TeX testing 2026

geomar · #2

\begin{aligned} \min_{\mathbf{x} \in \mathbb{R}^n} \quad & \mathcal{L}(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^{m} \left( y_i - \mathbf{a}_i^\top \mathbf{x} \right)^2 + \lambda \|\mathbf{x}\|_1 \\[1em] \text{s.t.} \quad & \mathbb{P} \!\left( \sup_{t \in [0,T]} \left| X_t - \int_0^t \mu(s)\,ds \right| > \varepsilon \right) < \delta, \\[1em] & \nabla^2 f(\mathbf{x}) = \left[ \frac{\partial^2 f} {\partial x_i \partial x_j} \right]_{i,j=1}^{n}, \\[1em] & \det\!\left( e^{A} \right) = e^{\operatorname{tr}(A)}, \\[1em] & \oint_{\partial \Omega} \mathbf{F}\cdot d\mathbf{r} = \iint_{\Omega} \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) \, dA, \\[1em] & \zeta(s) = \sum_{k=1}^{\infty} \frac{1}{k^s}, \qquad \Re(s) > 1, \\[1em] & \hat{\theta}_{\mathrm{MAP}} = \arg\max_{\theta \in \Theta} \left\{ \log p(D \mid \theta) + \log p(\theta) \right\}. \end{aligned}

Λήψη ggb

Δεύτερη δοκιμή

f(x,t)= \begin{cases} \displaystyle \sum_{n=1}^{\infty} \frac{\sin(n\pi x)}{n^2} e^{-n^2\pi^2 t}, & \text{if } 0 < x < 1 \text{ and } t > 0, \\[1.2em] \displaystyle \lim_{\varepsilon \to 0^+} \int_{-\infty}^{\infty} \frac{e^{-u^2}} {(u-x)^2+\varepsilon^2}\,du, & \text{if } x \in \mathbb{R}\setminus\{0\}, \\[1.2em] \displaystyle \frac{\partial^2}{\partial x^2} \left( \int_0^x \frac{\log(1+t^2)} {1+t^4}\,dt \right), & \text{if } x = 0, \\[1.2em] \displaystyle \arg\max_{y\in\mathbb{R}} \left\{ -\frac12 y^\top \Sigma^{-1} y + \lambda \|y\|_1 \right\}, & \text{otherwise.} \end{cases}

Δοκιμή tikz:

$\displaystyle{\begin{tikzpicture} \coordinate (A) at (0,0); \coordinate (B) at (4,0); \coordinate (C) at (2,3); \draw[thick] (A) -- (B) -- (C) -- cycle; \fill (A) circle (2pt) node[below left] {A}; \fill (B) circle (2pt) node[below right] {B}; \fill (C) circle (2pt) node[above] {C}; \end{tikzpicture}}$

Λήψη ggb

TeX testing 2026

TeX testing 2026

Re: TeX testing 2026

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