphysics occur on a scale smaller than the grid-scale o... | Hurricane dynamics and cloud microphysics | 0.777477 |
98,014 | The most recognizable cloud system in the tropics is the hurricane. In addition to the important climatic effects of tropical weather systems, hurricanes possess enough energy to cause massive death and destruction. Therefore, their accurate prediction is of utmost importance. Cloud microphysics describe the structure ... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,015 | Schemes that produce heavier particles that will fall faster (like K) produce worse results. They conclude by warning that any changes in storm track or speed that are initially caused by microphysics could be amplified by other dynamic factors such as the steering flow or sea surface temperatures. == References == | Hurricane dynamics and cloud microphysics | 0.777476 |
98,016 | The K microphysics scheme produced particle fall speeds that were slower than the others, thereby increasing the size of its anvil. F09 report that the most important factor that influences the size of the anvil is the terminal velocity, and that the terminal velocity of the particles depends on their geometry, density... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,017 | An earlier study by Fiorino and Elsberry (1989) showed that hurricane track and speed can be changed by simply changing the tangential winds in the outer part of the storm because they helped determine the orientation and strength of the beta gyres. The F09 storm with the K microphysics parameterization had the largest... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,018 | The model had a constant sea surface temperature, no background wind, but with Earth rotation. They then inserted a vortex with varying microphysics schemes and noted that the tracks diverged. They used the same microphysics schemes as F07, and like F07 the noted that the K storm moved faster and further westward than ... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,019 | On a constant f-plane experiment, there was no movement of the storms. They note that variations among the NWS consensus model results could be primarily due to how the different models parameterize their cloud microphysics and other subgrid-scale processes.Recently, Fovell et al. (2009) conducted a modeling study of h... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,020 | However, the different microphysical schemes tracked at different directions. Since there was no large-scale flow, they conclude that the differences in the track represent changes in the vortex motion caused by changes in the microphysics. | Hurricane dynamics and cloud microphysics | 0.777476 |
98,021 | The differences between the crystalline nature of cloud ice and snow, compared with the spherical nature of raindrops, and the semi-spherical shape of graupel will likely produce different fall velocities when frozen water is included in the parameterizations. They used the most accurate member of the Rita simulations ... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,022 | The hurricane that most similarly simulated Rita's track was when the WSM3 microphysics scheme was paired with BMJ convection. The worst simulated track was when the K microphysics was paired with KF convection, which produced a weaker storm that tracked well west of the actual storm. The spread from simply changing th... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,023 | They attribute this difference to the differences in grid spacing between the studies.The first paper published that specifically looked at the impacts of cloud microphysics on hurricane track wa Fovell and Su (2007). They use simulations of Hurricane Rita (2005) and an idealized hurricane simulation to see how differe... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,024 | There are several different cloud microphysics parameterization schemes. Depending on the sophistication of the scheme, the number of ice-phase categories can vary. Many schemes use at least three categories: cloud ice, graupel, and snow. The classification of ice into categories is necessary because different forms of... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,025 | The total number of droplets was between 600 and 1000 m−3, the liquid water content was around 1 g m−3, and a rain rate of approximately 20 mm per hour. The droplets had a mean mass diameter of ~1.6 mm and the maximum diameter recorded was 4.11 mm. There results indicate that prior rain rate estimates from tropical cyc... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,026 | Graupel is found mostly in regions of weak updrafts. Particle size tends to decrease with increasing altitude because at lower altitudes the larger particles collide and aggregate with the smaller particles. Because updrafts are important for cloud microphysics, it is also necessary to consider how convection parameter... | Hurricane dynamics and cloud microphysics | 0.777476 |
98,027 | The study of stable isotope biogeochemistry involves the description of the relative abundances of various isotopes in a certain chemical pool, as well as the way in which physicochemical processes change the fraction of those isotopes in one pool vs. another. Various type of notation have been developed to describe th... | Hydrogen isotope biogeochemistry | 0.777473 |
