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{{Short description|Theorem in plasma physics}} ...last1=Kholodenko |first1=Arkady L. |title=Applications of Contact Geometry and Topology in Physics |date=2013 |publisher=World Scientific |location=New Je ...

...ent spectral line intensities can be used to achieve information about the plasma, as well. == Theory == ...

...m energy|minimum energy state]] of a [[plasma (physics)|plasma]] while the plasma is conserving [[magnetic flux]].<ref>{{cite book ...e = Spheromaks: A Practical Application of Magnetohydrodynamic dynamos and plasma self-organization ...

...behavior on perpendicular spatial scales comparable to the [[gyroradius]] and frequencies much lower than the particle [[Cyclotron motion|cyclotron frequ ...atial, 2 velocity, and time) rather than the seven (3 spatial, 3 velocity, and time). Because of this simplification, gyrokinetics governs the evolution o ...

...erforming [[Coulomb collision|Coulomb collisions]] in a [[Plasma (physics)|plasma]]. ...|title=Entropy dissipation estimates for the relativistic Landau equation, and applications|journal=Journal of Functional Analysis|volume=277|issue=4 |pag ...

...e PET studies in human subjects | journal=[[Journal of Cerebral Blood Flow and Metabolism]] | volume=10 | issue=5 | pages=740&ndash;747 |date=September 19 ...}}</ref> at [[NIH]]. Based on the original work of Patlak, [[Jean Logan]] and her colleagues<ref name="Logan1990" /> from [[Brookhaven National Laborator ...

* [[Sturm–Liouville theory]] of [[orthogonal polynomials]] and separable partial differential equations ===Dynamical systems and Chaos theory=== ...

...zero. Since <math>\beta</math> equals zero, the distribution is symmetric, and thus an example of a symmetric alpha-stable distribution. The Holtsmark dis ...smark]] proposed the distribution as a model for the fluctuating fields in plasma due to the motion of charged particles.<ref>{{Cite journal ...

In [[physics]] and [[mathematics]], the '''Clebsch representation''' of an arbitrary [[three-d ...ed after [[Alfred Clebsch]] (1833–1872) and [[Gaspard Monge]] (1746–1818), and <math>\boldsymbol{\nabla}</math> is the [[gradient]] operator. ...

....457C|pmc=534220}}</ref> The functions were independently derived by both, and the two decided to publish their findings in the same paper. ...mbda\mathbf{H}</math>, where <math>\mathbf{H}</math> is the magnetic field and <math>\lambda</math> is the force-free parameter, with the assumption of di ...

...ribe light emission in semiconductors and they are suited for a systematic modeling of semiconductor emission ranging from [[exciton]]ic luminescence to [[lase ...ntanglement|entanglement]]. Such investigations are the basis of realizing and developing the field of [[quantum-optical spectroscopy]] which is a branch ...

...cies. Since surface plasmon polaritons cannot exist naturally in microwave and terahertz frequencies due to [[Dispersion (optics)|dispersion]] properties ...They were first theorized by [[John Pendry]] et al.<ref name="tang-concept-theory"/> ...

...er Engineering]], the Department of [[Computer science|Computer Science]], and the Department of [[Electrical engineering|Electrical Engineering]]. ...irst professor for [[calculus]], [[Analytic geometry|analytical geometry]] and [[analytical mechanics]]. Over the years, several institutes for mathematic ...

{{Short description|Theory of laser diodes}} ...t only from a fundamental point of view, but also in order to generate new and improved designs. It is common to all systems that the laser is an inverted ...

...er a drug or nutrient is infused or ingested at a relatively constant rate and when a constant fraction is eliminated during each time interval. Under the ...of Body Constituents. Harvard University Press, Cambridge, MA, 1942.</ref> and [[David Rittenberg]].<ref>{{Cite journal |doi=10.1016/s0021-9258(18)71388-4 ...

| image3 = Plasma-lamp 2.jpg ...Space Station]]. Bottom left: A [[fire]] in a fire pit; fires may produce plasma if hot enough. Bottom right: The [[Sun]]'s [[Stellar corona|corona]] as see ...

...y quantities such as density, bulk velocity, temperature, pressure tensor, and heat flux from the microstate of the gas. To describe non-equilibrium pheno ...x.doi.org/10.1093/oso/9780198561958.001.0001 |title=Molecular Gas Dynamics And The Direct Simulation Of Gas Flows |date=1994-05-05 |publisher=Oxford Unive ...

...t7=Koumoutsakos|first7=P.|date=2020-03-21|title=Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of com ...quation|journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=471|issue=2179|year=2015|pages=20140932|issn=13 ...

...В. Соболева}}) as a utility function for [[multi-objective optimization]] and [[choice modelling]] in [[decision-making]].<ref name="Soboleva-Beskorovain The function has since been introduced into [[neural network]] theory and practice.<ref name="Malinova-Golev-Iliev-Kyurkchiev_2017"/> ...

...lecular vibration]]s, interband transitions (semiconductors), [[phonon]]s, and collective excitations.<ref name = "Lorentz1909"/><ref name = "Dressel2002" ...ization density|polarization]], [[Electric dipole moment|susceptibility]], and [[Relative permittivity|dielectric function]].<ref name = "Colton2020"/> ...