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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
In mathematical physics the Knizhnik–Zamolodchikov equations, or KZ equations, are linear differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level.
In the classical sense, if f(x) ∈ C k, and g(x) ∈ C k−1, then u(t, x) ∈ C k. However, the waveforms F and G may also be generalized functions, such as the delta-function. In that case, the solution may be interpreted as an impulse that travels to the right or the left.
The multipole expansion circumvents this difficulty by expanding not E or B, but r ⋅ E or r ⋅ B into spherical harmonics. These expansions still solve the original Helmholtz equations for E and B because for a divergence-free field F, ∇ 2 (r ⋅ F) = r ⋅ (∇ 2 F). The resulting expressions for a generic electromagnetic field are:
In mathematics, the annihilator method is a procedure used to find a particular solution to certain types of non-homogeneous ordinary differential equations (ODEs). [1] It is similar to the method of undetermined coefficients, but instead of guessing the particular solution in the method of undetermined coefficients, the particular solution is determined systematically in this technique.
And although Washington, D.C., isn't a state, it leads the nation in declining non-mortgage debt. Average balances there fell by 4.5% in 2024, to $24,258. Adjacent Maryland was runner-up with a 3. ...
Even if cold, wet weather doesn't directly cause a cold, take the change in seasons as a reminder that respiratory illnesses are likely to be circulating right now — and you have tools available ...
A Washington, D.C. man has been arrested for threatening flight attendants on a United Airlines plane traveling from Houston to New Jersey. Kedus Yacob Damtew, 38, was charged with one count of ...