Compare Complexity of Graph (Landau) February 7

Assume I know that there is an algorithm of complexity$ \mathcal{O}( \vert V \vert^2 \vert E \vert ) $ for a Graph $G(E,V)$.How do I compare this for example to the complexity of$ \mathcal{O}( \vert V \vert^2 + \vert E \vert ) $ or other complexity a

A faithful positive Radon measure February 7

Let $X$ be a locally comapct and Hausdorff space. We say a positive Radon Measure on $X$ is faithful if $$0\leq f ~~~,~~~\int fd\mu=0\rightarrow f=0$$Q: True or false: If there is a faithful positive Radon measure on $X$ then $X$ has a countable dens

Support of a Radon measure February 7

Let $X$ be a locally compact and Hausdorff space. For given a Radon measure $\mu$ on $X$, the support of $\mu$ is the smallest closed subset of $X$ with $|\mu|(X)=||\mu||$.Q: Let $E$ be a closed subset in $X$. Does there exist any (positive) measure

Question about angular velocity February 7    1

If $z=r\cos\theta +ir\sin \theta$, show that $\dfrac{dz}{dt}=r\dfrac{d\theta}{dt}(-\sin\theta+i\cos \theta)$ and that if $\dfrac{d\theta}{dt}$ is constant, then $\arg\dfrac{dz}{dt}=\theta-\pi/2$.I managed to do everything apart from the argument, whi

Russell's paradox question February 7    3

Tao's analysis book uses following example for Russell's paradox: $$P(x) \Longrightarrow `` x\text{ is a set, and }x \notin x"\\ \Omega := \{x : P(x)\text{ is true} \} = \{x : x\text{ is a set and }x \notin x\}$$ then conclude that $­\Omega \in \Omeg

separation and russell's paradox February 7

I just want to be sure that I understand the connection between "Naive Comprehension", the Axiom of Separation, Russell's Paradox, and the existence of a universal set. Is the following correct?The Naive Comprehension Axiom has as an instance th

Physics Velocity Correction February 7

So, been up all night working on getting the velocity/angle of arrow simulations perfect. Running into an issue with the physics engine I'm using is ever so slightly off (probably a rounding issue)The Velocity is a fixed 55 "Units"Correction Req

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