Examples of using Displaystyle in English and their translations into Vietnamese
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The original definition of the Riemann integral does not apply to a function such as 1/ x 2{\displaystyle 1/{x^{2}}} on the interval 1,∞, because in this case the domain of integration is unbounded.
Here are some images of the unit ball for the two-dimensional ℓ p{\displaystyle\ell^{p}} space for various values of p(the unit ball being concave for p<
which is also called backward induction, the π{\displaystyle\pi} function is not used; instead, the value of π( s){\displaystyle\pi(s)} is calculated within V( s){\displaystyle V(s)} whenever it is needed.
These illustrate why the condition p≥ 1 is necessary in the definition of the ℓ p{\displaystyle\ell^{p}} norm, as the unit ball in any normed space must be convex as a consequence of the triangle inequality.
The relationship between these two masses is M t= M s+ M l{\displaystyle M_{ t}= M_{ s}+ M_{ l}}, where M l{\displaystyle M_{l}} is the mass of substances lost on oven drying(often, mostly water).
Where ϕ{\displaystyle\phi} is the phase difference between current and voltage, Re{\displaystyle\operatorname{Re}} means real part, Z is the complex impedance,
Where x n{\displaystyle x_{n}} and y n{\displaystyle y_{n}} are constants, s= j ω{\displaystyle s=\mathrm{j}\omega}, a n, b n> 0{\displaystyle a_{n}, b_{n}>0}, and H{\displaystyle H} is the transfer function.
In isotropic, linear elastic materials described by Lame coefficients λ{\displaystyle\lambda} and μ{\displaystyle\mu}, Rayleigh waves have a speed given by solutions to the equation.
and R{\displaystyle R} are the invariants of the symmetric matrix Γ j k{\displaystyle\Gamma_{jk}}.
Where δ β α{\displaystyle\delta_{\beta}^{\alpha}} is the Kronecker tensor and the Christoffel symbol Γ α β γ{\displaystyle\Gamma^{\alpha}{}_{\beta\gamma}} is defined as.
Using the time-independent Schrödinger equation, ignoring all spin-coupling interactions and using the reduced mass μ{\displaystyle\mu}, the equation is written as.
m⟩{\displaystyle|n,\ell,m\rangle} is the state represented by the wavefunction ψ n ℓ m{\displaystyle\psi_{n\ell m}} in Dirac notation, and δ{\displaystyle\delta} is the Kronecker delta function.[9].
The function v^( x, z, t){\displaystyle{\hat{v}}(x, z, t)} can be expressed as the superposition of harmonic waves with varying wave numbers( k{\displaystyle k}) and frequencies( ω{\displaystyle\omega}).
ρ{\displaystyle\rho} is the density, U j{\displaystyle U_{j}} is the component of the displacement vector U, and c i j k l{\displaystyle c_{ijkl}} represents the elastic tensor.
Sometimes, coefficients a i( x){\displaystyle a_{i}(x)} that are polynomial over a ring R are considered,
And the expected payoff to player i{\displaystyle i} for such a strategy profile is u i( S)= E ω∼ p i{\displaystyle u_{ i}( S)= E_{\ omega\sim p_{i}}}.
The length of the longest diagonal of a unit hypercube of n dimensions is n{\displaystyle{\sqrt{n}}}, the square root of n and the(Euclidean) length of the vector(1,1,1,… 1,1)
a 1,…{\displaystyle a_{0}, a_{1},\dots} are real numbers
Chebyshev's inequality can be seen as a special case of the generalized Markov's inequality applied to the random variable| X- E[ X]|{\displaystyle|X-\operatorname{E}[X]|} with Φ( x)= x 2{\displaystyle\Phi(x)=x^{2}}.
Finding an indefinite integral of a function f( x){\displaystyle f(x)} is the same as solving the differential equation d y d x= f( x){\displaystyle{\frac{ dy}{ dx}}= f( x)}.