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In physics, energy () is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).
In mathematical physics, Minkowski space (or Minkowski spacetime) (mɪŋˈkɔːfski,_-ˈkɒf-) combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics). A four-vector (x,y,z,t) consists of a coordinate axes such as a Euclidean space plus time. This may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally.
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
An introduction to methods of harmonic analysis.
Covers convergence of Fourier series, Hilbert transform, Calderon-Zygmund theory, Fourier restriction, and applications to PDE.
Le cours donne une introduction à la théorie des EDO, y compris existence de solutions locales/globales, comportement asymptotique, étude de la stabilité de points stationnaires et applications, en pa
This course will give an introduction to some aspects of nonlinear dispersive partial differential equations. These are time evolution problems that arise in many contexts in physics, such as quantum
We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into S2. Our admissible class of perturbations is an open set in some suf
We prove the semi-global controllability and stabilization of the (1+1)−dimensional wave maps equation with spatial domain 𝕊1 and target Sk. First we show that damping stabilizes the system when t
We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the