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is good or great.\n return if score > 2\n warning: ''\n suggestions: []\n\n # tie feedback to the longest match for longer sequences\n longest_match = sequence[0]\n for match in sequence[1..]\n longest_match = match if match.token.length > longest_match.token.length\n feed...
Here we need to find the integrating factor and it is then multiplied with the equation to solve it. The given equation is of the form: {eq}y'+Py=Q(x) {/eq} Integrating factor is calculated by the formula: {eq}I.F.=e^{\int Pdx} {/eq} Answer and ...
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Prove the following identity: (cosh x + sinh x)^n = cosh nx + sinh nx (n any real number) Prove that \cosh z = \cos iz for all z \in \mathbb C and hence, or otherwise, give all solutions to \cosh z = \cos 3 without using inverse trigonometric or inverse hyp...
denotes the class of all finite metric spaces isometrically embeddable into X. 2 Homogeneity A metric space X is said to be n-homogeneous for if for every isometry between subspaces with there exists an automorphism extending f, i.e. ; ultrahomogeneous if it is n-homogeneous for every ; ...
Within the scope of elementary number theory, we prove that, as the main\nresult, if $1 \\leq x < y < z$ are integers such that at least one of $y, z,\nx+y$ is prime then $x^{n}+y^{n} eq z^{n}$ for every odd integer $n \\geq 3$.\nThis re... ...
摘要" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer,the time and memory requirements generally scale exponentially with...
Use the quadratic formula to find the value of the variable. Factor the equation and find the values of the variable. If you factor the quadratic equation, it is done through a remarkable product or a common term. It must be in the general form {eq}ax^{2}+bx+c=0. {/eq}...
Ce-N-O system derived from doping of cerium oxide with nitrogen with general formula CeON, with the same structure as undoped CeO, and which can have 5 similar uses of great technological and strategic relevance, namely as a solid electrolyte and as a catalyser. The presence of cerium 3+ ...