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Step function Fourier series
How to do a step function based Fourier series? What I am confused about is how to calculate the time period since the step function doesn't end? And...
Apr 22, 2026
Archive: News
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Solving the following trigonometric equation: $\sin x + \cos x = \frac{1}{3} $
I have to solve the following equation: $$\sin x + \cos x = \dfrac{1}{3} $$ I use the following substitution: $$\sin^2 x + \cos^2 x = 1 \longrightarrow \s...
Apr 22, 2026
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Split up a double integral
Is it true that $\int_a^b \int_c^d f(x)g(y)dydx = \int_a^b f(x)dx \cdot \int_c^dg(y)dy $ My intuition says it is true, but I also have the feeling that I ...
Apr 21, 2026
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Multiplication operator
Let $M_{\phi}$ be a multiplication operator $M_{\phi}:L^{2}\left(\mu\right)\rightarrow L^{2}\left(\mu\right)$ defined by $M_{\phi}f=\phi f$. Show that $\k...
Apr 21, 2026
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Real Primitive Characters and Quadratic Forms
since I do not know algebra very well, I have some troubles with the following concepts: I want to ask something about quadratic fields and quadratic form...
Apr 21, 2026
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How many ways to colour a $4 \times 4$ grid using four colours subject to three constraints
In how many ways can a $4 \times 4$ square grid be coloured using four different colours so that no colour is repeated in any row, column, or along the tw...
Apr 21, 2026
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How to derive the 3D equation of a torus?
I'm doing a presentation on 3D surfaces for college and one of the equations I am using is a Torus. I know that the equation is $$z^2 = 25 - \left(10...
Apr 21, 2026
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What is the relationship between the width, height, and radius of an arc?
What is the relationship between the width ($w$), height ($h$), and radius ($r$) of an arc? Specifically, the relationship in terms of $h$. I know this is...
Apr 21, 2026
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Prove, that sequence $ b_n = \sin1/2 +\sin2/4 +\dots+ \sin(n)/2^n$ is Cauchy
I do not know, how to start proving that this sequence $$b_n = \sin1/2 + \sin2/4 +\dots+ \sin(n)/2^n$$ is Cauchy. Thanks for all your answers.
Apr 21, 2026
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Distribution of mixed random variable
Let $X$ have cdf $F(x)=(x/2+1/2)I_{[0,1)}(x)+I_{[1,\infty)}(x)$. Clearly, $P(X=0)=1/2$, so $X$ is a mixed random variable (is not discrete nor continuous)...
Apr 21, 2026
