# All Questions

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### A weak* dense subset intersected with norm ball contains no ball

I'm struggling with this problem in general. Represent $\ell^1$ as the space of all real functions $x$ on $S = \{(m,n): m\geq 1, n \geq 1\}$, such that $$\|x\|_1 = \sum |x(m,n)| < \infty$$ ...
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### The path of the shock

Here I am using the shock speed to work out the path the shock takes. I don't understand why we cannot take the value of $u_{-}$ at $t=1/u_0$ i.e $u_{-}=u_0$. and calculate the speed of the ...
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### Method of solving no-homogeneous recurrence equation

I need to obtain a closed form of $M(t)$, satisfying the following recurrence equation: $$M(t+1)=a+bM(t)+\frac{c}{t+1}\sum_{t'=0}^tM(t')+df(t)$$ Where $f(t)$ is a known function and $a$, $b$, $c$ ...