98,028 | This work on hydrogen isotopes won Urey the 1934 Nobel Prize in Chemistry. Also in 1934, scientists Ernest Rutherford, Mark Oliphant, and Paul Harteck, produced the radioactive isotope tritium by hitting deuterium with high energy nuclei. The deuterium used in the experiment was a generous gift of heavy water from the ... | Hydrogen isotope biogeochemistry | 0.777473 |
98,029 | The study of hydrogen isotope biogeochemistry relies on the fact that various physicochemical processes will preferentially enrich or deplete deuterium relative to protium (see kinetic isotope effect, etc.). There are various measures that have been developed to describe the fractionation in an isotope between two pool... | Hydrogen isotope biogeochemistry | 0.777473 |
98,030 | Hydrous incubation experiments suggest that 36–79% of bulk organic hydrogen may come from water at moderate maturity. While still under debate, it appears likely that incorporation of water hydrogen isotopes is the more dominant process for kerogen D- enrichment during catagenesis.In summary, D content of kerogen and c... | Hydrogen isotope biogeochemistry | 0.777473 |
98,031 | The complex composition and chemistry of kerogen complicates the results. Nevertheless, most research on hydrogen isotopes of kerogen show D enrichment with increasing maturity. | Hydrogen isotope biogeochemistry | 0.777473 |
98,032 | It was then possible to look at smaller samples with more precision. Hydrogen isotope applications quickly emerged in petroleum geochemistry by measuring oil, paleoclimatology by observing lipid biomarkers, and ecology by constructing trophic dynamics. | Hydrogen isotope biogeochemistry | 0.777473 |
98,033 | Another duo in 1970, Schiegl and Vogel, analyzed the composition of hydrogen isotopes as water became biomass, as biomass became coal and oil, and as oil became natural gas. In each step they found deuterium further depleted. A landmark paper in 1980 by Marilyn Epstep, now M. Fogel, and Thomas Hoering titled "Biogeoche... | Hydrogen isotope biogeochemistry | 0.777473 |
98,034 | Hydrogen isotope biogeochemistry is the scientific study of biological, geological, and chemical processes in the environment using the distribution and relative abundance of hydrogen isotopes. There are two stable isotopes of hydrogen, protium 1H and deuterium 2H, which vary in relative abundance on the order of hundr... | Hydrogen isotope biogeochemistry | 0.777473 |
98,035 | Both the δD values of sea water and the fractionations associated with hyptophyte biochemistry (εbio) are fairly well understood, so alkenones can be readily used to observe the secondary effect of salinity on δD. There is a well established positive linear correlation between salinity and εl/w, on the order of a ~3‰ c... | Hydrogen isotope biogeochemistry | 0.777473 |
98,036 | An important goal of environmental chemistry is tracing the source and degradation of pollutants. Various methods have been employed for fingerprinting pools of environmental pollutants such as the bulk chemical composition of a spill, isotope ratios of the bulk chemical mixture, or isotope ratios of individual constit... | Hydrogen isotope biogeochemistry | 0.777473 |
98,037 | All isotopes of a chemical element contain the same number of protons with varying numbers of neutrons. The element hydrogen has three naturally occurring isotopes, 1H, 2H and 3H, which are sometimes referred to as protium (H), deuterium (D) and tritium (T), respectively. Both 1H and 2H are stable indefinitely, while 3... | Hydrogen isotope biogeochemistry | 0.777473 |
98,038 | The discovery of hydrogen isotopes also impacted the field of physics in the 1940s, as Nuclear Magnetic Resonance (NMR) spectroscopy was first invented. Today, organic chemists utilize NMR for mapping protein interactions or identifying small compounds, but NMR was first a passion project of physicists. All three isoto... | Hydrogen isotope biogeochemistry | 0.777473 |
98,039 | The lighter isotope has a higher energy state in the quantum well and will thus be preferentially formed into products. Thus under kinetic conditions the product will be relatively depleted in deuterium. Kinetic isotope effects are common in biological systems and are especially important for hydrogen isotope biogeoche... | Hydrogen isotope biogeochemistry | 0.777473 |
98,040 | Cellulose and methane studies in the 1970s and 1980s set the standard for modern hydrogen isotope geochemistry. Measurements of individual compounds was made possible in the late 1990s and early 2000s with advancements in mass spectrometry. The Thermo Delta+XL transformed measurements as the first instrument capable of... | Hydrogen isotope biogeochemistry | 0.777473 |
98,041 | In biogeochemistry, scientists focused primarily on the stable isotope of deuterium as a tracer for environmental processes, especially the water cycle. The American geochemist Harmon Craig, once a graduate student of Urey's, discovered the relationship between rainwater's hydrogen and oxygen isotope ratios. The linear... | Hydrogen isotope biogeochemistry | 0.777473 |
