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 Mar 15 awarded Curious Mar 14 revised Asymptotic expansion of integrals of the form $\int_{\mathcal{D}} \exp(\lambda\, \phi(x))\, g(x) \,dx$ for small $\lambda.$ added 172 characters in body Mar 14 asked Asymptotic expansion of integrals of the form $\int_{\mathcal{D}} \exp(\lambda\, \phi(x))\, g(x) \,dx$ for small $\lambda.$ Feb 5 asked Is it possible to construct a 1-D linear differential operator with given spectrum $0\leq\lambda_0\leq \lambda_1\leq\dots\leq\lambda_n\le\dots$? Feb 1 comment How to compute $\int_{0}^{\infty}dx\:\frac{\exp(-ax^2+bx)}{x+1}\:\text{ for }\: a>0, b\in \mathbb{C}$? Thanks. But I don't want an answer as a power series in b. Actually I am trying to see the behaviour of $\displaystyle\sum_{k=1}^{\infty}\displaystyle\int_{0}^{\infty}dx\: \frac{\exp(-a(x+1)^2+2\pi i k x)}{x+1}$ for small values of $a$. Expanding in $b=-2a+2\pi i k$ doesn't seem helpful in this problem. Feb 1 asked How to compute $\int_{0}^{\infty}dx\:\frac{\exp(-ax^2+bx)}{x+1}\:\text{ for }\: a>0, b\in \mathbb{C}$? Dec 8 comment Proof of a theorem about oscillation You are right. I see it now. Thanks. Dec 8 comment Proof of a theorem about oscillation Can you include this calculation in your answer ? I am not sure if the method of variation of parameters applies to nonlinear equations Dec 8 comment Proof of a theorem about oscillation Hmm.. but I can't see how the derivative of second equation is same as the first? Dec 8 comment Proof of a theorem about oscillation I think the difference of x and y satisfies $\displaystyle \frac {d (x-y)}{dt}=A(x-y)+R$? Dec 8 answered Proof of a theorem about oscillation Dec 8 comment Proof of a theorem about oscillation Since the first derivatives of $x$ and $y$ are given so we can write a Taylor series expansion of $x(t)$ and $y(t)$. It gives a result of the form $x(t)-y(t)= x_0^2 h(t,x_0)$ for some function $h$. If one can show that $h$ is bounded in a rectangular region $[0,T]\times[-a,a]$ with some upper bound $M$, then the theorem will follow. Since then $|x(t)-y(t)|<\delta \epsilon$ if we take $|x_0|<\delta$ and $\delta<\epsilon/M$ Sep 1 awarded Scholar Sep 1 accepted Probability for the sum of two random numbers being a prime number? Aug 31 comment Probability for the sum of two random numbers being a prime number? If the choice of numbers is in the range $N_1$ to $N_2$ (where both $N_1$ and $N_2$ are 'large') then the probability will be roughly $N_2/((N_2-N_1)log(N_2))−N_1/((N_2-N_1)log(N_1))$. Right ? Aug 30 awarded Commentator Aug 30 asked Probability for the sum of two random numbers being a prime number? Jun 28 awarded Yearling Jun 28 answered why symplectic form should be closed when we work on a manifold Jun 28 comment why symplectic form should be closed when we work on a manifold Now when you are asking for an example I think my statement is not correct;) It should be other way around - every symplectic vector space is also a symplect manifold. Doesn't the condition $d\omega=0$ follow from bilinearity? Since matrix elements of $\omega$ will have no dependence on coordinates.