Scaling - Rigid or Non-Rigid Transformation
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Scaling - Rigid or Non-Rigid Transformation

I am trying to look for a precise definition of what rigid and non-rigid transformation is, and to which categories does 'scaling' belong. This ...

Published: Aug 10, 2026

How to find the vector equation of a plane given the scalar equation? [closed]
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How to find the vector equation of a plane given the scalar equation? [closed]

How would I find the vector equation of the plane: $x + 2y + 7z - 3 = 0$ So far, I found the normal vector: it's $(1, 2, 7)$.

Published: Aug 10, 2026

The Coercivity of uniformly positive definite Matrix of Sobolev function
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The Coercivity of uniformly positive definite Matrix of Sobolev function

For $u=(u^1,\ldots, u^N)\in W^{1,2}(\Omega,R^N)$ where $\Omega$ is bounded. We define $$ E[u]=\int_\Omega g_{ij}(u)\nabla u^i\nabla u^jdx$$ where $G=(g_{i...

Published: Aug 10, 2026

In English, is there a difference between square and squared?
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In English, is there a difference between square and squared?

For example, if I say "one over $x$ square/squared" Do I mean: $1/\sqrt{x}$ or $1/x^2$? Is there some other way to distinguish between the Engli...

Published: Aug 10, 2026

Real Analysis, Folland Problem 1.5.29 Lebesgue measurable set
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Real Analysis, Folland Problem 1.5.29 Lebesgue measurable set

1.5.29 - Let $E$ be a Lebesgue measurable set. a.) If $E\subset N$ where $N$ is the nonmeasurable set described in section 1.1, then $m(E) = 0$. b.) If $m...

Published: Aug 10, 2026

Evaluating Surface Integral Using Stokes' Theorem
general

Evaluating Surface Integral Using Stokes' Theorem

Let $\vec{F}$ be the vector field $\vec{F}\left(x,y,z\right)=\left(z,x,y\right)$. Let $\rm S$ be portion of the surface $x^{2}+y^{2}+z=1$ lying above the ...

Published: Aug 10, 2026

Prove that the planar curve obtained by projecting $\alpha$ into its osculating plane at $P$ has the same curvature at $P$ as $\alpha$.
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Prove that the planar curve obtained by projecting $\alpha$ into its osculating plane at $P$ has the same curvature at $P$ as $\alpha$.

Let $\alpha(s)$ be a regular curve with $\kappa\neq0$ at P, where $\kappa$ is the curvature. Prove that the planar curve obtained by projecting $\alpha(s)...

Published: Aug 10, 2026

Write $2+\log_3 x+\log_9 x^4-\log_{27} x^5$ into one single logarithm
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Write $2+\log_3 x+\log_9 x^4-\log_{27} x^5$ into one single logarithm

I'm trying to answer this problem: Write $$2+\log_3 x+\log_9 x^4-\log_{27} x^5$$ into one single logarithm. This is what I'm stuck with: $$\frac...

Published: Aug 10, 2026

How to find the potential function of a vector field?
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How to find the potential function of a vector field?

I calculated that $\frac{dP}{dy} = \cos(y) = \frac{dQ}{dx}$ This tells me that the potential function exists, however I can't figure out what it is. ...

Published: Aug 10, 2026

Is the term *monotone* used fairly consistently to mean non-decreasing or non-increasing but not strictly?
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Is the term *monotone* used fairly consistently to mean non-decreasing or non-increasing but not strictly?

In BBFSK, (~1960, Germany) at least in the section I am currently reading, the authors use the term monotone increasing (decreasing) to mean what I often ...

Published: Aug 10, 2026

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