98,042 | On the other hand, tertiary carbocations are relatively stable and are often intermediates in organic chemistry reactions. This stability, which increases the likelihood of proton loss, is due to the electron donation of nearby carbon atoms. Resonance and nearby lone pairs can also stabilize carbocations via electron d... | Hydrogen isotope biogeochemistry | 0.777473 |
98,043 | The location where the organism lives and substrate concentration also affect isotopic composition: rumen methanogenesis, which occurs in a more closed system and with higher partial pressures of hydrogen, exhibits a greater fractionation (−300 to −400‰) than wetland methanogenesis (−250 to −170‰). Recent advances in a... | Hydrogen isotope biogeochemistry | 0.777473 |
98,044 | Carnivores at the same trophic level tend to exhibit the same level of 2H enrichment. Because, as mentioned earlier, the amount of organic hydrogen produced from water varies between species, a model of trophic level related to absolute fractionation is difficult to make if the participating species are not known. Cons... | Hydrogen isotope biogeochemistry | 0.777473 |
98,045 | Duan et al. reported a strong kinetic isotope effect(KIE) during the desaturation from oleic acid to linoleic acid.In summary, the underlying physics of the SNIF-NMR makes it capable of measuring isotopomers. Another advantage of doing NMR measurements over mass spectrometry is that it analyzes samples non-destructivel... | Hydrogen isotope biogeochemistry | 0.777473 |
98,046 | This fundamental difference in 1H and 2H manifests in many physical properties. Integer spin particles like deuterium follow Bose-Einstein statistics while fermions with half integer spins follow Fermi-Dirac statistics. | Hydrogen isotope biogeochemistry | 0.777473 |
98,047 | Oxygen cells behave in a similar way to electrical batteries in that they have a finite lifespan which is dependent upon use. The chemical reaction described above causes the cell to create an electrical output that has a predicted voltage which is dependent on the materials used. In theory they should give that voltag... | Oxygen analyser | 0.777471 |
98,048 | Mikrotron cameras capture images from 1.1 up to 25 MPixel resolution and frame rates from several hundred to more than 250,000 frames per second (fps). They are used for process optimization, quality testing, engineering and motion analysis. Mikrotron develops and designs all of the hard- and software that is used in i... | Mikrotron-GmbH | 0.77747 |
98,049 | (The approach uses a fair bit of algebraic geometry but yields a very quick proof.) The invariant theoretic approach: one constructs irreducible representations as subrepresentations of a tensor power of the standard representations. This approach is essentially due to H. Weyl and works quite well for classical groups. | Theorem of the highest weight | 0.777469 |
98,050 | There are at least four proofs: Hermann Weyl's original proof from the compact group point of view, based on the Weyl character formula and the Peter–Weyl theorem. The theory of Verma modules contains the highest weight theorem. This is the approach taken in many standard textbooks (e.g., Humphreys and Part II of Hall)... | Theorem of the highest weight | 0.777469 |
98,051 | If K {\displaystyle K} is simply connected, this distinction disappears. The theorem was originally proved by Élie Cartan in his 1913 paper. The version of the theorem for a compact Lie group is due to Hermann Weyl. The theorem is one of the key pieces of representation theory of semisimple Lie algebras. | Theorem of the highest weight | 0.777469 |
98,052 | In representation theory, a branch of mathematics, the theorem of the highest weight classifies the irreducible representations of a complex semisimple Lie algebra g {\displaystyle {\mathfrak {g}}} . There is a closely related theorem classifying the irreducible representations of a connected compact Lie group K {\disp... | Theorem of the highest weight | 0.777469 |
98,053 | Little is known about their biology, though Zikan reported the larvae of Gauromydas heros live in the subterranean detritus "pans" of Atta ants in southern Brazil, where they appear to be feeding on detritivorous Dynastinae (Coelosis spp.) larvae. In the U.S., Mydas brunneus, Mydas clavatus, and Mydas tibialis larvae a... | Mydas fly | 0.777466 |
98,054 | A feed-in premium (FIP) is a policy mechanism designed to support investment in renewable energy. In a FIP, renewable energy producers sell to the electricity market and receive a payment (premium) in addition to the market price. | Feed-in premium | 0.777466 |
98,055 | A binoviewer is an optical device designed to enable binocular viewing through a single objective. In contrast to binoculars, it allows partially stereoscopic viewing and partially monoculair viewing, this because the eyes and brain still process the image binocularly, as both images are produced by the same objective ... | Binoviewer | 0.777464 |
98,056 | These processes are studied in the field of nonlinear optics. In the specialized literature, "ultrashort" refers to the femtosecond (fs) and picosecond (ps) range, although such pulses no longer hold the record for the shortest pulses artificially generated. Indeed, x-ray pulses with durations on the attosecond time sc... | Femtosecond pulse | 0.777463 |
