Examples of using Mathbf in English and their translations into Vietnamese
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Colloquial
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Ecclesiastic
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Computer
Mathbf{R}$ is the set of real numbers.
In the direction of N{\displaystyle\mathbf{N}}.
And u{\displaystyle\mathbf{u}} is said to be solenoidal.
Gives the distance between the point P{\displaystyle\mathbf{P}}.
Where x{\displaystyle\mathbf{x}} denotes the vector(x1, x2).
This vector will proceed to precess around z^{\displaystyle\mathbf{\hat{z}}}.
Where E{\displaystyle{\mathbf{}}E} denotes the expected value.
Any hyperplane canbe written as the set of points x{\displaystyle\mathbf{x}} satisfying.
Given the solution S( t),0≤ t≤ T{\displaystyle{\mathbf{}}S(t), 0\leq t\leq T} the feedback gain equals.
Moreover, this bilinear form is positive definite,which means that a⋅ a{\displaystyle\mathbf{a}\cdot\mathbf{a}}.
The final time(horizon) T{\displaystyle{\mathbf{}}T} may be either finite or infinite.
This relation is stable under addition and multiplication: for a, b, c∈ N{\displaystyle a, b,c\in\mathbf{N}}, if a≤ b, then.
Evaluating u( ρ){\displaystyle\scriptstyle\mathbf{u(\rho)}} often includes solving a differential equation.
Consider the case of a spin-1/2 particle in a magnetic field B= B n^{\displaystyle\mathbf{B}=B\mathbf{\hat{n}}}.
To keep the costs finite instead of J{\displaystyle{\mathbf{}}J}one has to consider J/ N{\displaystyle{\mathbf{}}J/N} in this case.
The linearity of the Stokes equations in the case of an incompressible Newtonian fluid means that a Green's function,J(r){\displaystyle\mathbb{J}(\mathbf{r})}, exists.
H( x)= 1 0,∞( x).{\displaystyle H(x)=\mathbf{1}_{0,\infty}(x).} The corresponding probability distribution is the degenerate distribution.
For this we need to guarantee that$\mathbf{B}$ is a basis.
The real number system( R;+;⋅;<){\displaystyle\mathbf{R}\cdot can be defined axiomatically up to an isomorphism, which is described hereafter.
An important property of PA- is that any structure M{\displaystyle M} satisfying this theory has an initial segment(ordered by≤{\displaystyle\leq})isomorphic to N{\displaystyle\mathbf{N}}.
And the material can be shown to satisfy Ohm's law J= σ 0 E{\displaystyle\mathbf{J}=\sigma_{0}\mathbf{E}} with a DC-conductivity σ0.
We want to choose the w{\displaystyle{\mathbf{w}}} and b{\displaystyle b} to maximize the margin, or distance between the parallel hyperplanes that are as far apart as possible while still separating the data.
Both additive white Gaussian system noise v(t){\displaystyle\mathbf{v}(t)} and additive white Gaussian measurement noise w( t){\displaystyle\mathbf{w}(t)} affect the system.
Using$\ mathbf{ a}=-\ omega^ 2/\mathbf{r}$ the speed required to obtain a modest 1/6 of Earth gravity in order to provide a small but meaningful experience of"laying down" rather than floating is $\omega=1.3\text{s}^{-1}$ which works out to one revolution every 5 seconds, or a rotation frequency of 0.2 Hz.
For example, suppose that f: R n→ R{\displaystyle f\colon\mathbf{R}^{n}\to\mathbf{R}} is a differentiable function of variables x 1,…, x n{\displaystyle x_{1},\ldots,x_{n}}.
Here i{\displaystyle\mathbf{} i} represents the discrete time index and v i, w i{\displaystyle\mathbf{v}_{i},\mathbf{w}_{i}} represent discrete-time Gaussian white noise processes with covariance matrices V i, W i{\displaystyle\mathbf{}V_{i},W_{i}} respectively.
Given this system the objective is to find the control input history u( t){\displaystyle{\mathbf{u}}(t)} which at every time t{\displaystyle{\mathbf{}}t} may depend only on the past measurements y( t′), 0≤ t′< t{\displaystyle{\mathbf{y}}(t'), 0\leq t'.
At each time t{\displaystyle{\mathbf{}}t} this filter generates estimates x^( t){\displaystyle{\hat{\mathbf{x}}}(t)} of the state x( t){\displaystyle{\mathbf{x}}(t)} using the past measurements and inputs.
In our problem, we know c{\displaystyle\mathbf{c}}, r{\displaystyle r}, s{\displaystyle\mathbf{s}}(e.g. the position of a light source) and d{\displaystyle\mathbf{d}}, and we need to find t{\displaystyle t}.
The RPA vacuum| R P A⟩{\displaystyle\left|\mathbf{RPA}\right\rangle} for a bosonic system can be expressed in terms of non-correlated bosonic vacuum| M F T⟩{\displaystyle\left|\mathbf{MFT}\right\rangle} and original boson excitations a i†{\displaystyle\mathbf{a}_{i}^{\dagger}}.