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# Michael Renardy

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## Registered User

 Name Michael Renardy Member for 2 years Seen 1 hour ago Website Location Blacksburg, VA Age 58
 2d comment Is a free alternative to MathSciNet possible?Scraping titles and abstracts is no problem, the web site doing that already exists! It is called Google. The "user-base of open-source reviewers" may be a bit trickier. Why should I spend my time reviewing for some upstart web site which lacks the tradition and reputation of the established review journals? Jun11 answered Integrating the complete elliptic integral K Jun7 accepted System of quadratic equations with 18 unknown Jun7 answered System of quadratic equations with 18 unknown Jun6 accepted I have this linear PDE… Jun4 comment Please recommend some literature on the systematical theory of the elliptic systems!The original papers of Agmon, Douglis and Nirenberg are a good place to start. May30 comment Boys and Girls RevisitedWell, it does not have to be the blue-eyed islanders. Maybe it will come back as the surprise test. May30 answered I have this linear PDE… May27 comment Estimates for Green’s functionOn a compact manifold, how is a bound other than near the singularity an issue? Am I missing something here? May23 comment Phase transition in dynamical systemsThis question is much too imprecise for an intelligent answer. For starters, what are P, f and $\phi$? I can sort of guess what $t$ is, but ... Voting to close as "not a real question." May8 comment Asymptotics of a functionThe last term is $n^{-3n}$, which is certainly not dominant! The asymptotics is probably obtainable by comparing with $$\int_0^\infty x^n n^{-4x}\,dx=\frac{n!}{(4\ln n)^n}.$$ May8 answered Functional equations Apr26 revised Is $f$ continuous?removed tag Apr26 comment Is $f$ continuous?Why was this tagged special functions? I am going to remove this tag. Apr25 comment Volume of a convex setWell, yes, but I thought you were looking for a formula given by an integral in terms of w. Apr25 comment Volume of a convex setI see a formula for the perimeter there, not for the area. Apr24 answered Volume of a convex set Apr24 comment Finding Center of Union of CirclesFrom the figure in the link, I am guessing that you want the center of mass of the area common to all the circles. You can always decompose this area into a finite union of polygons and lens-shaped areas which are bounded by a straight line and a circular arc. For each of those parts, you can find the area and center of mass by elementary means. Apr24 comment Finding Center of Union of CirclesI take back my earlier comment. I think the way the problem is intended, the mass density where the circles overlap is supposed to be 1 rather than adding up the masses of the circles. With that interpretation, the problem does not seem trivial. Apr24 comment Finding Center of Union of CirclesFor one thing, you need to define "center" for something that is not a circle. I presume you mean the center of gravity. Now consider what happens if you concentrate the mass of each circle at its midpoint ... This site is for research level questions. Voting to close. Apr23 answered Double Integral of plane wave squared over a circular domain Apr1 accepted Riemann-Lebesgue lemma for measures Mar26 accepted Choosing boundary conditions for $(\frac{-d^2}{dx^2})^m$ on $H^m((0,1))$? Mar26 answered Riemann-Lebesgue lemma for measures Mar21 comment Finding an optimal $p$ such that $u \in L^p$The monograph of Lions and Magenes, for instance. Mar19 comment Finding an optimal $p$ such that $u \in L^p$It is supposed to mean $H^{2/3}$ (as a function of x) with values in $L^2$ (as a function of y). Mar19 answered Finding an optimal $p$ such that $u \in L^p$ Mar14 revised Spherical Bessel functionscorrected minor error Mar13 accepted Spherical Bessel functions Mar12 answered Spherical Bessel functions Feb25 awarded ● Nice Answer Feb25 answered weak*-compactness of unit ball in equivalent norm Feb19 accepted nonnegative Fourier Transform Feb19 revised nonnegative Fourier Transformdeleted 1 characters in body Feb19 answered nonnegative Fourier Transform Feb5 comment What is the solution of $u_t=u_{xx}+\frac{1}{x}u_x$?The ODE you give can be solved in terms of Bessel functions. But, perhaps more fundamentally, you did not specify boundary conditions for your problem. Feb5 answered Control of the $C^1$ norm of a diffeomorphism Feb5 comment Boundedness of a given boundary value problem.Homework, voting to close. Jan29 comment Generator of a generated $C_0$ semigroup.If U is bounded, this is rather obvious. However, if U is unbounded, there is in general an issue of domains. It is easy to come up with example where $U\rho$ is an unbounded operator, but $A(\rho)$ is bounded. Hence the generator of $P_t$ will in general be an extension of $A$. Jan9 awarded ● Yearling Jan7 comment Are All Irrational Elementary Numbers Conjectured to Be Normal?Since it seems to unknown even whether such popular numbers as e or $\sqrt{2}$ are normal, what would be the point of formulating such a conjecture? Jan7 comment Looking for higher order Sobolev inequalityIf you put the $H^2$ norm on the right hand side instead of the $H^1$ norm, this is Ehrling's lemma, which is well known. Jan6 comment Who discovered the winding number?No. If you reverse orientation on every successive day, you will have marched around the city seven times. The instructions were to march around the city once on each of days 1-6 and then seven times on the seventh day. Jan5 comment Boundary Problem with an Area ConstraintIn addition to voting to close, I removed the tag "Laplace transforms." Jan5 revised Boundary Problem with an Area Constraintremoved inappropriate tag Jan5 comment Dirac Delta function with a complex argumentFunctions like $e^{cx}$ are distributions, but not tempered distributions. Hence the theory of the Fourier transform as expounded in most textbooks does not apply to them. The Fourier transforms of distributions are a class of objects known as analytic functionals. An exposition of the theory can be found in Gelfand and Shilov, Generalized Functions. Jan3 comment Shortlists and job offersI wonder who publishes short lists of applicants. My department certainly does not, neither before nor after positions are filled. And, of course I cannot speak for our lawyers, but I cannot imagine them embracing the idea. Dec31 comment Approximating erf by tanhNot an answer but related: mathapps.net/Holmes/Holmes.pdf Dec30 comment The logarithmic fast diffusion equation in one space variable with periodic boundary conditions.Diffusion is fast only for $u\to 0$. In your problem, however, the maximum principle ensures that the solution remains within the range of the initial data. This makes the analysis fairly routine. Dec23 comment The origin of sets?This is often referred to as Galileo's paradox. Galilei discusses it in some detail, but it goes back further. The following web site gives references going back as far as Plutarch: earlham.edu/~peters/writing/infinity.htm