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Apr
8
reviewed Approve suggested edit on Confused on a proof that $\langle X,1-Y\rangle$ is not principal
Apr
8
reviewed Approve suggested edit on Intuition behind Descartes' Rule of Signs
Apr
8
reviewed Approve suggested edit on How to find maximum/minimum of $y=\frac{x(x^2-x+2)}{x^2-9}$?
Mar
28
reviewed Approve suggested edit on Finding coordinates of nodes in a graph
Mar
24
reviewed Approve suggested edit on Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
Mar
23
comment convolution a continuous function?
I think the second part of the proof can be slightly simplified if we approximate continuous functions by smooth functions, and use the fact that a convolution with a smooth function is smooth, therefore continuous a fortiori.
Mar
18
reviewed Approve suggested edit on Location of Prime Gaps Subsequence
Feb
26
comment singular parabolic equation
In any case, the method of sub and super solutions might be applicable.
Feb
26
comment singular parabolic equation
Can you give a concrete example of $H$?
Feb
25
comment Pseudodifferential operators and Hypoellipticity problems..
Have a look at Hormander's 1963 book, before reading the 3rd volume of Hormander's 4 volume treatise.
Feb
25
reviewed Approve suggested edit on Linear Regression Question (Linear Algebra) Help!!
Feb
18
reviewed Approve suggested edit on integral computation $\int_{-\infty}^{\infty} \frac{1}{(1+x+x^2)^2} dx $
Feb
14
comment About inequalities (general)
Take f=1 and g=1.
Jan
21
reviewed Approve suggested edit on Graph Connectivity
Jan
2
comment Geometric intuition for the concept of analytical function
Conformal maps are one way to understand them geometrically.
Dec
29
awarded  Custodian
Dec
27
comment Relation of Hodge Theorem to Eigenfunction Basis of Laplacian
In general, 0 is not a simple eigenvalue when k>0.
Dec
24
comment Scalar product and uniform convergence of polynomials
Let us define the bilinear form $b(\cdot,\cdot)$ by $$ b(u,v) = \int_0^1 (u'-u)(v'-v), $$ and let $X_n$ be the space of polynomials of degree $n$. Then the question regarding the first example can be rephrased as follows. Let $u_n\in X_n$ be the solution of $$ b(u_n,v) = 0, \qquad \textrm{for all}\quad v\in X_{n-1}, $$ satisfying $u_n(0)=1$. Is it true that $u_n\to u$ uniformly in $[0,1]$, where $u(t)=e^{t}$? This is an instance of the so-called Petrov-Galerkin approximation, and can in principle be handled by the Babuska-Brezzi theory.
Dec
24
comment Motivation of Weierstrass-approximation Theorem?
The proof using Bernstein polynomials not only shows the possibility of approximation, but also gives the best polynomial that does the job (i.e., it is not just any polynomial that approximates the function well, but in fact it is (one of) the best one).
Dec
23
comment $f$ is a non-constant polynomial, $A $ is a set of measure zero, Is this true that $m(f^{-1}A)=0$, where $m$ stands for the Lebesgue measure.
How about multivariate polynomials?