98,057 | Physicists also contributed to the war effort, developing wireless communication technologies and sound-based methods of detecting U-boats, resulting in the first tenuous long-term connections between academic science and the military.World War II marked a massive increase in the military funding of science, particular... | History of military technology | 0.777462 |
98,058 | The complex histories of computer science and computer engineering were shaped, in the first decades of digital computing, almost entirely by military funding. Most of the basic component technologies for digital computing were developed through the course of the long-running Whirlwind-SAGE program to develop an automa... | History of military technology | 0.777462 |
98,059 | Because of the success of academic science in solving specific military problems, the NRC was retained after the war's end, though it gradually decoupled from the military.Many industrial and academic chemists and physicists came under military control during the Great War, but post-war research by the Royal Engineers ... | History of military technology | 0.777462 |
98,060 | In the United States, the established tradition of engineering was explicitly competing with the rising discipline of physics for World War I military largess. A host of inventors, led by Thomas Edison and his newly created Naval Consulting Board, cranked out thousands of inventions to solve military problems and aid t... | History of military technology | 0.777462 |
98,061 | A slightly different outcome came from the longitude prize of the 18th century, offered by the British government for an accurate method of determining a ship's longitude at sea (essential for the safe navigation of the powerful British navy): intended to promote—and financially reward—a scientific solution, it was ins... | History of military technology | 0.777462 |
98,062 | Following the end of the Cold War and the dissolution of the Soviet Union, military funding of science has decreased substantially, but much of the American military-scientific complex remains in place. The sheer scale of military funding for science since World War II has instigated a large body of historical literatu... | History of military technology | 0.777462 |
98,063 | Quantum electronics permitted both revolutionary new methods of analyzing the universe and—using the same equipment and technology—the monitoring of Soviet electronic signals.Military interest in (and funding of) seismology, meteorology and oceanography was in some ways a result of the defense-related payoffs of physic... | History of military technology | 0.777462 |
98,064 | Even for geodetic data, new secrecy guidelines worked to restrict collaboration in a field that had formerly been fundamentally international; the Figure of the Earth had geopolitical significance beyond questions of pure geoscience. Still, geodesists were able to retain enough autonomy and subvert secrecy limitations ... | History of military technology | 0.777462 |
98,065 | The history of earth science and the history of astrophysics were also closely tied to military purposes and funding throughout the Cold War. American geodesy, oceanography, and seismology grew from small sub-disciplines in into full-fledged independent disciplines as for several decades, virtually all funding in these... | History of military technology | 0.777462 |
98,066 | and elsewhere.Other wartime physics research, particularly in rocketry and radar technology, was less significant in popular culture but much more significant for the outcome of the war. German rocketry was driven by the pursuit of Wunderwaffen, resulting in the V-2 ballistic missile; the technology as well as the pers... | History of military technology | 0.777462 |
98,067 | If World War I was the chemists' war, World War II was the physicists' war. As with other total wars, it is difficult to draw a line between military funding and more spontaneous military-scientific collaboration during World War II. Well before the Invasion of Poland, nationalism was a powerful force in the German phy... | History of military technology | 0.777462 |
98,068 | Historian Paul Forman, in his seminal 1987 article, proposed that not only had military funding of science greatly expanded the scope and significance of American physics, it also initiated "a qualitative change in its purposes and character." Historians of science were beginning to turn to the Cold War relationship be... | History of military technology | 0.777462 |
98,069 | The biological sciences were also affected by military funding, but, with the exception of nuclear physics-related medical and genetic research, largely indirectly. The most significant funding sources for basic research before the rise of the military-industrial-academic complex were philanthropic organizations such a... | History of military technology | 0.777462 |
