Search results for "Symbol"

showing 10 items of 7541 documents

Characteristics of Mesozoic fluvio-lacustrine formations of the western Central African Republic (Carnot Sandstones) by means of mineralogical and ex…

1990

Abstract The so-called Carnot Sandstones, Mesozoic fluvio-lacustrine detrital formation, which stretch over an area of more than 40 000 km 2 in the western part of the Central African Republic, are made of a succession of conglomerates, sandstones and argilites which can reach 300 m in thickness. Heavy mineral analyses and quartz exoscopic studies of this detrital material allow to understand the geology of these formations. The detrital material origin: heavy mineral distribution in the lower levels indicates mostly a meridional origin with a quantitatively poor peripheral supply. The importance of the transport: quartz exoscopic observations show that the main part of the detrital materia…

symbols.namesakePaleontologyHeavy mineralsymbolsErosionAlluviumContext (language use)Ecological successionMesozoicCarnot cycleQuartzGeologyJournal of African Earth Sciences (and the Middle East)
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Itô-Stratonovitch Formula for the Wave Equation on a Torus

2010

We give an Ito-Stratonovitch formula for the wave equation on a torus, where we have no stochastic process associated to this partial differential equation. This gives a generalization of the classical Ito-Stratonovitch equation for diffusion in semi-group theory established by ourself in [18], [20].

symbols.namesakePartial differential equationDiffusion equationMathematics::ProbabilityDifferential equationMathematical analysisFirst-order partial differential equationsymbolsFokker–Planck equationFisher's equationWave equationd'Alembert's formulaMathematics
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Random Walk and Diffusion

2014

The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.

symbols.namesakePartial differential equationHeterogeneous random walk in one dimensionDiffusion equationFourier transformLaplace transformDifferential equationMathematical analysissymbolsEinsteinRandom walkMathematics
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Bounds for Bessel functions

1989

We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.

symbols.namesakeParticle in a spherically symmetric potentialCylindrical harmonicsBessel processGeneral MathematicsMathematical analysisBessel polynomialsStruve functionsymbolsBessel's inequalityBessel functionLommel functionMathematicsRendiconti del Circolo Matematico di Palermo
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Spin-lattice relaxation of deuterated methyl groups: Implications of the pauli principle

1999

The high-field spin-lattice relaxation of deuterated methyl groups undergoing rotational tunneling is investigated theoretically. It is found that for systems showing a tunneling frequency comparable to accessible Larmor frequencies the relaxation to equilibrium of the Zeeman energy does not follow a simple exponential time dependence even in powdered samples due to a finite coupling to the relaxation of the tunneling system. This finding contrasts to the high-temperature behavior of reorienting methyl groups which undergo simple exponential relaxation. The nonexponentiality has its origin in the statistical coupling of the three deuteron spins due to the Pauli principle.

symbols.namesakePauli exclusion principleDeuteriumCondensed matter physicsSolid-state physicsSpinsChemistrysymbolsSpin–lattice relaxationRelaxation (physics)Zeeman energyAtomic and Molecular Physics and OpticsQuantum tunnellingApplied Magnetic Resonance
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Memories and Legacies of Emmy Noether

2021

Those who knew Emmy Noether best were her fellow Germans in exile, in particular her former colleague in Gottingen, Hermann Weyl.

symbols.namesakePhilosophyHermann weylsymbolsNoether's theoremClassics
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Noether’s International School in Modern Algebra

2020

Pavel Alexandrov and Heinz Hopf met for the first time in Gottingen in the spring of 1926, soon after Alexandrov departed from Blaricum. Hopf had recently taken his doctorate in Berlin under Ludwig Bieberbach and Erhard Schmidt, and his research interests differed sharply from Alexandrov’s work in general topology.

symbols.namesakePhilosophysymbolsGeneral topologySpring (mathematics)Noether's theoremMathematical economicsAbstract algebraInternational school
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Erzwingt die Quantenmechanik eine drastische Änderung unseres Weltbilds? Gedanken und Experimente nach Einstein, Podolsky und Rosen

1989

Von den Anfangen der Quantenmechanik bis heute gibt es Versuche, sie als statistische Theorie uber Ensembles individueller ‚klassischer’ Systeme zu interpretieren. Die Bedingungen, unter denen Theorien verborgener Parameter zu deterministischen Beschreibungen dieser individuellen Systeme als ‚klassisch’ angesehen werden konnen, wurden von Einstein, Podolsky und Rosen 1935 formuliert: 1. Physikalische Systeme sind im Prinzip separierbar. 2. Zu jeder physikalischen Grose, deren Wert man ohne Storung des betrachteten Systems mit Sicherheit voraussagen kann, existiert ein ihr entsprechendes Element der physikalischen Realitat. Zusammen sind sie, wie Bell 1964 gezeigt hat, prinzipiell unvertragl…

symbols.namesakePhysical realityVerstehenPhilosophyHidden variable theorysymbolsGeneral Physics and AstronomyEinsteinHumanitiesClassical physicsMathematical physicsAnnalen der Physik
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A Place for Life

2010

The belief in the existence of extraterrestrial civilizations starts from the so-called principle of mediocrity. This principle postulates that Earth is a normal planet that rotates around a normal star, which in turn is located in a normal galaxy. That is to say, there is nothing so special in our world as to make it unique. This is a logical conclusion, toward which we are guided by the successive “Copernican turns” that science has suffered throughout its long history, and which has ­removed us from the central position we once believed to occupy in the universe.

symbols.namesakePlanetNothingMediocrity principleExtraterrestrial lifePhilosophysymbolsCopernican principleLogical consequenceExoplanetEpistemology
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Second harmonic ac polarography of strongly adsorbed electroactive species

1981

Abstract The second harmonic ac current is calculated for the case of a quasi-reversible surface redox system: both species are strongly adsorbed according to a Langmuir isotherm and the kinetics of the process are controlled by the electron transfer. The current is measured with a phase-sensitive detector and the variation of the in-phase and quadrature components vs. the frequency leads to the surface rate constant ks. The experimental results obtained for benzo-(c)cinnoline are in good agreement with the theoretical predictions and with the results of impedance measurements. The advantages of the two methods are compared.

symbols.namesakePolarographyElectron transferReaction rate constantAdsorptionChemistryKineticssymbolsAnalytical chemistryLangmuir adsorption modelRedoxElectrical impedanceJournal of Electroanalytical Chemistry and Interfacial Electrochemistry
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