Reputation
9,254
Next privilege 10,000 Rep.
Access moderator tools
Badges
3 18 65
Newest
 Good Answer
Impact
~114k people reached

Jul
20
comment Hamiltonian action: what does $d^3x$ mean?
This notation is used in physics because it makes immediately evident the dimensionality of $d^nx$ (when $n=3$, it is a volume). The alternative notation $dx^n$ is not used because coordinates are often listed by a superscript: $x^0, x^1, x^2, x^3 \ldots$. Therefore confusion might arise between $(dx)^n$ and $d(x^n)$.
Jul
20
reviewed Approve Problem with one of the order property proofs
Jul
20
reviewed Approve Check if the weak law of large numbers holds true for the following sequence of random variables
Jul
20
comment What are some easy to understand applications of Banach Contraction Principle?
I completely agree with the point of view of this good answer. As you know very well, this point of view is so important in computational mathematics that it has its own terminology: one speaks of attractive fixed points, and the concept is by no means limited to linear equations, but nonlinear equations as well.
Jul
19
comment Is there continuous $f: [0, 1] \rightarrow [0, \infty)$ such that for all $x$ there is $y$ with $f(y) < f(x)$?
Some (complicated) transfinite induction argument might be necessary if you want to eliminate the continuity assumption on $f$.
Jul
19
reviewed Approve Is there continuous $f: [0, 1] \rightarrow [0, \infty)$ such that for all $x$ there is $y$ with $f(y) < f(x)$?
Jul
19
reviewed Close Conditions for $X\times Y=X\oplus Y$ holds?
Jul
19
reviewed Close Difference quotients and weak derivatives (Evans 5.8.2 theorem 3)
Jul
19
reviewed Approve Eigenvalues of Hermitian matrix, reflexion matrix
Jul
19
reviewed Approve How to compute an expected value in shorter ways (when taking all possibilities into account isn't plausible.)
Jul
17
revised Computing the total energy of Nonlinear Schrödinger (NLS) equation
edited tags
Jul
17
comment Need to prove continuous periodic function of $\varphi (x) \equiv \psi(x)$
Nice proof! @Nemo: As a side note, the continuity assumption is not needed if the periods $S$ and $T$ are commensurable, that is, if there exists a rational number $n/k$ such that $nS=kT$.
Jul
16
revised What can be a Fourier transform's domain?
added 13 characters in body
Jul
16
comment What can be a Fourier transform's domain?
@Minethlos: Yes, exactly. You are right it is not great notation! Editing
Jul
16
comment What can be a Fourier transform's domain?
@Minethlos: What exponent? You mean, some factor of $\pi$?
Jul
16
answered What can be a Fourier transform's domain?
Jul
16
comment How to prove this inverse of Holder inequality?
This inequality is invariant with respect to rescaling of $(a, b)$ and of $(x, y)$. (That is, the transformations $a=\lambda \tilde{a},\ b=\lambda\tilde{b}$ and $x=\mu\tilde{x},\ y=\mu\tilde{y}$, where $\lambda > 0$ and $\mu>0$, leave the inequality unchanged). You can exploit this symmetry. This means that it is enough to prove the inequality with the additional assumptions $a^p+b^p=1$ and $x^q+y^q=1$.
Jul
15
comment Are there non-holomorphic or non-analytic polynomials of several complex variables?
In real variable theory one usually distinguishes between "real-analytic" and "complex-analytic". I suppose that here that's the same. The polynomial $p(x, y)=x^2+y^2$, for example, can be seen as a function defined on the complex plane, but it is not complex-analytic.
Jul
14
awarded  Good Answer
Jul
14
comment Unknowledgable of single variabled integral
Sometimes one also writes one integration extreme, because the other doesn't matter, e.g. in the following formula: $$\frac{d}{dt}\int^t f(x)\, dx=f(t),$$ where the lower integration extreme does not matter.