98,070 | Military patronage benefited a large number of fields, and in fact helped create a number of the modern scientific disciplines. At Stanford and MIT, for example, electronics, aerospace engineering, nuclear physics, and materials science—all physics, broadly speaking—each developed in different directions, becoming incr... | History of military technology | 0.777462 |
98,071 | The Air Force became an independent service branch from the Army and established its own research and development system, and the Army followed suit (though it was less invested in academic science than the Navy or Air Force). Meanwhile, the perceived communist menace of the Soviet Union caused tensions—and military bu... | History of military technology | 0.777462 |
98,072 | In many podsols, Iron Pans are created. This can cause water logging which may then saturate the A horizon leading to mottling or a gleyed podsol. Also useful: soil chemistry == References == | Podsolisation | 0.777461 |
98,073 | )Example 4 Being at least 30 years old is necessary for serving in the U.S. Senate. If you are under 30 years old, then it is impossible for you to be a senator. That is, if you are a senator, it follows that you must be at least 30 years old.Example 5 In algebra, for some set S together with an operation ⋆ {\displayst... | Necessary cause | 0.777461 |
98,074 | Launched in September 2017, PocketBeagle offers identical computing performance to BeagleBone Black in a physical form factor that offers over 50% reduction in size and 75% reduction in weight, along with over 40% cheaper purchase price (December 2018 MSRP US$25 vs. US$45 for BeagleBone Black). The miniaturization was ... | Beagle Board | 0.777457 |
98,075 | The criterion is related to Routh–Hurwitz theorem. From the statement of that theorem, we have p − q = w ( + ∞ ) − w ( − ∞ ) {\displaystyle p-q=w(+\infty )-w(-\infty )} where: p {\displaystyle p} is the number of roots of the polynomial f ( z ) {\displaystyle f(z)} with negative real part; q {\displaystyle q} is the nu... | Routh stability criterion | 0.777456 |
98,076 | Let f ( z ) = a z 2 + b z + c {\displaystyle f(z)=az^{2}+bz+c} (for the sake of simplicity we take real coefficients) where c ≠ 0 {\displaystyle c\neq 0} (to avoid a root in zero so that we can use the Routh–Hurwitz theorem). First, we have to calculate the real polynomials P 0 ( y ) {\displaystyle P_{0}(y)} and P 1 ( ... | Routh stability criterion | 0.777456 |
98,077 | With the advent of computers, the criterion has become less widely used, as an alternative is to solve the polynomial numerically, obtaining approximations to the roots directly. The Routh test can be derived through the use of the Euclidean algorithm and Sturm's theorem in evaluating Cauchy indices. Hurwitz derived hi... | Routh stability criterion | 0.777456 |
98,078 | To sum it up: Integration of the metadata across the organization Build relationship between various metadata types Build relationship between various disparate systems Define business golden copy of definitions Version control of the changes at structure level Interaction with Reference data Link view to master data A... | Metadata repository | 0.777454 |
98,079 | This statistic was consistent across the Caucasian, African American, and Hispanic races.A report by the Washington Post found that 385 Americans were fatally shot by law enforcement officers in the first five months of 2015, an average of more than two fatal shootings a day, which was more than twice the rate reported... | Use of force | 0.777453 |
98,080 | Ultra-high-purity steam is used in key industries including semiconductors, photovoltaics, MEMS and nanotechnology. Water vapor plays an important role in deposition processes, as well as in annealing, release etching and bonding. Water vapor can be the source of oxygen for the generation of oxides as well as a humidif... | Ultra-high-purity steam for oxidation and annealing | 0.777452 |
98,081 | As microelectronic device size and geometry shrink, the susceptibility to damage from contaminants grows. This requires intervention through the use of filters, selective membranes or other techniques to clean the water or steam before delivery to process. Metals: Metals can be in the source water or gases and can migr... | Ultra-high-purity steam for oxidation and annealing | 0.777452 |
98,082 | Same is true for the Arens-Mackey topology, the ultrastrong*, and the strong* topology. In locally convex spaces, closure of convex sets can be characterized by the continuous linear functionals. Therefore, for a convex subset K of B(H), the conditions that K be closed in the ultrastrong*, ultrastrong, and ultraweak to... | Uniform operator topology | 0.777452 |
98,083 | On norm bounded sets of B(H), the weak (operator) and ultraweak topologies coincide. This can be seen via, for instance, the Banach–Alaoglu theorem. For essentially the same reason, the ultrastrong topology is the same as the strong topology on any (norm) bounded subset of B(H). | Uniform operator topology | 0.777452 |
98,084 | The continuous linear functionals on B(H) for the weak, strong, and strong* (operator) topologies are the same, and are the finite linear combinations of the linear functionals (xh1, h2) for h1, h2 ∈ H. The continuous linear functionals on B(H) for the ultraweak, ultrastrong, ultrastrong* and Arens-Mackey topologies ar... | Uniform operator topology | 0.777452 |
