In all these tests below the following latex structure is used
\documentclass[12pt]{article} \input{preamble.tex} \input{font_setting.tex} \begin{document} \input{body.tex} \end{document}
The file preamble.tex and body.tex is the same for all tests. The only specific part is
font_setting.tex file.
Below is listing of preamble.tex and body.tex.
In the font specific section, there is a link to download the complete Latex file also, and
also it shows there the specific font_setting.tex used for each font.
\usepackage[letterpaper,left=1in,right=1in,top=.9in,bottom=1in, headsep=.25in]{geometry} \usepackage{ntheorem} \newtheorem{theorem}{Theorem} \usepackage{amsmath} \usepackage{mathtools} \DeclarePairedDelimiter\abs{\lvert}{\rvert} \DeclarePairedDelimiter{\norm}{\lVert}{\rVert} \newcommand{\envert}[1]{\left\lvert#1\right\rvert} \DeclareMathOperator*{\esssup}{ess\,sup} \DeclareMathOperator{\meas}{meas} \newcommand{\wh}{\widehat} \newcommand{\wt}[1]{\widetilde{#1}} \DeclareMathOperator{\Res}{Res} \usepackage[tracking]{microtype} %\usepackage{resizegather} \setlength{\parindent}{0pt} % Removes all indentation globally
\begin{theorem}[Residue Theorem] Let $f$ be analytic in the region $G$ except for the isolated singularities $a_1,a_2,\dots,a_m$. If $\gamma$ is a closed rectifiable curve in $G$ which does not pass through any of the points $a_k$ and if $\gamma\approx 0$ in $G$, then \[ \frac{1}{2\pi i}\int_\gamma\! f = \sum_{k=1}^m n(\gamma;a_k)\Res(f;a_k)\,. \] \end{theorem} % \[ \begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\ -a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\ \hdotsfor[2]{4}\\ -a_{n1}t_1&-a_{n2}t_2&\dots&D_nt \end{pmatrix} \] % \begin{multline} \biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr) \det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\ =\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr) \sum_{I\subseteq\mathbf{n}-\{l \}} (-1)^{\envert{I}}\mathbf{A}^{(\lambda)}(I|I) \det\mathbf{A}^{(\lambda)} (\overline I\cup\{l \}|\overline I\cup\{l \}). \label{sum-ali} \end{multline} % \[v^{k}_{i}= \begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\ 0 &\text{otherwise.} \end{cases} \] % \[ \frac{\partial x}{\partial y} \pmb{\bigg\vert} \frac{\partial y}{\partial z} \] % \[ \sum_{\substack{i<B\\\text{$i$ odd}}} \prod_\kappa \kappa F(r_i)\qquad \mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}} \mathop{\pmb{\prod}}_\kappa \kappa(r_i) \] % \begin{align*} \overrightarrow{\psi_\delta(t) E_t h}& =\underrightarrow{\psi_\delta(t) E_t h}\\ \overleftarrow{\psi_\delta(t) E_t h}& =\underleftarrow{\psi_\delta(t) E_t h}\\ \overleftrightarrow{\psi_\delta(t) E_t h}& =\underleftrightarrow{\psi_\delta(t) E_t h} \end{align*} % Then we have the series $A_1,A_2,\dotsc$, the regional sum $A_1+A_2+\dotsb$, the orthogonal product $A_1A_2\dotsm$, and the infinite integral \[ \int_{A_1}\int_{A_2}\dotsi \] % \[ \Hat{\Hat{H}}\quad\Check{\Check{C}}\quad \Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad \Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad \Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad \Bar{\Bar{B}}\quad\Vec{\Vec{V}} \] % \[ \dddot{Q}\qquad\ddddot{R} \] % \[ \sqrt[\leftroot{-2}\uproot{2}\beta]{k} \] % \[ \boxed{W_t-F\subseteq V(P_i)\subseteq W_t} \] % \[ 0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1] \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b} \] % \[ \sideset{_*^*}{_*^*}\prod_k\qquad \sideset{}{'}\sum_{0\le i\le m} E_i\beta x \] % \[ \mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad y'_k=\delta_k y_{\tau(k)} \] % \[ \norm{f}_\infty= \esssup_{x\in R^n}\abs{f(x)} \] % \[ \meas_1\{u\in R_+^1\colon f^*(u)>\alpha\} =\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\} \quad \forall\alpha>0. \] % \begin{align} &\varlimsup_{n\rightarrow\infty} \mathcal{Q}(u_n,u_n-u^{\#})\le0\\ &\varliminf_{n\rightarrow\infty} \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\ &\varinjlim (m_i^\lambda\cdot)^*\le0\\ &\varprojlim_{p\in S(A)}A_p\le0 \end{align} % \begin{align} x&\equiv y+1\pmod{m^2}\\ x&\equiv y+1\mod{m^2}\\ x&\equiv y+1\pod{m^2} \end{align} % \begin{equation} \begin{split} \sum_{\gamma\in\Gamma_C} I_\gamma& =2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\ &\quad+\dots+(-1)^l\binom{k}{l}2^{k-l} +\dots+(-1)^k\\ &=(2-1)^k=1 \end{split} \end{equation} % \begin{align*} \frac {\partial ^2 u}{\partial t^2} &= c^2 \left ( \frac {\partial ^2 u}{\partial r^2} + \frac {1}{r} \frac {\partial u}{\partial r} +\frac {1}{r^2} \frac {\partial ^2 u}{\partial \theta ^2} \right ) \end{align*} % \begin{align*} u\left ( r,\theta ,0\right ) & =0\\ u_{t}\left ( r,\theta ,0\right ) & =\left \{ \begin {array} [c]{ccc}\frac {1}{\pi \epsilon ^{2}} & & \text {if }r\leq \epsilon \\ 0 & & \text {otherwise}\end {array} \right . \end{align*} % \[ \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+\dotsb }}}}} \] % \begin{equation} P_{r-j}= \begin{cases} 0& \text{if $r-j$ is odd},\\ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. \end{cases} \end{equation} % \[ \begin{matrix} \vartheta& \varrho\\\varphi& \varpi \end{matrix}\quad \begin{pmatrix} \vartheta& \varrho\\\varphi& \varpi \end{pmatrix}\quad \begin{bmatrix} \vartheta& \varrho\\\varphi& \varpi \end{bmatrix}\quad \begin{Bmatrix} \vartheta& \varrho\\\varphi& \varpi \end{Bmatrix}\quad \begin{vmatrix} \vartheta& \varrho\\\varphi& \varpi \end{vmatrix}\quad \begin{Vmatrix} \vartheta& \varrho\\\varphi& \varpi \end{Vmatrix} \] % This is a small matrix \begin{math} \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) \end{math} % \[ W(\Phi)= \begin{Vmatrix} \dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\ \dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}& \dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\ \hdotsfor{5}\\ \dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}& \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots& \dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}& \dfrac{\varphi}{(\varphi_n,\varepsilon_n)} \end{Vmatrix} \] % \[ \sum_{\begin{subarray}{l} 0\le i\le m\\ 0<j<n \end{subarray}} P(i,j) \] % \[\biggl(\mathbf{E}_{y} \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds \biggr) \] % {\Large \[\biggl(\mathbf{E}_{y} \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds \biggr) \]} % \begin{equation} \begin{split} f_{h,\varepsilon}(x,y) &=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon} L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\ &= h\int L_{x,z}\varphi(x)\rho_x(dz)\\ &\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y} \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\ &\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon} \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)} \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon} L_{x,y_\varepsilon(\varepsilon s)} \varphi(x)\,ds\biggr)\biggr]\\ &=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y), \end{split} \end{equation} % \begin{align} \begin{split}\abs{I_1} &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\ &\le C_3\left[\int_\Omega\left(\int_{a}^x g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\ &\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k} \left(\int_{a}^x cu_t\,d\xi\right)^2\right\} c\Omega\right]^{1/2}\\ &\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-} W_2(\Omega,\Gamma_l)\right\rvert\right\rvert \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} (\Omega;\Gamma_r,T)\right\rvert\right\rvert. \end{split}\label{eq:A}\\ \begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t) -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)} \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\ &\le C_6\left\lvert \left\lvert f\int_\Omega \left\lvert \wt{S}^{-1,0}_{a,-} W_2(\Omega,\Gamma_l)\right\rvert\right\rvert \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} (\Omega;\Gamma_r,T)\right\rvert\right\rvert. \end{split} \end{align} % \begin{multline}\label{eq:E} \int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy \end{multline} % \begin{gather} D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\ seg(a,r)\equiv\{z\in\mathbf{C}\colon \Im z= \Im a,\ \abs{z-a}<r\},\notag\\ c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C} \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\ C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r). \end{gather} % \begin{align} \gamma_x(t)&=(\cos tu+\sin tx,v),\\ \gamma_y(t)&=(u,\cos tv+\sin ty),\\ \gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv, -\frac\beta\alpha\sin tu+\cos tv\right). \end{align} % \begin{align*} \gamma_x(t)&=(\cos tu+\sin tx,v),\\ \gamma_y(t)&=(u,\cos tv+\sin ty),\\ \gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv, -\frac\beta\alpha\sin tu+\cos tv\right). \end{align*} % \begin{align} x& =y && \text {by eq:C}\\ x'& = y' && \text {by eq:D}\\ x+x' & = y+y' && \text {by Axiom 1.} \end{align} % \begin{gather} \begin{split} \varphi(x,z) &=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\ &=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n \end{split}\\[6pt] \begin{align*} \zeta^0 &=(\xi^0)^2,\\ \zeta^1 &=\xi^0\xi^1,\\ \zeta^2 &=(\xi^1)^2, \end{align*} \end{gather} % \begin{gather*} \begin{split} \varphi(x,z) &=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\ &=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n \end{split}\\[6pt] \begin{align} \zeta^0&=(\xi^0)^2,\\ \zeta^1 &=\xi^0\xi^1,\\ \zeta^2 &=(\xi^1)^2, \end{align} \end{gather*} % \begin{alignat}{3} V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j, & \qquad U_i & = u_i, \qquad \text{for $i\ne j$;}\label{eq:B}\\ V_j & = v_j, & \qquad X_j & = x_j, & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i. \end{alignat} % \begin{align*} u_{\theta \theta }+\frac {v^2}{1-\frac {v^2}{c^2}} u_{vv} + v u_v&=0 \end{align*} % \begin{align*} u \left (\theta , v\right ) &= \frac {{\mathrm e}^{\frac {-4 \sqrt {\textit {\_c}_{1}}\, \theta \,c^{2}+v^{2}}{4 c^{2}}} \left (\operatorname {WhittakerW}\left (-\frac {\textit {\_c}_{1}}{2}+\frac {1}{2}, \frac {i \sqrt {\textit {\_c}_{1}}}{2}, \frac {v^{2}}{2 c^{2}}\right ) c_{4} +\operatorname {WhittakerM}\left (-\frac {\textit {\_c}_{1}}{2}+\frac {1}{2}, \frac {i \sqrt {\textit {\_c}_{1}}}{2}, \frac {v^{2}}{2 c^{2}}\right ) c_{3} \right ) \left (c_{1} {\mathrm e}^{2 \sqrt {\textit {\_c}_{1}}\, \theta }+c_{2} \right )}{v} \end{align*} % \begin{equation} u\left ( x,t\right ) =\sum _{n=1}^{\infty }\left ( D_{n}\cos \left ( c\frac {n\pi }{L}t\right ) +E_{n}\sin \left ( c\frac {n\pi }{L}t\right ) \right ) \Phi _{n}\left ( x\right ) \tag {1} \end{equation} % \begin{align*} \int _{0}^{L}f\left ( x\right ) \Phi _{n}\left ( x\right ) dx & =D_{n}\int _{0}^{L}\Phi _{n}^{2}\left ( x\right ) dx\\ & =\frac {L}{2}D_{n} \end{align*} % \begin{align*} \int _{0}^{L}g\left ( x\right ) \Phi _{n}\left ( x\right ) dx & =E_{n}c\frac {n\pi }{L}\int _{0}^{L}\Phi _{n}^{2}\left ( x\right ) dx\\ & =\frac {L}{2}E_{n}c\frac {n\pi }{L}\\ & =\frac {1}{2}E_{n}cn\pi \end{align*} % \begin{align} \Delta F_0 &= \sqrt{\sum_{i=1}^n\left(\frac{\delta F_0}{\delta x_i}\Delta x_i\right)^2}\\[0.2cm] \Delta F_0 &= \sqrt{6.044 \cdot 10^{-6}\text{m}^2} \end{align} % \begin{gather}\tag{1} \begin{aligned} a &= b + c \\ d &= e + f + g +r+ c +e + f + g +r+ c+e + f + g +r\\ h + i &= j \end{aligned} \end{gather} % \begin{equation} \frac {du}{dt}=\frac {\partial u}{\partial x}\frac {dx}{dt}+\frac {\partial u}{\partial t} \tag {2} \end{equation} % Integrating the above w.r.t $t$ gives \begin{align*} \int \left(x^{\prime} x^{\prime \prime}+6 x^{\prime} x^{5}\right)d t &= 0 \\ \frac{{x^{\prime}}^{2}}{2}+x^{6} &= c_1 \end{align*} % \begin{gather*}\begin{aligned} \int (1-x)^{20} x^4 \, dx&=-\frac {1}{21} (1-x)^{21}+\frac {2}{11} (1-x)^{22}-\frac {6}{23} (1-x)^{23}+\frac {1}{6} (1-x)^{24}-\frac {1}{25} (1-x)^{25} \end{aligned}\end{gather*} % And \begin{gather*}\begin{aligned} \int \frac {\left (-15+x^2\right ) \log \left (x^2\right )+\left (180+24 x-12 x^2\right ) \log \left (\log \left (x^2\right )\right )+\left (-45-3 x^2\right ) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}{\left (225-240 x+94 x^2-16 x^3+x^4\right ) \log \left (x^2\right )+\left (1350-540 x-96 x^2+60 x^3-6 x^4\right ) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )+\left (2025+540 x-234 x^2-36 x^3+9 x^4\right ) \log \left (x^2\right ) \log ^4\left (\log \left (x^2\right )\right )} \, dx&=\frac {x}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \end{aligned}\end{gather*} % % \begin{gather*} \frac {d}{dx}\phi \left ( x,y\right ) =0 \end{gather*} Hence \begin{equation} \frac {\partial \phi }{\partial x}+\frac {\partial \phi }{\partial y}\frac {dy}{dx}=0\tag {B} \end{equation} % Integrating (1) w.r.t. $x$ gives \begin{align*} \int \frac{\partial \phi}{\partial x} \mathop{\mathrm{d}x} &= \int M\mathop{\mathrm{d}x}\\ \int \frac{\partial \phi}{\partial x} \mathop{\mathrm{d}x} &= \int -2 x -1\mathop{\mathrm{d}x}\\ \phi &= -x^{2}-x+ f(y)\tag{3} \end{align*} Where $f(y)$ is used for the constant of integration since $\phi$ is a function of both $x$ and $y$. Taking derivative of equation (3) w.r.t $y$ gives \begin{align*} \frac{\partial \phi}{\partial y} = 0+f'(y)\tag{4} \end{align*} But since $\phi$ itself is a constant function, then let $\phi=c_2$ where $c_2$ is new constant and combining $c_1$ and $c_2$ constants into the constant $c_1$ gives the solution as \begin{align*} c_1 &= -x^{2}-x +y \end{align*} %