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prolong-data-64K-prompt-target

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" that case the discrepancy was not improved.\n\n\\section{Summary}\n\nThe formation energy, $\\Delt(...TRUNCATED)

"_1}{\\epsilon} = \\lim_{n \\rightarrow \\infty} \\frac{EX_n^{\\epsilon, p_k, \\nu}}n - \\frac{||q-p(...TRUNCATED)

" rotating convection systems are used to make predictions about their convective behaviors in Secti(...TRUNCATED)

"To prove this it suffices to check it on representables for which it is clear.\n\n\n\\begin{cor} \\(...TRUNCATED)

"# \\mathcal{M}_2 ) \\cdot ( \\# \\mathcal{M}_3)\n\\]\nof the numbers of elements of $\\mathcal{M}_m(...TRUNCATED)

"\\!P}\\xspace}^{\\alpha}$/$\\ensuremath{A_{\\CP}}\\xspace^{\\alpha}(\\Lambda)$ are taken as the sum(...TRUNCATED)

"}), we get ${\\rm rank\\,}L_gH_{k-1}(x)=const.$ for all $x\\in M^c_{k-1}$ around $x_p$ (condition ((...TRUNCATED)

" \ncontinuous\nparameter $\\lambda$ (Tikhonov, Eq.~(\\ref{eq:Ti})). This choice is specially import(...TRUNCATED)

".5cm\n\\begin{centering}\n\\epsfig{file=fig4.eps,height=8.5cm,width=6cm,angle=-90}\n\\caption{Total(...TRUNCATED)

"\\begin{lemma} Let $x,x_1,...,x_s\\in\\frak{m}$ be an $R$-regular sequence and $\\frak{a}=(x_1,...,(...TRUNCATED)

"$, and $\\eta^\\text{r} = 1.0\\times 10^{-5}$ as in \\ref{sec:mainSimulations}. \n\nFigure~\\ref{fi(...TRUNCATED)

"_{\\infty}+[g']_{0,\\alpha}+\\left\\|g''\\right\\|_{\\infty}+[g'']_{0,\\alpha}). $\n\\end {proposit(...TRUNCATED)

"1+2*#4/2+#3*#4/2,#2)}\n\\def\\mult(#1,#2)[#3,#4]{\\draw (#1,#2) arc (180:360:0.5*#3 and 0.5*#4) (#1(...TRUNCATED)

" -- (0.5,-5); \\map(1.5,-4)[\\scriptstyle \\Pi^{\\!L}];\n\\end{scope}\n\\begin{scope}[xshift=15.8cm(...TRUNCATED)

"1}}(h_{2+\\ep_1}(\\lam))$. \n\n\\noindent \n(3) Define $L_2(\\lam)=D_0 L_1(\\lam)(1+L_1(\\lam))^{(...TRUNCATED)

"SSM. The limits for each corresponding mass value have been scaled by orders of ten as indicated in(...TRUNCATED)

"{R},\n\\label{31}\n\\end{equation}\nsee Figure \\ref{pic7}, left.\nThe restriction of the field \\e(...TRUNCATED)

" $\\langle P\\rangle$ leads to average values for $\\langle \\dot{n}_{\\rm GJ}\\rangle$ and $\\lang(...TRUNCATED)

"modes. To this end we consider dimensionless quantities (in geometric units) that are formed from t(...TRUNCATED)

"_{\\rm NLO}= 0.248$ GeV.\nThis corresponds to a value of the strong coupling constant in Eq.~(\\ref(...TRUNCATED)