98,085 | (Warning: the weak Banach space topology and the weak operator topology and the ultraweak topology are all sometimes called the weak topology, but they are different.) The strong-* operator topology or strong-* topology is defined by the seminorms ||x(h)|| and ||x*(h)|| for h ∈ H. It is stronger than the strong and wea... | Uniform operator topology | 0.777452 |
98,086 | Warning: in spite of the name "strongest topology", it is weaker than the norm topology.) The σ-weak topology or ultraweak topology or weak-* operator topology or weak-* topology or weak topology or σ(B(H), B(H)*) topology is defined by the family of seminorms |(w, x)| for elements w of B(H)*. It is stronger than the w... | Uniform operator topology | 0.777452 |
98,087 | It is stronger than all topologies below. The σ-strong topology or ultrastrong topology or strongest topology or strongest operator topology is defined by the family of seminorms pw(x) for positive elements w of B(H)*. It is stronger than all the topologies below other than the strong* topology. | Uniform operator topology | 0.777452 |
98,088 | It is stronger than all topologies below. The σ-strong-* topology or ultrastrong-* topology is the weakest topology stronger than the ultrastrong topology such that the adjoint map is continuous. It is defined by the family of seminorms pw(x) and pw(x*) for positive elements w of B(H)*. | Uniform operator topology | 0.777452 |
98,089 | It is stronger than the ultraweak and weak operator topologies. (Warning: the weak Banach space topology and the weak operator topology and the ultraweak topology are all sometimes called the weak topology, but they are different.) The Mackey topology or Arens-Mackey topology is the strongest locally convex topology on... | Uniform operator topology | 0.777452 |
98,090 | It is stronger than all the other topologies below. The weak (Banach space) topology is σ(B(H), B(H)*), in other words the weakest topology such that all elements of the dual B(H)* are continuous. It is the weak topology on the Banach space B(H). | Uniform operator topology | 0.777452 |
98,091 | The seminorm pw(x) for w positive in the predual is defined to be B(w, x*x)1/2. If B is a vector space of linear maps on the vector space A, then σ(A, B) is defined to be the weakest topology on A such that all elements of B are continuous. The norm topology or uniform topology or uniform operator topology is defined b... | Uniform operator topology | 0.777452 |
98,092 | (In topology proper, these terms can suggest the opposite meaning, so strong and weak are replaced with, respectively, fine and coarse.) The diagram on the right is a summary of the relations, with the arrows pointing from strong to weak. If H is a Hilbert space, the Hilbert space B(X) has a (unique) predual B ( H ) ∗ ... | Uniform operator topology | 0.777452 |
98,093 | There are many topologies that can be defined on B(X) besides the ones used above; most are at first only defined when X = H is a Hilbert space, even though in many cases there are appropriate generalisations. The topologies listed below are all locally convex, which implies that they are defined by a family of seminor... | Uniform operator topology | 0.777452 |
98,094 | Let ( T n ) n ∈ N {\displaystyle (T_{n})_{n\in \mathbb {N} }} be a sequence of linear operators on the Banach space X. Consider the statement that ( T n ) n ∈ N {\displaystyle (T_{n})_{n\in \mathbb {N} }} converges to some operator T on X. This could have several different meanings: If ‖ T n − T ‖ → 0 {\displaystyle \|... | Uniform operator topology | 0.777452 |
98,095 | In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(X) of bounded linear operators on a Banach space X. | Uniform operator topology | 0.777452 |
98,096 | Polaris is a Texas hold 'em poker playing program developed by the computer poker research group at the University of Alberta, a project that has been under way for 16 years as of 2007. Polaris is a composite program consisting of a number of bots, including Hyperborean08, the winner of the limit equilibrium series in ... | Polaris (poker bot) | 0.777452 |
98,097 | The peacetime application of military geology includes the building of infrastructure, typically during local emergencies or foreign peacekeeping deployments.Warfare can change the physical geology. Examples of this include artillery shattering the bedrock on the Western Front during World War I and the detonation of n... | Military geology | 0.777451 |
98,098 | Military geology is the application of geological theory to warfare and the peacetime practices of the military. The formal practice of military geology began during the Napoleonic Wars; however, geotechnical knowledge has been applied since the earliest days of siege warfare. In modern warfare military geologists are ... | Military geology | 0.777451 |
98,099 | Military activity affects the physical geology. This was first noted through the intensive shelling on the Western Front during World War I, which caused the shattering of the bedrock and changed the rocks' permeability. New minerals, rocks, and land-forms are also a byproduct of nuclear testing. | Military geology | 0.777451 |
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